Encyclopedia of Nanoscience and Nanotechnology 9781588830616, 1588830616

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Encyclopedia of Nanoscience and Nanotechnology Volume 5 Number 1 2004 Magnetostrictive Nanomaterials for Sensors

1

Keat G. Ong; Craig A. Grimes Magnetotransport in Nanogranular Materials

29

Jinke Tang Manganite Nanocomposites

41

B. K. Chaudhuri; Aritra Banerjee; Sudipta Pal Mechanical Behavior of Nanomaterials

53

A. Li Bassi; C. E. Bottani Mechanical Molecular Nanodevices

73

Laura Frankfort; Xiange Zheng; Karl Sohlberg Mechanical Processing for Nanomaterials

91

E. Gaffet; G. Le Caër Mechanical Properties of Nanostructured Materials

131

S.-P. Hannula; J. Koskinen; E. Haimi; R. Nowak MEMS-Based Nanotechnology

163

H. V. Jansen; N. R. Tas; J. W. Berenschot Mesoscopic Organizations of Metal Nanocrystals

277

G. U. Kulkarni; P. John Thomas; C. N. R. Rao Mesoscopic Phenomena in Nanotubes and Nanowires

291

Junji Haruyama Metal Nanoclusters

337

Yuan Wang; Yongge Wei Metal Nanoclusters by Ion Implantation

369

Elti Cattaruzza; Francesco Gonella Metal Nanoclusters as Quantum Dots

387

Günter Schmid Metal Nanoclusters on Oxide Surfaces

399

Gianfranco Pacchioni Metal Nano-Optics

411

J. R. Krenn; A. Leitner; F. R. Aussenegg

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Metal Nanoparticle Superlattices

421

Toshiharu Teranishi; Mikio Miyake Metal Nanoparticles

449

Colin C. Baker; Anshu Pradhan; S. Ismat Shah Metal Nanoparticles in Catalysis

475

Qiang Wang; Agnes E. Ostafin Metal Oxide Nanostructures as Gas Sensors

505

Oomman K. Varghese; Craig A. Grimes Metal Polyhedral Nanorods

523

Jeong Won Kang; Ho Jung Hwang Metallic State in Conducting Polymers

537

Kwanghee Lee Micro and Nanocantilever Sensors

551

P. G. Datskos; T. Thundat; Nickolay V. Lavrik Micro- and Nanomechanics

561

Barton C. Prorok; Yong Zhu; Horacio D. Espinosa; Zdenĕk P. Ba ant; Zaoyang Guo; Yufeng Zhao; Boris I. Yakobson Modeling of Carbon-Based Nanojunctions

607

Juyeon Yi; Gianaurelio Cuniberti; Markus Porto Modification of Carbon Nanotubes

619

Hansoo Kim; Wolfgang M. Sigmund Molecular Electronic Devices

633

J. Chen; T. Lee; J. Su; W. Wang; M. A. Reed Molecular Gradient Nanoassemblies

663

Jan Genzer; Rajendra R. Bhat; Tao Wu; Kirill Efimenko Molecular Logic Gates

677

Françisco M. Raymo; Silvia Giordani Molecular Nanotechnology with 2D Protein Crystals

693

Uwe B. Sleytr; Dietmar Pum; Margit Sára; Bernhard Schuster Molecular Planar Technology

703

J. M. Köhler; W. Fritzsche Molecular Sieve Silica Membranes

723

João C. Diniz da Costa; Victor Rudolph; G. Q. Lu Molecular Tectonics in Sol-Gel Chemistry

743

Marc Henry

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Molecular Wires and Switches

821

Chen Wang; Chunli Bai Monolayer-Assisted Electrochemical Nanopatterning

835

O. Azzaroni; P. L. Schilardi; R. C. Salvarezza Monolayer-Based Scanning Probe Lithography

851

Ryan R. Fuierer; Christopher B. Gorman Monolayer-Coated Au and Ag Nanoclusters

861

Nirmalya K. Chaki; T. G. Gopakumar; M. Aslam; K. Vijayamohanan Multiwall Carbon Nanotubes

879

Dojin Kim Copyright © 2004 American Scientific Publishers

4/21/2007 10:06 PM

Encyclopedia of Nanoscience and Nanotechnology

www.aspbs.com/enn

Magnetostrictive Nanomaterials for Sensors Keat G. Ong, Craig A. Grimes The Pennsylvania State University, University Park, Pennsylvania, USA

CONTENTS 1. Introduction 2. Principles of Magnetism 3. Ferromagnetic Glass Preparation and Properties 4. Sensor Applications 5. Summary List of Symbols Glossary References

1. INTRODUCTION Amorphous ferromagnetic glasses are noncrystallized ferromagnetic alloys free from defects such as grain boundaries, precipitates, or phase segregation [1, 2]. The amorphous structure of these materials gives rise to unique magnetic and mechanical properties, such as high mechanical strength [3], large magnetoelastic coupling, large magnetostriction [4], and the so-called giant magnetoimpedance effect (GMI) [5], which make them suitable for various sensor applications. The large magnetostriction allows the permeability of the materials to significantly change with applied stress and also causes the ferromagnetic glasses to exhibit a strong mechanical vibration when excited by a time-varying magnetic field. The high degree of magnetoelastic coupling allows efficient conversion between mechanical and electrical energies [6], so the response of the ferromagnetic glasses can be remotely detected by measuring the magnetic flux change. Furthermore, the GMI effect, wherein the electrical impedance of a ferromagnetic glass significantly changes with applied magnetic field, allows them to be used as ultrasensitive magnetic field sensors. Since there are few defects in the amorphous glass to restrict magnetic domain wall motion, magnetically soft ferromagnetic glasses have properties useful in sensor design including low coercivity, low hysteresis loss, and high permeability. The soft magnetic

ISBN: 1-58883-061-6/$35.00 Copyright © 2004 by American Scientific Publishers All rights of reproduction in any form reserved.

properties increase the performance and the stability of ferromagnetic glass-based sensors by allowing them to have good reversibility with little hysteresis in response to applied mechanical stresses and magnetic fields. Ferromagnetic glasses are fabricated by rapid quenching techniques (e.g., melt-spinning) to prevent crystallization. Material properties are largely dependent upon the alloy composition, generally a combination of transition metals, rare-earth metals, and glass-forming metalloids. The lack of long-range order in the amorphous glasses eliminates the crystalline anisotropy energy, rendering them magnetically soft. However, inhomogeneous cooling of the alloy melt creates internal stresses that increase stress anisotropy energy. Since the amorphous nanostructure of these materials allows atomic rearrangement at a temperature far below crystallization, the stress anisotropy can be removed by relaxing the materials with low-field annealing at a moderate temperature. Alternatively, depending upon the application an anisotropy field can be introduced in a ferromagnetic glass by annealing under applied stress or magnetic field at moderate temperatures [7–9]. For certain amorphous alloys, annealing can be preformed above the crystallization temperature (500–900
C) to create nanocrystalline structures of 10–20 nm in size for enhancing the soft magnetic properties of the materials [10]. Although there are many types of ferromagnetic glasses with a range of mechanical and magnetic properties, as dependent upon the composition and annealing history, the most generally useful type of ferromagnetic glass for sensor applications is magnetically soft transition-metalloid-based alloys with a high Fe or Co content. For example Fe-rich alloys have magnetostriction constants as high as
S ≈ 10−5 , and magnetoelastic couplings as high as 0.98, while Co-rich transition-metalloid alloys have low magnetostriction on the order of 10−7 . Rare-earth amorphous alloys, which exhibit large magnetostriction as high as 10−4 , are useful as transducers since a small applied field can causes a large change in the material dimensions. Some of the commercially available ferromagnetic glasses [11] for sensor applications are the Fe-rich Metglas 2605SC (Fe81 B135 Si35 C2 ) and 2826MB (Fe40 Ni38 Mo4 B18 ) that have a magnetostriction coefficient Encyclopedia of Nanoscience and Nanotechnology Edited by H. S. Nalwa Volume 5: Pages (1–27)

2 on the order of 10−5 and a high magnetoelastic coupling coefficient, and the Vitrovac amorphous alloys that have a near zero magnetostriction and excellent soft magnetic properties (BS = 055 T, max = 105 ). Ferromagnetic glasses were initially used as the sensing materials for induction-based sensors to measure stress/strain and torque [12], magnetic field [13], and displacement [14] since their permeability varies with applied stress and field. These sensors, usually composed of solenoids loaded with ferromagnetic glass cores, are simple in design, stable over a wide range of temperature, and have a good linearity and low hysteresis. Ferromagnetic glasses are also used as field and stress sensors based on the GMI effect. The GMI magnetic sensors are highly sensitive, with maximum impedance variation reaching 400%. Ferromagnetic glasses have been used to construct magnetostrictive delay lines (MDL) for the measurement of stress, torque, and displacement [15–22]. The MDL sensor is usually a long ferromagnetic glass wire or ribbon surrounded with an excitation coil at one end and a sensing coil at the opposite end. An acoustic wave is excited by passing a voltage pulse to the excitation coil and is captured by a sensing coil as an induced voltage. The parameters of interest, such as stress, torque, and weight, are determined from the attenuation of the acoustic wave, which is obtained by normalizing the measured voltage amplitude to the excitation voltage amplitude. Magnetoelastic resonant sensors, which are based on the change in the magnetoelastic resonant frequency of a ferromagnetic glass ribbon in response to applied stress and field, have become popular in the past decade due to their remote-query capability, simple design, and low cost. These sensors have been used to measure pressure [23], liquid viscosity and density [24], liquid flow velocity [25], temperature [26], and thin-film elasticity [27]. Magnetoelastic resonance chemical and gas sensors have also been built by applying a layer of mass-changing chemically responsive material, the mass loading of which changes the mechanical resonant frequency of the sensor, as does the elasticity of the applied coating [28–33]. Ferromagnetic glass thin films are also used as the active layer of a magnetic surface acoustic wave (MSAW) sensor [34]. Due to the stress and field dependencies in the ferromagnetic glass, the MSAW sensor can be used to measure stress, magnetic field, or displacement. Recently, a viscosity sensor [35] was built based on the spontaneous mechanical rotation of a large magnetostrictive ferromagnetic glass wire when subjected to an ac magnetic field.

Magnetostrictive Nanomaterials for Sensors

2.1. Origin of Magnetic Fields Although a magnetic compass was apparently used over 4000 years ago [see for example T. C. Lucretius, On The Nature of the Universe (≈100 B.C.), translated by R. Latham, Penguin Books, New York, 1992], the mechanism and principles of magnetism were not put to paper until 1819, when Oersted [36] discovered that an electric current produces a magnetic field, resulting in the modern field of magnetism. The reader requiring greater knowledge on the subject of magnetism is encouraged to seek one or more of the many excellent books extensively dealing with the topic of magnetism that have been published over the past 50 years [37–43].

2.1.1. Magnetic Dipoles and Moments Magnetic fields originate from electrical charges in motion, be they electrical currents (free moving electrons) flowing in a conductor, or the orbital motions of electrons (the socalled “Amperian currents”). Since magnetic fields are generated by electrical currents, the basic unit of the magnetic field, H , is amperes per meter (A/m). It is common to treat magnetic fields as lines of force that originate and terminate from magnetic poles or magnetic charges, just like those in an electrostatic system. However, magnetic poles exist as opposing dipoles—there are no magnetic monopoles. Figure 1 is a simple illustration of the magnetic fields generated by a permanent magnet, represented by the lines of force originated from the north (N) pole and terminated at the south (S) pole; the field lines form a closed loop inside the magnet from the S to N pole. Similar to electrical charges, physically separating two magnetic poles generates a force. For two magnetic poles separated by a distance l the force between them is quantified by the Coulomb magnetic moment pm given in voltsecond-meters (V · s · m) as pm = Qm l

(1)

where Qm is the Coulomb magnetic pole strength, in Webers (Wb) or volt-seconds (V · s), which depends on the magnetic properties of the materials. Under a homogeneous H field,

2. PRINCIPLES OF MAGNETISM In this section the fundamental principles of magnetism and magnetic materials are reviewed. It begins by introducing the concept and origin of magnetic fields and fluxes, followed by a discussion on the constitutive relations and some basic magnetism principles, such as Faraday’s induction law, Lorentz’s force equation, and Maxwell’s equations. Different types of magnetic materials are then introduced. Intrinsic properties of ferromagnetic materials, such as magnetic domains, anisotropy, and magnetization processes, are detailed.

S

N

Figure 1. Magnetic field represented by lines of force originating from the N pole and terminated at the S pole.

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Magnetostrictive Nanomaterials for Sensors

the magnetic moment experiences a torque T : (2)

T = pm × H

Equation (2) describes the fundamental principle of the first magnetic sensor, the compass; earth’s magnetic generates a torque on the needle shaped compass magnet and orients it parallel to the direction of earth’s field along a north–south direction.

A current-carrying conductor consists of moving electrical charges that generate a magnetic field. The fundamental principle that describes the generation of magnetic fields by an electrical current is the Biot–Savart law, an empirical equation discovered in 1820. According to the Biot–Savart law, the field contributed by a segment of current-carrying conductor with length l is I l × u 4r 2

(3)

where I is the current in the conductor segment, u is the unit vector of the current direction, and H is the contribution to the magnetic field at r due to the current element I l. Figure 2 illustrates the generation of magnetic fields with conduction currents. A flowing current in a conductor loop generates a magnetic field H passing through the loop, while a current in a straight wire generates a circumferential field around the wire. The direction of the H field is given by the right-hand rule as illustrated in Figure 2. Although the Biot–Savart law provides great understanding on how electrical currents generate magnetic fields, it can only be solved analytically when the current conductor contains high symmetry and the observation point is at the symmetry axis. For example, the field generated by a long straight wire at a distance r is given as H = I/2r, the field along the axis of an N -turn solenoid with length l is H = NI/l, and the field along the z-axis of a circular loop of diameter d that is centered on the xy-plane is H = Id 2 d 2 + 4z2 −3/2 .

2.2. Magnetic Principles This section shows the connection between magnetic fields and fluxes in vacuum and in magnetic materials. This section also introduces the fundamental magnetic principles that describe the relations between magnetic and electric H

I

H I

2.2.1. Magnetic Constitutive Relations In the MKS unit system, the vacuum magnetic flux density B, in Webers per meter2 (Wb/m2 ) or volt-seconds per meter2 (V · s/m2 ), is related to H as B = 0 H

2.1.2. Magnetic Fields around Current-Carrying Conductors

H =

quantities, such as Ampere’s law [44] and Faraday’s law [45]. Lorentz’s force equation, which links magnetic fluxes to force and torque, is also discussed in this section.

H I

H

(4)

where 0 is the free space magnetic permeability that has a value of 4 × 10−7 Wb/A · m. When a magnetic field passes through a magnetic material, the magnetic dipoles in the material tend to align with the applied field. This phenomenon is called magnetization, and the intensity of magnetization is generally represented by M having the same unit basis as H . The direction and intensity of the magnetization depend on the material: for nonmagnetic materials the value is close to zero, but for ferromagnetic materials the number can reach 106 (see Section 2.4). The magnetization process effectively increases the density of magnetic fields in the magnetic material, so the flux density inside the material becomes B = 0 H + M

(5)

To simplify Eq. (5) so the flux B only depends on the applied field H , the magnetic permeability  (in Wb/A · m) and the relative permeability r (unitless) are introduced as B = H = r 0 H

(6)

Comparing Eqs. (5) and (6), the permeability  can be expressed as  = 0 1 + M/H = 0 1 + 

(7)

The ratio of magnetization to applied field M/H is defined as the relative magnetic susceptibility  (unitless). Most magnetic materials used for engineering applications are ferromagnetic materials with large magnetization M. As a result, the susceptibility and relative permeability are often treated as approximately equal (r ≈ ). At high frequency, many materials dissipate field energies as the field passes through them. To compensate for the field dissipation, the relative complex permeability ∗r is used, ∗r = ′r − j′′r

(8)

where the real part represents the magnetization and the imaginary part represents the energy loss. For anisotropic materials where the permeability varies with directions, ∗r is replaced by the relative complex permeability tensor ¯ ∗r = ¯ ′r − j ¯ ′′r .

I

(a)

(b)

Figure 2. A flowing current in a loop or a straight wire generates a magnetic field H, the direction of which is given by the right-hand rule.

2.2.2. Ampere’s Circuital Law Consider a long circular conductor carrying a current I. By the Biot–Savart law, the magnetic field integrated along a circular path outside the conductor with radius r can be

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Magnetostrictive Nanomaterials for Sensors

expressed as


c

H · dl =

I 2r




c

dl = I

(9)

Replacing the current I with the current density Jc in the conductor, Eq. (9) becomes 
(10) H · dl = Jc · ds

The term IA is defined as the magnetic moment m . Note the similarity between the magnetic moment m and the Coulomb magnetic moment pm in Eq. (13) and Eq. (2), respectively. In vacuum, they are scaled by the free space permeability 0 . Equation (13), similar to Eq. (2), describes the operational principle of electrical motors that generate rotational motion by passing a current within a magnetic field.

s

c

Equation (10) is the Ampere’s circuital law, which states the line integral of H around a closed path is equal to the total current crossing any surface bounded by the line integral path.

2.2.3. Faraday’s Induction Law

2.2.5. Maxwell’s Equations Maxwell combined the observations discovered by Ampere, Faraday, and Gauss into a final form for governing electric and magnetic fields, charges, and currents [46]. These equations, known as the Maxwell’s equations, are useful for understanding magnetism and electromagnetism. In differential form, Maxwell’s equations can be written as

According to Faraday’s induction law, an electromotive force (emf) will be induced in a closed-path electrical circuit if there is a change of magnetic flux linking to the circuit. In equation form, Faraday’s law is expressed as dB emf = −A dt

(11)

where A is the surface area, and B is the magnetic flux. The negative sign in the equation is a result of Lenz’s law, which states the direction of the induced voltage is such that the induced flux opposes the incident flux. Faraday’s induction law is demonstrated in Figure 3 with a moving bar magnet and a closed loop. The movement of the permanent magnet results in a change in the magnetic flux linking to the loop, causing an induction voltage in the loop with a sense that would produce a current whose magnetic field opposes the flux change. Faraday’s induction law is important for induction and search coil sensors, which detect magnetic fields by the induction voltage.

2.2.4. Lorentz’s Force in Magnetic Fields According to Lorentz’s force equation, an electric charge qe traveling at a velocity v inside flux B experiences a force F perpendicular to B and v: (12)

F = qe v × B

For a current I flowing in a closed loop of area A, a torque T appears on the conductor according to the Lorentz’s force: (13)

T = IA × B

Moving Direction I

B (decreasing)

N

# ·B =0

(14) (15) (16) (17)

where Jc is the conduction current and (es is the surface charge density. A more familiar form of Faraday’s induction law can be obtained from Eq. (14) by integrating over an open surface S bounded by a curve C and applying Stoke’s theorem on the left-hand side as
%  B · ds (18) E · dl = − %t s c Equation (18)  is essentially identical to (11) because emf is defined as E · dl. Applying Stokes’ theorem on Eq. (15) yields


c

H · dl =



s

Jc · ds +

%  B · ds %t s

(19)

Equation (19) is identical to Ampere’s law except for the second term on the right-hand side, which is the displacement current added by Maxwell to complete Ampere’s law under ac conditions. Equations (16) and (17) are Gauss’ electric and magnetic field laws, which state that electrical charges can operate as sources or sinks, originating or terminating electric flux, while magnetic flux forms closed loops with no known sources and sinks.

2.3. Types of Magnetism

Induced B

S

%B %t %D # × H = JC + %t # · D = (es # ×E =−

Induced emf

Figure 3. Illustration of Faraday’s induction law. The decrease in the magnetic flux creates an induced emf, which produces a current I that in turn generates an induced flux opposing to the initial change.

All materials exhibit unique magnetization behavior and from the magnetization profiles can be categorized. Among the categories, diamagnetic and paramagnetic materials are considered as “weak magnetic” materials because the magnetization is relatively small,  ≈ 0 and  ≈ 0 (although there are exceptions such as superconductors that exhibit a perfect diamagnetism,  ≈ −1). Ferromagnetic and ferrimagnetic materials exhibit large magnetization with applied field; for some ferromagnetic materials r can reach ≈106 .

5

Magnetostrictive Nanomaterials for Sensors

2.3.1. Diamagnetism All materials exhibit diamagnetism; however, the effect of diamagnetism is small and often shadowed by other magnetic effects. A diamagnetic material has the ability to “repel” magnetic fields, with the flux density in diamagnetic materials actually being less than in vacuum. Classically, diamagnetism is explained by the reduction of the electron velocity due to an external magnetic field. To understand diamagnetism, first consider an atom with an electron moving clockwise in an orbit perpendicular to an applied field. Since the electron carries an electrical charge, the orbital motion of the electron is equivalent to a current on a conductor loop. By Faraday’s law, the increase in the applied field generates an induction current on the loop to produce an opposing field. For an orbiting electron the opposing field is generated by decreasing the electron velocity. Now consider another electron orbit adjacent to this orbit, with its plane parallel to the first one but the electron moving counterclockwise. In the absence of an external applied field, the moments of these two electrons cancel each other, yielding zero net moment. As the applied field increases, both orbits produce a magnetic moment opposing the applied field. The classical explanation for diamagnetism is illustrated in Figure 4. For a diamagnetic material with Z electrons per atom, N atoms per cubic meter, and at effective equilibrium distance of 2r, the susceptibility  is given by  = −0 N

qe2 Zr 2 6me

(20)

where qe is the electron charge and me is the electron mass. For most diamagnetic materials, the value of  is very small, about 10−5 . As a result, diamagnetic materials have almost no effect on magnetic fields under most conditions, and they are commonly used as materials that do not disturb magnetic fields. Examples of diamagnetic materials are noble gases such as helium, neon, and argon, diatomic gases such as hydrogen and nitrogen, ionic solids such as sodium chloride (NaCl), and almost all organic compounds. Many metals also exhibit diamagnetic properties, for example, copper, zinc, silver, cadmium, gold, mercury, lead, and bismuth. Superconductors exhibit the most unusual diamagnetic behavior. Superconductors are typically metals such as lead and tantalum, or compounds such as Nb3 Sn. At normal operating temperatures these materials are either diamagnetic or paramagnetic. However, when they are cooled to µm = 0

µm = 2 µm

ν

ν−∆ν

−ν

−ν−∆ν

H=0

a critical temperature, they repel all magnetic flux by generating a thin layer of nondissipating surface currents. This effect is known as the Meissner effect. Ideally, superconductors have a perfect diamagnetism, which is  = −1. Superconductors such as lead and tantalum exhibit perfect diamagnetism. Superconductive diamagnetic materials are the key elements for superconducting quantum interference device field sensors.

2.3.2. Paramagnetism Paramagnetic materials are composed of atoms or molecules that have a net magnetic moment because the spin and orbital moments of electrons do not completely cancel out. In the absence of applied fields, the magnetic moments are oriented randomly and thus macroscopically the net moment of a paramagnetic material is zero. When a magnetic field is applied on the material, the magnetic moments tend to align with the field. However, thermal agitation in the atoms or molecules opposes this tendency and tries to keep the moments in random states. This will result in a partial alignment of the magnetic moments; thus a small positive susceptibility is observed in paramagnetic materials. Increasing temperature increases the thermal energy in the atoms or molecules and therefore reduces the susceptibility. In general, the magnetization M in a paramagnetic material is nonlinear, which can be given by the Langevin function L with s = m B/kB T as M = Nm

ses + e−s  − es − e−s  = Nm Ls es − e−s 

(21)

where m is the magnetic moment of each atom, T is the temperature, kB is the Boltzmann constant (kB = 538 × 10−23 ), and N is the number of atoms. In room temperature (T ≈ 300 K) and at a moderate field B ≈ 1 T, which is the operation condition for most technical applications, s ≈ 0 and Eq. (21) becomes =

C 2m N0 = 3kB T T

(22)

Equations (21) and (22) are the results from classical Langevin paramagnetism [47]. The paramagnetic behavior can also be predicted using quantum mechanic theorems, and the results are identical to Eq. (22) for moderate fields at room temperature. The typical value for  is generally on the magnitude of 10−3 . Examples of paramagnetic substances are diatomic gases such as oxygen and nitric oxide, polyatomic gases such as NO2 and ClO2 , and metals such as aluminum, titanium, platinum, palladium, magnesium, molybdenum, and vanadium.

2.3.3. Ferromagnetism and Ferrimagnetism H

Figure 4. In the absence of an external field, the orbital motions of two electrons with velocity v and −v create two opposing moments, resulting in zero net moment. When a field is applied, additional moments, *m , are created at both atoms due to the change in the electron velocity. These two moments add up to reduce the applied field.

Ferromagnetic and ferrimagnetic materials are perhaps the most useful materials for technical applications. Like paramagnetic materials, each molecule in the ferro- and ferrimagnetic materials contains a net magnetic moment. However, because of the existence of a strong molecular field that aids the applied field in the magnetization process, the susceptibility of ferro- and ferrimagnetic materials is much larger than paramagnetic materials, ranging from 102 to 106 . Even

6

Magnetostrictive Nanomaterials for Sensors

under zero applied field, the atomic moments of ferromagnetic materials are oriented in parallel due to the strong molecular field (in quantum magnetism, it is the exchange energy that causes the alignment of the moments), causing a large spontaneous magnetization. The moments of antiferromagnetic alloys are oriented in antiparallel, resulting in a zero net moment in the absence of an orienting magnetic field. Ferrimagnetic materials are composed of antiparallel atomic moments that do not completely cancel out. The moment alignments in ferro-, antiferro-, and ferrimagnetic materials are shown in Figure 5. Due to the strong molecular field, ferro- and ferrimagnetic materials are self-saturating, or “spontaneously magnetized” in the absence of an external field. However, it is still easy to find a ferro- or ferrimagnetic sample in the unmagnetized state. This is because ferro- and ferrimagnetic contain many small regions, called “domains,” which are spontaneously magnetized to saturation Ms but oriented at different directions to minimize the energy potential within the material. The Ms in these domains cancel each other, yielding zero macroscopic magnetization. When an external field is applied, these domains align with the field, and a large magnetization is observed. A permanent magnet sample consists of domains that do not cancel out macroscopically due to the crystal structure, applied stress, or mechanical defects. Section 2.5 details the domains and magnetization processes in ferro- and ferrimagnetic materials. Magnetization in ferromagnetic magnetic materials is a critical function of temperature. The spontaneous magnetization below the Curie temperature T- of a ferromagnetic material is given by   H + 0 .Ms Ms = Nm tanh 0 m (23) kB T

Ferromagnetic

 = 0

m N 3kB T − T- 

(24)

Ms

1/χ

Tc

Figure 6. The transition of a material from ferromagnetic state to paramagnetic. The material is ferromagnetic below T- , but becomes paramagnetic above T- according to the Curie–Weiss law.

Quantum theory explains ferromagnetism on the basis of exchange forces, which are caused by the exchange orbit of two adjacent electrons from two atoms. The exchange energy Eex is given as (25)

Eex = −2Jex s1 · s2

where s1 and s2 are the spins of two adjacent electrons, and Jex is the exchange integral. Since the moments of ferromagnetic materials are parallel (i.e., s1 and s2 have the same sign), Jex must also be positive for a ferromagnet to minimize Eex . The same argument goes for antiferromagnetic, where Jex must be negative. Figure 7, known as the Bethe–Slater curve [49, 50], shows that the exchange integral varies with the ratio of the atomic distance to the 3dshell distance, ra /r3d . The curve shows that ferromagnetism only appears in some metals such as Fe, Co, and Ni because their ra /r3d ratios correspond to positive Jex . Following a similar argument, ferromagnetic materials can be created by alloying two or more nonferromagnetic materials by changing in the effective ra /r3d . Examples of ferromagnetic alloys are manganese–aluminum–chromium, manganese–copper– tin, and all rare-earth magnets. Although later Herring and others [51] showed that this method of determining ferromagnetism is unreliable, the Bethe–Slater curve still provides insights on the origin of ferromagnetism.

2.4. Anisotropy Due to defects, shape, and crystallographic structure, the applied field required for magnetizing a magnetic material commonly varies with the direction of the applied field Ferromagnetic α-Fe

Co Ni

Jex

Equation (24) is actually an extension of the Curie law in Eq. (22). Figure 6 depicts the transition of a material from ferromagnetism to paramagnetism with increasing temperature. At low temperature, the material exhibits strong ferromagnetism with a large magnetization Ms0 . As the temperature increases, the saturation magnetization decreases and becomes zero at T- . Above T- , the susceptibility of the material decreases with temperature following the profile given by Eq. (24).

Mso

χ

where . is the Weiss constant. At T- , the thermal energy kB Tc is equal to the molecular exchange energy, and this makes Ms zero. All ferromagnetic materials become paramagnetic above T- , and the susceptibility above T- is given by Curie–Weiss law [48] as

Paramagnetic

Mn

Gd

ra / r3d

Cr Antiferromagnetic

Ferromagnetic

Antiferromagnetic

Ferrimagnetic

Figure 5. The atomic moment alignment of the ferromagnetic, antiferromagnetic, and ferrimagnetic materials.

Figure 7. Bethe–Slater curve shows that the exchange integral varies with the ratio of the atomic distance to the 3d-shell distance.

7

Magnetostrictive Nanomaterials for Sensors 1 0.5 0

Z

relative to the direction of the magnetization vector within the material. The minimum field needed to magnetize a sample is for a field parallel to the magnetization vector direction. Conversely, the maximum field needed to magnetize a sample is when the applied field is perpendicular to the easy axis, the so-called hard axis. This phenomenon is called anisotropy, and there are three major causes of anisotropy: magnetocrystalline anisotropy, shape anisotropy, and magnetostriction anisotropy. Anisotropy determines the magnetic hardness of materials and is usually controlled for enhancing the magnetic materials as needed for specific applications.

-0.5 -1 1

cobalt

The energy function of cobalt, plotted in Figure 8a, indicates that in the absence of an applied field, the magnetization seeks the lowest energy orientation, namely, along the z-axis. The anisotropy of a magnetic material is also commonly defined by a fictitious anisotropy field Hk , which for the simplified case of a uniaxial structure is given by Hk =

2K1 Ms

-0.5 -1 -1

Y

X

(a)

Z

0.5 0 -0.5 -1 1 1

0.5 0.5

0

0

-0.5

-0.5 -1 -1

Y

(27)

The energy function for a cubic system can be written as     ua = K0 + K1 321 322 + 322 323 + 323 321 + K2 321 322 323 + · · · (28) where 31 , 32 , and 33 are the directional cosines of the magnetization along the main coordinate axes (3i = Mi /Ms ).

X

(b) 1

Z

0.5 0

-0.5 -1 1 1

0.5 0.5

0

0

-0.5

(26)

where - is the angle between Ms and the main axis of the uniaxial structure. In Eq. (26), K0 has no meaning for anisotropy properties because it is directional independent. The first term K1 describes the shape of the energy function, where K1 > 0 means an oblate spheroid and K1 < 0 a prolate spheroid. An example of material having this geometry is cobalt, which at room temperature has K2 = 55 × 105 J/m3

0

-0.5

1

The electron orbits of a crystalline magnetic material, such as iron, are fixed on certain crystallographic directions due to a strong orbit–lattice coupling. When an external field is applied the electron orbits tend to reorient. However, the strong orbit–lattice coupling force creates a resistance that hinders the reorientation of the electron orbits. The energy needed to overcome this orbit–lattice coupling is equal to the energy needed to rotate the electron spin away from the easy direction, which is known as the crystalline anisotropy energy ua . The anisotropy of a magnetic material is generally represented by an energy function that describes the equilibrium orientation of the magnetization under different fields, stresses, temperatures, etc. The easiest way to approximate the energy function is by applying a power series expansion on a set of directional basis functions. The anisotropy energy function for the simplest geometry, the hexagonal uniaxial structure, is expressed as

K1 = 41 × 105 J/m3

0.5

0

2.4.1. Magnetocrystalline Anisotropy

ua = K0 + K1 sin2 - + K2 sin4 - + · · ·

1

0.5

-0.5 -1 -1

Y

X

(c) Figure 8. Anisotropy energy for (a) uniaxial cobalt, (b) fcc iron, and (c) bcc nickel. The length of the radius at the surface of the wire frame defines the anisotropy energy in that direction.

The anisotropy constants at room temperature for the facecentered cubic (fcc) iron and body-centered cubic (bcc) nickel are K1 = 48 × 104 J/m3 3

K1 = −45 × 103 J/m

K2 = −50 × 104 J/m3

K2 = −23 × 103 J/m

3

iron nickel

Figure 8b and c shows the energy plots of, respectively, iron and nickel. For iron and nickel the change in the sign of K1 changes the number of easy directions (the nulls in the energy patterns). Iron has six easy directions and hence three easy axes, while nickel has eight easy directions and four easy axes. Cobalt has a uniaxial anisotropy that results in an omnidirectional energy pattern with one easy axis. Notice how the sign of K1 inverses the anisotropy pattern in Figures 8b and c by turning nulls into peaks and vise versa. At the point when K1 changes sign (K1 = 0), the anisotropy pattern becomes spherical (no anisotropy or Hk = 0). By alloying iron and nickel that have opposite signs

8

Magnetostrictive Nanomaterials for Sensors

in K1 , Hk can become very small, allowing easy magnetization at every direction. A good low Hk alloy is the permalloy (NiFe) material (see Section 2.6 for details). Figure 9 plots the magnetization Ms in iron, nickel, and cobalt as a function of applied H field. As shown in the plot, the materials have the lowest saturation fields when the applied field is along the easy axis, which is 100 for iron, 111 for nickel, and 001 or the c-axis for cobalt.

2.4.2. Shape Anisotropy and Demagnetizing Fields A magnetized material is composed of small magnetic dipoles. As illustrated in Figure 10, these dipoles cancel out within the material body, but not on the surface. The surface dipoles create a demagnetizing field Hd , which is proportional but antiparallel to the magnetization M,

(30)

Hi = H + Hd

The energy density of the demagnetizing field, ud , of a general ellipsoid is given as  0 Ms2  Na 321 + Nb 322 + Nc 323 2

(31)

where 31 , 32 , and 33 are the directional cosines of the magnetization with respect to the ellipsoid axes a, b, and c. Generally, the demagnetizing field is larger along a shorter direction. The demagnetizing factor for a long rod parallel to the a-axis is Na ≈ 1/2 and Nb ≈ Nc ≈ ln 2r − 1/r 2 , for a thin disc centered on the bc-plane is Na ≈ 1 and Nb = Nc ≈ 0, and for a sphere is Nd = 1/3. By choosing an appropriate

Ms (10 5 A/m)

Ms (10 5 A/m)

α-Fe H (10 4 A/m)

Ni H (10 4 A/m)

5

(a)

3

(b)

Ms (105 A/m)

|| c

S

N

S

N

S

N

N

S

N

S

N

S

N

S

N

S

N

S

N

S

N

S

N

S S

N

M, Hi

N

Hd

N

Figure 10. The magnetized sample is composed of nano/microscopic dipoles. The dipoles cancel out within the sample, but the surface dipoles remain, creating a demagnetizing field.

shape, ud can become much larger than the magnetocrystalline anisotropy energy ua , thus providing an easy way to control the direction of the anisotropy without worrying about the crystal structure of the material.

Many magnetic materials exhibit the magnetostriction effect, a phenomenon that elongates the material dimension parallel to the applied magnetic field and shortens the dimension perpendicular to the field, or vice versa. Not all materials exhibit the isotropic magnetostriction effect; for example, magnetization of an iron crystal in its 100 direction causes an elongation along 100 but magnetizing in the 111 direction causes an contraction along the 111 direction. The anisotropic magnetostriction effect, or the magnetostriction anisotropy, couples with the magnetocrystalline anisotropy, so the total energy function u of a cubic material becomes u = ua + ume + uel   = K0 + K1 321 322 + 322 323 + 323 321 + K2 321 322 323 + · · ·   + B1 321 exx + 322 eyy + 323 ezz   + B2 321 322 exx + 322 323 eyy + 323 321 ezz

+ c11 /2exx + eyy + ezz  + c11 exx eyy + eyy ezz + ezz exx 

c

Co 8

(c) Figure 9. The magnetization of (a) iron, (b) nickel, and (c) cobalt at different crystalline axes.

(32)

where ua is the anisotropy energy shown in Eq. (28), ume is the magnetoelastic energy, uel is the pure elastic energy, B is the magnetoelastic coefficient that relates the coupling between the strain eij and the magnetization direction given by 3i , and the c terms in the uel are the elastic coefficients. The strain or magnetostriction
= *l/l is derived form Eq. (32) as
=

H (10 4 A/m)

N

S

S

H

14.4

T

S

N

2 2 2 + eyz + ezx  + const × eij + c44 /2exy

4.9



N

S

2.4.3. Magnetostriction Anisotropy

where Nd is the demagnetizing factor, Nd = Na 5 Nb 5 Nc , defined over a general ellipsoid with axes a, b, and c. The field inside the material Hi is the sum of the applied H field and the demagnetizing field:

17.1

S

(29)

Hd = −Nd M

ud =

H

  3
32 92 + 322 922 + 323 923 2 100 1 1   + 3
111 31 32 91 92 + 32 33 92 93 + 33 31 93 91 (33)

where 9 gives the direction of the measured strain, and
100 and
111 are the saturation magnetostriction along the crystallography axes 100 and 111 given by
100 = −

2 B1 3 c11 − c12


111 = −

1 B2 3 c44

(34)

9

Magnetostrictive Nanomaterials for Sensors

For an isotropic polycrystalline material, the isotropic saturation magnetostriction
S is

M

c b

3 2
S =
100 +
111 5 5

(35)

For an isotropic material where
100 =
111 =
s , the relative length change is dependent only on the angle - between the measured strain and the magnetization:   3 1
= cos2 - − (36) 2 3

a

H

Domain wall

2

2 (a)

1

(b)

H

2.5. Magnetic Domains and Magnetization Process This section explains the formation of magnetic domains in ferromagnetic materials, and the motion of domain walls that is responsible for dynamic magnetization processes. This section also presents the magnetization curve of ferromagnetic materials and some common parameters that characterize ferromagnetic materials.

2.5.1. Domains and Domain Walls In the absence of an external field, the magnetic moments inside a ferromagnetic material are self-segregated into different domains of 10–100 m in size to reduce the fringing fields so the potential energy in the material is minimized. Within each domain, the magnetic moments are all oriented in parallel due to the strong exchange force. Figure 11 illustrates the formation of magnetic domains in the absence of an external field. The magnetic sample starts out with two opposing domains and gradually splits into more domains to reduce the fringing fields until reaching a pattern for which the a minimum potential energy level is reached. Since the domains in the sample are opposing each other, the net moment is zero and the sample is unmagnetized. In some cases, due to crystalline structures, defects, and stresses, these domains do not align such that the moments cancel each other, and the sample is said to have a net spontaneous magnetization. When the sample is subjected to an external field, it magnetizes along the direction of the field. To explain the magnetization process, first consider the sample shown in Figure 12, which has only two opposing domains, Domains

N N S S

N S N S

S NS N

(a)

(b)

H

1 and 2, separated by a boundary known as the domain wall or the Bloch wall. In the absence of an applied field, these two domains are oriented antiparallel so the net moment is zero. When an external field is applied, the size of Domain 1 increases, and the domain wall moves toward Domain 2. The change in domain size creates a net magnetic moment parallel to the field direction. Eventually, Domain 1 dominates the whole sample, and further increases in the magnitude of the applied field no longer increase the net magnetic moment. The sample is referred to as being in saturation. If the sample is free from structural defects and stress, the magnetization will return to zero when the applied field is removed; this type of material is classified as “magnetically soft.” In the case of nonideal materials with imperfections such as grain boundaries and precipitates, the magnetization will be irreversible due to the pinning of domain walls at the defects. Figure 13 illustrates the irreversible magnetization due to imperfections (represented by the black dots). The domain wall is initially pinned on the defects, so further field energy is needed to force the wall to jump over the defects until it is pinned again. The jump, known as the Barkhausen jump, dissipates energy due to spin relaxation and microscopic eddy currents. As a result, the domain wall motion will be different dependent upon whether the applied field is increasing or decreasing; hence the sample demonstrates hysteresis (history dependent) in its magnetization. Magnetically hard materials exhibit large hysteresis.

(a) (c)

H

1

Figure 12. Illustration of the magnetization process. Initially the two opposing domains are equal in size, so the net moment is zero. As the external field increases, the domain wall moves toward Domain 2, resulting in an increase in the net moment. Eventually, only Domain 1 remains, and increasing field will have no effect on the magnetization.

H=0

S S NN

(c)

1

H

(b)

H

(c)

(d)

Figure 11. The change of the domain pattern from two domains to an optimized pattern where the total energy is lowest.

Figure 13. Illustration of domain wall (dashed line) pinning at defects (black dots). The process from (a) to (b) is reversible, but the process from (b) to (c) is not.

10

Magnetostrictive Nanomaterials for Sensors

The domain wall, separating regions (domains) having different magnetization directions, has a width that depends upon the anisotropy and exchange energies of the materials. To understand and determine the width of the domain wall of a given sample, first consider a hypothetical scenario where the change in direction between two adjacent domains is abrupt (i.e., the domain wall is infinitesimally thin as shown in Fig. 14). The sample has an easy direction along the ±z direction, which means the anisotropy energy is smallest when the domains are parallel or antiparallel along the z direction. However, the exchange energy in a ferromagnet is minimal only when the moments are in parallel. Therefore, the domain wall in Figure 14 has a minimum anisotropy energy but a large exchange energy. To minimize the exchange energy, the direction of the moments must change gradually within the domain walls so the angle between two consecutive moments is less than 180
see Fig. 15). However, this will increase the anisotropy energy because some domains are no longer aligned along the easy axis. As a result, there are two competing energies trying to minimize the total energy: the anisotropy energy that tries to reduce the width of the domain wall, and the exchange energy that tries to widen the wall. The actual thickness of the domain wall is determined when these two competing effects are minimum. For a cubic sample with length a, is given by  Jex S 2  2 (37) = Ka where K is the anisotropy constant, Jex is the exchange integral, and S is the electron spin. The details of determining are given in Cullity [37]. Generally, the domain wall is about 10–100 nm wide. The magnetization of fine magnetic particles is explained by single-domain rotation. When an external field is applied to a single-domain particle, the Ms vector of the particle rotates toward the field direction from its easy axis, working against the anisotropy field.

2.5.2. Magnetization Curve As indicated in Section 2.2, the magnetic flux B and field H are scaled by the permeability ; similarly the magnetization M and field H are scaled by the susceptibility . For ferro- and ferrimagnetic materials,  and  are not constants; instead they are nonlinear functions that depend on the previous state of magnetization (hysteresis). Figure 16 is a plot of B and 0 M versus H, known as the BH or MH loop, where  and  are the tangents of the curve at different operating H . Note that from Figure 16, the BH and

Figure 15. To minimize the exchange energy associated with the infinitely thin domain wall of Figure 35, the directions of the moments (represented by the arrows) change gradually so the angle between two consecutive moments is less than 180
.

MH curves are offset by the vacuum induction 0 H . For most ferro- and ferrimagnetic materials, the susceptibility is much larger than 1, so the BH and MH loops are commonly considered the same. The BH loop begins with an initial curve, which is obtained by applying a field on a demagnetized sample. As the field increases, the sample magnetizes through reversible domain wall movement including irreversible Barkhausen jumps until reaching the saturation magnetization BS . As the H field reduces to zero, the magnetization does not reduce to zero but remains at the remanence Br due to the irreversible rotation of the magnetization vectors within the material. The magnetization becomes zero only when H reaches to the coercive field H = −Hc . As the H field continues to decrease, the sample will saturate at −BS . When the H field increases again, the MH curve reaches Br , Hc , and BS sequentially. Note that the BH loop will not go back to the origin. To reset the BH loop to the origin the sample needs to be demagnetized by either annealing the sample over Tc or by applying a time-varying amplitude-decaying ac field. Annealing over Tc is the best way to erase all magnetic memory of the sample; however, the process may also alter the mechanical properties of the material. Applying a decaying ac field is the most common way because it is easy to implement and imposes no permanent physical damage, but it yields no random distribution of the domain magnetization B, µ0M BH loop

Bs µ0Ms Br = µ 0Mr

MH loop

-HcB -HcM

Happl H Initial Curve

Domain Wall z

Easy axis

-Br = -µ0Mr

y

x

-µ 0Ms -B s

Domain 1

Domain 2

-z

Figure 14. A hypothetical infinitely thin domain wall separating two domains with a 180
difference in direction.

Figure 16. MH and BH hysteresis loops. The remanence, saturation magnetization, and coercive force are shown.

11

Magnetostrictive Nanomaterials for Sensors

over the easy axis. An improvement for the decaying-field demagnetization is to rotate the sample (or the field) while undergoing a demagnetizing field that yields a more random domain distribution. Although the MH loop or BH loop provides a complete picture on the magnetization, numerical permeability values are more convenient for general engineering applications. A material can have many different permeability values depending upon which part of the BH loop the material is at (biasing field magnitude). A commonly used value is the initial permeability

Easy Axis

B

Hard Axis

H

(a)

B i = lim H→0 H B→0

(38)

which is the tangent line at the origin of the initial BH curve, the maximum permeability B max = (39) H max

which is the tangent line of the BH  curve at B = 0, the reverse permeability *B (40) rev = lim *H→0 *H Bt 5 H t

which is the limit of the superposition permeability of a small ac field on the operating point Ht , Bt , and the differential permeability diff =

dB dH

B Hard Axis

(41)

which is the derivative of the BH curve. For an anisotropic material, the magnetization curve varies when the field is applied from different directions. As a result, many magnetic materials, especially thin films, are categorized with two BH loops, one measured along the easy axis and the other along the hard axis. Figure 17a illustrates the BH loop measured along the easy and hard axes. Notice that along the hard axis, a larger applied field is needed to saturate the material. The anisotropy field Hk can also be determined from the hard axis by measuring the linearized minor loop and extrapolating the linear line until it reaches saturation BS (see Fig. 17b).

2.6. Magnetic Materials Strong magnetic materials such as ferro- and ferrimagnetic alloys that exhibit large magnetization are by far the most useful materials and are commonly categorized by the coercive force Hc . Generally, materials with Hc < 1000 A/m are considered magnetically soft, materials with Hc between 1 and 30 kA/m are semihard, and materials with Hc > 30 kA/m are considered hard (for calibration, earth’s magnetic field is approximately 50 A/m at the pole, 25 A/m at equator). This section includes an overview of magnetically soft and hard ferromagnetic materials, as well as magnetoelastic and magnetostrictive materials (soft magnetic materials that react magnetomechanically with stress).

Bs

Minor Loop

Hk

H

(b) Figure 17. (a) The BH loop measured along the easy and hard axes. (b) The anisotropy field Hk can be determined by extrapolating the small-signal linearized minor loop.

2.6.1. Soft Magnetic Materials Magnetically soft materials have a low coercivity and high permeability, which result from the low crystalline and strain anisotropy energies. The low anisotropy energy minimizes the domain wall energy, allowing the rotation of domain wall with minimum energy loss when subjected to an external field. Due to reversible magnetization and a correspondingly low hysteresis loss, soft magnetic materials are largely used in field sensors, power transformers, induction motors, etc. Soft magnetic materials include various crystalline ferrites, as well as nanocrystalline and amorphous alloys. Some common magnetically soft materials and their BS , Hc , and max are listed in Table 1. Metallic crystals without impurities are good soft magnetic materials. For example, pure iron, which has a small magnetocrystalline anisotropy of K1 = −48 × 104 J/m3 , has a relatively large saturation flux density of 2.15 T and a max of 5000. The low anisotropy energy in pure iron allows domain wall movement with little resistance, hence the low coercivity and high permeability. Other good magnetically soft crystalline materials are iron–nickel (FeNi) alloys such as Permalloy, Supermalloy, Mumetal
, cobalt–iron (CoFe) alloys, silicon steels (SiFe), and Sendust (FeAlSi). Amorphous ferromagnetic alloys produced by rapid quenching do not exhibit long-range order, resulting in zero magnetocrystalline anisotropy; generally a cooling rate of approximately 105
C/s is needed to achieve such materials. Amorphous magnetic materials have a higher electrical resistance (120–200 :) compared to crystalline magnetic

12

Magnetostrictive Nanomaterials for Sensors

Table 1. A list of common magnetically soft materials with their saturation magnetization, coercive force, and maximum permeability.

Material e

Iron Cobalte Nickele Silicon steela5 e Senduste Hipercoe Permalloye Permendure Supermendure Mumetal 3e Supermalloye Ferroxcube 3F3b5 f Manifer 230c5 f Metglas 2605SCd5 g

Composition

BS T

Hc A/m

max

Fe998 Co998 Ni998 Fe96 Si4 Fe85 Si10 Al5 Fe64 Co35 Cr05 Fe22 Ni78 Fe50 Co50 Fe49 Co49 V2 Fe17 Ni76 Cu5 Cr2 Fe16 Ni79 Mo5 Mn–Zn–Fe2 O3 Ni–Zn–Fe2 O3 Fe81 Ni135 Si35 C2

215 579 061 597 500 242 508 245 240 090 079 050 035 055

80 800 60 40 4 80 4 160 16 08 016 15 8 10

5000 250 600 7000 1205000 105000 1005000 5000 605000 1005000 150005000 1800 150 3005000

a

Nonoriented. At 100 kHz. At 100 MHz. d Annealed. e Crystalline. f Soft ferrite. g Amorphous. b c

materials (30–50 :), making them a better choice for high frequency and high power applications due to reduced eddy currents. Amorphous alloys are widely used as field and stress sensors and high-power distribution transformers. Typically these glasses are composed of metals such as iron, cobalt, and nickel. To stabilize the alloys in an amorphous state metalloids such as silicon, boron, and molybdenum are added. Amorphous glasses of the transition metals (Zr, Nb, Hf), or rare-earth metals (Tb, Dy, Er, Gd) can also be made; however, the addition of rare-earth metals increases the magnetic anisotropy. Due to the presence of the glassforming metalloids the saturation magnetizations of amorphous alloys are lower than their crystalline counterparts. As-cast amorphous alloys typically contain large stress anisotropies, which reduce the soft magnetic properties of the materials. In practice, amorphous alloys are relaxed by low-temperature annealing to remove the internal stress. When used as stress sensors, amorphous alloys are annealed under magnetic field to create an anisotropy to increase the stress sensitivity. Nanocrystalline grains of 10–15 nm can be formed in the amorphous alloys by annealing them at their crystallization temperature (∼450–550
C). These nanostructured alloys have excellent soft magnetic properties with the permeability on the order of 105 , and a low hysteresis loss. However, due to the increase of phase segregation and precipitation, these nanocrystalline materials are mechanically brittle making them difficult to handle. Soft ferrites are generally composed of 70% of iron oxide Fe2 O3 and 30% of metal oxides such as zinc oxide and nickel oxide. Although ferrites are relatively inexpensive to fabricate the low magnetization (∼0.5 T) limits their applications. However, ferrites have high resistivity and therefore can be used at higher frequencies.

2.6.2. Hard Magnetic Materials Magnetically hard materials are categorized by their large coercive force (104 –106 A/m) that makes them hard to magnetize and a large remanence that allows them to exhibit significant spontaneous magnetization in zero applied field. Magnetically hard materials encompass permanent magnets, magnetic data storage, and sensors. A common way to characterize hard magnetic materials is to determine the maximum B-H energy product, BHmax . Figure 18 illustrates how to determine (BH)max from the second quadrant of a BH loop. Hard magnetic materials are made so that they have a large number of grain boundaries that act to pin the magnetization vector in a given direction. Early magnets were ironbased, such as magnetite (Fe3 O4 ) and iron carbon magnets (Fe3 C). These magnets were replaced by tungsten, Co–Mo, and Co–Cr steels with larger coercive force and magnetization during the 1940s. Another magnet widely used since the 1930s was the Alnico (Fe2 NiAl) magnet, which has subsequently been phased out by the rare-earth–transition metal magnets. Examples are SmCo5 , R2 Co7 , and Sm2 (CoFe)17 . These magnets have coercive fields of 0.8–2.4 MA/m and an energy product reaching a few hundred kJ/m3 ; common permanent magnets are listed in Table 2.

2.6.3. Magnetoelastic and Magnetostrictive Materials The most common magnetoelastic materials are the rareearth intermetallic compounds and amorphous magnetically soft ferromagnetic glasses. Crystalline rare-earth intermetallic compounds, such as Terfenol-D (Tb03 Dy07 Fe595 ), have a magnetostriction on the order of 10−3 , a magnetoelastic coupling of k = 07, and a low compliance. As a result, such materials are useful actuators for a range of applications including sonar transducers. Other examples of rare-earth compounds are GdCo and GdFe. Amorphous ferromagnetic alloys with high iron content exhibit magnetostrictions on the order of 10−5 and a magnetoelastic coupling close to 1 after annealing. Amorphous ferromagnetic alloys, such as Fe81 B135 Si35 C2 , have a low anisotropy field (Hk = 70 A/m), which allows the rotation of magnetization and accompanying magnetostrictive strain with low applied fields and stresses, resulting in a high magnetoelastic coupling. Ferromagnetic glasses are widely used as stress/strain sensors and field sensors and as cores of power transformers. Some

B

B

(BH)max

(BH)max H

(a)

BH

(b)

Figure 18. (a) Second quadrant of a BH loop. The location of the BHmax corresponds to a rectangular area where the product of BH is maximal. (b) The (BHmax can be determined by plotting B versus BH and determining the maximum of the curve along the x-axis.

13

Magnetostrictive Nanomaterials for Sensors Table 2. A list of common magnetically hard materials with their remanence, coercive force, and energy product.

Material

Composition

Iron carbon Tungsten steel Alnico 5 Fe–Cr–Co Hexagonal ferrites Co–rare earth Fe–rare earth

Fe3 C Fe92 W8 Fe50 Co25 Ni15 Al8 Cu2 Fe–Cr–Co isotropic BaO–Fe2 O3 SmCo5 (aligned) Fe14 Nd2 B (aligned)

Hc BH max Br (T) (kA/m) (kJ/m3  524 2 52 56 022 50 56

4 7 50 65 145 2900 1600

4 8 42 80 9 200 350

common magnetoelastic materials, along with their saturation magnetization, magnetostriction, and magnetoelastic coupling coefficients, are listed in Table 3.

3. FERROMAGNETIC GLASS PREPARATION AND PROPERTIES This section describes some fabrication processes, properties, and methods of enhancing the properties of the ferromagnetic glass alloys.

3.1. Preparation of Ferromagnetic Glasses Ferromagnetic glasses are commonly fabricated using melt quenching methods such as melt-spinning [52] and atomic condensation techniques such as electrodeposition [53, 54] and sputtering [55]. The key to successfully fabricating a ferromagnetic glass is rapid removal of heat from the melt, to preclude crystallization in the alloy. In most cases, cooling rates of 105
C/s are needed. Most of the magnetically soft ferromagnetic glasses are based on 3d transition metals (T) with glass forming metalloids (M) such as boron, carbon, silicon, or phosphors to stabilize the amorphous state. The composition of transition-metalloid-based alloys, T1−x Mx , is usually in the range of 15 < x < 30 at%, such as Fe80 B20 , Fe40 Ni40 P14 B6 , and Co74 Fe5 B18 Si3 . The late transition metals (TL = Fe, Co, Ni) can also be stabilized in an amorphous state by alloying with early transition metals (Zr, Nb, Hf), forming TE1−x TLx , with x in the range 5–15 at% such as Co90 Zr10 . Ferromagnetic glasses are also built by alloying transition metals (TL = Fe, Ni, Co) with rare-earth metals (R = Tb, Dy, Er, Gd), forming R1−x TLx with x typically 10–25 at%. Among these ferromagnetic glasses, the Table 3. A list of magnetoelastic materials and their saturation magnetization, magnetostriction, and magnetoelastic coupling coefficient. Material

Composition a

Metglas 2605SC Metglas 2826MBa Ferromagnetic glassa Ferromagnetic glassa Terfenol-Db a b

Amorphous. Crystalline.

Fe81 B135 Si35 C2 Fe40 Ni38 Mo4 B18 Fe45 Co6815 Si125 B15 Co725 Si125 B15 Tb03 Dy07 Fe595

BS (T)
S (ppm) kmax 561 088 07 05 52

30 12 −01 −1 1500

098 05 — — 075

transition-metalloid-based alloys have the most useful properties for sensor applications, such as high magnetostrictive and magnetoelastic coupling coefficient and low magnetic anisotropy. Although transition-rare-earth-based amorphous alloys such as TbDyFe and TbCo have a lower magnetoelastic coupling coefficient, of ∼0.5–0.7, they have the largest known values of magnetostriction on the order of 10−4 [56, 57].

3.2. Summary of Physical and Magnetic Properties of Ferromagnetic Glasses As-cast ferromagnetic glasses are flexible, with Young’s moduli of around 100 GPa, about 20–30% lower than their crystalline counterparts [58]. As-cast ferromagnetic glasses also exhibit high mechanical strength and ductility. For example, the tensile strength of as-cast Metglas 2605SC and 2826MB alloys is approximately 1000 to 1700 MPa, and for as-cast FC20 alloys (Fe933 Si29 C34 B04 ) it can reach to 3400 MPa. However, annealing processes, although improving the soft magnetic properties by creating nanocrystalline structures, can destroy the mechanical properties and render these materials brittle by increasing precipitation and phase segregation. In general, the tensile strength and Vicker’s hardness of the ferromagnetic glasses show a small increase at low temperature annealing but decrease significantly when the annealing temperature reaches the crystallization temperature Tc [59]. Nanocrystalline alloys, produced by annealing ferromagnetic glasses at temperatures at or above Tc , have a lower mechanical strength compared to their amorphous counterparts. Ferromagnetic glasses contain localized random anisotropies, which act like the crystalline anisotropy but on the scale of few nanometers. The strength and direction of the localized anisotropy vary with position, resulting in zero macroscopic crystalline anisotropy (although most ferromagnetic glasses still contain stress anisotropy as a result of the fabrication process). Ferromagnetic glasses made of transition metals and metalloids have weak coupling between the local anisotropies; as a result they are magnetically soft and can be easily magnetized. However, rare-earth-based ferromagnetic glasses have strong localized coupling forces; hence saturation magnetization is much harder to achieve, and the materials are magnetically harder to a significant degree. Common magnetically soft ferromagnetic glasses have magnetic susceptibilities on the order of 105 , saturation magnetizations of about 1 T, and compared to their crystalline counterparts low hysteresis loss. Annealed and nanocrystalline ferromagnetic glasses have a higher susceptibility due to the reduction of stress anisotropy energy. The electrical resistivity of ferromagnetic glasses are generally one order of magnitude higher than their crystalline counterparts, with typical values of 100–200 : · cm. The high resistivity significantly reduces eddy currents making the ferromagnetic glasses more suitable for high frequency applications. Note that the values given above are those of common materials, as generally fabricated and used; properties can be altered by changing alloy composition and performing annealing, as will be detailed in Section 3.3. In addition to

14

Magnetostrictive Nanomaterials for Sensors

these properties, ferromagnetic glasses also exhibit attractive properties for sensor applications such as magnetoelastic and magnetostriction effects, magnetoelastic resonance, and the GMI effect, which will be explained in the following sections.

3.2.1. Magnetoelastic and Magnetostriction Effects Most ferromagnetic glasses exhibit magnetostriction, a phenomenon where the dimensions of an object change when subjected to the influence of an external magnetic field. Magnetostriction is generally quantified with the saturation magnetostriction
S , which is defined as the ratio of the change in length *l/l at magnetic saturation. Although it is well known that the magnetostriction of a ferromagnetic glass varies with alloy composition, predicting the effects of alloy composition on the magnetostriction is still difficult, and most existing theoretical models are only applicable to specific binary or ternary alloys. In general, rare-earth-based alloys exhibit the highest magnetostriction with
S ≈ 10−4 , followed by Fe-rich alloys with
S ≈ 10−5 , while Co-rich alloys have a low magnetostriction of
S ≈ 10−7 . Magnetostriction also depends upon applied stress, structural relaxation [60, 61], and fabrication parameters [56, 62]. Generally,
S increases when ferromagnetic glasses are relaxed under low field annealing but decreases when the annealing temperature is beyond the crystallization temperature. The magnetoelastic effect, which describes the coupling between the elastic energy and magnetic energy, is usually quantified by the magnetoelastic coupling coefficient k, defined as the ratio of the coupled elastic-magnetic energy to the pure elastic and magnetic energies. Magnetoelastic and magnetostriction are related but not necessarily proportional to each other due to the influence of other parameters such as applied stress. For example, rare-earth-based alloys have a very high
S , but their magnetoelastic coupling is lower than the Fe-rich alloys, which have a lower
S . The most common model for understanding the effects of applied stress and field on the susceptibility, magnetoelastic coupling, and the Young’s modulus of a ferromagnetic ferromagnetic glass ribbon is shown in Figure 19. The model considers a ribbon-shaped ferromagnetic glass having a widthwise magnetic easy axis and a uniaxial anisotropy with an energy contribution of KU cos - per unit volume. In the absence of an applied field and applied stress the magnetization in the domains aligns across the width of the ribbon. When a longitudinal field H and stress < are applied

the magnetization rotates from the width toward the length direction (see Fig. 19), yielding a magnetostrictive strain = given by [63]   3
S H 2 1 < + H < Hk (42) − == EM 2 Hk2 3 where EM is the Young’s modulus at a constant magnetization, and the anisotropy field Hk is given by Hk =

=

Ms

(b) Figure 19. (a) Magnetic domain of a transverse-field annealed ferromagnetic glass ribbon at (a) zero bias field (H = 0) and (b) 0 < H < Hk .

Ms2 2KU − 3
S
1, generating nonlinear dispersion, two or even three film properties, such as the density and Poisson’s ratio, may be accessible. An important property that can be studied with this technique is also the mechanical strength. Except for a few materials, the theoretical strength may be orders of magnitude higher than the measured value. With laser-excited nonlinear SAW pulses, it is possible to generate steep shocks with stresses that exceed the mechanical strength of covalent brittle materials such as silicon. These stresses lead to transient fracture by impulsive loading. The influence of rapidly rising stress pulses of very short duration on the dynamics of fracture is currently not well understood. Nonlinear SAW pulses provide a new tool to study transient fracture dynamics without seed cracks.

5.2.2. Brillouin Scattering A very powerful, nondestructive, and sensitive technique for the characterization of elastic properties of materials, and in particular for thin films or multilayers, but also for nanostructured materials, is Brillouin spectroscopy. Brillouin light scattering is the inelastic scattering of an incident optical wave field by thermally excited elastic waves (usually called acoustic phonons). Since the advent of lasers, Brillouin scattering has received considerable interest for the characterization of elastic and optoelastic bulk and surface properties of materials. Due to the small frequencies of acoustic phonons for small wavevectors, the Brillouin lines are separated by small frequency shifts, of the order of less than 1 cm−1 , from the elastic line. For this reason it is not possible to use a grating monochromator as for Raman scattering, but rather a Fabry–Perot interferometer must be used. In terms of the corpuscular theory of light, first-order Brillouin scattering corresponds to an inelastic collision of a photon with an acoustic phonon. As for Raman scattering, the photon either loses a quantum of vibrational energy (Stokes line) or acquires such a quantum (anti-Stokes line). For a complete presentation of Brillouin scattering theory the reader is referred to [63, 65, 66]. Brillouin scattering by SAWs is called surface Brillouin scattering (SBS). The measurement is intrinsically contactless and local. Since spontaneous Brillouin scattering relies on thermally excited acoustic waves, interaction occurs with waves having an amplitude much smaller than that of the waves excited in the other techniques cited before, implying that Brillouin scattering measurements are more time consuming. However, the acoustic wavelengths probed in a Brillouin scattering experiment can be significantly smaller than those probed by other techniques: this gives Brillouin scattering a unique potential in terms of spatial resolution, particularly relevant in the case of ultrathin films. In the case of thin or ultrathin films, this technique proves really powerful. The velocities of surface acoustic waves can be measured by Brillouin spectroscopy. If independent measurements of film thickness and mass density are available, the elastic constants can be derived from the measured acoustic velocities. Such measurements can be performed, for example, by X-ray reflectivity (see, e.g., [67]). Combining Brillouin scattering and X-ray reflectivity measurements

Mechanical Behavior of Nanomaterials

of thickness and density, the elastic constants of films have been measured for film thicknesses ranging from hundreds to tens of nanometers. It has been demonstrated that it is possible to extend the limits of the sensitivity of both the X-ray and Brillouin scattering techniques, in order to characterize films down to a few nanometers thick.

5.2.3. Surface Brillouin Spectroscopy In the bulk of a material, the interaction between acoustic waves and electromagnetic waves occurs by the elasto-optic effect, that is, the dynamical modulation of the electrical susceptibility by the strain field of the acoustic wave. At a surface, interaction also occurs by the ripple effect, that is, the dynamical modulation of the surface geometry due to the acoustic wave. The ripple mechanism is the only one in metallic materials, and is however typically dominant in SBS, since the strain field of SAWs is confined in the vicinity of the surface. In a Brillouin scattering measurement, a monochromatic laser beam of wavelength 40 , circular frequency /i , and wavevector ki ( ki = 25/40 ) is focused onto the specimen, and scattered light of wavevector ks is collected along a given direction. The scattering geometry selects the exchanged wavevector, that is, the acoustic wavevector q being probed q = ±ks − ki 

(19)

the − and + signs referring to Stokes and anti-Stokes events, respectively. The wavevectors ki and ks have essentially the same modulus, and the relative difference is at most twice the ratio of the acoustic velocity to the light velocity. The spectrum of the scattered light is dominated by the elastically scattered light at the incident circular frequency /i . If light is inelastically scattered by an acoustic wave of velocity v, the spectrum also contains a doublet at frequencies /s = /i ± 8

(20)

the − and + signs referring again to Stokes and anti-Stokes events, respectively; the frequency shift 8 = vq immediately gives the acoustic velocity. In SBS only the wavevector component parallel to the surface is conserved: Eq. (19) takes the form q = ±ks − ki 

(21)

and the SAW velocity v = 8/q is obtained. In SBS the backscattering configuration is often adopted because it maximizes q , and because it allows a simpler set-up, since the same lens is exploited to focus and to collect. In backscattering with incidence angle 9, the nominal exchanged wavevector is q = 45/40  sin 9. This means that SAWs are probed having wavelength 4 = 40 /2 sin 9 and, although 9 seldom exceeds 70 , acoustic wavelengths are probed down to about 40 /2. With visible light this means that wavelengths 4 below 300 nm can be probed. They are completely determined by the scattering geometry alone, and with common values of material properties they correspond to SAW frequencies up to above 20 GHz. This gives SBS its unique sensitivity to submicrometric films; with other techniques the frequency rather than the wavelength is determined by the experimental set-up, and the frequencies typically lie in the tens to

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hundreds of megahertz range. A dispersion relation vq  is obtained varying the incidence angle 9. Measurements are performed at a set of incidence angles 9 i obtaining a set of measured circular frequencies 8im and a set of measured i velocities vm = vm qi  = 8im /qi .

5.2.4. Derivation of the Elastic Constants From the measured acoustic velocities the elastic properties of materials can be derived. Both bulk acoustic waves [68] and SAWs [69] have been exploited. The velocities of the SAWs in layered structures, and namely for a single film on a substrate, can be computed by the continuum elastodynamics equations as a function of the material properties of both the film and the substrate, of the film thickness, and of the wavevector. In particular, materials are characterized by the mass density 7 and the elements Cij of the elastic constants tensor, and the computed velocities vc are obtained as vc = vc ;7 Cij 850  C). Such a noticeable temperature lowering is a consequence of the high-energy milling enhancing the formation of BaFe2 O4 . A ternary mixture BaCO3 –Al2 O3 –SiO2 was mechanically activated for different lengths of time [252]. The obtained data show that reaction rate increases with prolonged activation time, under the same conditions of thermal treatment ranging from 750 to 1200  C. Formation of hexacelsian via a series of solid state reactions involving Ba silicates was favored with increasing activation time. Direct formation of monoclinic celsian has been found to be retarded with prolonged activation.

110 BaAl2 O4 /aluminum bearing composites have been synthesized [253] via the low temperature oxidation of Ba–Al precursors. Ba–Al powder mixtures were prepared via highenergy vibratory milling, then unixially pressed into barshaped samples which were then exposed to heat treatment in pure flowing oxygen at temperatures up to 640  C. Oxidation at 300  C resulted in the formation of barium peroxides (BaO2 . Heat treatment at 550  C leads to the consumption of BaO2 and of some aluminum to yield to BaAl2 O4 and Al4 Ba. The oxidation of Al4 Ba at 640  C has been found to produce additional BaAl2 O4 . The fast synthesis of YBa2 Cu3 Oz superconductor at low temperatures of its orthorhombic modification existence using mechanically activated and densified two-powder precursors has been investigated by Goodilin et al. [254]. Mechanically activated and densified two-powder precursors yield reproducibly an YBa2 Cu3 Oz phase when using internal oxygenation of soft chemistry produced Cu2 O by YBa2 O3 5 (containing BaO2  in their mixture (Y:Ba:Cu = 1:2:3) mechanically activated in a planetary mill and warmly compacted at 250  C into a dense pellet. A “mild” mechanochemical synthesis based on mechanical activation of highly reactive compounds in the grinders (solid acids and bases, hydrated oxides, acidic or basic salts, crystallohydrates) has been used for the preparation of cordierite [255]. Mechanical activation accelerates the mixing and mass transfer processes at an atomic level. Sometimes, this treatment suffices to complete thermodynamically favorable reactions. However, in the majority of cases, the amorphous phases are formed and a subsequent thermal treatment is necessary at temperatures which are 200–300  C lower than that of common thermal synthesis.

4.3.3. Nanotubes/Nano“cage” Synthesis Mechanically activated solid state reaction has been found to be a suitable method for the production of carbon and boron nitride nanotubes [256]. Both carbon and boron nitride nanotubes have been produced by first ball-milling of graphite and boron nitride powders at room temperature and then by isothermal annealing at temperatures less than 1500  C. Ball milling has been found to create the nuclei for nanotubes and the subsequent isothermal annealing is responsible for nanotube growth. The investigation [257] of morphological and structural changes during high-energy ball-milling and thermal annealing of the mixtures soot–iron and soot–nickel demonstrated that the activation is accompanied by the formation of nanosized metal particles (10–50 nm) distributed over the amorphous carbon matrix. Prolonged mechanical activation of the amorphous soot iron has been found to lead to the formation of nanosized cementite Fe3 C compound. Morphological characteristics of the annealed, mechanically activated soot–metal samples depend on the time of the mechanical activation step. Annealing after shorttime mechanical activation has been demonstrated to cause a crystallization of the amorphous carbon as onionlike graphite–metal structures. Annealing of the soot–metal samples after mechanical treatment for more than 5 min leads to the formation of metal nanoparticles (40–50 nm) encapsulated by graphite. The longer the preliminary mechanical activation, the smaller the size of encapsulated particles.

Mechanical Processing for Nanomaterials

5. MECHANOCHEMISTRY Mechanochemical processing is broadly the use of mechanical energy to cause reactions, which normally require elevated temperatures, to occur at ambient temperatures. For example reduction reactions which are normally carried out at temperatures close to 1000  C can be achieved at ambient temperatures through the mechanochemical process [258, 259]. Normally the reaction products formed by the process are ultrafine powders with a wide distribution of particle size ranging from a few nanometers to micrometers [260]. In a paper entitled “Recent development of materials design through a mechanochemical route,” Senna [261] wrote a critical overview of the principle and practice of modern mechanochemical processes for the preparation and design of high-value-added materials. The importance of the low coordination states and effects of symmetry disturbance of crystal and ligand fields are emphasized. Several successful examples of applications are displayed, such as inorganic complexes for electronic and construction materials, bioceramic materials, and metal organic coordination compounds. Starting from the binary system, Ca(OH)2 –SiO2 , it was shown that a proton from a surface silanol group transfers to an OH group of Ca(OH)2 , a so-called mechanochemical dehydration, leaving a bridging bond, Ca–O–Si [262]. Similar reactions lead to heterobridging bonds or heterometaloxane bonds when two dissimilar metal atoms, Me(I) and Me(II), are connected by an oxygen atom serving as a hinge. Several conditions must be associated for such a reaction mechanism to occur. One is the state of the low coordination number of atoms. The coordination number of Ca in Ca(OH)2 is equal to 6 in the crystal bulk but it may decrease to 5, 4, or even 3, not only for atoms located on surfaces (edge or corner atoms) but, more importantly, due to various lattice defects. The second condition, not less important, is the loss of crystal field symmetry. Knowing that bridging bond formation is a consequence of a redox reaction between two metal oxides or hydroxides, it has been applied to complex oxide syntheses such as that of perovskite compounds Pb(Mg1/3 Nb2/3 O3 . The same principle has been applied to complex oxides other than perovskites, for example, the formation of MgTiO3 starting from Mg(OH)2 and TiO2 · H2 O hydrogel [263, 264] or of Sr0 6 FeO4 from Sr(OH)2 and alpha-FeOOH. Another field of successful applications is the synthesis of rapid hardening agents for cement which are necessary for emergency construction and for shortening construction time. It has been realised via a mechanochemical activation. When Al(OH)3 was milled by an agitation mill and subsequently mixed with Ca(OH)2 in equimolar proportions, the mixture served as an excellent hardener [265].

5.1. Formation of Ultrafine Oxide Nanoparticles Various ultrafine particles have been reported to be prepared by a combination of mechanochemical and thermal processes. Several examples are described.

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One is the synthesis of pure ZrO2 by mechanochemical reaction of ZrCl4 with MgO, as given by ZrCl4 + 2MgO → ZrO2 + 2MgCl2 . The degree of interparticle agglomeration was found to be significantly reduced by postmilling heat treatments and also by the use of alcohol wash solvents [266]. The solid-state reduction of haematite (alpha-Fe2 O3 ) with carbon mainly to nanocrystalline wüstite by room-temperature dry ball-milling was investigated by Matteazzi and Le Caër [267]. In addition to wüstite, a small amount of nanocrystalline magnetite is also formed, possibly by a disproportionation reaction of wüstite. In some cases, the chemical reaction has been found to not occur during milling but during a postmilling annealing step. The formation of alumina via the reaction 2AlCl3 + 3CaO → Al2 O3 + CaCl2 does not occur during mechanical milling. Annealing at 150–200  C leads to the formation of AlCaCl5 . CaCl2 was found to form by annealing at temperatures higher than 300  C, indicating the formation of alumina. After washing to remove the chloride, the samples were found to consist of gamma alumina nanoparticles (10–20 nm). This phase, which is metastable at room temperature, transforms into alpha alumina during annealing at 1250  C [268]. Such a feature is also the case for the mechanochemical synthesis of ultrafine ZrO2 powders [269]. They are obtained by a subsequent annealing of ground powders at 300–400  C, according to the expected milling induced reaction ZrCl4 + 2CaO → ZrO2 + 2CaCl2

G = −440 kJ

In fact, the absence of diffraction peaks for the ZrCl4 phase just after milling suggests that amorphization occurs during milling, leading to an embedding of separated CaO crystallites in an amorphous ZrCl4 matrix. After annealing, the ZrO2 nanophase is dispersed in a CaCl2 matrix which can then be dissolved in methanol. The same behavior is observed in the case of hematite powders synthesized by mechanochemical processing [270] according to the following chemical reactions: 2FeCl3 + 3CaO → Fe2 O3 + 3CaCl2

G = −508 kJ

2FeCl3 + 3CaOH2 → Fe2 O3 + 3CaCl2 + 3H2 O G = −341 kJ The diffraction pattern for the as-milled powder indicates that CaO remained unreacted during milling. Annealing at 50 and 100  C did not result in any changes of the as-milled mixture. After annealing at 150  C, X-ray diffraction peaks associated with the CaCl2 and Fe2 O3 phases were observed indicating that the reaction has occurred. A methanol washing was used to remove the CaCl2 phase. The Fe2 O3 powder exhibits particle sizes ranging from 100 to 500 nm. Dilution of the starting materials with CaCl2 resulted in the reduction of the Fe2 O3 particle size down to 10–30 nm. Milling of a starting mixture which contains Ca(OH)2 results in the formation of FeOOH. Annealing at temperatures below 150  C did not lead to any significant changes in

the XRD patterns. Annealings above 200  C are needed to form crystalline CaCl2 and hematite Fe2 O3 , due to dehydration of FeOOH. The hematite particle size ranges between 20 and 50 nm. The synthesis of ultrafine (Sn, Zn, Ce) oxides by mechanochemical reaction and subsequent calcinations was studied [271]. A simple washing process has been found to remove the by-product phase, resulting in the production of nanopowders of SnO2 , ZnO, and CeO2 with mean particle size of 40, 28, and 10 nm, respectively: SnCl2 + CaOH2 → SnO + CaCl2 + H2 O

G = −59 kJ

ZnCl2 + Na2 CO3 + 8 6NaCl → ZnO + 10 6NaCl + CO2 gaz

G = −80 kJ

CeCl3 + 3NaOH → CeOH3 + 3NaCl

G = −345 kJ

To prevent the occurrence of a combustion reaction, 12 moles of NaCl diluent were added to the starting mixture yielding the reaction CeCl3 + 3NaOH + 12NaCl → CeOH3 + 15NaCl which takes place progressively instead. In the cases of the SnCl2 and CeCl3 initial chlorides, such reactions lead to the hydroxide phase formation during milling. The removal of H2 O and the final oxidation step occur on heating ground powders above 100  C in air. With the ZnCl2 /Na2 CO3 reaction, the ZnCO3 phase is stable at room temperature and calcinations above 200  C were required to form ZnO.

5.2. Formation of Ultrafine Metallic Nanoparticles Mechanochemical synthesis has been successfully applied to the synthesis of ultrafine metallic powders.

5.2.1. Na Reducing Agent Such a method has been applied to the production of ultrafine Fe powders [272]. The formation of Fe is due to the reduction of FeCl3 by Na via the reaction FeCl3 + Na → Fe + 3NaCl An important requirement for the formation of nanoscale particles is that the volume fraction of the by-product phase has to be sufficient to prevent the particle agglomeration resulting in an increase of the crystallite size. In the case of ultrafine Cu particles prepared by the mechanochemical process [273], the milling induced solid state displacement reaction is CuCl2 + 2Na → Cu + 2NaCl Depending on the reaction modes (continuous or combustion ones), two distinct morphologies of Cu particles have been observed; Cu particles with sizes uniformly distributed

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in the range 20–50 nm are formed by a steady state reaction during mechanical milling, whereas larger particles were observed in the combustion reaction case. McCormick et al. showed such an addition of Na to metal chlorides [274] to produce ultrafine Co and Ni particles, with particle sizes of 10–20 nm, according to the following reactions: CoCl2 + 2Na → Co + 2NaCl

G = −495 kJ

NiCl2 + 2Na → Ni + 2NaCl

G = −507 kJ

The formation of ultrafine particles requires again the volume fraction of the metallic phase being formed to be small relative to that of the by-product phases and combustion during milling must be avoided to prevent particle coarsening.

5.2.2. Mg Reducing Agent Instead of using Na as reactant, a solid state displacement reaction between NiCl2 and Mg, induced by mechanical milling [275], was employed for the production of fine Ni powders. The end product was leached with dilute HCl to obtain the nickel powder with sizes ranging between about 10 to 500 nm. It has been observed that unlike the results on reduction reaction in ZnO/Ti and CuO/Fe systems, interruption during milling of NiCl2 /Mg prolongs the start of ignition. A critical combination of intimate mixing of the reactants with freshly formed surfaces, structural strains, and a milling induced temperature rise is necessary for the ignition to take place. Such a Mg reactant chemical reaction has also been used for the reduction of tantalum chloride by magnesium during reaction milling [276]. The reaction used is 2TaCl5 + 5Mg → 2Ta + 5MgCl2

G = −356 kcal

The vial temperature, which was measured during milling, indicated that the in-situ mechanochemical reaction which has been found to occur is a combustion one. Crystalline Ta and MgCl2 were identified immediately after the combustion (corresponding to an abrupt increase of the vial temperature) while further milling led to chloride amorphization. The ball mass has an important effect on the conditions required for combustion to occur. A mechanochemical reduction of nickel oxide by graphite has been tested to produce ultrafine Ni [277]. Milling at ambient temperature did not result in the reduction of nickel oxide to nickel. However, milling significantly decreased the critical reaction temperature for the reduction, from 1350 K for the unmilled sample to 650 K for samples milled for 12 hours or longer. Reduction of NiO to Ni occurred during milling at elevated temperatures. The extent of the reaction during milling at elevated temperatures was dependent on the partial pressure of CO2 in the sealed vial. Ultrafine Mo particles can be produced as a result of the slow burning transition into detonation in the MoS2 –Mg mixture [see N. G. Danielian et al. Mod. Phys. Lett. B 5, 1301 (1991)] according to the following reaction: MoS2 + 2Mg → 2MgS + Mo

The mechanical treatment of the reactant mixture results in a considerable decrease of the ignition temperature and in a strong increase of the burning speed. To close this section about the description of the mechanochemical synthesis of ultrafine metallic particles, we notice that similar methods can be used to prepare nanostructured intermetallic compounds [278]. The basis for the synthesis of Ti–Al alloys is the coreduction reaction induced mechanically: 6TiCl4 + 2AlCl3 + 7CaH2 + 8Mg → 2Ti3 AlH + 7CaCl2 + 8MgCl2 The reaction product after leaching is Ti3 Al(H) with hydrogen in interstitial sites of the Ti3 Al structure. The use of CaH2 as a reducing agent in the given example results in the formation of Ti3 Al(H) which is more passive to oxidation than Ti3 Al. Nanocrystalline TiC was synthesized by the displacement reaction TiCl4 + 2CaC2 → TiC + 2CaCl2 + 3C The reaction has also been modified to avoid the formation of free carbon, by the addition of Mg: 2TiCl4 + CaC2 + 3Mg → 2TiC + CaCl2 + 3MgCl2

5.2.3. Si, Fe Reducing Agents The mechanochemical synthesis of refined Ag and Zn composite powders starting from oxides using Si and Fe as reducing agents was reported by de la Torre et al. [279]. Ag2 O and ZnO powders were reduced by a mechanochemical process using Si and Fe as reducing agents. A number of advantages are conferred to the end products Ag–SiO2 , Ag–Fe2 O3 , Zn–SiO2 , and ZnO–Fe2 O3 submicrometric composite products prepared in that way. The active oxides, with nanometer-sized tailored particles, are for instance homogeneously dispersed into the reduced metal matrix.

5.3. Formation of Semiconductor Nanoparticles Mechanochemical synthesis has been applied to the large scale preparation of ultrafine Si nanoparticles by ball-milling [280]. Si nanoparticles were synthesized by ball-milling of mixtures of graphite and of SiO2 powders followed by subsequent annealing at 150  C.

5.4. Sulphide Reduction or Production Mechanical milling [281] of ZnCl2 and CaS mixtures resulted in the formation of 500 nm ZnS particles containing aggregates of 12 nm crystallites according to the following reactions: ZnCl2 + CaS → ZnS + CaCl2 ZnCl2 + CaS + 3 6CaCl2 → ZnS + 4 6CaCl2 ZnCl2 + CaS + 8 2CaCl2 → ZnS + 9 2CaCl2

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The addition of 71 vol% CaCl2 as a diluent to the reactants resulted in the formation of separated 16 nm particles of ZnS. Using mechanically alloyed CaS (10–50 nm particle size) enabled the synthesis of isolated ZnS particles 7–9 nm in size. Such a method is claimed to be applicable for the production of nanoparticles of other II–VI semiconductors, of ternary II–VI semiconductors such as CdHgSe and CdSTe, or of heavily doped semiconductors such as Zn(Mn)S as well as that of metal sulphide compounds. Solid-state room temperature reduction and exchange reactions of metal (M) sulphides (FeS, WS2 , MoS2 , Cu2 S, CoS, PbS, ZnS) [282] were driven by ball-milling of powder mixtures of a sulphide and of either a reductant (R = Al, Mn, Fe, Si) or an exchange compound (CaO). Milling results in a complete reduction of the metal sulphide and in the formation of nanocomposites made of M and R sulphide. Exchange reactions with CaO show the formation of M oxide–CaS nanocomposites: MS + R → RS + M MS + CaO → CaS + MO Iron sulphides were for instance reduced by aluminum, manganese, and silicon, copper sulphides by aluminum and iron, and cobalt, lead, and zinc sulphides by aluminum. Exchange reactions took place for iron, tungsten, and molybdenum sulphides.

5.5. Nanocomposite Formation 5.5.1. Magnetic Nanocomposites Magnetic nanocomposites [283] of small iron particles embedded in nonmagnetic zinc oxide have been prepared by ball-milling (Spex machine) via in-situ displacement reactions: Fe3 O4 + 4Zn → 3Fe + 4ZnO The final particle size is about 9 nm as estimated from X-ray diffraction line broadening. The end product is a semihard magnetic material exhibiting a significant volume fraction of superparamagnetic Fe particles. Solid-state room temperature exchange reactions of iron nitride, fluoride, and cementite Fe3 C with silicon or aluminum, carbon, and chromium respectively were investigated [284] according to (iron nitride) + Al → AlN + Fe (iron nitride) + Si → Si3 N4 + Fe FeF3 + C → C fluoride + Fe fluoride Fe3 C + Cr → (Fe, Cr) carbide A partial transfer of nitrogen from iron nitride to aluminum and silicon, with the formation of aluminum and silicon nitrides, was evidenced. Partial transfer of fluorine was obtained too by reaction milling. A mixed, largely amorphous (Fe,Cr) C alloy was formed. The as-milled powders have small crystallite sizes (10–20 nm) and may

thus be considered as nanocomposites composed of AlN– Fe2 5 N–(FeAl) alloy, Si3 N4 –Fe2 5 N–(FeSi) alloy, FeF3 –FeF2 – FeF3 (H2 O)0 33 –CFn –(CF1 1 )n and (Fe,Cr)carbide–(Fe,Cr)C amorphous alloy.

5.5.2. Synthesis of Nanocermets (Oxide–Metal Nanocomposites) Metal–matrix composites (MMCs) have been of interest for several decades. Several methods have been developed to incorporate large volume fractions of oxides, carbides, borides, and other particles into metallic matrices. The mechanical alloying technology has been used to produce strengthened MMCs with oxide dispersions and controlled fine microstructures. Derived from mechanical alloying, the mechanochemical process is suited for the formation of complex precursor oxides for advanced materials technology applications. Schaffer and McCormick [285] reported the direct synthesis of metallic Cu by milling mixtures made of its oxide and of various reducing elements such as Al, Ca, Ti, Mg, Mn, Fe, and Ni.

5.5.3. Alumina–Metal Nanocomposites Nanometer sized alpha-Al2 O3 –M composites (M = Fe, V, Cr, Mn, Co, Ni, Cu, Zn, Nb, Mo, W, Si, Fe alloys) were synthesized by solid-state reduction reactions occurring during room-temperature ball-milling of mixtures of a metal oxide (Mx Oy ) and aluminum (Al2y/3 ) [286, 287]. The sizes of both alumina and metal crystallites obtained in that way are close to 10 nm for powders processed in a vibratory mill (24 hours). In a planetary mill, nanocrystalline phases have crystallite sizes about 2–3 times larger after milling for about one hour with a smaller powder-toball ratio. Nanocomposite powders [(Fe or Fe–Cr alloy)/alpha alumina (75 and 85 vol%)] were prepared [288] by room temperature high-energy milling powder mixtures of haematite (and chromium oxide) with aluminum and alumina in a high-capacity mill according to the following reactions: Fe2 O3 + 2Al + 0 7 or 2 1 Al2 O3 → 1 7 or 3 1Al2 O3 + 2Fe Fe2 O3 + 0 16Cr2 O3 + 2 32Al + 0 77 or 2 49 Al2 O3 → 1 93 or 3 65 Al2 O3 + 2Fe + 0 32Cr Both the metallic and ceramic phases have crystallite sizes smaller than 15 nm for all the investigated compositions. A spinel oxide, hercynite, FeAl2 O4 , is formed during the reduction reaction and is retained in small amounts in the final powders. In the Fe–Cr/Al2 O3 composite, the metallic matrix has a lower Cr content than expected as a significant amount of Cr is dissolved in alumina. The solid-state reduction of Fe2 O3 (haematite) by ballmilling with Al or Mg has been investigated by Nasu et al. [289] according to the following equations: Fe2 O3 + 2Al → 2Fe + Al2 O3 Fe2 O3 + 3Mg → 2Fe + 3MgO

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A partial substitution of Fe by Al in the alpha-Fe lattice has been revealed by Mössbauer analyses. For the second reaction, the reduction of Fe2 O3 results in the formation of alpha-Fe, MgO, and an unknown compound (presumably a wustite-like Fe1−x Mgx O compound). Takacs has studied the reduction of magnetite by aluminum by the way of a displacement reaction induced by mechanical alloying [290]. An explosive solid-state reaction occurs in a wide composition range as revealed by the sudden temperature rise of the grinding media. The reduction of Fe3 O4 to Fe by metallic Al is consistent with the following reaction:

In the first reaction, oxygen is directly transferred from NiO to Si which is completely oxidized into silica, while the stoichiometric quantity of NiO is reduced to Ni. The sizes of the Ni crystallites are in the nanometer range. Similar milling processing conditions, which have applied to mixtures containing CuO, give rise to the formation of Cu(I) intermediate products.

5.5.5. Other Nanocomposite Formation

Off–stoichiometry lengthens the incipient stage of the reaction and changes the reaction products. A slight reduction of the amount of Al results in the formation of hercynite, FeAl2 O4 , instead of Al2 O3 ; an excess of Al suppresses the formation of the metastable gamma-Al2 O3 phase and of FeAl2 O4 and results in a disordered bcc alpha-FeAl solid solution and alpha-Al2 O3 . Shengqi et al. have investigated the solid-state reaction of the Al/CuO couple by high-energy ball-milling [291]. A sole reduction occurs for an Al content of 20 wt%. When the amount of Al exceeds 20 wt%, along with the reduction leading to the formation of alumina, a synthesis reaction occurs simultaneously. As the amount of Al increases, the reaction products are Cu9 Al4 , CuAl2 , or a Al(Cu) solid solution, respectively.

In a study of the dynamics of planetary ball mills, Dallimore and McCormick have investigated the CuO/Ni displacement reaction milling kinetic [295]. A two-dimensional, discrete element method software (so-called DEM simulation) has been developed to predict ball motion in a planetary ball mill. Various models have been assessed to simulate actual milling impacts. They have been used to study the relevant parameters of the kinetics of the CuO/Ni displacement reaction propagated under these conditions. It was concluded that the distribution of the impact energies does not significantly affect reaction propagation over the range of the investigated speeds. The structural evolution of rod-milled Cu2 O and Ti powders during mechanical solid-state reactions has been studied by El-Eskandarany [296]. Cuprous oxide is reduced to metallic copper by elemental titanium in such processing conditions. The end product is a mixture of nanocrystalline Cu and TiO2 powders with an average crystallite size of 7 nm.

5.5.4. Silica–Metal Nanocomposite Formation

5.5.6. Reduction of Minerals: The Case of Ilmenite

The reduction induced by ball-milling of hematite (Fe2 O3 ) by silicon takes place through the formation of intermediate phases containing divalent iron [292]. The phases are oxides (magnetite and wüstite) and silicates (fayalite and iron silicate glass). In the stoichiometric conditions, the reduction is not fully achieved leading to an end product consisting of alpha-Fe and divalent iron in a silicate glass. In the case of an Fe2 O3 excess in the starting powder mixture, the final product is also composed of fayalite and magnetite. On the basis of the intermediate compounds which were characterized by Mössbauer spectrometry, during the evolution of the reaction, the following steps have been proposed to describe the oxygen transfer:

The mechanochemical reactions of ilmenite with different additives have been investigated by several authors. Chen et al. [297] have reported the reactions with Si and Ti. The results can be summarised as follows:

3Fe3 O4 + 8Al → 9Fe + 4Al2 O3

(1)

2Fe2 O3 + Si → 4FeO + SiO2 FeO + Fe2 O3 → Fe3 O4

(2)

2FeO + SiO2 → Fe2 SiO4 xFeO + SiO2 → Fex SiO2+x FeO + Si → Fe + SiO2

(3)

Fe3 O4 + 2Si → 3Fe + 2SiO2 Fex SiO2+x + x/2 → xFe + x/2SiO2

Corrias et al. have prepared Ni–silica, Cu–silica [293], and Fe–silica [294] nanocomposites by ball-milling according to the following reactions: 2NiO + Si → 2Ni + SiO2 2CuO + Si → 2Cu + SiO2

2FeTiO3 + Si → 2Fe + 2TiO2 (nanocrystalline) + SiO2 amorph  G = −76 3 kcal mol−1  2FeTiO3 + Ti → 2Fe + 3TiO2 G = −84 2 kcal mole−1  The reactions with Al and Zr differ from the previous ones as they result in the formation of a mixture of alphaFe and of a multinary amorphous phases. Therefore, ballmilling induces not only reduction/oxidation reactions but also new chemical reactions: 3FeTiO3 + 2Al → 3Fe + 3TiO2 + Al2 O3 G = −185 5 kcal mole−1  2FeTiO3 + Zr → 2Fe + 2TiO2 + ZrO2 G = −120 1 kcal mole−1  Mechanically induced chemical reactions between FeTiO3 and Si [298] lead to the formation of elemental iron, TiO2 ,

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and metal silicides, depending on the Si content. The products are increasingly reduced as the molar ratio of silicon to ilmenite increases from 1:2 to 2:1. The reaction has been found to lead to the formation of TiO2 and elemental iron. Further reduction of the TiO2 to Tin O2n−1 phases then occurred in parallel with iron silicide formation. The final stage is the reduction of the Tin O2n−1 phase to titanium silicide. Under a high intensity impact, the reaction proceeds more rapidly than under low intensity impact. Milling of a mixture of ilmenite and aluminum [299] leads to reaction within the mill forming TiAl3 , Fe4 Al13 , Al2 O3 . The same reaction occurs in unmilled powders after heating to a temperature higher than 850  C for 1 h. To increase the efficiency of the preceeding reduction process, the carbothermic reactions were extensively investigated [300]. The chemical reactions that occur during the reduction process can be conveniently separated into a solid-state reduction (typically from 860 to 1000  C), FeTiO3 + C → Fe + TiO2 + CO gas a gaseous reduction (typically above 1000  C), FeTiO3 + CO g → TiO2 + Fe + CO2 g and a reduction of rutile (typically above 1200  C), 3TiO2 + CO g → Ti3 O5 + CO2 g After ball-milling of a carbon–ilmenite mixture at room temperature, ilmenite was found to be reduced to rutile and alpha iron during subsequent low temperature annealing. The reduction temperature and the reduction kinetics for production of this intermediate reduction state (TiO2  depend critically on the milling conditions: (1) With increasing milling time, the reduction temperature decreases and the reaction rate increases. (2) High milling intensity also leads to a lowering of the annealing temperature for the main reduction step to rutile. A parametric study of the mechanically activated carbothermic reduction of ilmenite has been performed by Welham [301]. As reported by Welham, ilmenite (FeTiO3  is the primary global source of titanium dioxide which is commonly used as a whitening agent in paper manufacture and as a pigment in paint manufacture: FeTiO3 + C → Fe + TiO2 + CO C + CO2 → 2CO FeTiO3 + CO → Fe + TiO2 + CO2 nTiO2 + CO → Tin O2n−1 + CO2 The separation of iron from titanium has been enhanced by milling ilmenite and coal powder together prior to annealing. The subsequent solubility of iron was maximized when the fraction of the elemental iron after annealing was at a maximum. On the other hand, titanium solubility was minimized when rutile was the predominant titanium product.

The leaching step is much faster than conventional processing, primarily due to the much finer particle size. No elemental iron could be detected by X-ray diffraction after leaching. Leaching indicated that the reduction of rutile was detrimental to iron removal and led to increased titanium dissolution.

5.5.7. Reduction of Minerals: The Case of Bastnaesite A nonthermal process for extracting rare earths from bastnaesite by means of mechanochemical treatment has been developed by Zhang and Saito [302]. Bastnaesite (ReCO3 F, Re = rare earths) is one of the most important resources containing rare earth elements such as La and Ce. There are several hydrometallurgical methods for extracting them from bastnaesite. They can be classified into two process methodologies: one is the acidic method using H2 SO4 solution; the other the alkali method using NaOH. In the former, bastnaesite is dissolved in a concentrated acid solution which is heated to 473 K to form rare earth sulfates. Another method is the dissolution of bastnaesite in acid solution after roasting at 1073 K. In this case, the initial material is decomposed into oxide forms Re2 O3 . One of them, Ce2 O3 , is oxidized to CeO2 which is hard to dissolve in the acid solution. Therefore acid leaching is used for separating soluble rare earths from CeO2 . In contrast, several investigations using the alkali method have been reported. One is the decomposition of bastnaesite by a 45% NaOH solution heated at near the boiling point. Another involves the decomposition of minerals by a NaOH solution in an autoclave or by a molten NaOH medium. In any case, high temperature treatments are needed to extract the rare earths from bastnaesite. Therefore an alternative process operated at relatively low temperature and mild conditions would be desirable: LaCO3 F + 3NaOH → LaOH3 + Na2 CO3 + NaF Extraction of the rare earth elements such as La, Ce, Pr, Nd, Sm included in bastnaesite was attempted with NaOH powder using a planetary mill. (1) Milling of the mixture composed of bastnaesite and NaOH powders permits the formation of rare earth hydroxides and Na compounds. The Ce(OH)3 and Pr(OH)3 so formed are changed into the respective oxides in the high oxidation state during and after the milling operation. (2) The rare earth hydroxides/oxides can be separated from the Na compounds by washing with distilled water at room temperature. Most of the carbonates and 75% of the fluorides are removed from the milled mixture by the washing operation. (3) The rare earth oxides are dissolved by either H2 SO4 or HCl solutions at room temperature. Controlling the concentration of the H2 SO4 solution is a key to the preferential extraction of La, Nd, Sm from Ce and Pr in the leaching stage. In addition, milling of the mixture composed of bastnaesite and NaOH powders plays a significant role in achieving a high yield of rare earth elements in the leaching of the washed sample.

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6. ORDER–DISORDER TRANSFORMATIONS AND BALL-MILLING 6.1. Introduction Order–disorder transformations, which have played a major role in the development of modern physical metallurgy, attract still a great deal of attention both for theoretical reasons and for their applications as high-temperature structural materials [303–307]. Further, recent potential applications of ordered alloys are based on peculiar combinations of magnetic, transport, and structural properties which are strongly dependent on chemical order (among others [308–311] and references therein). Notable examples are Heusler alloys such as Co2 MnGe, Co2 MnSi, or Ni2 MnIn for spin-sensitive electronic devices which include magnetic memory and hard disk read-heads, or Ni2 MnGa for actuators and sensors because giant deformations can be induced by an externally applied magnetic field to which the alloy responds much faster than to heating or cooling. Another notable ordered alloy is Fe65 Co35 , which has the largest room-temperature magnetization, but it is a soft magnet. A way to enhance the properties of permanent magnets is through “exchange coupling” between a hard material and a soft material with a large magnetization. Models show that the soft phase must have grains of about 10 nm diameter and that the hard phase too must have nanosized grains ([312] and references therein). An ideal exchange-coupled magnet, consisting of aligned grains of Sm2 Fe17 N3 and of Fe65 Co35 , is expected to reach an energy product of about 125 MGOe [313]. For both applied and fundamental aspects, it is thus necessary to characterize and master the state of order of alloys, in particular for the more demanding class of nanostructured materials for which there are prospects of improved properties with respect to those of their classical counterparts and expectations of extended fields of applications. Ordered intermetallics are usually found in rather narrow compositional ranges around simply expressed stoichiometric compositions which reflect the underlying existence of superlattices which are few in number. Reversibly ordered alloys have their critical ordering temperature TC which is lower than their melting temperature Tm (examples are L12 Cu3 Au, DO3 Fe3 Al, DO19 Ti3 Al, L10 CuAu, B2 FeCo, B2 CuZn). By contrast, permanently ordered alloys have only a virtual ordering temperature TC as it is higher than Tm (examples are L12 Ni3 Al, B2 NiAl, L10 TiAl) [303, 304]. Reversibly ordered alloys are the sole alloys which can in principle be retained in a disordered nonequilibrium state at temperatures lower than TC by a heat treatment followed by a quench. As discussed by Cahn [303, 304] thermal treatments of the latter alloys falls into three categories: (1) alloys which are easily disordered or ordered by slow cooling, (2) alloys in which the self-diffusivity is so high that disordering is difficult at normal quenching rates, and (3) alloys in which the self-diffusivity is so low that it is difficult to order them even by very slow cooling. Other methods may be used to drive order–disorder transformations, notably irradiation [35, 314]. As reviewed (and modeled) by Martin and Bellon [35], two contradictory processes compete under

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irradiation for establishing a steady-state configuration, on the one hand a chemical disordering proportional to the irradiation flux, on the other hand a reordering promoted by thermally activated point defects at a rate proprotional to the product of their concentration, their jump frequency, and their temperature-dependent driving force for ordering. The eventual steady-state configurations achieved by such alloys depend on the “forcing” conditions. Dynamical equilibrium phase diagrams have been determined theoretically and experimentally [35]. Plastic deformation is also a means of changing the state of order of alloys which was and is still used to prepare and investigate structures far from equilibrium. The changes of magnetic properties of B2 Fe1−x Alx (0 30 ≤ x ≤ 0 40) alloys during compression testing were for instance studied recently [315]. A technique to plastically deform particles is simply ball-milling and the focus will be hereafter on its effect on order–disorder transformations. Earlier works are about the influence of grinding on the magnetic properties and on the hyperfine magnetic properties [nuclear magnetic resonance (NMR), Mössbauer spectroscopy] of B2 FeAl [316] and of L21 Heusler alloys X2 MnY (X = Ni, Cu, Pd, Y = Al, In, Sn, Sb) [317, 318] (Fig. 7). The crushing of some Heusler alloys to prepare powdered samples was indeed observed to change drastically their magnetic properties, for instance reducing the saturation magnetization to about one-third of its value, increasing the NMR signal intensity, and generating satellite lines in Pd2 MnSn [318, 319]. These investigations were thus motivated by the need to eliminate the defects produced by cold-work (dislocations, antiphase boundaries, atomic disorder) by annealing treatments. More recent studies of ball-milling of ordered alloys are still aimed at characterizing ground alloys with nanometer-sized grains and their reordering kinetics if disordered but the determination of steady states “under” milling has become central to that research field [35, 314]. The studies of ball-milled ordered alloys typically show a large accumulation of defects during milling which can drive phase transformations such as amorphization [320–322]. The reverse transformation, disordering a B2-ordered Fe60 Al40 nanocrystalline alloy during high-energy ball-milling, has also been studied recently [323]. We shall first describe a study of mechanical milling of X2 MnSn Heusler alloys to emphasize the possibility that thermally induced disorder differs from mechanically induced disorder. Then, we will describe an example of reordering of disordered nanocrystalline FeV alloys by low-temperature annealing.

L21

DO3

B2

Figure 7. The ordered structures: L21 , D03 , and B2, shown on an underlying lattice of eight bcc unit cells. In the L21 structure of X2 MnSn, the X atoms occupy the white sites, the Mn occupy the gray, and the Sn occupy the black.

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70

25

60

M (emu/g)

Heusler alloys X2 YZ, more particularly X2 MnSn alloys in which Mn atoms carry a magnetic moment of more than 3
B , are excellent candidates for evidencing such behavior. Their structure is indeed reasonably simple (Fig. 7) and their magnetic (and hyperfine magnetic) properties are well documented (see [324–331] among others). The L21 structure may contain two types of antiphase boundaries (APBs) with fault vectors of a/4111 (B2 APBs) and a/2100 (L21 APBs) respectively, where a is the lattice parameter [317, 318]. First and second nearest-neighbor Mn atoms are altered in the APBs with the formation of first nearest-neighbor Mn–Mn pairs in L21 APBs and of second nearest-neighbor Mn–Mn pairs in B2 APBs. As the magnetic properties are strongly dependent on the interactions between Mn atoms, a difference in the nature of thermal APBs and of APBs formed during plastic deformation may produce large magnetic differences between thermally and mechanically disordered alloys. The effect of cold work simply produced by crushing samples with a pestle in an agate mortar varies indeed considerably from one Heusler alloy to another [316–319]. A significant reduction of saturation magnetization, by about 60%, with cold work is for instance observed to occur in Pd2 MnSn [317–319] and is attributed to a high density of B2 antiphase boundaries created by plastic deformation [317, 318]. By contrast, crushing is supposed to bring about only L21 APBs in Pd2 MnSb because the reduction of magnetization is very small for that alloy [318]. The Heusler alloys Cu2 MnSn [332] and Cu2 MnAl [333] were found to be unstable when milled for short and for long times respectively. The disorder induced thermally in Ni2 MnSn was compared to the disorder induced by ball-milling using neutron diffraction and 119 Sn Mössbauer spectrometry [332]. As-cast Ni2 MnSn alloys were annealed under low-pressure argon at a temperature Ta (Ta = 773, 973, 1023, 1073, 1173, 1273 K) for 1 month and were quenched into water. Samples were milled under an argon atmosphere in a Fritsch P7 planetary mill for different times from 0.5 to 20 h with different powder-to-ball weight ratios, R, from 1/15 to 1/50. The magnetic properties (Fig. 8) and the hyperfine magnetic field distributions P H , where P H H is the fraction of 119 Sn atoms whose hyperfine magnetic field is between H and H + H (Fig. 9), of as-milled samples differ strongly from those of samples quenched from high temperatures. The Curie temperature Tc decreases sligthly from 343(3) to 333(3) K when Ta increases from 773 to 1073 K. The magnetization curves of all as-quenched samples are similar to those of Figure 8 (left). In contrast, Figure 8 (right) shows that drastic changes of the magnetic structure take place in ground samples. As-milled Ni2 MnSn, which remains of the L21 type with a tendency toward B2 type of order, has a disordered magnetic structure while as-quenched samples remain basically ferromagnetic [332]. Further, neutron diffraction patterns indicated that the disorder retained by quenching from Ta is similar to the disorder measured by in-situ diffraction experiments at temperatures identical or

80

M (emu/g)

6.2. Disordering of Ordered Alloys by Ball-Milling: The Example of X2 MnSn Heusler Alloys

50 40 30

20 15 10

20 5

10 0

0 0

10000 20000 30000 40000 50000

0

10000 20000 30000 40000 50000

Magnetic Field (G)

Magnetic Field (G)

Figure 8. Magnetization curves at 5, 30, 50, 100, 150, 200, 250, 300 K (from top to bottom) of Ni2 MnSn quenched from 1273 K (left) and ground (right) (note the difference in scales).

close to Ta . High-temperature neutron diffraction measurements at 1080, 1180, and 1265 K show that the structure of Ni2 MnSn is still of the L21 type above 980 K and not of the B2 type as proposed in the literature [334]. Moreover, the lattice parameter of as-quenched samples decreases regularly from 0.6045(1) to 0.6015(2) nm for 973 K = Ta = 1273 K while it is 0.6022 nm for the ground sample. Figure 9 shows the 119 Sn Mössbauer spectra at 80 K of as-quenched samples and the associated hyperfine magnetic field distributions P H . The 119 Sn hyperfine magnetic field distributions of as-quenched samples at 80 K have two characteristics: a main peak near 90 kG, the sole contribution expected for a perfectly ordered alloy, and a broad RT

80K

P(H) 80K

Ta = 773K

Ta = 973K

Ta = 1073K

ground

–10 –5

0

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mm/s

–10 –5

0

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0

40 80 120

H(kG)

Figure 9. 119 Sn Mössbauer spectra at room temperature and at 80 K of Ni2 MnSn either quenched from Ta or ground and hyperfine magnetic field distributions P H  associated with the spectra recorded at 80 K.

118 low-field tail (Fig. 9) [332]. The increase of the weight of the latter contribution with Ta reflects the greater chemical disorder retained by quenching from higher Ta . This increase reflects the greater chemical disorder retained by quenching from higher Ta . The main peak of P H  remains at the same position for all Ta . In contrast, spectra from the asmilled samples differ strongly from those of as-quenched samples with broad, almost featureless, field distributions without a main peak near 90 kG. The mean field at 5 K was found to be reduced from 92 kG for perfect order to 69 kG for Ta = 1273 K and to 55 kG for ground samples milled long enough to be in a steady state. Hyperfine properties show thus that the magnetic disorder in ground samples differs from the magnetic disorder in as-quenched samples in agreement with magnetic measurements. These results suggest that in the as-milled samples there is a broad distribution in both magnitudes of Mn moments and angles between them. Changes of magnetic (and hyperfine magnetic) properties combined with the strong reduction of the intensity of the (111) superlattice neutron diffraction line in milled samples confirm that disorder induced by the shear deformation of grinding differs from the disorder induced by temperature. Therefore, it appears impossible to find an annealing temperature that can provide as-quenched Ni2 MnSn samples with the same chemical disorder as for milled samples. These conclusions appear to be consistent with the preferential formation of L21 APBs and of B2 APBs in annealed alloys and in as-milled alloys respectively. Similar differences between thermal and mechanical disorder were found for Co2 MnSn alloys [332]. Doubt is thus cast upon the universal validity of phase diagrams of ground ordered alloys which consider that mechanical energy and thermal energy have identical effects.

6.3. Reordering of Ground Disordered Alloys The high density of defects of materials disordered by milling, especially vacancies and grain boundaries, enhance the kinetics of ordering, enabling studies at lower temperatures and more practical times than in coarse-grained quenched alloys. For example, a metastable B2 phase has been prepared in Fe–V alloys with equiatomic compositions by quenching from above ∼1500 K and annealing the unstable bcc phase for a few hours at 870 K [335–337], or for a few days at temperatures between 700 and 800 K [337]. Annealing for only 8 h at 723 K is needed to reach the steady state of B2 order for as-milled bcc Fe0 53 V0 47 [338]. The study of ordering in nanocrystalline alloys is itself a topic of widespread current interest. The formation of B2, L12 , and D03 order in several nanocrystalline alloys has been reported, including Ti–Al, Fe–Al, Fe–Si, Fe–Co, Ni– Al, and Cu–Au, sometimes with ternary additions [339–358]. These studies have emphasized various aspects of defects and diffusion in nanostructured alloys, with comparison to coarse-grained materials. A number of features seem common to the reordering of chemically disordered nanocrystalline materials, in spite of differences in their methods of synthesis (e.g., ball-milling [339–340, 344, 346–349, 352– 353, 355], plastic deformation [356], gas-phase condensation with compaction [350, 351], sputtering [345], ion irradiation

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[357]), microstructures (isolated clusters [345] or more typically micrometer-sized particles composed of nanometersized grains), and ordered structures. Reordering can occur at low temperatures and involves only few jumps of nonequilibrium vacancies that were not promptly annihilated at sinks [346, 350–353, 356–358]. Grain boundaries probably prevent order from propagating from one grain to another [344, 348]. It is less clear if chemical disorder exists near grain boundaries or antiphase boundaries. A curious feature of ordered nanocrystals is that the steady-state value of the long-range order (LRO) parameter is generally lower than that of bulk samples [345, 348–351]. For example, the relative long-range order parameter of Fe0 53 Al0 47 synthesized by gas-phase condensation and highpressure compaction, annealed at 800 K and below, stabilizes at 0.8 instead of increasing to 1.0 [350, 351]. Recent studies lead to the conclusion that this suppressed order parameter is not intrinsic to the nanocrystalline structure but that it is a kinetic effect associated with low temperatures of annealing. The example of the ordering of ground nearly equiatomic Fe–V alloys is described.

6.4. Ordering of Nearly Equiatomic Nanostructured Fe–V Alloys The equilibrium Fe–V phase diagram shows complete mutual solubility of Fe and V in a bcc -phase at high temperatures and shows a 2-phase below ∼1500 K in the central part of the diagram. Owing to the slow kinetics of the  → 2 transformation, as also found for nearly equiatomic Fe–Cr alloys, the 2-phase formation can be bypassed kinetically, and a disordered bcc phase can be obtained at low temperatures by rapid cooling [335]. A chemical ordering transformation into an ordered B2 phase can then occur on the bcc lattice during annealing at low temperatures [336, 337]. For example, a metastable B2 phase has been prepared in Fe–V alloys with equiatomic compositions by quenching from above ∼1500 K, and annealing the unstable -phase for a few hours at 870 K, or for a few days at temperatures between 700 and 800 K [335]. Although the B2 phase does not appear on the equilibrium phase diagram, a metastable Fe–V phase diagram for the A2 and B2 phases, without 2-phase, has been theoretically calculated [336]. Nanocrystalline nearly equiatomic bcc Fe–V alloys can be synthesized by mechanical alloying for instance [337] and then ordered by annealing at low temperatures [338]. The values of the LRO parameter S are most reliable for the lower annealing temperatures, where enhanced kinetics in nanocrystalline materials allow steady state to be reached in reasonable times. The high density of grain boundaries in nanocrystals promotes the formation of 2-phase at higher temperatures. Although the formation of 2-phase is relatively sluggish, it is indeed much faster in these nanocrystalline Fe–V alloys than in coarse-grained Fe–V. In a conventional coarse-grained Fe0 50 V0 50 alloy annealed for 120 h at 873 K, 2-phase forms only near free surfaces, and negligibly in the bulk [338]. A Fe0 53 V0 47 alloy annealed for 100 h at 873 K is fully transformed into 2-phase while only 30 min suffice at 973 K. In contrast, the metastable steady state of Fe0 53 V0 47 is in the B2 single-phase region between 700 and 873 K [338]. The LRO parameter, S,

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of a B2 Fe1−x Vx alloy is S = 2([Fe]Fe−1+x ), where [X]Y (X4 Y = Fe4 V) is the concentration of atomic species X on sublattice Y, where the designation Y for the sublattice refers to its majority species. The LRO parameter reaches its minimum value, S = 0, when the alloy is fully disordered while its maximum value is Sm = 1 − 2x, where x = x − 0 5, for a negligible concentration of vacancies. Figure 10 presents the LRO parameter measured by neutron diffractometry as a function of annealing time at 723 K and other temperatures. At 723 K, S increases rapidly at first and reaches a plateau between 8 and 24 h. The very small size of the ordered domains in the as-milled Fe0 53 V0 47 is comparable to the 2.5 nm domain size reported for ballmilled B2 FeAl [352]. At 723 K, the ordered domain size increases with annealing time and matches the crystallite size after some hundreds of hours. Figure 11 compares the steady-state experimental values of the LRO parameter, S, as a function of T /Tc , along with LRO calculated by the cluster variation method, and from the classical Bragg–Williams model [338]. The experimental LRO parameters, ∼0.80, are smaller than the values expected for equilibrium. The measured steady-state LRO parameters for different V contents were found to be consistent with the aforementioned metastable Fe–V phase diagram [338]. The previous LRO parameters are close to those reported for nanocrystalline materials reordered at low temperature [350, 351]. The thermal stability of disordered mechanosynthesized Ni40 Al40 T20 (T = Cr, Fe) was recently investigated [359]. The highest value of the long-range order parameter in mechanosynthesized NiAl was measured to be about 0.75 during reordering at 873 K. Grain growth was found to slow down once the order parameter reaches a steady value at any annealing temperature for the investigated alloys. Preliminary investigations indicate that reordering of disordered Ni2 MnSn occurs already by annealing at 523 K for times as short as 5 hours [360]. The kinetics and mechanisms of chemical ordering could be altered by the nanocrystalline nature of the material. Any material with a ∼7 nm grain size has indeed a high density of grain boundaries. An even higher density of antiphase boundaries exists in these materials, since the

LRO

0.8

723 K

0.4

773 K 823 K 873 K 0 0.1

1

10

100

1000

annealing time (h)

Figure 10. Long-range order parameter at room temperature of asmilled Fe0 53 V0 47 as a function of annealing time at different temperatures. Reprinted with permission from [338], T. Ziller et al., Phys. Rev. B 65, 024204 (2002). © 2002, American Physical Society.

S(T) / S(0)

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CVM

0.8

0.6

0.4 Bragg-Williams 0.2

0 0.6

0.7

0.8

0.9

1

1.1

T/Tc

Figure 11. Reduced long-range order parameter of Fe1−x Vx as a function of T /Tc calculated with the CVM model and the Bragg–Williams model. Full circles are experimental values of the steady state values for x = 0 47 and full triangle are for x = 0 39. Reprinted with permission from [338], T. Ziller et al., Phys. Rev. B 65, 024204 (2002). © 2002, American Physical Society.

domain sizes are only 2–3 nm in the early stages of ordering. Monte Carlo simulations of ordering with a vacancy mechanism at low temperatures have revealed a high density of antisite defects once ordered domain formation is complete [361–363]. The high antisite population is quite different from the clean ordered domains during ordering by interchanges of atom pairs, for example, even when the domain structures are comparable [361]. Antiphase domain boundaries serve as traps for vacancies [361], reducing their effectiveness in annealing out the antisite atoms, and the motion of the APBs is not always conservative. This transient population of antisite atoms is responsible for a slow coarsening regime at low temperature [363]. Once the APBs are eliminated, the last antisite atoms are removed slowly [361–363]. Mössbauer spectroscopy proved useful to quantify the fraction of antisite Fe atoms in partially ordered FeV alloys and to evidence the role of antisite defects [338]. The fraction of antisite atoms was shown to decrease when S increases at early annealing times. A further reduction of the latter fraction was measured when nanocrystals are single domains without APBs. The steady-state LRO parameter is smaller than the equilibrium value because of residual antisite defects that do not anneal out on the time scale of the experiments. The LRO parameters in these Fe–V alloys were not sensitive to grain growth. Little change in S (about 0.7) was for instance observed at 723 K when most grain growth occurred [338]. The elimination of antisite defects requires some longer range diffusion, which is very slow in ordered domains at low temperatures. The kinetics at the later stages of annealing may also be suppressed by a low vacancy concentration. At the higher temperature of 873 K, however, once the domain size grows to the crystal size, S then increases from 0.64 to 0.75, which is close to the value expected in thermodynamic metastable equilibrium (Fig. 11) [338].

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In summary, reordering results first from the elimination of antiphase boundaries and second from the removal of the last antisite defects which is very slow in ordered domains at low temperatures. Thermal reordering takes place prior to recrystallization, and in a temperature range similar to the milling temperature [364]. The reduction of the steady-state value of the long-range order parameter is due to a kinetic effect associated with the low temperatures of annealing. Besides their historical and practical importance [303– 307], order–disorder transformations play an important role in the understanding of the physics of mechanical alloying. Some of the most convincing proof of the very existence of dynamical equilibrium under milling is for example provided by ground FeAl alloys [314, 358, 364] which further show that initially disordered alloys may reorder under milling if the pertinent parameters, a dynamical parameter and the milling temperature, are adequately chosen. As briefly described for Heusler alloys and as emphasized by Martin et al. [314, 358, 364], the destruction of long-range order is a result of the plastic shear of grains (e.g., one dislocation gliding along its slip plane leaves a planar stacking fault behind). Alternatively, one pair of jogged dislocations on a single slip plane leaves behind a tube of stacking faults, etc. Moreover, shear induced vacancies enhance the atomic mobility and hence speed up the reordering process in the time interval between two collisions. These mechanically induced “ballistic jumps” occur in a collective manner along the shear planes. As suggested by computer simulations, these space and time correlations of ballistic jumps might result in original microstructures [364].

fcc Cu(Fe) solid solution for iron contents lower than 45 at% and bcc Fe(Cu) solid solution for iron contents higher than 55 at% [15–17, 23–27]. In between, the two phases coexist [379, 381]. However, some results of Mössbauer spectrometry and atom probe investigations indicate that these solid solutions are chemically heterogeneous on a nanometer scale [379, 381, 389–391]. In a recent work on nanocrystalline Fey Cu1−y (0 141 ≤ y ≤ 0 450) alloys produced by ball-milling [390], Fernandez et al. used a small-angle X-ray scattering technique to conclude that the synthesized alloys are heterogeneous on a nanometer scale since composition fluctuations were detected inside nanocrystalline grains. Wanderka et al. [389] investigated the microstructure and composition on the nanometer scale of mechanically alloyed Cu50 Fe50 with a tomographic atom probe. They concluded that samples contain nanometer-sized regions with strongly varying composition. Further, supersaturated solid solutions formed deep inside a miscibility gap through rapid quenching or solid state routes may have decomposition features on the scale of a few nanometers as shown recently for sputtered fcc Ag– Cu solid solutions [397] or for mechanically alloyed Fe30 Cr70 alloys [392] and for milled as-cast Fe30 Cr70 alloys as will be further discussed. In the following, we denote as p-Ax By the initial mixture of powders of element A and of powders of element B in the atomic ratio x:y.

7. ALLOYING BY HIGH-ENERGY BALL-MILLING (SUPERSATURATED SOLID SOLUTIONS)

Given milling conditions, tm is defined as the current milling time and the synthesis time tf as the minimum time needed to enter a stationary state in which all kinds of powder characteristics remain unchanged when milling for tm ≥ tf (hardness, magnetic properties, average grain sizes, crystallographic structures, etc.). Besides the synthesis time, tf , a second characteristic milling time tcm was considered and termed “chemical mixing time” [399], tcm ≤ tf . To define it, let us consider for instance a binary mixture of elemental powders with a mean composition A1−x Bx (Fig. 12). Powder particles are initially either pure A or pure B. The time tcm is then the minimum milling time at which all powder particles have essentially the final chemical composition A1−x Bx . The particle scale is relevant because tcm can be measured, for instance using a microprobe [399], and because it is the shortest possible synthesis time, tf ≥ tcm . Even if they have the expected composition, powder particles may be made up of various phases whose structures and compositions may still evolve for tcm ≤ tm ≤ tf (Fig. 12). For tm ≤ tcm , mixing occurs simultaneously at different scales with a broad distribution of characteristics from particle to particle. Both tf and tcm were obtained, as will be described, for Fe1−x Tx elemental powder mixtures ground in a planetary ball mill, with x = 0 50, 0.70, 0.72 for T = V, Cr, and Mn respectively [399]. The synthesis time depends strongly on the considered Fe–T alloy while chemical mixing times were estimated to be similar whatever the element T , tcm ≈ 3–4 h, in the milling conditions described in [399] (planetary ball mill Fritsch Pulverisette 7 with a powder-to-ball weight ratio of 1/20).

7.1. Introduction The fundamental problems of the mechanisms of mixing of elements by milling and of the resulting formation of phases such as extended solid solutions, in particular in binary metallic systems of elements which have limited solid solubilities or are immiscible in equilibrium, intermetallic compounds, amorphous phases, or the two-phase coexistence in alloys for certain concentration ranges are still thoroughly investigated. Some examples are Cr–Sn, Fe–Cr, Fe–Cu, Fe– Sn, Fe–Ta, Co–Cu, Ni–Cu, Ni–Ag, Cu–Ta, Ag–Cu [365–392]. The interest in the characterization and modeling of supersaturated solid solutions formed in a large number of systems with positive heats of mixing is obviously not restricted to mechanosynthesized materials but extends to materials produced by all kinds of methods [393–398]. To reach sound conclusions about their actual structures on a nanometer scale (are they compositionally homogeneous or decomposed?), techniques which yield both global information and local information on ground powders must be combined. In that way, it is possible to follow not only the average properties of powder particles but also their fluctuations in the whole sample both during milling and in as-milled materials. Single-phase structures have been, for instance, obtained by mechanical alloying in a broad concentration range in the archetypal Fe–Cu system, for example,

7.2. Composition Fluctuations during Mechanical Alloying: Two Notable Times

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same average composition

same composition and stationary structure

Fe + T tcm

tf

Figure 12. Two characteristic times, the chemical mixing time tcm and the synthesis time tf , illustrated for milling of Fe–T elemental powder mixtures.

7.2.1. Simple Method to Estimate the Chemical Mixing Time To estimate the chemical mixing time tcm of A and B, a powder mixture p-A1−x Bx is ground for a time tm and the A content xi4 tm  of every powder particle (i = 14 4 N ) is imagined to be measured with standard methods. The fluctuation of the A content from particle to particle at time tm is then conveniently characterized by a standard deviation 2tm  of the distribution of composition found in that way: 2 2 tm  =

N 1  xi4 tm  − x2  N i=1

The chemical mixing time tcm is thus the shortest milling time for which 2tcm  ≈ 0 in the considered experimental conditions. For instance, microprobe analyses performed on about 20–30 powder particles for samples of p-Fe1−x Tx (T = V, Cr, Mn) ground for tm yield a good estimate of 2tm  (Fig. 13) [399]. The milling time dependence of the fluctuation 2tm  appears to be well approximated by an exponential decrease in the case of some Fe–T binary systems,   t 2tm  = 20 exp − m (1) 6cm with a time constant 6cm . Time constants 6cm = 39 ±3 min, 6cm = 55 ±5 min, and 6cm = 66 ±3 min were obtained for T = V, Cr, Mn respectively. The times for which 2 ≈ 0 are then found to be similar, tcm ≈ 46m ≈ 3–4 h, and for all alloys in the given milling conditions. The times, ≈4 h, needed to observe a stationary hardness and stationary shapes of hyperfine magnetic field distributions for T = V, Cr were found to both be of the order of tcm . Figure 13 further shows the milling time dependence of the relative fraction p-Fe0.50V0.50

p-Fe0.28Mn0.72 1

1 RFe σ/σ(0)

0,8 0,6

0,6

0,4

0,4

0,2

0,2

0

RFe σ/σ(0)

0,8

0 0

100

200

tm (min)

300

400

0

200

400

600

800

tm (min)

Figure 13. Milling time dependences of 2tm /20 [and of RFe tm  obtained from Mössbauer spectra] for p-Fe0 28 Mn0 72 (left) and p-Fe0 50 · V0 50 (right).

RFe tm  of Fe atoms which give rise to the “-Fe” contribution in Mössbauer spectra of p-Fe0 50 V0 50 · RFe tm  clearly shows that the chemical mixing time tcm is much less than the synthesis time tf for this alloy. The typical chemical mixing times estimated in these experiments are not short as compared to the synthesis times (more than about 50%) and must be borne in mind when characterizing ground powders which have not yet reached a stationary dynamical state. The importance of the chemical mixing time was evidenced too in a recent investigation of the mechanical alloying of Fe–Ge alloys [400]. For p-Fe0 75 Ge0 25 , mechanical alloying was indeed found to occur in two steps: for tm < tcm ≈ 4 h, the mixture of Fe and Ge refines down to a nanometer scale with the formation of solute supersaturated regions near interfaces, possibly by a dislocation pumping solute mechanism. The latter process consists of repeated sequences of solute diffusion in dislocation cores, pinning and depinning due to stresses applied during shocks. An homogenization process occurs for longer milling times [400]. The time tf needed to reach a final stationary state is obtained to be of the order of ≈8–10 h for V and Cr, a time much larger than tcm , while it is of the order of tcm , being ≈5–6 h, for Mn. The long synthesis times reflect the fundamental role of competing mechanisms in the establishment of dynamical stationary states with a trend to unmixing in nearly equiatomic Fe–Cr and a trend to ordering in nearly equiatomic Fe–V alloys. By contrast Fe and Mn tend to mix, as shown by the large equilibrium solubility of Fe in Mn.

7.3. Composition Fluctuations in Mechanosynthesized Materials: The Example of p-Fe0
30 Cr0
70 A considerable amount of theoretical and experimental work has been devoted to coarse-grained Fe–Cr alloys, a binary system which exhibits among others a wide miscibility gap, stable or metastable, below about 1000 K [400]. Mechanical alloying of p-Fe1−x Crx alloys has been thoroughly investigated for the whole range of x [392, 399, 401, 410]. Homogeneous solid solutions and an amorphous phase, for x ∼ 0 70 [403–405], were reported to be the dynamical equilibrium phases according to the composition and the milling conditions. However, recent investigations [409] demonstrate the favorable role of oxygen on the amorphous phase formation, particularly for contents larger than ∼1.5 wt%. Conclusions about the formation of homogeneous Fe–Cr solid solutions with nanosized grains were most often obtained from room-temperature (RT) Mössbauer spectra because heterogeneities can hardly be detected from broadened X-ray diffraction patterns of ground powders. Magnetization and magnetoresistance measurements [408] led, however, the reconsideration of the conclusions drawn from RT Mössbauer spectra about the formation of a solid solution in p-Fe0 30 Cr0 70 alloys milled in classical experimental conditions (Fritsch Pulverisette 7 planetary ball mill with steel vial and seven balls with a powder-to-ball weight ratio R = 1/22 and a disc rotation speed  = 640 rpm [392]) by evidencing the existence of composition fluctuations, whose amplitude x is ∼0.1, on a scale of a few nanometers inside grains [392, 399, 408]. As described, the average chemical

122 compositions of all particles of ground powders are essentially the same for tm > ≈3–4 h in these milling conditions.

7.4. Steady State Structure of Milled Fe0
30 Cr0
70 Detailed magnetic characterizations of Fe0 34 Cr0 66 synthesized by high-energy ball-milling from p-Fe0 30 Cr0 70 initial mixtures of chromium and iron powders are reported in [392]. They evidence the existence of a dominant superparamagnetic contribution from Fe-rich clusters at 400 K above the Curie temperature of the classical homogeneous alloy with the same composition, Tc < ≈380 K [411]. X-ray diffraction patterns, transmission electron microscopy, and Mössbauer spectra at 7 K show no evidence of the formation of an amorphous phase which is known to be nonmagnetic at least down to 5 K. This indicates that oxygen contained in the starting powders does not play a significant role in the steady state achieved in these experimental conditions, as further confirmed by the results of chemical anlayses and of annealing experiments. The final ground Fe0 34 Cr0 66 alloys were concluded to have complex structures with intragranular composition fluctuations of ≈0.1 in amplitude at a scale of a few nm (of the order of 2–4 nm) which reflect the strong trend of Fe and Cr toward segregation. To show that the latter microstructure is a true dynamical equilibrium state, an as-cast Fe0 30 Cr0 70 alloy was ball-milled in the same milling conditions as those used previously for mechanically alloyed powders of elemental Fe and Cr. Advantage was taken from a brittle–ductile transition located between room-temperature and liquid–nitrogen temperature to obtain coarse powder particles from a bulk as-cast alloy. The incorporation of steel from milling tools into ground powders was found to be negligible in such experimental conditions. The magnetic moment at 5 K is for instance 1.8
B /Fe atom for the as-cast alloy [412], in perfect agreement with the moment measured by Fischer et al. [411]. The reduced contamination explains why the Fe content is smaller in milled as-cast alloys than in alloys which were mechanosynthesized from elemental Fe0 30 Cr0 70 mixtures. Magnetic susceptibilities (Fig. 14) were measured with a commercial susceptometer between 5 and 350 K with an ac field of 2 Oe at four frequencies ranging from 10 Hz to 10 kHz. The experimental results were similar for all investigated frequencies. When T decreases, the ac susceptibility 7T  of the as-cast alloy (Fig. 14) exhibits a broad transition around ≈290 K, reaches a maximum at ≈200 K and then decreases when T decreases down to 5 K. These characteristics reflect the influence of short-range order, namely a strong tendency to clustering [411], on magnetic properties as clearly shown by the effect of annealing on Fe–Cr alloys with compositions similar to those investigated by Delcroix et al. [412]. The ac susceptibility of the mechanosynthesized alloy exhibits a clear ferromagnetic transition at ≈170 K, the Curie temperature of an alloy with a Cr content x ≈ 0 75. Then it reaches a maximum at ≈150 K and decreases when T decreases down to 50 K. It decreases more markedly below 50 K, as expected from the reentrant transition from a ferromagnetic phase to a cluster-glass-like state for x ≈ 0 75 [392]. The susceptibility of the as-cast alloy milled for 4 h 30 (Fig. 14) is very close to that of the MA alloy with

Mechanical Processing for Nanomaterials Susceptibility (emu/g/Oe) as-cast + 10 h 0.04

0.03

as-cast

0.02

MA 12h

as-cast + 4h30 0.01

f = 1000 Hz h = 2 Oe

0 0

50

100

150

200

250

300

350

400

T (K)

Figure 14. Ac susceptibility of Fe0 30 Cr0 70 (1) mechanically alloyed (crosses, MA, tm = 12 h), (2) as-cast (empty circles), (3) and as-cast and milled for various times (empty diamonds: tm = 4 h 30, solid diamonds: tm = 10 h).

a small temperature shift likely due to the composition difference. Finally, the susceptibility of the alloy ground for 10 h shows a transition at the same temperature as the alloy ground for 4 h 30, but it is more abrupt for the former alloy. This suggests that the distribution of Fe contents in Fe-rich clusters become narrower with milling time. As discussed in [392], the overall behavior of 7T  of as-milled samples is dominated by the contribution of Cr-rich zones. It complements the information drawn from high-temperature magnetization which is dominated by superparamagnetic Fe-rich clusters. In summary, both mechanically ground and mechanically alloyed Fe0 30 Cr0 70 alloys exhibit similar stationary microstructures with intragranular composition fluctuations of ≈0.1 in amplitude at a scale of a few nm. They differ from those found for a macroscopic phase separation. These results reinforce the conclusion of a recent study of Ag0 50 Cu0 50 alloys [397] about the likely phase separation on ultrafine scales that escaped detection in many alloys obtained inside miscibility gaps which are often believed to be homogeneous. He et al. further question the reliability of diffraction methods to determine the true level of supersaturation or the homogeneity of a solid solution (see also [413]). To conclude, the characterization of composition fluctuations is essential for a thorough description of the mechanical alloying process and of mechanosynthesized materials.

8. CONCLUSION Investigations performed for a period of about 20 years provide realistic ideas about the actual potentialities of synthesis methods which involve mechanical energy and about the problems they raise. Mechanosynthesis is a promising synthesis method for all kinds of nanomaterials, often with original features, and a step in the preparation of consolidated materials with improved properties. Milling must no more be kept in mind as the sole millenial method of

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powder processing but it must considered nowadays as being also a modern technique, mechanosynthesis, of preparation and transformation of materials which turns progressively simple mills into true “mechanoreactors” [414]. For both applied and fundamental aspects, it is necessary to characterize and master the “microstructures” of the demanding class of nanostructured materials for which there are expectations of improved properties and of promising applications. Besides the chemical engineering and materials synthesis aspects mentioned, the physical understanding of mechanosynthesis still requires detailed investigations particularly in systems for which thermal and mechanical energy compete (order–disorder, unmixing–mixing) to drive milled materials to dynamical stationary states far from equilibrium with original microstructural features. Mechanosynthesized nanostructured materials belong to a larger family whose properties still remain to be characterized and understood. For instance, how do such materials plastically deform when there is no apparent activity of dislocations? Which are the characteristics of phase separation in nanostructured materials? As already mentioned, important aspects of mechanosynthesis of nanostructured materials have not been covered in this chapter. This is the case for instance for computer simulations of mechanical alloying which provide already some information about original morphologies that may be formed thanks to competing interactions between elements to be mixed [35] but, as emphasized by Martin, a safe modeling of the shearing event itself is still lacking [314]. This is further the case for the synthesis of all kinds of compounds (intermetallic compounds, “Xides” where X stands for bor, carb, nitr, alumin, phosph, silic, etc., and metallic glasses) but many of them are prepared in a straightforward way simply by grinding elemental powder mixtures. Further, applications of nanostructured materials often require them to be processed in a temperature range in which they may undergo grain growth and thus risk losing their specific properties. Lund and Schuh [415–416] explored recently driven alloy systems (irradiation, mechanical alloying, severe plastic deformation) to test the assumption according to which only completely random configurations are dynamically stable in the limit where ballistic effects are dominant. Their molecular simulations of driven binary alloys suggest that complex ordered or segregated structures may evolve even in the absence of thermally activated diffusion [415]. They have indeed found that binary alloys can mix, demix, and even order under an external driving force at T = 0 K. Lund and Schuh emphasize that atoms would have a microscopic degree of freedom to select their preferred nearest neighbors, whenever there is a force enabling their motion, in systems with local stresses due to either an atomic size mismatch or a high density of crystalline defects. In the latter systems, the formation of preferred bonds would result from subatomic translations since there is no fixed lattice site for a given atom. “Micromégas,” the hero of the Voltaire’s Conte philosophique which echoes Swift’s Gulliver’s Travels, imagines an animal “not quite one 600,000th of an inch in height” [417] (“qui aurait à peu près la six-cent millième partie d’un pouce en hauteur”), that is, an animal whose height is about 40 nm. Micromégas seems thus to be the right giant we

need to close this chapter on mechanical alloying and nanostructured materials, a class of materials in which widely different scales are linked too [417]: “Quel plaisir sentit Micromégas en voyant remuer ces petites machines, en examinant tous leurs tours, en les suivant dans toutes leurs opérations!” “What pleasure Micromégas felt in watching the movements of those little machines, in examining all their feats, in following all their operations!”

GLOSSARY Ball milling (BM) A process consisting of mechanical mixing of powders based on prealloyed components (as example intermetallic phases, ceramic compounds). Combustion A reaction which is found to liberate quasiinstantaneously its exothermic energy. Field activated pressure assisted sintering (FAPAS) Compared to a classical sintering process under pressure, a current is applied in order to assist the sintering. A current exhibiting a high intensity (up to 8,000 A) under low voltage (10 V) is applied. Grinding Mechanical processing leading to a decrease in the crystallite grain size. The initial material is pure element or alone compound. Mechanical activated annealing processing (M2AP) Before an annealing treatment, a former mechanical step is introduced leading to a mechanical activation of the powders. Mechanical activated self-heat-sustaining (MASHS) For SHS (see SHS terms), before igniting SHS reaction, a first step is performed consisting of short duration mechanical alloying of elementary component. The duration is enough to generate a 3D nanoscale distribution of the elementary component inside each micrometer powder grain. Mechanical activation processing (MA processing) Before powder metallurgy processing (i.e., sintering, densification, reactive sintering), a step consisting of a short duration mechanical alloying is performed. Mechanical alloying (MA) A process consisting of a mechanical mixing at the nanoscale of elementary components. A long duration of such a mechanical process is expected to lead to the formation a stationary end product constituted by definite compounds. Mechanochemistry Processing involving mechanical treatment in order to achieve chemical reactions. Milling A mechanical processing for treatment of powders. Introduction of a component helping the milling is defined as wet milling. Without such an additive, it is the so-called dry milling. Nanocomposites Dense materials composed of various materials. One of the latter has a nanoscale dimension. Nanoparticles Isolated particles whose diameters are well below 100 nm, classically less than 10 nm. Self-heat-sustaining (reaction) (SHS) An exothermic reaction between two elementary components exhibiting enough energy to be self-sustaining (i.e., without the need for an external energy source).

124 Solid state reaction Reaction occurring below the melting point of any elementary component or compounds. Spark plasma sintering A process leading to bulk materials by a sintering step using pulse electric discharge. Due to the high intensity of the current, plasma may occur between the various powder grains. Thermomechanical treatment A treatment of materials combining thermal effect and mechanical solications, both being successive or simultaneously performed. Ultrafine (particles) Particles which are isolated each from each other and exhibiting a nanometer scale (less than 100 nm).

REFERENCES 1. J. Swift, “Gulliver’s Travels,” Ch. 6 (1726). http://www.on-line. literature.com/swift/gulliver/. 2. H. Gleiter, Acta Mater. 48, 1 (2000). 3. R. W. Cahn, “The Coming of Materials Science.” Pergamon, Amsterdam, 2001. 4. A. Caro and H. Van Swygenhoven, Phys. Rev. B 63, 134101 (2001). 5. J. S. Benjamin, Metall. Trans. 1, 2943 (1970). 6. J. S. Benjamin, Sci. Amer. 234, 40 (1976); Mater. Sci. Forum 88–90, 1 (1992). 7. R. L. White, Ph.D. Dissertation, Stanford University, 1979. 8. C. C. Koch, O. B. Kavin, C. G. Mckamey, and J. O. Scarbrough, Appl. Phys. Lett. 43, 1017 (1983). 9. J. J. De Barbadillo, Key Eng. Mater. 77–78, 187 (1993). 10. V. V. Boldyrev, N. Z. Lyakhov, Yu. T. Pavlyukhin, E. V. Boldyreva, E. Yu. Ivanov, and E. G. Avvakumov, Sov. Sci. Rev. B. Chem. 14, 105 (1990). 11. E. Gaffet, F. Bernard, J. C. Niepce, F. Charlot, C. Gras, G. Le Caër, J. L. Guichard, P. Delcroix, A. Mocellin, and O. Tillement, J. Mater. Chem. 9, 305 (1999). 12. B. S. Murty and S. Ranganathan, Int. Mater. Rev. 43, 101 (1998). 13. C. Suryanarayana, Progr. Mater. Sci. 46, 1 (2001). 14. L. Takacs, Progr. Mater. Sci. 47, 355 (2002). 15. R. Z. Valiev, R. K. Islamgaliev, and I. V. Alexandrov, Progr. Mater. Sci. 45, 103 (2000). 16. M. Atzmon, K. M. Unruh, and W. L. Johnson, J. Appl. Phys. 58, 3865 (1985). 17. F. Bordeaux and A. R. Yavari, J. Appl. Phys. 67, 2385 (1990). 18. L. Battezzati, P. Pappalepore, F. Durbiano, and I. Gallino, Acta Mater. 47, 1901 (1999). 19. H. J. Fecht, Scripta Mater. 44, 1719 (2001). 20. Y. Watanabe, K. N. Ishihara, and P. H. Shingu, Scripta Mater. 44, 1853 (2001). 21. A. Csanády, A Csordás-Pintér, L. Varga, L. Tóth, and G. Vincze, J. Phys. I France 6, 925 (1996). 22. C. Suryanarayana, E. Ivanov, and V. V. Boldyrev, Mater. Sci. Eng. A 304–306, 151 (2001). 23. L. Takacs, Progr. Mater. Sci. 47, 355 (2002). 24. B. S. Murty and S. Ranganathan, Int. Mater. Rev. 43, 101 (1998). 25. F. Bernard and E. Gaffet, Int. J. Self Propagating High Temp. Synthesis 10, 109 (2001). 26. E. Gaffet, N. Malhouroux, and M. Abdellaoui, J. All. Comp. 194, 339 (1993). 27. L. Lü and M. O. Lai, Kluwer Academic, Dordrecht, 1998. 28. R. Z. Valiev, R. K. Islamgaliev, and I. V. Alexandrov, Progr. Mater. Sci. 45, 103 (2000). 29. F. H. Froes, O. N. Senkov, and E. G. Baburaj, Mater. Sci. Eng. A 301, 44 (2001). 30. C. Suryanarayana, Cambridge International Science, England, 1995. 31. G. Le Caër (Issue Ed.), Special Issue, Ann. Chim. 22, 341 (1997).

Mechanical Processing for Nanomaterials 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55. 56. 57. 58. 59.

60. 61. 62. 63. 64. 65. 66.

67. 68. 69. 70. 71. 72. 73. 74. 75.

R. Z. Valiev (Issue Ed.), Ann. Chim./Sci. Mater. 21, 369 (1996). E. M. Gutman, World Scientific, Singapore, 1994. P. Y. Butyagin, Russian Chem. Rev. 63, 965 (1994). G. Martin and P. Bellon, Solid State Phys. 50, 189 (1996). http://www.bls.fr/amatech/Sciences/Mecanosynthese/mecanosynthese.htm E. Gaffet, M. Abdellaoui, and N. Malhouroux-Gaffet, Mater. Trans. JIM 36, 198 (1995). A. Calka and A. P. Radlinski, Mater. Sci. Eng. A 134, 1350 (1991). D. Basset, P. Matteazzi, and F. Miani, Mater. Sci. Eng. A 174, 71 (1994). P. Pochet, E. Tominez, L. Chaffron, and G. Martin, Phys. Rev. B 52, 4006 (1995). Y. Chen, M. Bibole, R. Le Hazif, and G. Martin, Phys. Rev. B 48, 14 (1993). P. Lebrun, L. Froyen, and L. Delaey, Mater. Sci. Eng. A 161, 75 (1993). R. B. Schwarz, Mater. Sci. Eng. 97, 71 (1988). T. H. Courtney, Mater. Trans. JIM 36, 110 (1995). T. H. Courtney and D. Maurice, Scripta Mater. 34, 5 (1996). R. M. Davis, B. McDermott, and C. C. Koch, Metall. Trans. A 19, 2867 (1988). M. Abdellaoui and E. Gaffet, Acta Metall. Mater. 43, 1087 (1995). B. K. Mishra and C. V. R. Murty, Powder Technol. 115, 290 (2001). A. Joisel, Rev. Mater. Construction 493, 234 (1952). A. A. Bradley, A. J. Freemantle, and P. J. D. Lloyd, J. South African Inst. Mining Metall. 10, 78 (1975). J. Schilz, M. Riffel, K. Pixius, and H.-J. Meyer, Powder Technol. 105, 149 (1999). J. Schilz, Mater. Trans. JIM 39, 1152 (1998). M. Riffel and J. Schilz, J. Mater. Sci. 33, 3427 (1998). H. Mio, J. Kano, F. Saito, and K. Kaneko, Mater. Sci. Eng. A 332, 75 (2002). M. Magini, C. Colella, A. Iasonna, and F. Padella, Acta Mater. 46, 2841 (1998). B. K. Mishra, Kona 13, 151 (1995). M. Abdellaoui and E. Gaffet, J. All. Comp. 209, 351 (1994). E. V. Shelekhov, V. V. Tcherdyntsev, L. Yu, S. D. Kaloshin, and I. A. Tomilin, J. Metast. Nanocryst. Mater. 8, 603 (2000). W. Shulin, Y. Xianqi, and L. Juguang, “Integrating Dynamics, Condition Monitoring and Control for the 21st Century” (Starr, Leung, Wright, and Sandoz, Eds.), pp. 465–470. Rotterdam, 1999. J. Raasch, Chem. Eng. Technol. 15, 245 (1992). M. Abdellaoui and E. Gaffet, Acta Mater. 44, 725 (1996). H. Watanabe, Powder Technol. 104, 95 (1999). J. Kano, N. Chujo, and F. Saito, Adv. Powder Technol. 8, 39 (1997). H. Watanabe, Powder Technol. 104, 95 (1999). D. R. Maurice and T. H. Courtney, Metall. Trans. A 21, 289 (1990). T. H. Courtney and D. R. Maurice, “Solid State Powder Processing” (A. H. Clauer and J. J. de Barbadillo, Eds.), Vol. 3. The Minerals, Metals and Materials Society, 1990. P. P. Chattopadhyay, I. Manna, S. Talapatra, and S. K. Pabi, Mater. Chem. Phys. 68, 85 (2001). K. Szymanski and Y. Labaye, Phys. Rev. E 59, 2863 (1999). R. Rahouadj and E. Gaffet, Mater. Sci. Forum 225–227, 249 (1996). H. Huang, M. P. Dallimore, J. Pan, and P. G. McCormick, Mater. Sci. Eng. A 241, 38 (1998). K. R. Shah and T.-F. Wong, Int. J. Rock Mech. Min. Sci. 34, 727 (1997). M. Zdujic, C. Jovlekic, Lj. Karanovic, M. Mitric, D. Poletti, and D. Skala, Mater. Sci. Eng. A 245, 109 (1998). J. Xu, G. S. Collins, L. S. J. Peng, and M. Atzmon, Acta Mater. 47, 1241 (1999). Y.-S. Kwon, K. B. Gerasimov, and S.-K. Yoon, J. All. Comp., in press. S. K. Pabi, D. Das, T. K. Mahapatra, and I. Manna, Acta Mater. 46, 3501 (1998).

Mechanical Processing for Nanomaterials 76. 77. 78. 79. 80. 81. 82. 83. 84. 85. 86. 87. 88. 89. 90. 91. 92. 93. 94. 95. 96. 97. 98. 99. 100. 101. 102. 103. 104. 105.

106. 107. 108. 109. 110. 111. 112. 113. 114. 115. 116. 117.

J. Kano, H. Mio, and S. Saito, J. Chem. Eng. Japan 32, 445 (1999). F. C. Bond, Mining Eng. 4, 484 (1952). E. P. Zemskov, Powder Technol. 102, 71 (1999). V. Buchholtz, J. A. Freund, and T. Pöschel, Europ. Phys. J., in press. J. R. Harris, J. A. D. Wattis, and J. V. Wood, Acta Mater. 49, 3991 (2001). B. J. M. Aikin and T. H. Courtney, Mater. Sci. Eng. A 147, 229 (1993). D. Gavrilov, O. Vinogradov, and W. J. D. Shaw, Powder Technol. 101, 63 (1999). F. Kh. Urakaev and V. V. Boldyrev, Inorganic Mater. 35, 189 (1999). F. Kh. Urakaev and V. V. Boldyrev, Inorganic Mater. 35, 405 (1999). G. Gonzalez, L. D’Angelo, J. Ochoa, B. Lara, and E. Rodriguez, Mater. Sci. Forum 386–388, 159 (2002). H. H. Tian and M. Atzmon, Acta Mater. 47, 1255 (1999). R. B. Schwarz, Mater. Sci. Forum 269–272, 665 (1998). P. Pochet, P. Bellon, L. Boulanger, L. Chaffron, and G. Martin, Mater. Sci. Forum 269–272, 655 (1998). P. Pochet, P. Bellon, L. Chaffron, and G. Martin, Mater. Sci. Forum 225–227, 207 (1996). F. Wu, P. Bellon, A. J. Melmed, and T. A. Lusby, Acta Mater. 49, 453 (2001). A. Y. Badmos and H. K. D. H. Bhadeshia, Metall. Mater. Trans. A 28, 2189 (1997). V. I. Levitas, V. F. Nesterenko, and M. A. Meyers, Acta Mater. 46, 5929 (1998). J. J. Gilman, Philos. Mag. B 71, 1057 (1995). H. Zhang and X. Liu, Int. J. Refractory Metals Hard Mater. 19, 203 (2001). H. J. Fecht, E. Hellstern, and W. L. Johnson, Metall. Trans. A 21, 2333 (1990). J. S. C. Jang and C. C. Koch, Scripta Metall. Mater. 24, 1599 (1990). P. Le Brun, E. Gaffet, L. Froyen, and L. Delaey, Scripta Metall. Mater. 26, 1743 (1992). J. Eckert, J. C. Holzer, C. E. Krill III, and W. L. Johnson, J. Mater. Res. 7, 1751 (1992). T. Tanaka, S. Nasu, B. Huang, K. N. Ishihara, and P. H. Shingu, Nucl. Instrum. Methods B 76, 195 (1993). A. M. Harris, G. B. Schaffer, and N. W. Page, J. Mater. Sci. Lett. 12, 1103 (1993). H. J. Fecht, Nanostruct. Mater. 6, 33 (1995). A. Benghalem and D. J. Morris, Acta Metall. Mater. 42, 4071 (1995). L. Daroczi, D. L. Becke, G. Posgay, and M. Kis-Varga, Nanostruct. Mater. 6, 981 (1995). T. D. Shen, C. C Koch, T. Y. Tsui, and G. M. Pharr, J. Mater. Res. 10, 2892 (1995). S. J. Campbell and W. A. Kaczmarek, in “Mössbauer Spectroscopy Applied to Magnetism and Materials Science” (G. J. Long and F. Grandjean, Eds.), Vol. 2, p. 273. Plenum, New York, 1996. D. Oleszak and P. H. Shingu, J. Appl. Phys. 79, 2975 (1996). C. C. Koch, Nanostruct. Mater. 9, 13 (1997). E. Bonetti, E. G. Campari, L. Pasquini, and E. Sampaolesi, J. Appl. Phys. 84, 4219 (1998). L. Del Bianco, C. Ballesteros, J. M. Rojo, and A. Hernando, Phys. Rev. Lett. 81, 4500 (1998). J. Rawers, D. Cook, and T. Kim, Mater. Sci. Eng. A 248, 212 (1998). A. Révész and J. Lendvai, Nanostruct. Mater. 10, 13 (1998). E. Bonetti, L. Del Bianco, D. Fiorani, D. Rinaldi, R. Caciuffo, and A. Hernando, Phys. Rev. Lett. 83, 2829 (1999). A. Hernando, J. Phys.: Condens. Matter 11, 9455 (1999). H. H. Tian and M. Atzmon, Acta Mater. 47, 1255 (1999). E. Gaffet, C. Meunier, S. Vives, and J. P. Itié, J. Metastable Nanocryst. Mater. 2–6, 587 (1999). J. Rawers and D. Cook, Nanostruct. Mater. 11, 331 (1999). D. X. Li, D. H. Ping, J. Y. Huang, Y. D. Yu, and H. Q. Ye, Micron 31, 581 (2000).

125 118. J. Balogh, D. Kaptas, T. Kemeny, I. Vincze, and G. Radnoczi, Phys. Rev. Lett. 82, 4150 (1999). 119. L. Del-Bianco, C. Ballesteros, J. M. Rojo, and A. Hernando, Phys. Rev. Lett. 82, 4151 (1999). 120. B. Fultz, J. L. Robertson, T. A. Stephens, L. J. Nagel, and S. Spooner, J. Appl. Phys. 79, 8318 (1996). 121. E. Bonetti, L. Pasquini, E. Sampaolesi, A. Deriu, and G. Cicognani, J. Appl. Phys. 88, 4571 (2000). 122. J. Balogh, L. Bujdoso, D. Kaptas, T. Kemeny, I. Vincze, S. Szabo, and D. L. Beke, Phys. Rev. B 61, 4109 (2000). 123. A. Hernando, J. Phys.: Condens. Matter 11, 9455 (1999); A. Hernando and A. Gonzalez, J. Non-Cryst. Solids 287, 256 (2001). 124. E. P. Elsukov, G. A. Dorofeev, A. I. Ul’yanov, A. V. Zagainov, and A. N. Maratkanova, Phys. Metals Metallography (Russia) 91, 258 (2001). 125. B. Chen, D. Penwell, M. B. Kruger, A. F. Yue, and B. Fultz, J. Appl. Phys. 89, 4794 (2001). 126. Y. H. Zhao, H. W. Sheng, and K. Lu, Acta Mater. 49, 365 (2001). 127. M. Murayama, J. M. Howe, H. Hidaka, and S. Takaki, Science 295, 2433 (2002). 128. Q. Meng, N. Zhou, Y. Rong, S. Chen, and T. Y. Hsu (Xu Zuyao), Acta Mater. 50, 4563 (2002). 129. N. R. Tao, Z. B. Wang, W. P. Tong, M. L. Sui, J. Lu, and K. Lu, Acta Mater. 50, 4603 (2002). 130. P. P. Chatterjee, S. K. Pabi, and I. Manna, J. Appl. Phys. 86, 5912 (1999). 131. P. Chatterjee and S. P. Sen Gupta, Philos. Mag. A 81, 49 (2001). 132. X. Zhang, H. Wang, J. Narayan, and C. C. Koch, Acta Mater. 49, 1319 (2001). 133. X. Zhang, H. Wang, M. Kassem, J. Narayan, and C. C. Koch, Scripta Mater. 46, 661 (2002). 134. X. Zhang, H. Wang, R. O. Scattergood, J. Narayan, C. C. Koch, A. V. Sergueeva, and A. K. Mukherjee, Acta Mater. 50, 3995 (2002). 135. S. Hwang, C. Nishimura, and P. G. McCormick, Mater. Sci. Eng. A 318, 22 (2001). 136. I. Lucks, P. Lamparter, and E. J. Mittemeijer, Acta Mater. 49, 2419 (2001). 137. E. Gaffet and M. Harmelin, J. Less-Common Met. 157, 201 (1990). 138. T. D. Shen, C. C. Koch, T. L. McCormick, R. J. Nemanich, J. Y. Huang, and J. G. Huang, J. Mater. Res. 10, 139 (1995). 139. J. Y. Huang, H. Yasuda, and H. Mori, Philos. Mag. Lett. 79, 305 (1999). 140. G. J. Fan, F. Q. Guo, Z. Q. Hu, M. X. Quan, and K. Lu, Phys. Rev. B 55, 11010 (1997). 141. F. Q. Guo and K. Lu, Phys. Rev. B 57, 10414 (1998). 142. F. Q. Guo and K. Lu, Philos. Mag. Lett. 77, 181 (1998). 143. Y. H. Zhao, Z. H. Jin, and K. Lu, Philos. Mag. Lett. 79, 747 (1999). 144. T. D. Shen, W. Q. Ge, K. Y. Wang, M. X. Quan, J. T. Wang, W. D. Wei, and C. C. Koch, Nanostruct. Mater. 7, 393 (1996). 145. S. Orimo, G. Majer, T. Fukunaga, A. Züttel, L. Schlapbach, and H. Fujii, Appl. Phys. Lett. 75, 3093 (1999). 146. X. H. Chen, H. S. Yang, G. T. Wu, M. Wang, F. M. Deng, X. B. Zhang, J. C. Peng, and W. Z. Li, J. Cryst. Growth 218, 57 (2000). 147. 148. D. Choulier, R. Rahouadj, and E. Gaffet, Ann. Chim. Sci. Mater. 22, 351 (1997). 149. A. Caro and H. Van Swygenhoven, Phys. Rev. B 63, 134101 (2001). 150. P. Keblinski, D. Wolf, S. R. Phillpot, and H. Gleiter, Scripta Mater. 41, 631 (1999). 151. D. Wolf, Current Opinion Solid State Mater. Sci. 5, 435 (2001). 152. H. Van Swygenhoven, D. Farkas, and A. Caro, Phys. Rev. B 62, 831 (2000). 153. H. Van Swygenhoven, Science 296, 2386 (2002). 154. H. E. Schaefer, K. Reimann, W. Straub, R. Phillipp, H. Tanimoto, U. Brossmann, and R. Würschum, Mater. Sci. Eng. A 286, 24 (2000).

126 155. Yu. R. Kobolov, G. P. Grabovetskaya, M. B. Ivanov, A. P. Zhilyaev, and R. Z. Valiev, Scripta Mater. 44, 873 (2001). 156. D. Jia, K. T. Ramesh, E. Ma, L. Lu, and K. Lu, Scripta Mater. 45, 613 (2001). 157. S. R. Agnew, B. R. Elliott, C. J. Youngdahl, K. J. Hemker, and J. R. Weertman, Mater. Sci. Eng. 285, 391 (2000). 158. H. H. Fu, D. J. Benson, and M. A. Meyers, Acta Mater. 49, 2567 (2001). 159. E. Arzt, Acta Mater. 46, 5611 (1998). 160. L. H. Qian, S. C. Wang, Y. Z. Zhao, and K. Lu, Acta Mater. 50, 3425 (2002). 161. Y. Estrin, G. Gottstein, E. Rabkin, and L. S. Shvindlerman, Scripta Mater. 43, 141 (2000). 162. C. E. Krill III, L. Helfen, D. Michels, H. Natter, A. Fitch, O. Masson, and R. Birringer, Phys. Rev. Lett. 86, 842 (2001). 163. C. C. Koch, J. Metastable Nanocryst. Mater. 18, 9 (2003). 164. S. Van Petegem, F. Dalla Torre, D. Segers, and H. Van Swygenhoven, Scripta Mater. 48, 17 (2003). 165. E. R. Kimmel, Int. J. Refract. Hard Met. 2, 84 (1983). 166. F. Cardellini and G. Mazzone, Philos. Mag. A 67, 1289 (1993). 167. G. Mazzone, Appl. Phys. Lett. 67, 1944 (1995). 168. J. Y. Huang, Y. K. Wu, and H. Q. Ye, Appl. Phys. Lett. 66, 308 (1995). 169. J. Y. Huang, Y. K. Wu, and H. Q. Ye, Appl. Phys. Lett. 67, 1945 (1995). 170. J. Y. Huang, Y. K. Wu, and H. Q. Ye, Acta Mater. 44, 1201 (1996). 171. J. Sort, N. M. Mateescu, J. Nogués, S. Suriñach, and M. D. Baró, J. Metastable Nanocryst. Mater. 12, 126 (2002). 172. M. S. El-Eskandarany, K. Sumiyama, K. Aoki, and K. Suzuki, Mater. Sci. Forum 88–90, 801 (1992). 173. H. Van Swygenhoven, M. Spaczer, A. Caro, and D. Farkas, Acta Mater. 47, 3117 (1999). 174. J. Schiotz, T. Vegge, F. D. Di Tolla, and K. W. Jacobsen, Phys. Rev. B 60, 11971 (1999). 175. P. M. Derlet, R. Meyer, L. J. Lewis, U. Stuhr, and H. Van Swygenhoven, Phys. Rev. Lett. 20, 205501 (2001). 176. E. Gaffet, Mater. Sci. Eng. A 136, 161 (1991). 177. E. Gaffet, F. Faudot, and M. Harmelin, Mater. Sci. Eng. A 149, 85 (1991). 178. E. Gaffet and J. P. Gaspard, J. Phys. Suppl. Coll. C 4, 205 (1990). 179. T. D. Shen, I. Shmagin, C. C. Koch, R. M. Kolbas, Y. Fahmy, L. Bergman, R. J. Nemanich, M. T. McClure, Z. Sitar, and M. X. Quan, Phys. Rev. B 55, 7615 (1997). 180. A. N. Streleskii, A. V. Leonov, and P. Yu Butyagin, Coll. J. 63, 630 (2001). 181. A. N. Strelestkii, A. V. Leonov, I. V. Beresteskaya, S. S. Mudretsova, A. F. Majorova, and P. Ju. Butyagin, Mater. Sci. Forum 386–388, 187 (2002). 182. C. Diaz-Guerra, A. Montone, J. Piqueras, and F. Cardellini, Semicond. Sci. Technol. 17, 77 (2002). 183. T. Nasu, F. Araki, O. Uemura, T. Usuki, Y. Kameda, S. Takahashi, and K. Tokumitsu, J. Metast. Nanocryt. Mater. 10, 203 (2001). 184. Y. Tani, Y. Shirakawa, A. Shimosaka, and J. Hidaka, J. Non-Cryst. Solids 293–295, 779 (2001). 185. J. Y. Huang, Acta Mater. 47, 1801 (1999). 186. N. J. Welham and J. S. Williams, Carbon 36, 1309 (1998). 187. F. Salver-Disma, J.-M. Tarascon, C. Clinard, and J.-N. Rouzaud, Carbon 37, 1941 (1999). 188. F. Disma, L. Aymard, L. Dupont, and J.-M. Tarascon, J. Electrochem. Soc. 143, 3959 (1996). 189. F. Salver-Disma, C. Lenain, B. Beaudoin, L. Aymard, and J.-M. Tarascon, Solid State Ionics 98, 145 (1997). 190. R. Janot and D. Guerard, Carbon, in press. 191. G. B. Schaffer and P. G. McCormick, Mater. Sci. Forum 88–90, 779 (1992). 192. G. B. Schaffer and P. G. McCormick, Appl. Phys. Lett. 55, 45 (1989).

Mechanical Processing for Nanomaterials 193. P. G. McCormick, Mater. Trans. JIM 36, 228 (1995). 194. J. Ding, T. Tsuzuki, P. G. McCormick, and R. Street, Mater. Trans. JIM 36, 228 (1995). 195. T. Tsuzuki and P. G. McCormick, Appl. Phys. A 65, 607 (1997). 196. J. Ding, T. Tsuzuki, and P. G. McCormick, J. Mater. Sci. 34, 5293 (1999). 197. P. Matteazzi and G. Le Caër, J. Am. Ceram. Soc. 75, 2749 (1992). 198. L. Takacs, Progr. Mater. Sci. 47, 355 (2002). 199. H. W. Sheng, K. Lu, and E. Ma, Acta Mater. 46, 5195 (1998). 200. K. Chattopadhyay and R. Goswami, Progr. Mater. Sci. 42, 287 (1997). 201. K. Lu and Z. H. Jin, Current Opinion Solid State Mater. Sci. 5, 39 (2001). 202. Y. Wang, M. Chen, F. Zhou, and E. Ma, Nature 419, 912 (2002). 203. G. He, J. Eckert, W. Löser, and L. Schultz, Nature Mater. 2, 33 (2003). 201. M. Zeghmati, E. Duverger, and E. Gaffet, in “Proc. CANCAM 95” (B. Tabarrock and S. Dost, Eds.), Cong. Canad. Mécan. Appl. 2, 952 (1995). 202. F. Charlot, E. Gaffet, B. Zeghmati, F. Bernard, and J.-C. Niepce, Mater. Sci. Eng. A 262, 279 (1999). 203. F. Bernard, F. Charlot, E. Gaffet, and J. C. Niepce, Int. J. Self Prop. High Temp. Synth. 7, 233 (1998). 204. F. Charlot, E. Gaffet, F. Bernard, Ch Gras, and J. C. Niepce, Mater. Sci. Forum 312–314, 287 (1999). 205. F. Charlot, F. Bernard, D. Klein, E. Gaffet, and J.-C. Niepce, Acta Mater. 47, 619 (1999). 206. F. Charlot, C. Gras, M. Grammond, F. Bernard, E. Gaffet, and J. C. Niepce, J. Phys. Suppl. Coll. IV, 497 (1998). 207. Ch Gras, D. Vrel, E. Gaffet, and F. Bernard, J. All. Comp. 314, 240 (2001). 208. Ch. Gras, F. Charlot, F. Bernard, E. Gaffet, and J. C. Niepce, Acta Mater. 47, 2113 (1999). 209. Ch. Gras, N. Bernsten, F. Bernard, and E. Gaffet, Intermetallics 10, 271 (2002). 210. Ch. Gras, E. Gaffet, F. Bernard, and J. C. Niepce, Mater. Sci. Eng. A 264, 94 (1999). 211. H. Shouha, E. Gaffet, F. Bernard, and J. C. Niepce, J. Mater. Sci. 35, 3221 (2000). 212. F. Bernard, H. Souha, and E. Gaffet, Mater. Sci. Eng. A 284, 301 (2000). 213. H. Shouha, F. Bernard, E. Gaffet, and B. Gillot, Thermochem. Acta 351, 71 (2000). 214. V. Gauthier, F. Bernard, E. Gaffet, D. Vrel, and J. P. Larpin, Intermetallics 10, 377 (2002). 215. V. Gauthier, F. Bernard, E. Gaffet, C. Josse, and J. P. Larpin, Mater. Sci. Eng. A 272, 334 (1999). 216. V. Gauthier, C. Josse, F. Bernard, E. Gaffet, and J.-P. Larpin, Mater. Sci. Eng. A 265, 117 (1999). 217. V. Gauthier, J. P. Larpin, M. Vilasi, F. Bernard, and E. Gaffet, Mater. Sci. Forum 369–372, 793 (2001). 218. R. M. L. Neto and C. J. da Rocha, Key Eng. Mater. 189–191, 567 (2001). 219. K. Uenishi, T. Matsubara, M. Kambara, and K. F. Kobayashi, Scripta Mater. 44, 2093 (2001). 220. T. Matsubara, K. Uenishi, and K. F. Kobayashi, Mater. Trans. JIM 41, 631 (2000). 221. J. Lagerbom, T. Tiainen, M. Lehtonen, and P. Lintula, J. Mater. Sci. 34, 1477 (1999). 222. F. Maglia, U. Anselmi-Tamburini, G. Cocco, M. Monagheddu, N. Bertolino, and Z. A. Munir, J. Mater. Res. 16, 1074 (2001). 223. S. Murali, T. Sritharan, and P. Hing, Int. J. Powder Metall. 37, 67 (2001). 224. D. Vrel, N. Girodon-Boulandet, S. Paris, J.-F. Mazué, E. Couqueberg, M. Gailhanou, D. Thiaudière, E. Gaffet, and F. Bernard, Rev. Sci. Instrum. 73, 422 (2002).

Mechanical Processing for Nanomaterials 225. F. Bernard, E. Gaffet, M. Gramond, M. Gailhanou, and J. C. Gachon, J. Synchrotron Radiation 7, 27 (2000). 226. Z. A. Munir, F. Charlot, F. Bernard, and E. Gaffet, One Step Synthesis and Consolidation of Nanophase Materials, U.S. Patent 6, 200, 515, 2001. 227. F. Charlot, E. Gaffet, F. Bernard, and Z. A. Munir, J. Amer. Ceram. Soc. 84, 910 (2001). 228. Ch. Gras, F. Bernard, F. Charlot, E. Gaffet, and Z. A. Munir, J. Mater. Res. 13, 542 (2002). 229. V. Gauthier, F. Bernard, E. Gaffet, Z. Munir, and J.-P. Larpin, Intermetallics 9, 571 (2001). 230. R. Orru, J. Woolmann, G. Cao, and Z. A. Munir, J. Mater. Res. 16, 1439 (2001). 231. M. Sannia, R. Orru, J. E. Garay, G. Cao, and Z. A. Munir, Mater. Sci. Eng., in press. 232. O. Coreno-Alonso, J. G. Cabanas-Moreno, J. J. Cruz-Riverra, H. A. Calderon, M. Umemoto, K. Tschiya, S. Quintana-Molina, and C. Falcony, J. Metast. Nanocryst. Mater. 8, 635 (2000). 233. Y. D. Kim, S.-T. Oh, K. H. Min, H. Jeon, and I.-H. Moon, Scripta Mater. 44, 293 (2001). 234. J. W. Lee, Z. A. Munir, and M. Ohyanagi, Mater. Sci. Eng. A 325, 221 (2002). 235. M.-S. El-Eskandarany, M. Omori, T. J. Konno, K. Sumiyama, T. Hirai, and K. Suzuki, Metall. Mater. Trans. A 32, 157 (2001). 236. S. D. de la Torre, D. E. Garcia, N. Claussen, R. Janssen, Y. Nishikawa, H. Miyamoto, R. Martinez-Sanchez, A. Garcia-L., and D. Rios-Jara, Mater. Sci. Forum 386–388, 299 (2002). 237. T. Murakami, C. N. Xu, A. Kitahara, M. Kawahara, Y. Takahashi, H. Inui, and M. Yamaguchi, Intermetallics 7, 1043 (1999). 238. G. Farne, F. G. Ricciardiello, L. K. Podda, and D. Minichelli, J. Europ. Ceram. Soc. 19, 347 (1999). 239. S. S. Ryu, Y. D. Kim, and I. H. Moon, J. All. Comp. 335, 233 (2002). 240. E. Gaffet, N. Malhouroux, and M. Abdellaoui, J. All. Comp. 194, 339 (1993). 241. N. Malhouroux-Gaffet and E. Gaffet, J. All. Comp. 198, 143 (1993). 242. E. Gaffet and N. Malhouroux-Gaffet, J. All. Comp. 205, 27 (1994). 243. E. Gaffet, N. Malhouroux-Gaffet, M. Abdellaoui, and A. Malchère, Rev. Métal. 757 (1994). 244. G. A. Roberts, E. J. Cairns, and J. A. Reimer, J. Power Sources, in press. 245. D. L. Zhang and D. Y. Ying, Mater. Sci. Eng. A 301, 90 (2001). 246. R. Ren, Z. Yang, and L. L. Shaw, Mater. Sci. Eng. A 286, 65 (2000). 247. R.-M. Ren, Z.-G. Yng, and L. L. Shaw, Scripta Mater. 38, 735 (1998). 248. V. Berbenni and A. Marini, Mater. Res. Bull. 37, 221 (2002). 249. V. Nivoix, F. Bernard, E. Gaffet, P. Perriat, and B. Gillot, Powder Technol. 105, 155 (1999). 250. H. Hu, Q. Chen, Z. Yin, P. Zhang, J. Zou, and H. Che, Thermochim. Acta 389, 79 (2002). 251. V. Berbenni, A. Marini, N. J. Welham, P. Galinetto, and M. C. Mozzati, J. Europ. Ceram. Soc. 23, 179 (2003). 252. S. Boskovic, D. Kosanovic, Dj. Bahloul-Hourlier, P. Thomas, and S. J. Kiss, J. All. Comp. 290, 230 (1999). 253. R. Citak, K. A. Rogers, and K. H. Sandhage, J. Amer. Ceram. Soc. 82, 237 (1999). 254. E. A. Goodilin, D. Pyoryshkov, A. V. Knot’ko, V. V. Lennikov, N. N. Oleynikov, and Y. D. Tretyakov, Physica C 349, 278 (2001). 255. E. G. Avvakumov, E. T. Devyatkina, N. V. Kosova, O. A. Kirichenko, N. Z. Lyakhov, and A. A. Gusev, Kinetics Catal. 39, 663 (1998). 256. Y. Chen, L. T. Chadderton, J. S . Williams, and J. FitzGerald, J. Metast. Nanocryst. Mater. 8, 63 (2000). 257. B. Bokhonov and M. Korchagin, J. All. Comp. 333, 308 (2002). 258. P. G. McCormick and F. H. Froes, JOM 50, 61 (1998).

127 259. E. G. Baburaj, O. N. Senkov, and F. H. Froes, Reduction of Metal Oxides through Mechanochemical Processing, U.S. Patent Pending 60/074693, 1998. 260. F. H. Froes, O. N. Senkov, and E. G. Baburaj, Mater. Sci. Technol. 17, 119 (2001). 261. M. Senna, Int. J. Inorganic Mater. 3, 509 (2001). 262. T. Watanabe, T. Isobe, and M. Senna, J. Solid State Chem. 130, 284 (1997). 263. K. Hamada, T. Isobe, and M. Senna, J. Mater. Sci. Lett. 15, 603 (1996). 264. JG Baek, T. Isobe, and M. Senna, Solid State Ionics 90, 269 (1996). 265. M. Kitamura, M. Kamitani, and M. Senna, J. Amer. Ceram. Soc. 83, 523 (2000). 266. A. C. Dodd, K. Raviprasad, and P. G. McCormick, Scripta Mater. 44, 689 (2001). 267. P. Matteazzi and G. Le Caër, Mater. Sci. Eng. A 149, 135 (1991). 268. J. Ding, T. Tsuzuki, and P. G. McCormick, J. Am. Ceram. Soc. 79, 2956 (1996). 269. J. Ding, T. Tsuzuki, and P. G. McCormick, Nanostruct. Mater. 8, 75 (1997). 270. J. Ding, T. Tsuzuki, and P. G. McCormick, Nanostruct. Mater. 8, 739 (1997). 271. Tsuzuki and McCormick, Mater. Sci. Forum 343–346, 383 (2000). 272. J. Ding, W. F. Miao, P. G. McCormick, and R. Street, Appl. Phys. Lett. 67, 3804 (1995). 273. J. Ding, T. Tsuzuki, P. G. McCormick, and R. Street, J. All. Comp. 234, L1 (1996). 274. J. Ding, T. Tsuzuki, P. G. McCormick, and R. W. Streep, J. Phys. D 29, 2365 (1996). 275. E. G. Baburaj, K. T. Hubert, and F. H. Froes, J. All. Comp. 25, 146 (1997). 276. H. Yang and P. G. Mc Cormick, J. Mater. Sci. Lett. 12, 1088 (1993). 277. H. Yang and P. G. McCormick, Metall. Mater. Trans. B 29, 449 (1998). 278. F. H. Froes, O. N. Senkiv, and E. G. Baburaj, Mater. Sci. Technol. 17, 119 (2001). 279. S. D. de la Torre, K. N. Ishihara, P. H. Shingu, D. Rios-Jara, and H. Miyamoto, Proc. Innovative Processing/Synthesis: Ceramics Glasses Composites 2, 287 (1999). 280. C. Lam, Y. F. Zhang, Y. H. Tang, C. S. Lee, I. Bello, and S. T. Lee, J. Cryst. Growth 220, 466 (2000). 281. T. Tsuzuki, J. Ding, and P. G. McCormick, Physica B 239, 378 (1997). 282. P. Matteazzi and G. Le Caër, Mater. Sci. Eng. A 156, 229 (1992). 283. L. Takacs and M. Pardavi-Horvath, J. Appl. Phys. 75, 5864 (1994). 284. P. Matteazzi and G. Le Caer, J. All. Comp. 187, 305 (1992). 285. G. B. Schaffer and P. G. Mc Cormick, Mater. Sci. For. 88–90, 779 (1990). 286. P. Matteazzi and G. Le Caër, J. Amer. Ceram. Soc. 75, 2749 (1992). 287. P. Matteazzi, G. Le Caër, and A. Mocellin, Ceram. Int. 23, 39 (1997). 288. P. Matteazzi and M. Alcalà, Mater. Sci. Eng. A 230, 161 (1997). 289. T. Nasu, K. Tokumitsu, K. Miyazawa, A. L. Greer, and K. Suzuki, J. Metast. Nanocryst. Mater. 2–6, 185 (1999). 290. L. Takacs, Mater. Lett. 13, 119 (1992). 291. S. Xi, X. Qu , M. Ma, J. Zhou, Zheng, and X. Wang, J. All. Comp. 268, 211 (1998). 292. G. Concas, F. Congiu, A. Corrias, C. Muntoni, G. Paschina, and D. Zedda, Z. Naturforsch. 51, 915 (1996). 293. A. Corrias, G. Paschina, and P. Sirigu, J. Non-Cryst. Solids 232–234, 358 (1998). 294. A. Corrias, G. Ennas, A. Musinu, G. Paschina, and D. Zedda, J. Mater. Res. 12, 2767 (1997). 295. M. P. Dallimore and P. G. McCormick, Mater Trans JIM (1996). 296. M. S. El-Eskandarany, Mater. Trans. JIM 36, 182 (1995). 297. Y. Chen, J. S. Williams, and B. Ninham, Colloids Surfaces A 129– 130, 61 (1997).

128 298. N. J. Welham, J. All. Comp. 274, 303 (1998). 299. N. J. Welham, J. All. Comp. 270, 228 (1998). 300. Y. Chen, T. Hwang, M. Marsh, and J. S. Williams, Metall. Mater. Trans. A 28, 1115 (1997). 301. N. J. Welham, Minerals Eng. 9, 1189 (1996). 302. Q. Zhang and F. Saito, Hydrometallurgy 47, 231 (1998). 303. R. W. Cahn, Mater. Sci. Forum 179–181, 53 (1995). 304. R. W. Cahn, in “Physics of New Materials” (F. E. Fujita, Ed.), 2nd updated ed., p. 179. Springer, Berlin, 1998. 305. C. T. Liu and K. S. Kumar, JOM 45, 38 (1993). 306. K. S. Kumar and C. T. Liu, JOM 45, 28 (1993). 307. Y. W. Kim, JOM 46, 30 (1994). 308. K. A. Kylian and R. H. Victora, J. Appl. Phys. 87, 7064 (2000). 309. S. Picozzi, A. Continenza, and A. J. Freeman, IEEE Trans. Mag. 38, 2895 (2002). 310. B. Ravel, M. P. Raphael, V. G. Harris, and O. Huang, Phys. Rev. B 65, 184431 (2002). 311. T. Kakeshita and K. Ullakko, MRS Bull. 27, 105 (2002). 312. D. J. Sellmyer, Nature 420, 374 (2002). 313. R. Skomski and J. M. D. Coey, Phys. Rev. B 48, 15812 (1993). 314. G. Martin, Current Opinion Solid State Mater. Sci. 3, 552 (1998). 315. S. Takahashi, X. G. Li, and A. Chiba, J. Phys.: Condens. Matter 8, 11243 (1996). 316. G. P. Hufman and R. M. Fisher, J. Appl. Phys. 38, 735 (1967). 317. A. J. Lapworth and J. P. Jakubovics, Philos. Mag. 29, 253 (1974). 318. T. Shinohara, K. Sasaki, H. Yamanchi, H. Watanabe, H. Sekizawa, and T. Okada, J. Phys. Soc. Japan 50, 2904 (1981). 319. J. Schaf, K. Le Dang, P. Veillet, and I. A. Campbell, J. Phys. F 13, 1311 (1983). 320. E. P. Elsukov, V. A. Barinov, V. R. Galakhov, E. E. Yurchikov, and A. E. Ermakov, Phys. Metals Metallograph. 55, 119 (1983). 321. H. Bakker, G. F. Zhou, and H. Yang, Progr. Mater. Sci. 39, 159 (1995). 322. C. C. Koch and J. D. Whittenberger, Intermetallics 4, 339 (1996). 323. D. Negri, A. R. Yavari, and A. Deriu, Acta Mater. 47, 4545 (1999). 324. P. J. Webster, Contemp. Phys. 10, 559 (1969). 325. J. S. Brooks and J. M. Williams, J. Phys. F 4, 2033 (1974). 326. C. C. M. Campbell, J. Phys. F 5, 1931 (1975). 327. J. C. Suits, Phys. Rev. B 14, 4131 (1976). 328. Le Dang Khoi, P. Veillet, and I. A. Campbell, J. Phys. F 8, 1827 (1978). 329. Y. Watanabe, Y. Murakami, and S. Kachi, J. Japan Inst. Metals 45, 551 (1981). 330. R. A. Dunlap, R. H. March, and G. Stroink, Can. J. Phys. 59, 1577 (1981). 331. A. Ayuela, J. Enkovaara, K. Ullakko, and R. M. Nieminen, J. Phys.: Condens. Matter 11, 2017 (1999). 332. G. Le Caër, P. Delcroix, B. Malaman, R. Welter, B. Fultz, and E. Ressouche, Mater. Sci. Forum 235–238, 583 (1997). 333. J. S. Robinson, P. G. McCormick, and R. Street, J. Phys.: Condens. Matter 7, 4259 (1995). 334. E. Wachtel, F. Henninger, and B. Predel, J. Magn. Magn. Mater. 38, 305 (1983). 335. J. I. Seki, M. Hagiwara, and T. Suzuki, J. Mater. Sci. 14, 2404 (1979). 336. R. J. Chandross and D. P. Shoemaker, J. Phys. Soc. Jpn. Suppl. B-III 17, 16 (1962). 337. J. M. Sanchez, M. C. Cadeville, V. Pierron-Bohnes, and G. Inden, Phys. Rev. B 54, 8958 (1996). 338. T. Ziller, G. Le Caër, O. Isnard, P. Cénédèse, and B. Fultz, Phys. Rev. B 65, 024204 (2002). 339. A. R. Yavari, Acta Metall. Mater. 41, 1391 (1993). 340. C. Bansal, Z. Q. Gao, L. B. Hong, and B. Fultz, J. Appl. Phys. 76, 5961 (1994). 341. Z. Q. Gao and B. Fultz, Hyp. Interact. 94, 2213 (1994); 94, 2361 (1994). 342. Z. Q. Gao and B. Fultz, Nanostruct. Mater. 4, 939 (1994).

Mechanical Processing for Nanomaterials 343. C. Bansal, Z. Q. Gao, and B. Fultz, Nanostruct. Mater. 5, 327 (1995). 344. F. Cardellini, V. Contini, and G. Mazzone, Scripta Metall. Mater. 32, 641 (1995). 345. U. Herr, M. Pollack, D. L. Olynick, J. M. Gibson, and R. S. Averback, Mater. Res. Soc. Symp. Proc. 398, 575 (1996). 346. P. Scherrer, C. Dimitropoulos, F. Borsa, and S. Rubini, Phys. Rev. B 57, 10462 (1998). 347. A. Hernando, X. Amils, J. Nogués, S. Surinach, M. D. Baro, and M. R. Ibarra, Phys. Rev. B 58, R11864 (1998). 348. S. Gialanella, X. Amils, M. D. Barò, P. Delcroix, G. Le Caër, L. Lutteroti, and S. Surinach, Acta Mater. 46, 3305 (1998). 349. R. A. Varin, J. Bystrzycki, and A. Calka, Intermetallics 7, 785 (1999); 7, 917 (1999). 350. K. Reimann and H. E. Schaefer, Nanostruct. Mater. 12, 633 (1999). 351. H. E. Schaefer, K. Reimann, W. Straub, R. Phillipp, H. Tanimoto, U. Brossmann, and R. Würschum, Mater. Sci. Eng. A 286, 24 (2000). 352. X. Amils, J. Nogués, S. Surinach, M. D. Baro, M. A. MunozMorris, and D. G. Morris, Intermetallics 8, 805 (2000). 353. L. Pasquini, A. A. Rempel, R. Würschum, K. Reimann, M. A. Müller, B. Fultz, and H. E. Schaefer, Phys. Rev. B 63, 134114 (2001). 354. S. Sarkar and C. Bansal, Acta Mater. 49, 1789 (2001). 355. D. G. Morris, X. Amils, S. Surinach, M. D. Baro, and M. A. Munoz-Morris, Mater. Sci. Forum 360–362, 195 (2001). 356. K. Reimann, H. J. Fecht, and H. E. Schaefer, Scripta Mater. 44, 1999 (2001). 357. J. C. Evert and G. Schmitz, Eur. Phys. J. B 17, 391 (2000). 358. P. Pochet, E. Tominez, L. Chaffron, and G. Martin, Phys. Rev. B 52, 4006 (1995). 359. J. Joardar, S. K. Pabi, H. J. Fecht, and B. S. Murty, Philos. Mag. Lett. 82, 469 (2002). 360. E. A. Leonova, P. Delcroix, G. Le Caër, S. D. Kaloshkin, and Yu. V. Baldokhin, in “Ninth International Symposium on Metastable Mechanically Alloyed and Nanocrystalline Materials,” ISMANAM 2002, 8–12 September 2002, Seoul, South Korea, J. Metastable Nanocryst. Mater., in press. 361. B. Fultz, J. Chem. Phys. 88, 3227 (1988). 362. B. Fultz and L. Anthony, Philos. Mag. Lett. 59, 237 (1989). 363. D. Le Floc’h, P. Bellon, and M. Athènes, Phys. Rev. B 62, 3142 (2000). 364. L. Chaffron, Y. Le Bouar, and G. Martin, C.R. Acad. Sci. Paris Ser. IV 2, 749 (2001). 365. A. R. Yavari, P. J. Desre, and R. Benameur, Phys. Rev. Lett. 68, 2235 (1992). 366. C. Gente, M. Oehring, and R. Bormann, Phys. Rev. B 48, 13244 (1993). 367. J. Xu, U. Herr, T. Klassen, and R. S. Averback, J. Appl. Phys. 79, 3935 (1996). 368. L. B. Hong and B. Fultz, J. Appl. Phys. 79, 3946 (1996). 369. G. Mazzone and M. Vittori Antisari, Phys. Rev. B 54, 441 (1996). 370. T. Klassen, U. Herr, and R. S. Averback, Acta Mater. 45, 2921 (1997). 371. J. Y. Huang, Y. D. Yu, Y. K. Wu, D. X. Li, and H. Q. Ye, Acta Mater. 45, 113 (1997). 372. J. Xu, J. H. He, and E. Ma, Metall. Mater. Trans. A 28A, 3935 (1997). 373. E. P. Yelsukov, E. V. Voronina, G. N. Konygin, V. A. Barinov, S. K. Godovikov, G. A. Dorofeev, and A. V. Zagainov, J. Magn. Magn. Mater. 166, 334 (1997). 374. G. Martin and P. Bellon, Metall. Sci. Techn. 9, 61 (1991); Solid State Phys. 50, 189 (1997). 375. R. Bormann, Mater. Sci. Eng. A 226–228, 268 (1998). 376. G. Martin, Current Opinion Solid State Mater. Sci. 3, 552 (1998). 377. M. Zhu, X. Z. Che, Z. X. Li, J. K. L. Lai, and M. Qi, J. Mater. Sci. 33, 5873 (1998).

Mechanical Processing for Nanomaterials 378. J. Rüsing, V. Naundorf, N. Wanderka, and H. Wollenberger, Ultramicroscopy 73, 267 (1998). 379. L. B. Hong and B. Fultz, Acta Mater. 46, 2937 (1999). 380. J. Xu, G. S. Collins, L. S. J. Peng, and M. Atzmon, Acta Mater. 47, 1241 (1999). 381. P. J. Schilling, J. H. He, R. C. Tittsworth, and E. Ma, Acta Mater. 47, 2525 (1999). 382. E. Gaffet, F. Faudot, and M. Harmelin, J. Alloys Comp. 194, 23 (1993). 383. S. Zghal, M. J. Hÿtch, J. P. Chevalier, R. Twesten, F. Wu, and P. Bellon, Acta Mater. 50, 4695 (2002). 384. S. Zghal, R. Twesten, F. Wu, and P. Bellon, Acta Mater. 50, 4711 (2002). 385. U. Czubayko, N. Wanderka, V. Naundorf, V. A. Ivchenko, A. Ye. Yermakov, M. A. Uimin, and H. Wollenberger, Mater. Sci. Eng. A 327, 54 (2002). 386. H. W. Sheng, G. Wilde, and E. Ma, Acta Mater. 50, 4711 (2002). 387. J. Z. Jiang, C. Gente, and R. Bormann, Mater. Sci. Eng. A 242, 268 (1998). 388. P. Crespo and A. Hernando, Recent Res. Devel. Nanostruct. 1, 63 (1999). 389. N. Wanderka, U. Czubayko, V. Naundorf, V. A. Ivchenko, A. Ye. Yermakov, M. A. Uimin, and H. Wollenberger, Ultramicroscopy 89, 189 (2001). 390. M. B. Fernandez van Raap, L. M. Socolovsky, F. H. Sanchez, and I. L. Torriani, J. Phys.: Condens. Matter 14, 857 (2002). 391. S. D. Kaloshkin, I. A. Tomilin, G. A. Andrianov, U. V. Baldokhin, and E. V. Shelekhov, Mater. Sci. Forum 235–238, 565 (1997). 392. P. Delcroix, T. Ziller, C. Bellouard, and G. Le Caër, Mater. Sci. Forum 360–362, 329 (2001). 393. J. H. He, H. W. Sheng, P. J. Schilling, C. L. Chien, and E. Ma, Phys. Rev. Lett. 86, 2826 (2001). 394. J. H. He and E. Ma, Phys. Rev. B 64, 144206 (2001). 395. H. R. Gong, L. T. Kong, W. S. Lai, and B. X. Liu, Phys. Rev. B 66, 104204 (2002). 396. H. W. Sheng, J. H. He, and E. Ma, Phys. Rev. B 65, 184203 (2002).

129 397. J. H. He, H. W. Sheng, J. S. Lin, P. J. Schilling, R. C. Tittsworth, and E. Ma, Phys. Rev. Lett. 89, 125507 (2002). 398. R. Enrique, F. Wu, and P. Bellon, Surface Coat. Technol. 150, 1 (2002). 399. G. Le Caër, T. Ziller, P. Delcroix, and C. Bellouard, Hyp. Interact. 130, 45 (2000). 400. A. F. Cabrera and F. H. Sanchez, Phys. Rev. B 65, 094202 (2002). 401. J. S. Benjamin and T. E. Volin, Metall. Trans. 5, 1929 (1974). 402. H. Kuwano, H. Ouyang, and B. Fultz, Mater. Sci. Forum 88–90, 561 (1992). 403. S. K. Xia, E. Baggio-Saitovitch, F. C. Rizzo Assunçao, and V. A. Pena Rodriguez, J. Phys.: Condens. Matter 5, 2729 (1993). 404. T. Koyano, T. Takizawa, T. Fukunaga, U. Mizutani, S. Kamizuru, E. Kita, and A. Tasaki, J. Appl. Phys. 73, 429 (1993). 405. S. K. Xia, F. C. Rizzo Assunçao, and E. Baggio-Saitovitch, Mater. Sci. Forum 225–227, 459 (1996). 406. G. Le Caër, P. Delcroix, T. D. Shen, and B. Malaman, Phys. Rev. B 54, 12775 (1996). 407. G. Le Caër, P. Delcroix, and J. Foct, Mater. Sci. Forum 269–272, 409 (1998). 408. C. Bellouard, G. Le Caër, and P. Delcroix, Mater. Sci. Forum 343–346, 819 (1998). 409. C. Lemoine, A. Fnidiki, D. Lemarchand, and J. Teillet, J. Phys.: Condens. Matter 11, 8341 (1999); C. Lemoine, Ph.D. Thesis, Université de Rouen, 2000. 410. B. F. O. Costa, G. Le Caër, and B. Luyssaert, J. Alloys Comp. 350, 36 (2003). 411. S. F. Fischer, S. N. Kaul, and H. Kronmüller, Phys. Rev. B 65, 064443 (2002). 412. P. Delcroix, C. Bellouard, and G. Le Caër, in preparation. 413. C. Michaelsen, Philos. Mag. A 72, 813 (1995). 414. H. Heegn, Chem. Ing. Tech. 73, 1529 (2001). 415. A. C. Lund and C. A. Schuh, Phys. Rev. Lett. 91, 235505 (2003). 416. A. C. Lund and C. A. Schuh, Appl. Phys. Lett. 82, 2017 (2003). 417. http://wondersmith.com/scifi/micro.htm

Encyclopedia of Nanoscience and Nanotechnology

www.aspbs.com/enn

Mechanical Properties of Nanostructured Materials S.-P. Hannula, J. Koskinen VTT Industrial Systems, Finland

E. Haimi Helsinki University of Technology, Finland

R. Nowak Helsinki University of Technology, Finland, and Hiroshima University, Kagamiyama, Japan

CONTENTS 1. Introduction 2. Theoretical Background of Mechanical Properties 3. Modeling of Mechanical Properties of Nanostructured Materials 4. Experimental Methods Designed for Probing of Mechanical Properties of Nanostructured Materials 5. Mechanical Properties of Nanostructured Materials 6. Application of Nanomaterials Relevant to Mechanical Properties 7. Summary Glossary References

1. INTRODUCTION In recent years a wide range of nanostructured materials has been introduced. These novel materials are produced in various forms such as nanopowders, nanostructured particulates, fibers, tubes, thin films, as well as bulk by using a number of processing routes. Nanostructured materials have many interesting properties. These include a number of ISBN: 1-58883-061-6/$35.00 Copyright © 2004 by American Scientific Publishers All rights of reproduction in any form reserved.

useful mechanical properties related to strength, hardness, elastic properties, toughness, plasticity, etc. In this chapter these properties are described and discussed in detail with a reference to existing or potential practical applications. Distinction of different forms of nanostructured materials may be made by their dimensionality [1, 2]. Nanostructural materials may exist in (i) zero-dimensional atomic clusters (all three dimensions in nanoscale), (ii) one- or twodimensional multilayers or filamentary structures (one or two dimensions in nanoscale, one or two in macroscale), and (iii) bulk (all dimensions in macroscale) with threedimensional nanocrystalline grains (see Fig. 1). There is a variety of processes suitable for producing nanocrystalline materials. Bulky nanocrystalline materials may be produced, for example, by electrodeposition, severe plastic deformation (SPD) of preforms, or by using various powder metallurgical routes to consolidate nanopowders or powders with nanocrystalline structure produced by, for example, mechanical alloying (MA). The bulk form of these materials includes electrodeposited sheets, equal channel angular pressed (ECAP) rods, ball-milled and consolidated pellets, composite films produced by a variety of deposition techniques, etc. It should be noted that their properties are related not only to their nanostructure, but also to the processing method by which they are produced, because the detailed microstructural features may differ after various processing routes even at the same nominal composition and grain size. These microstructural features include type of grain boundaries, grain shape, crystal defects, pores

Encyclopedia of Nanoscience and Nanotechnology Edited by H. S. Nalwa Volume 5: Pages (131–162)

132

Mechanical Properties of Nanostructured Materials

2. THEORETICAL BACKGROUND OF MECHANICAL PROPERTIES

Figure 1. Schematic illustration of various nanomaterials having a different number of dimensions [1, 2]; zero-dimensional powder, onedimensional thin deposited layer, surface coating with nanostructure in two-dimensions, and three-dimensional bulk nanomaterial.

and their distribution, other flaws, impurities, and surface condition. Mechanical testing of nanocrystalline materials is generally different from that used for their coarse-grained counterparts because the amount of nanocrystalline material is in many cases so small that conventional test methods with large bulk samples cannot be used. Therefore, methods using small amounts of material have often been used instead of conventional testing. Results have been obtained either by modified traditional testing methods or by specially designed tests that probe materials with small dimension, such as instrumented nanoindentation. Most of the data that exist are from the nanostructured thin films or bulk materials processed by powder metallurgy (PM) techniques or by severe plastic deformation (SPD). These data are not always as reliable as those obtained from conventional bulk samples. Further elaboration of results is also subject to uncertainty because the determination of the grain size in nanoscale is more tedious and subject to larger experimental errors than in materials with conventional grain sizes. Nevertheless, it has been shown that nanocrystalline materials have special mechanical properties. Typically the strength of crystalline materials is increased with decreasing grain size and materials with small grain size often exhibit also superplastic behavior. Nanocrystallinity may also have a positive influence on fatigue properties of metals and toughness of ceramic materials. Ductility, however, may also be decreased due to increased tendency to flow localization, but hardness and wear properties of materials and coatings can be improved. There are several recent reviews on mechanical properties of nanocrystalline materials (e.g., [3–5], to mention a few) and the reader is referred also to them for a more thorough review of different particular subjects. In this chapter, we wish to give a collective view on various current developments related to mechanical properties of nanocrystalline materials.

The main feature distinguishing nanomaterials from conventional materials is the large fraction of atoms located in the grain/interphase boundaries. Grains are typically equiaxed with a narrow and lognormal size distribution and dislocations are seldom seen inside the grains. Those that are seen are typically in sessile configurations [6]. Level of various defects arising from processing may be present in significant amounts and they all influence the mechanical properties. Even in nominally fully dense nanocrystalline materials there are 1- to 2-nm-sized pores and smaller nanovoids [7]. Two divergent views exist on the nature of grain boundaries in nanomaterials. According to the classic interpretation, the nature of grain boundaries in nanomaterials is no different from the nature of grain boundaries in coarsegrained materials [8]. However, based on a more recent study by computer simulation, it has been suggested that in nanomaterials a long-range periodicity does not exist, the grain boundary energy and width distributions are narrower and the grain boundaries wider than in bicrystals, and that the grain boundaries are an isotropic, cementlike phase different from glasses or bicrystals [9]. The grain boundary structure results in enhanced solute solubilities and enhanced diffusion as well as a different thermodynamic behavior [10]. Therefore, retention of nanocrystallinity at elevated temperatures either during processing or in service is quite difficult.

2.1. Scale Dependence of Strength and Elastic Properties 2.1.1. Dependence of Strength (and Hardness) on the Grain Size It has been known for a long time that refining the grain size of materials increases their strength, that is, the yield and flow stress as well as stress to rupture. The theoretical background for increasing strength with decreasing crystalline size lies in the theory for dislocation slip in crystalline materials. This tendency has been explained by using three different models, that is, the pile-up model, the work-hardening model, and the composite model; see, for example, the review of Lasalmonie and Strudel [11]. In nanocrystalline materials the conventional dislocation mechanisms cease to be operational. As the size of a Frank–Read dislocation source cannot exceed the size of a grain, such sources become inoperable with decreasing grain size under typical loads. Recent simulations on nanocrystalline Al have also demonstrated that the nucleation of complete dislocations at the grain boundary becomes impossible as the grain size becomes smaller than the so-called splitting distance of the dislocation [12]. The grain size (d) dependence of the yield strength (y ) with materials of conventional grain size in the micrometer range typically follows an expression of the type y = 0 + k/d 1/2

(1)

where 0 is the friction stress and k is a material-dependent constant. This relation is known as the Hall–Petch relation

Mechanical Properties of Nanostructured Materials

originally proposed by Hall [13] and Petch [14]. However, this relation has been found to break in nanometer-scale materials. At fine grain sizes (in the submicron range), the slope becomes lower and at ultrafine grain sizes, k may become negative [15–17]. The latter occurs when the grain size decreases to the range of few tens of nanometers although in some cases increase in flow stress has been reported down to the grain size of 10 nm [18, 19]. Several models have been proposed to explain the inverse Hall–Petch relation, that is, grain boundary deformation mode effect [20], triple junction volume effect [21], sizedependent line tension effect [22, 23] composite model [24, 25], and that of Takeuchi [26]. All the models incorporate a softening mechanism at fine grain sizes. Wang et al. [27] have been able to explain the different deviations from the Hall–Petch relation at different grain sizes by describing the material as a composite consisting of four different phases (crystal, grain boundary, triple line junctions, and quadruple node phases) with different strengths and relative volume fractions. Due to four fitting parameters, this model is capable of describing any kind of strength variations with grain size. However, it does not provide a physical explanation for the operational mechanisms. One plausible physical explanation for the softening is grain boundary sliding and rotation, which can explain both the accelerated deformation rates and the softening at the finest grain sizes and the hardening at larger grain sizes. This explanation is decribed by Padmanathan and coworkers [28–31]. According to their model, the deviation from the Hall–Petch behavior, which eventually leads to the inverse Hall–Petch behavior, can be attributed to competition between the grain boundary sliding controlled process and dislocation dominated deformation. These mechanisms are independent and the one that in particular conditions of grain size, alloying, temperature, and strain rate requires lower stress to operate will be the favored mode of deformation. In general, when the deformation is dislocation controlled, the grain refinement increases the stress required, and when the grain boundary sliding is the dominant mechanism, the grain refinement will decrease the stress to deformation. The latter explanation is finding support from the atomistic modeling of deformation in nanocrystalline materials. Recent molecular-dynamics simulations have revealed an inverse Hall–Petch behavior for very small grain sizes attributed to grain boundary (GB) sliding [32–35]. The simulation of nanoindentation in 5- and 12-nm nanocrystalline gold has shown that GBs act as a sink for partial dislocations emitted under the indenter and there is a collective motion of grains pointing towards the presence of GB sliding; that is, grain boundaries for a number of grains that are randomly oriented may straighten and slide collectively. Neighboring grains may rotate and form also larger grains [36, 37]. This mechanism supposedly works without diffusion accommodation and has been criticized by Yamakov et al. [12], who claim observation of GB sliding does not rule out the diffusion-assisted creep mechanisms even at room temperature. One should also note that the experimental results are influenced by the detailed GB structure of the nanostructured materials, which in turn is dependent on the particular

133 method with which the materials have been produced. For instance, despite the similar grain size, the deformation behavior of Cu produced by ECAP is significantly different in the as-pressed state than after a short anneal at 473 K, which results in recovery of the defect structure at grain boundaries and a sharp decrease of internal stresses [5]. This means that in addition to the mean grain size, the defect density at grain boundaries influences the strength properties of nanostructured materials. See Figure 2.

2.1.2. Elastic and Anelastic Properties of Nanocrystalline Materials There are very few theoretical considerations related to the elasticity of nanocrystalline materials. Some early experimental results have prompted ideas on elastic properties being dependent on the volume fraction of lower-density grain boundary phase in relation to the bulk phase [39]. Later, however, the experimental results [40, 41] have, according to Morris [2], quite convincingly showed that the grain size refinement does not play any obvious role in modifying Young’s modulus, shear modulus, or bulk modulus, but the observed reduction is inherited from the quality (porosity content) of the processed material. On the other hand, detailed studies of nanostructured copper samples processed by equal channel angular (ECA) pressing have been carried out by using ultrasound method [42]. According to this study, the values of elastic moduli in nanocrystalline copper were lower by 10–15% as compared to coarse-grained copper. The explanation was based on the differences of elastic properties of near grain boundary regions and grain interiors. The change in elastic values of nanostructured copper could be explained if it was assumed that the elastic modulus of the near grain boundary regions is 15–17% of the value of the elastic modulus of the coarse-grained copper. Reduction of elastic modulus in ECA pressed copper and copper composites has also been obtained in other studies [43–45]. Some new modeling results support the decreasing of elastic modulus values at very small grain sizes. However, this is realized in a substantial level only at grain sizes below 10 nm [46]. Internal friction studies are used to study the deviation of the material from Hooke’s law and its anelastic behavior. Internal friction studies show that the damping for nanocrystalline materials is significantly higher than in coarse-grained

Figure 2. Schematic illustration in two dimensions of grain arrangements in a nanocrystalline (a) and conventional polycrystalline (b) material. Forming of a mesoscopic planar interface can occur if atoms in the darker regions rearrange [38]. Rearrangement is favored in the nanocrystalline material because of the three orders of magnitude smaller thickness of the critical region.

134 materials. For example, studies on ECA pressed copper have revealed that damping in nanocrystalline material is higher by a factor of 4–5 than in coarse-grained material processed by annealing at high temperatures and even higher by a factor of 2–3 as compared to the level of damping in gray cast iron (50 × 10−4 ), typically used as a reference for damping [40, 47]. Previous studies have also shown that the onset of the intense growth of internal friction is significantly lower (by 120 K) in nanocrystalline materials than in coarsegrained materials. Similar results have been obtained for the nanocrystalline copper obtained by consolidating mechanically milled powders by hot isostatic pressing [48]. Furthermore, it has been noticed that the dislocation-associated peak typically present in coarse-grained materials at low temperatures is absent, indicating that there are only few mobile dislocations in nanocrystalline materials. The internal friction curve of nanocrystalline ECA copper has a strong maximum of the so-called grain boundary peak at 475 K associated with the intensification of grain boundary sliding in the material. According to Valiev et al. [4], these anomalies are associated not only with small grain sizes but also with specific structure connected with nonequilibrium grain boundaries formed in ECA processed material and their transformation from nonequilibrium grain boundaries to equilibrium grain boundaries. Internal friction studies have been performed also in other nanocrystalline materials, such as Pd [49], Al [50–52], Au [53], and Fe [54]. In general, a damping peak superimposed on a background increasing with temperature is observed. Furthermore, some additional peaks may be observed related to, for example, grain boundary impurities and films [49].

2.1.3. Fatigue of Nanocrystalline Materials In fatigue (cyclic loading), material undergoes reversed deformation which results in accumulation of damage and finally fracture. Cyclic deformation produces typically at some advanced stage microstructural features, that is, dislocation cells that are typical of the plastic strain amplitude in question. The relaxed dislocation cell structure that develops during fatigue testing is typically in the half-micron level. In nanostructured materials, it may therefore be expected that the continuous deformation will lead to cyclic softening and an extensive growth of crystal structure. Data obtained on low cycle fatigue of nanocrystalline ECA processed copper seems to support this idea [55–58]. On the other hand, it has been shown that the fatigue behavior of nanocrystalline Ni produced by electrodeposition is exactly similar to that of conventional Ni [59] and in another study that the formation of nanostructures by severe plastic deformation results in a significant increase in fatigue strength and life [3]. These contradictory results may at least partly be explained by the differences in the details of the nanostructures. Hashimoto et al. [60] have studied the fatigue response of different types of nanostructures produced by ECA. At a constant plastic amplitude fatigue, the material having a rather homogeneous nanocrystalline structure showed cyclic hardening while the material having a banded structure with elongated grains and fragments of low angle boundaries showed cyclic softening. Similarly, significant changes in the anelastic response of materials having

Mechanical Properties of Nanostructured Materials

nominally the same grain size have been observed [53]. The extent of Bauschinger effect in nanocrystalline ECA pressed copper was found to increase substantially in a short lowtemperature annealing, which did not alter the grain size but recovered the grain boundary structure. These results demonstrate the significant influence of the type of nanostructure on the cyclic response. After the early studies, the cyclic response of nanocrystalline materials has been a subject of growing interest and several investigations on different materials have been carried out [61–67]. As a conclusion from these studies, ECA-produced copper and 5056 Al-Mg alloy exhibit notable improvement of fatigue properties in load-controlled cycling while under constant strain amplitude they last considerably shorter than their coarse-grained counterparts. On the other hand, ECA pressed titanium shows no cyclic softening or degradation in strain-controlled cyclic loading [58]. Based on these studies, Vinogradov et al. have proposed a oneparameter dislocation-based model to describe the experimental results. According to this model the cyclic saturation stress at high strains takes the form s = o + b/ Ly1/2

(2)

where o is the minimum stress for the dislocations to move, is a geometrical factor of the order of 0.5, is the shear modulus, L is the slip path of the dislocations with a Burgers vector b, and y is the so-called annihilation length. This simple relation seems to be applicable both for an aluminum alloy [64] and for titanium [61]. Most of the characteristic features of the fatigue behavior of ultrafine grain size materials can be understood based on the ordinary dislocation kinetic, dislocation hardening, and Hall–Petch hardening. On the other hand, the susceptibility of the ECA pressed materials to strain localization limits their tensile and fatigue ductility and in practice to a large extent determines the fatigue performance. However, there still exists very little information on the fatigue behavior of nanocrystalline materials in the range of few nanometers up to few tens of nanometers.

2.1.4. Creep of Nanocrystalline Materials In creep, the material gradually undergoes straining under the load which may be well below the loads causing macroscopic deformation, for example, in tension. It is well known that creep may be ascribed to a number of different deformation processes, which typically operate more or less in parallel under given conditions. Under particular conditions of stress and temperature, it may be possible to identify a single process responsible for the measured creep rate. At very low stresses and small grain sizes, vacancies rather than dislocations are generally held responsible for the observed creep rate. Two models, Nabarro–Herring creep and Coble creep, can be used to account for plastic flow under those circumstances [5]. Nabarro–Herring creep involves the vacancy diffusion through the grain volume and Coble creep involves vacancy diffusion along grain boundaries. Nabarro–Herring creep has an inverse square dependence and Coble creep has an inverse cubic dependence of grain size with creep rate. Coble creep predominates over Nabarro–Herring creep at low homologous temperatures

Mechanical Properties of Nanostructured Materials

and very small normalized grain sizes. A number of studies have been designed to study the low-temperature creep in nanocrystalline materials since, for example, in nanocrystalline copper the diffusivity at room temperature has been reported to be orders of magnitude higher than the grain boundary diffusivity of regular polycrystalline copper [68]. Such high diffusivities have been proposed to be responsible for the additional modes of deformation which may contribute to softening at fine grain sizes [15]. The studies on creep behavior of nanostructural materials have established that they typically exhibit very high creep rates. The behavior has typically been explained in terms of grain boundary diffusional creep in combination with triple point diffusion [69–71], but as Mohammed and Li [5] have pointed out, some of the characteristics reported, such as instantaneous strain and primary creep with decreasing creep rate [72, 73], are not typical of diffusional creep. Although a number of studies on creep of nanocrystalline materials have already been conducted, the full picture of creep deformation is still somewhat unclear. However, it may be concluded that the creep properties of nanocrystalline materials are very sensitive to their microstructure. Therefore two nanocrystalline materials with the same nominal composition and structure may exhibit different deformation behavior. A current review on the subject is given by Mohammed and Li [5].

2.2. Plasticity of Nanocrystalline Materials Plasticity of nanocrystalline materials is of interest from both theoretical and practical points of view. The practical aspects are related both to the ease of producing complicated forms by plastic deformation as well as to the service performance of these materials. As discussed in the previous section, the susceptibility of, for example, fine-grained ECA pressed materials to strain localization limits their tensile and fatigue ductility and in practice to a large extent determines their fatigue performance. On the other hand, the increasing relative amount of atoms at grain boundaries and grain junctions with decreasing grain size results in enhanced diffusion rates in nanocrystalline materials as compared to standard polycrystalline materials.

2.2.1. Ductility of Nanocrystalline Materials The ductility of nanocrystalline materials can be examined by tensile testing. In a tensile test ductility is related to the elongation at fracture or the reduction of area (at necking) at fracture. A classical approach to theoretical consideration of the ductility of nanomaterials is that of Morris [2], who uses the so-called Considére construction to describe the respective importance of stress level and work-hardening rate in controlling the geometric instability responsible for the onset of necking. Generally, a high work-hardening rate will result in large strain at the instability while a low workhardening rate, typical of nanomaterials, will result in a small strain to failure or in extreme case no strain at all. However, the stability of flow and consequently the degree of ductility of a (ductile) material in tensile test depends, in addition to its strain hardening, also on strain rate hardening characteristics (see, e.g., Hart [74]). As both of these characteristics may differ from those of the coarse

135 (or conventional) grain size materials, it is expected that the ductility of nanostructural materials differ from that of their coarse-grained counterparts. A more complete treatment of the conditions for necking would include the strain rate sensitivity of the flow stress of nanostructural materials, which as already mentioned, typically also is different from that of coarse-grained materials. Hart [74] has shown that the instability in tensile test is determined by the equation +m≥1

(3)

where  is the strain-hardening rate and m is the strain rate sensitivity of the flow stress. Since for metals m is generally less than unity (in fact, generally much less than unity), the strain-hardening exponent  must be clearly greater than zero for the flow to be stable. As nanocrystalline metals show only little strain hardening in tension, their tensile strain at the flow at necking often remains small.

2.2.2. Superplasticity Many materials are known to exhibit superplasticity in proper conditions. In the superplastic state, elongations of several hundred or even more than one thousand percent are obtained. Typical attributes to superplastic deformation are a proper temperature–strain rate regime (typically temperature around 0.5–0.6Tm , where Tm is the melting point of the material, and strain rates around 10−3 –10−4 s−1 ), a small grain size (typically less than 10 m), and a relatively stable microstructure of the material during deformation [75, 76]. It is possible to describe superplasticity by a constitutive equation of the form ˙ = A DGb/KT  b/dp /En

(4)

where ˙ is the strain rate, A is a constant, D is the coefficient of grain boundary diffusion, G is the shear modulus, b is the Burgers vector, K is the Boltzmann constant, T is the temperature, d is the grain size, p is the grain size exponent (usually equal to 2),  is the flow stress, E is Young’s modulus, and n is the stress exponent. This law would predict the decrease of the temperature or increase in strain rate regime with decreasing grain size where superplasticity occurs. A closer examination of this relation shows that the slow strain rates associated with superplasticity in the conventional materials having a grain size around 1 m could be accelerated by several orders of magnitude or correspondingly the temperature may be decreased even by several hundreds of degrees. The superplasticity in nanocrystalline materials is therefore of special interest as it would extend the phenomenon to lower temperatures or higher strain rates, thus opening new technological opportunities. One of the requirements in order to technologically utilize the low-temperature or high strain rate superplasticity of nanomaterials is to control the grain growth during processing. During superplastic deformation both static and dynamic grain growth may occur. The static grain growth can be described by [3] DsN − D0N = kt

(5)

Mechanical Properties of Nanostructured Materials

136 where Ds is the grain size after temperature exposure, D0 is the grain size at the beginning of temperature exposure, N is the grain size exponent (2 in pure materials near the melting point and 3–4 in many practical cases), k is a rate constant with an Arrhenius dependence (k = k0 exp Q/RT ), and t is time. Because of the processing time needed for superplastic forming, static grain growth is always a concern. However, dynamic grain growth is in practice much more severe than static grain growth. Dynamic grain growth occurs because of the applied strain and may cause the grain size to grow severalfold during forming even at low temperatures. The increment of grain growth solely of dynamic origin (Dd ) is independent of time and temperature and may be described by [3] Dd = Df − Ds = c

(6)

where Df is the grain size after forming, Ds is the grain size before forming, c is a material constant, and  is the strain in forming. Because of the grain growth (both static and dynamic), deformation becomes increasingly difficult with increasing strain. So far superplasticity has been demonstrated at elevated temperatures for several nanocrystalline metal and ceramic systems. The major systems investigated so far include several Al-Ni-Mm alloys [77, 78], Ti, Al, or Mg-based SPD alloys [79–82], boron doped Ni3 Al-alloy [83, 84], Y-TZP [85–88], TiO2 [89–91], and MgO·Al2 O3 spinels [92]. Evidence of superplasticity in ceramic nanomaterials has mainly been obtained by other than tensile testing, that is, compressive testing, hardness testing, or bulge testing, because of difficulties in producing fully dense nanocrystalline specimens of adequate size for tensile testing. Large ductility in compression is not necessarily an evidence of superplasticity since neck instability and cavitation failure are absent in compressive deformation [93]. An example of excellent compressive properties but poor tensile behavior is that of Fe-28Al-2Cr alloy [94]. It was possible to deform this to a strain of >1.4 in compression, whereas no tensile ductility was observed. The flow stress in compression (2.1 GPa) was considerably higher than the tensile fracture stress (0.65 GPa). Tensile superplasticity of nanocrystalline materials has been studied more extensively over the last years since the first evidence of tensile superplasticity was reported [95] in 1993. According to studies so far, superplasticity of nanomaterials occurs most likely as a result of grain boundary sliding and some diffusional accommodation without visible dislocation activity in the grains. In order to limit the grain growth, both solute and second-phase additions have been used to pin the grain boundaries with a mixed success [96, 97].

2.3. Fracture Toughness of Nanocrystalline Materials Fracture toughness of the material is related to the ability of the material to sustain the creation and propagation to failure of local flaws and cracks. During loading the pre-existing subcritical flaws or cracks will grow as some localized straining will take place ahead of the flaw. When the critical size is reached, a catastrophic failure will take place. Fracture

toughness of nanocrystalline materials may be quite different from that of bulk materials. [Chan [98] assumed that the fracture toughness and the yield stress remain constant, but that the starting flaw size is decreased as the grain size is decreased the critical stress to be imposed for a flaw to grow will increase.] As a result, the strain to failure will be increased as the grain size is reduced. A dramatic increase in fracture strain will occur as the grain size reaches a characteristic value for the material (combination of fracture toughness and yield stress). Of course, then the flaw size has to decrease with grain size (which may not always be the case). Other assumptions must also be valid for the theory to work; that is, the critical stress intensity factor at the point of catastrophic failure should be constant and independent of grain size, and the plastic properties including yielding must be independent of grain size. Morris [2] has criticized especially the last assumption and refined the analysis of Chan by adapting the classical Hall–Petch relationship (Eq. (1)) to describe the dependence of yield strength on grain size. He arrived at the following critical crack length (c) at the failure point for a material of toughness Kc when a stress equal to the yield stress is applied: c = 1/"#Kc / 0 + kd −n $2

(7)

where 0 is the friction stress, k is a material-dependent constant, and d is the grain size. This equation gives a possibility to examine whether the material tends to become more or less brittle as the grain size changes for a material at a given fracture toughness level. Using this equation Morris and Morris [99, 100] have shown that the critical flaw size is only slightly and subtly different from the change of grain size, and in the absence of any change in the intrinsic property of fracture toughness, the critical flaw size and the grain size change in a closely correlated manner. Based on the analysis, Morris and Morris conclude that it is impossible to tell whether the nanocrystalline state will offer any improved ductility/failure characteristics. A complete analysis on the subject can be found in [98] with the further refinements in [2].

3. MODELING OF MECHANICAL PROPERTIES OF NANOSTRUCTURED MATERIALS Mechanical behavior of nanostructured materials is frequently investigated using various simulation techniques, due to difficulties associated with in-situ observation of deformed nanostructured material components. Hence, the modeling by finite element method, molecular dynamics, or atomistic calculations enables us to conclude on the phenomena that govern the mechanical response of these particular solids, and in consequence, to conclude on their mechanical properties. Since the cross-sectional dimensions of nanostructured components or entire material approach the scale of interatomic distances (it is already possible to fabricate the 1- to 5-unit-cells-thick ceramic plates [101] or SiO2 /SiC nanorods with 100 atoms across [102, 103]), their size challenges the classical approach used in continuum mechanics, and as a result, the scale effects cannot be ruled

Mechanical Properties of Nanostructured Materials

out in the modeling. This makes it difficult to perform the simulation of deformation of nanostructures, which is based in the classical continuum approach. Furthermore, it should be noted that all the above listed methods of modeling are used to simulate also nanoindentation testing, the probing technique which is frequently used to test nanostructured materials. The FEM-based analysis of the contact problems is already well developed, while molecular dynamics and atomistic simulations have recently gained common interest (refer to the next section).

3.1. Finite Element Method Despite the drawbacks of the traditional mechanical approach, finite element simulation of the deformation and fracture of nanostructures is widely used. It appears, however, in this area of research as a hybrid method supplemented by either empirical atomistic models such as this used by Robertson et al. [104] to study uniaxial tensile and compressive response of carbon nanotubes, or multiscale robust simulation of surface deformation (see, e.g., [105]) that allowed the authors to conclude on the microscopic aspects of phase transformation in silicon while investigating different interatomic potentials and various finite element meshes. In the latter approach the constitutive response of the material is obtained from atomistic calculations, which contrasts standard FEM methodology that employs empirical-phenomenological rule. Moreover, the recent comparison of finite element modeling and artificial neural network (ANN) appears quite beneficial for nanostructured materials and contacts in nanoscale. This type of approach allowed Muliana et al. [106] to resolve the long-persisting dilemma concerning the nanoindentation deformation of hard films/multilayer structure deposited on soft substrate—something already investigated by Myers et al. [107] and Nowak et al. [108, 109]. The ANN models have demonstrated excellent predictive capability for indentation of nonlinear materials. FEM modeling on the mechanical behavior of nanostructures proved to be efficient when one tackles the problems associated directly with application of a new structure. The proper example is here mechanical analysis of micromechanical clips for optical fibers, offered recently by Lu et al. [110], that targets the performance and reliability of new silicon nitride fiber-clips [111, 112] which might make the production and assembly process of full integrated optoelectronic systems cheap and reliable. Consequently, Lu et al. [110] used FEM to determine stress fields near the corner of the clip/substrate system and developed theoretical models to predict its failure. Furthermore, the finite element simulation has become widely used in studying deformation phenomena in microscale and in new mechanical processing oriented towards nanotechnology. The FEM-assisted analysis of anomalous surface deformation of sapphire [113], stress and cracks in nanostrip casting process [114], tribology in nanomanufacturing and nanopowders for solid lubrication [115], nanomechanical properties of cutting tools for nanomanufacturing [116], material removal during submicroscale polishing [117], estimation of nanoscale zone in corroded surface ceramic layers [118], and cohesive strength

137 of thin films [119], serve as selected examples of the present trend in research. These studies are again followed by FEMaided nanoindentation exploration of mechanical response of microsprings and microcantilevers—the subject being in the center of interest for microfabrication [120].

3.2. Molecular Dynamics and Atomistic Simulation Given the recently used direct machining of material surface to fabricate nanostructured components, it became necessary to achieve better understanding of such processes as adhesion, cutting, or surface deformation at atomistic level, where continuum mechanics cannot be applied. Hence, the molecular dynamic (MD) simulation method that allows one to study the behavior of atoms during short time interactions appears as a proper tool to model indentation, friction, adhesion, fracture, and ultraprecise cutting on the atomic scale [121]. In particular, nanoindentation is the area of research in which MD simulation was already exercised for several years, since the nanoscale contact problem falls clearly beyond the frames of continuum mechanics. The studies of this kind made use of realistic many-body interatomic potentials to obtain information concerning the way in which the defects are created under the tip as well as the fate of individual atoms. This provides a new insight into such phenomena as pressure-induced phase transformations, elastic to plastic transition, or amorphization of the tested material, as demonstrated in the case of nanoindentation of silicon structure [121–124], as well as FCC and BCC crystalline lattices in contact with a rigid [125] or atomistic modeled [126] tip. The above-mentioned conventional MD studies were followed by ab initio quantum mechanical approach [127] and local strain diagnostics [128] that provided a complete picture of atomic distribution near elastic contact and clarified origins of plastic deformation and amorphization in nanoindented silicon, respectively. Furthermore, the similar classical two-dimensional MD analysis applied to nanocutting process by Zhang and Tanaka [129] and Shimizu et al. [130] was improved in terms of a three-dimensional approach offered by Fang and Weng [131], who used canonical MD ensemble corresponding to their copper crystal processed with the diamond pin tool. It should be emphasized at this stage that the MD approach to nanoindentation or nanocutting reviewed in this section are in fact nothing other than hybrid FEM-MD methods which we discussed in the previous section [104, 105]. In contrast to this combined approach, the atomistic simulation represented here by the work of Astala et al. [127] has different character and provides better insight into atomistic processes, despite the fact that the size of the simulated cluster is considerably smaller than the experimental contact area (the common problem for the atomistic numerical models of this kind). The excellent example of the atomistic simulation of elastic properties of nanostructured materials was given by Miller and Shenoy [132] who used direct simulation of nanoscale structures using embedded atom method for FCC lattice and Stillinger–Weber potentials for diamond structures. Their size-dependent modeling of effective stiffness

Mechanical Properties of Nanostructured Materials

138 properties D of nanosized elements such as plates and beams led to the general formulation of the deviation of elastic property from that defined by conventional mechanics Dc [132]: D − DC S 1 = DC Eh

(8)

where defines nondimensional constant that is function of geometry, S stands for surface elastic constant, E is elastic modulus of bulk material, and h denotes length—the size of the structure. The authors found that S/E parameter sets the scale at which the effect of the free surface becomes significant [132]. They verified their simulated results by both uniaxial loading and pure bending of small-size plates and bars. For the sake of completeness of the present review, one should mention interesting modeling of dendrimers for nanoapplication [133] as well as recent numerical approach to phase transitions in nanoscopic layered systems [134]. Moreover, the detailed review of the status and perspectives of nanoscale device modeling was presented by Macucci et al. [135] who targeted development of nanoelectronic devices and quantitative predictive capabilities.

3.3. Simulation of Nanotribology Tribology describes phenomena on the contacting surfaces of materials in motion related to each other. The interactions at the contacting surfaces are closely related to atomic and molecular size effects, that is, nanosize effects. The MD simulation methods have successfully been used to describe a number of such phenomena [136]. However, most realistic tribological systems are of such complexity, including surface topography variations, impurities, and lubricants, that the present computers are capable to simulate tribology only partially [137]. When using empirical interatomic potentials, it is possible to simulate relatively large systems containing millions of atoms. MD methods have been used, for example, to simulate the elastohydrodynamic contact of real rough surfaces in the presence of hydrocarbon lubricants [138]. FEM modeling of sliding contact surfaces has been carried out by taking into account realistic asperity textures of the surfaces. Dimensions down to 100 nm have been assessed in the simulations of the contact area and coefficient of friction [139, 140]. Molecular dynamic simulation of contacting surfaces has been done mostly to simulate an indentation to a solid surface. Recently simulations of indentation of an ideal rigid tip to Al have taken into account the melting of material [136]. Common phenomena in the indentation simulation, such as local melting and dislocation nucleation, were observed. The effect of Al orientation and temperature were investigated. The results provided information on nanoscale phenomena present in such processes as wear in engine piston rings and metal forming. Modeling of stress distributions related to crack initiation and delamination of thin films has been investigated [141]. Simulations have also been used to design coated surfaces with multilayer and gradient structure with high adhesion and crack growth inhibition [142]. Recently, FEM modeling

has been used successfully to simulate the contact scratch testing experiment in order to experimentally determine the fracture toughness of the coated surface [143].

4. EXPERIMENTAL METHODS DESIGNED FOR PROBING OF MECHANICAL PROPERTIES OF NANOSTRUCTURED MATERIALS Many of the traditional methods used for testing of mechanical properties of materials may be used also for nanomaterials provided that adequate amount of material is available. However, in a number of occasions that is not possible. Then other methods must be used. Among them instrumented nanoindentation is the most important and will be described in detail here. Other methods are also briefly discussed.

4.1. Instrumented Nanoindentation 4.1.1. Principle and Equipment Conventional hardness measurement is insufficient to estimate the properties of, for example, thin nanostructured films, because of its low accuracy in the low-load indentation region that is due to limitations of the resolution of the optical systems attached to the hardness testers of conventional type. The development of the testing equipment has enabled the users to continuously monitor the load experienced by the indenter and the depth of penetration. This made it possible to overcome the limitations of the optical system and allowed us to derive new information on the complex mechanical behavior of materials deformed in a very small area. Thus, the nanoindentation appears as a unique method for studying the mechanical properties of solids with a tiny volume. The idea of depth-sensing indentation measurements was already realized for the first time more than two decades ago [144], while the first nanoindentation testers were designed ten years later [145–148]. Further, the pioneering results of ultra low-load indentation reported by Pethica et al. [146] resulted in a rapid development of this new area of research that recently has found its important application in a case of nanostructured materials. The nanoindentation experiments achieved a “new level,” owing to the new phenomena available for study as a consequence of recent developments in this particular research equipment. This has stimulated an urgent need for a general theory of indentation-induced deformation, which would yield a sound basis for interpreting experimental results. Considerable effort has already been undertaken to analyze the data of depth-sensing tests and to relate them to the observed phenomena [146, 148–152]. The significant progress has been achieved in this area through numerical modeling based on the finite element method [113, 153, 154]. However, the critical issue of this approach lies in the formulation of the pertinent constitutive equations as well as in the difficulty in estimating the elastic/plastic stress-state in the vicinity of the contact. The only case solved analytically is the pure elastic contact of spherical (Hertzian indentation [155, 156]) and axisymmetric

Mechanical Properties of Nanostructured Materials

139

sharp indenters (cone indentation—Boussinesq stress field [157]). Nanoindentation devices which allow us to use loads as low as fraction of millinewtons have recently been developed in response to an increasing number of requirements for the mechanical testing of crystalline thin films designed for electronics. Some commercial instruments operate automatically after initial setup and measure independently force and displacement experienced by the indenter tip. The successful examination of nanomaterials is in a part due to the selected tester. Indeed, the precision of measurements is of primary importance when one deals with new, advanced materials, which have never been characterized so far. Indentation techniques may be broadly classified according to the shape of the indenter used in experiments. It was found that sharp indenters, for example, the Berkovich pyramid, are useful in the investigation of mechanical properties in the smallest possible region, while the spherical tip is recommended for crystalline material with remarkable anisotropy.

4.1.2. Determination of Elastic Modulus Hertzian theory [156] of contact between two nonrigid bodies yields the relationship between their Young’s moduli:

Pmax S

(11)

while the elastic modulus of the examined solid E1 [Eq. (9)] may be calculated using the relationship 1 − (12 1 − (22 1 1 − (22 2 √ A− = − = √ E1 Eeff E2 E2 S "

(12)

where S defines the slope of the unloading curve (S = dP /dh), Pmax is the maximum load, and A is the contact area.

(9)

(10)

holds for cylindrical, conical, and spherical indenters. The above universal formula seems to be valid for all indenter shapes being a body of revolution of a smooth function, as proved by King [162]. Oliver and Pharr [163] proposed the method of analyzing indentation data obtained with sharp indenter, while taking advantage of the punch contact problem. The authors assumed that, during the unloading cycle, the deformation of the tested solid is entirely elastic, and they applied the relationships derived for elastic contact of an axisymmetric punch, along with the approach by Doerner and Nix [149]. The latter is based on the assumption that a considerable

Indentation load, P

Pmax

where Eeff is the effective elastic modulus, which can be obtained from load-depth indentation results. Hence, one is able to determine the elastic modulus of the tested solid (E1 ) based on the indentation data. However, the contact of a sharp indenter into a solid surface inevitably involves plastic deformation, which makes it difficult to model the process and analyze the experimental data. Since an analytical solution of the elastic/plastic contact problem is not available [157], and the elastic contact between axisymmetric punches and isotropic and anisotropic half-spaces has been the subject of thorough investigations (see, e.g., [158–160]), most researchers assume elastic punch contact as suitable for modeling elastic/plastic surface deformation. Consequently, Bulychev et al. [161] proved that the relationship between stiffness S, effective elastic modulus Eeff , and the projected area of the contact A: √ 2 A S = √ Eeff "

he = hmax − hp =

loading unloading S

hr hp

he hmax

Indentation depth, h

(a) Pmax

Indentation load, P

1 1 − (12 1 − (22 = + Eeff E1 E2

part of the unloading P − h curve possesses a linear character, which makes the equations derived for punch problem [refer to Eqs. (9) and (10)] to hold when one considers the indentation unloading. The assumptions by Doerner and Nix, followed by Pharr and Oliver, require contact area to remain unchangeable during the indentation cycle. Doerner and Nix [149] argued that the residual indentation depth hr (see Fig. 3a) is affected by elastic recovery within the contact and it cannot be used to determine the contact area. In order to estimate the size of the plastic contact region and residual plastic depth hp , the authors suggested subtraction of the elastic contribution from the maximum indentation depth hmax . Consequently, the elastically recovered depth he can be obtained in the form

loading unloading S ε=1 ε=0.75 hr hc hmax

Indentation depth, h

(b) Figure 3. (a) Schematic of the indentation load–displacement curve with the parameters used in the Doerner and Nix analysis. (b) Schematic of the indentation load–displacement curve with the parameters used in the Oliver and Pharr analysis.

Mechanical Properties of Nanostructured Materials

140

P = B · h − hf m

(13)

where hf is the residual displacement after unloading determined by the curve fitting with B and m values as fitting parameters. Oliver and Pharr stated that the depth at the contact hc (see Fig. 3b) appears to be dependent on the initial unloading slope S as well as the maximum penetration depth hmax . The discussed dependence yields the simple relationship for the hc parameter: hc = hmax −  ·

Pmax S

(14)

where -value equals 1, 0.75, and 0.73 for a flat punch, the Berkovich tip, and cone-shaped indenter, respectively. The essential point of the Oliver and Pharr analysis [163] is the evaluation of the shape function A = f dc , which expresses the relation between the projected contact area A and its distance dc from the indenter tip. The method employs the P − h data obtained for a model-specimen for which the authors developed a simple empirical calibration procedure which avoids the imaging of indents. As a result, Oliver and Pharr found the value of effective elastic modulus Eeff using the following equation [163]: √ " S Eeff = (15) √ 2/ A where / depends on the geometry of the indenter and equals 1.034 for the Berkovich tip. It should be emphasized that the method by Oliver and Pharr [163] is perhaps the most widely used nowadays to routinely analyze the data obtained by means of various nanoindentation systems. The measurement of Young’s modulus proposed by Field and Swain for the spherical indenter employs stepwise indentation with multiple partial unloading [164–166]. The stress field is well-defined in the solid deformed by an axisymmetric tip, whose radius may be selected to control the depth of penetration [164–167]. Furthermore, the indentation with multiple partial unloading produced data which allowed Field and Swain to separate the elastic and plastic components of indentation (Fig. 4) and, in a consequence, to estimate the elastic modulus at each step of the penetration. The above-mentioned fact is of great importance for the application of the method, since such a separation is essential for extracting information relating to material properties [166]. Taking advantage of the basic relationship between force P and the depth of the elastic penetration for a spherical indenter which was derived originally by Hertz [155, 156], and reviewed by Johnson [157], Field and Swain were able to derive a simple formula for calculating the elastic modulus Eeff [165]: Eeff =

0075 · P a · ht − hr 

where ht − hr denotes the elastic depth recovery.

(16)

50 Indentation load, P [mN]

The Oliver–Pharr analysis of depth-sensing indentation [150, 163] approximates the unloading curve by a power-law relationship:

40 30 20 10 0 0

50 100 150 Penetration depth, h [nm]

200

Figure 4. Typical load–partial-unload force-displacement data obtained for an elastic/plastic material.

The stepwise indentation allowed the authors a nearcontinuous assessment of the effective Young’s modulus with the depth of penetration. Hainsworth et al. [168] noticed that the unloading cycle hardly fits the existing models by Oliver and Pharr [163, 169] or Field and Swain [165, 170], and proposed the original method of Young’s modulus evaluation by using the loading part of an indentation cycle. Hainsworth et al. [168] concluded that the information on elastic and plastic properties of a tested solid may be obtained by analysis of the loading curve that follows the quadratic relationship. They found the simple relationship between the contact radius a, indentation load P , and hardness H :
P a= (17) H Further, following the approach by Loubet et al. [171], Hainsworth et al. [168] derived the power-law dependence between indentation load and depth: P = Km h2

(18)

where 

Km = E · 2 ·




E +3· H




H E

−2

(19)

The empirically determined 2 and 3 values depend on the indenter geometry, while E stands for Young’s modulus of the material. They verified Eq. (18) for a number of materials with widely varying E/H ratio (steel, bronze, copper, iron, silicon crystals, as well as TiN and CNx thin films) and concluded that the P − h2 relationship holds for 2 = 00194 and 3 = 0930 [168]. In sum, Hainsworth et al. [168] predicted the shape of the loading indentation curves which allows us to determine the commensurate value of Young’s modulus E of the indented material in the case when hardness H is known. Taljat et al. [172] investigated the unloading cycle of a ball-indentation process by the FEM analysis with the stressstrain curve of the indented material used as independent variable (input) in FEM calculations. They defined Young’s modulus of the indented solid as a functional dependence on

Mechanical Properties of Nanostructured Materials

141

a normalized unloading slope Su and the estimate of deformation d/D (ratio of the diameter of the impression and indenter) [172]: 

d E = f Su 5 D





= C1



d D

C ′ 

(20)

· Su

where C1 and C ′ constants were determined using FEM analysis. The authors estimated the indenter deformation employing an analytical solution for the displacement of the center of the contact circle and subtracted it from the total indenter compliance—the correction essential in the calculation of elastic modulus [172]. The complete study of elastic loading and elastic/plastic unloading of a spherical indenter was accomplished by Gerberich et al. [173]. Their method of Young’s modulus evaluation suits the requirements of ultra low-load experiments and was scrutinized for numerous materials [173]. The original analysis of the elastic displacement above (h1 ) and below (h2 ) the contact line (refer to Fig. 5) by Gerberich et al. [173] contrasts the elastic analysis by Field and Swain [166] who assumed the simplified relationship h1 = h2 . The solution of elastic and rigid plastic contact problems with the boundary conditions allowed the authors to determine elastic displacements (hE , ht ), contact radius (a), the total indentation load (P ), that led to the expression which describes the unloading curve, and consequently, the effective modulus Eeff [173]: Eeff =

4·



2−

hmax E hmax t



3·R·P  · RhE − 1 −

hmax E 2hmax t



· h2E

1/2

(21)

where R is a radius of the spherical indenter. Hence, Gerberich et al. [173] were the first to provide a complete method of estimating the elastic modulus of an indented material. It has been demonstrated that accurate simulation of elasticity may be in special cases elaborated to yield even compositional differences in the nanolayer composites [174].

4.1.3. Determination of Hardness The physical importance of hardness H—denoted according to Meyer’s concept—lies in the relationship between the H -value and the fundamental physical parameters such as yield strength Y or Young’s modulus E. Despite being

widely used by engineers, hardness appears to be an illdefined parameter which does not describe a single material property, as criticized by Söderlund and Rowcliffe [175]. The measured hardness is affected by indentation-induced cracking, densification, strain hardening, and creep, and it depends on Young’s modulus E, yield strength Y , toughness KIC , work-hardening exponent n, stress-dependent creep rate c , as well as the applied maximum indentation load Pmax . With the advent of nanostructured materials and nanoindentation instruments, confusion arose as to how to determine the hardness parameter from the monitored displacement of the indenter. Starting with the pioneering work by Oliver et al. [176], efforts were being made to settle the characteristic contact area A′ at each step of the penetration, and consequently to determine Meyer’s hardness as H = P /A′

As a result, the estimation of the depth–hardness profile became the standard procedure in the commercially available nanodepth-sensing indentation instruments. Furthermore, the original definition of hardness H, which appears a load-independent parameter, was introduced by Sakai and Nowak [177]. In contrast to the other approaches, H is a physical parameter defined on the basis of the energy consumed for the irreversible deformation of an indented material. Doerner and Nix [149] considered the hardness as the average pressure under the acting indenter. They proposed the subtraction of the elastic contribution he from indentation depth h measured during a depth-sensing test, in order to evaluate the level of hardness. Further, they have shown that plastic indentation depth hp may be determined by extrapolating to zero load the line which is fit tangent to the unloading P − h curve (see Fig. 3). Doerner and Nix were well aware of the drawbacks of their assumption of a perfect shape of a pyramidal indenter [149]. They also admitted that the estimation of the influence of the strain rate on the obtained results was beyond the resolution of the proposed method. Since the main difficulty associated with evaluation of the level of hardness lies in the estimation of the projected area A′ of permanent indentation [refer to Eq. (22)], Pharr, Oliver, and co-workers determined the empirically assessed shape of indenter at the contact depth hc A = f dc  [150, 163]. The f dc  function can be assessed from the depth-sensing indentation data which allow us to evaluate the relationship between the area A and the contact depth hc . The shape-function derived for a perfect Berkovich geometry, f dc  = 24056dc2

R

h1 hE h2 Figure 5. The geometry of elastic penetration of spherical indenter into a solid surface. Model by Gerberich et al. [173].

(22)

(23)

was used by Oliver and Pharr as a first estimate of the contact area [150], while to determine a realistic shape of the indenter, they used a standard specimen [150, 163, 169]. They carried out numerous indentations under various maximum loads Pmax in fused quartz or fused silica materials with well-defined isotropic properties, and the fitting procedure was applied several times in an iteration method to achieve suitable accuracy [163]. Once the f dc  function was determined, it was possible to evaluate the hardness from the

Mechanical Properties of Nanostructured Materials

142 indentation results according to Eq. (22). Recently, Pharr and associates have provided us with a new insight into hardness analysis by investigating the influence of pileup on the hardness of the indented solid [169]. Since the direct measurement of the contact area is usually impossible, the FEM simulation is effectively used to determine hardness. Numerical simulation allows us nowadays to conclude on a variety of mechanical parameters, such as contact stiffness, the effective elastic modulus, and yield strength, and may be used to predict the actual surface profile or the shape of the plastic zone created directly under an acting indenter. All these advantages, combined with the high computational capabilities that are readily available today, have caused interest in FEM-aided analysis of indentation data particularly in the case of unknown materials or nanostructures. Hill, Storåkers, and co-workers derived general expressions for the influence of the Brinell head-shape on the load and surface deformation by solving a class of boundaryvalue problems in elasticity [178, 179]. They also applied a novel FEM procedure to the deformation theory of plasticity [178, 180, 181]. Numerical simulations were performed for the elastoplastic homogeneous half-space, indented to a fixed depth by a smooth rigid ball. The solid was deformed according to the power-law hardening rigid-plastic model. Hill et al. determined the distribution of contact pressure, the profile of the deformed surface, and the contours of representative strain. Further, Storåkers and Larsson derived the universal relationship for hardness at creep applicable in the case of the Boussinesq and Brinell indentation [180]: P = · c " 2



/ 2n + 1D

2 

 1/ 2n+1 P t −2 " c

(24)

where a is the contact radius under the ball indenter of diameter D, t denotes time, and / are constants and c , n are material parameters defined by the stress-strain ( − ) creep law given by Norton [182]. The studies by Storåkers, Hill, Larsson, and associates proved that the indentation-deformation occurs in the lowstrain-hardening materials close to the indenter [178–181], which indicates the necessity to contract the mesh to a smaller size during subsequent stages of the simulation. FEM analysis of sharp indentation was first performed by Bhattacharya and Nix [183] and subsequently, by Lursen and Simo [154]. The authors performed their calculations for an axisymmetric cone of equal volume with a pyramid shape indenter in order to reduce computer time necessary for calculations. Bhattacharya and Nix provided the computer-simulation study of the frictionless penetration process of perfectly rigid tip as well as completely adhesive indentation contact using incremental elastoplasticity [153]. The authors applied constitutive equations of an elastic-plastic von Mises type with no strain hardening and with a linear, isotropic strain hardening. The mesh used in FEM procedure was fine right under the tip (four node elements, 0.02 m thick) which made it possible to estimate the radius of the contact area, the parameter being essential to determining the hardness value. The authors extended their considerations to the various combinations of hard/soft thin films and substrates [183]

and their report introduces the evaluation of the thin-film hardness. Hence, Bhattacharya and Nix were the first to demonstrate the successful simulation of the ultra-low-load indentation using the finite element method with simple constitutive data. Following the pioneering research by Bhattacharya and Nix [153, 183], Lursen and Simo presented a detailed numerical simulation of surface deformation of elastic/power-law plastic materials [154]. The work addressed axisymmetric cone indentation into bulk aluminum and silicon as well as thin films of various degrees of thickness. They emphasized numerical evaluation of the contact area and the surface profile near impression. Recently, Nowak et al. had applied the FEM simulation of the penetration by an axisymmetric indenter into the multilayer system to explain the surprising difference in the hardness of virgin and ion-treated, 50- to 300-nm thin HfN films [109]. The FEM calculations allowed them to conclude that bombardment with highly energetic ions (MeV energy range) results in formation of the amorphous silicon interlayer located under the top-film. The axisymmetric approximation of the pyramidal tip is hardly acceptable in the case of anisotropic materials. Thus, the three-dimensional (3D) FEM analysis of a sharp indentation has become highly required. The first attempt to perform a 3D finite element simulation of indentation by Wang and Bangert [184] was soon followed by a complete analysis of the Vickers indentation by Giannakopoulos et al. [185]. The latter formulated the problem as the penetration of a rigid indenter into a homogeneous, isotropic, rate-independent body. It was assumed that Hook’s law and the Prandl–Reuss equations govern the elastic and elastoplastic behavior of the deformed material, respectively [185]. The small strain formulation, elastic analysis by Giannakopoulos et al. allowed them to conclude on the parabolic relationship between the indentation load P and depth h at the loading cycle, and to determine hardness as the average contact pressure pav , while the deformation was found to be directly dependent on indentation depth [185]. Elastoplastic examination of the loading process led to the evaluation of the effect of the pileup and yield stress on the Vickers hardness H V (pav = H V ). This resulted in the universal formula for the Vickers hardness: pav = C · u



 1+ v u

     E · tan 22

u2 max · 1 + ln · 1− 3y h (25)

where C is constant, u2 max defines the maximum positive surface displacement caused by material pileup, while u and Y stand for the ultimate stress and yield stress, respectively. Calculations of steady-state hydrostatic stress and Mises effective stress profiles for materials with and without strain hardening, indicate that strain hardening suppresses pileup at the contact boundary [185]. The maximum tensile principal stress at loading, predicted in the vicinity of indenter tip, helped the authors to localize the region in which the fracture is likely to be initiated.

Mechanical Properties of Nanostructured Materials

143

E pav = 002201 · 1 − 0021( − 0001( 2 − 0041( 3  · 1 − (2     E · tan 2407

u · 1 + ln pav = 00245 · y 1 + y 3y

(26) (27)

This accounts for the pileup effect and provides the universal formula for Berkovich hardness. The complete 3D FEM analysis of sharp indentation into pressure-sensitive materials was offered by Giannakopoulos and Larsson in 1997 [188], who introduced pressure sensitivity of the studied material according to the classic model of pressure-sensitive flow, proposed by Drucker and Prager for ideal soils [189]. The results obtained using such an incremental elastoplastic law comprised the solution of complete load-unload cycles, the determination of the contact area, evaluation of the average contact pressure, local mechanical fields (the Mises effective stress), and their singularities near the tip and edges of the indenter. A large plastic strain and small elastic strain approach, as well as high and low, linearly isotropic strain-hardening effects were considered. It was found that the relationship between the indentation load P and depth h is parabolic, similar to earlier FEM-aided studies by Giannakopoulos and Larsson [185, 187]: P = − 2j Nj d:c = Ch2 (28) where :c denotes the actual contact area, Nj stands for an inward vector normal to the surface within the contact area, and C is constant. The calculations proved that the total energy Ur spent for indentation depends on the maximum indentation load to power 3/2: Ur =



hmax

0

Pdh =

3/2 Pmax 3C 1/2

(29)

The general formula for the average contact pressure pav (equivalent to the Meyer hardness) derived for pressuresensitive materials reads 3 1 + q y + qp0  3+q  2q/ 3 1+q 3 + qE · − y + qp0  3 1 + ( y + qp0 

pav = 0077 ·

The recent FEM simulations resulted in the general theory of indentation of piezoelectric solids [190] and clarified the evolution of the surface residual stress and deformation field in compositionally graded materials [191, 192]. Furthermore, the research is coming closer to the requirements imposed by the structure of nanomaterials targeting smallscale structures. In the latter case the FEM analysis which works yet for thin multilayered systems [107–109, 193] must be replaced by atomistic simulations (see, e.g., [124, 194]) or hybrid methods which combine advantages of FEM and elements of molecular dynamics calculations (refer to [105]). Another trend observed nowadays is improvement of FEM analysis by employing artificial neural network within the code [106]. All of this indicates that, despite unavoidable simplifications, the finite element calculations proved to be quite useful when studying the mechanics of indentation. Without the FEM approach, several complicated problems which concern surface deformation of solids would be still unsolved. A new concept of hardness, based on the amount of energy irreversibly consumed to create a unit volume of indentation impression in a perfectly plastic material, was proposed by Sakai and Nowak in 1992 [177], while its complete version was published by Sakai in 1993 [195]. The propounded theory—the energy principle of indentation (EPI)—is quite revolutionary in the traditional engineering field of hardness testing, where all the definitions have only been made on an empirical basis. Although not as popular as the approach by Oliver and Pharr [163], the EPI method has been widely recognized. Starting with the idea of hardness being a measure of the material resistance against plastic deformation induced by a rigid indenter, the EPI approach is based on the assumption that hardness should be directly related to the energy Ur expended for irreversible deformation of the tested solid [177, 195]. The above-mentioned energy can be readily determined from depth-sensing indentation data (P − h), since it is represented by the area bound by loading and unloading curves (see Fig. 6). In the case of the perfectly elastic contact, the energy Ur equals zero (see Fig. 6a), while it attains the maximum value for the indentation in perfectly plastic material (Fig. 6b). Usually one deals with a combined response typical for elastoplastic contact (Fig. 6c). Taking advantage of the determined shape of the P − h function, it was possible for Sakai and Nowak to calculate the Pmax

Indentation load, P

Pursuing their successful FEM-added study of the Vickers indentation [185, 186], the authors provided a common analysis of the deformation induced around a triangular indenter of Berkovich type which is mostly used in nanoindentation testers [187]. Larsson et al. [187] found that the P − h relationship for a triangular tip is again parabolic, when the indentation is simulated using either an elastic or an elastoplastic approach. Corresponding formulae denoting the average contact pressure under a Berkovich indenter (the estimation of the Berkovich hardness) were also derived for elastic [Eq. (26)] and elastoplastic [Eq. (27)] cases [187]:

(a)

(b)

(c)

Ur hmax

(30)

where q = 3a0 / 3 − a0 ), while a0 is the material constant that measures pressure sensitivity and p0 is a far-field hydrostatic compression.

h=he

Ur hmax

h=hp

hr

he

hmax

h=hr+he

Indentation depth, h

Figure 6. Typical loading–unloading indentation curves for the perfectly elastic (a), plastic (b), and elastic-plastic material which exhibits an appreciable elastic recovery (c).

Mechanical Properties of Nanostructured Materials

144 energy expended for an irreversible indentation deformation of the tested solid [177, 195]. In the case of an elastic-plastic material illustrated in Figure 6c, the Ur energy was obtained through integrating P h function with respect to h: Ur =



hmax

0

PL h dh −



hmax hr

PUL h dh

(31)

where PL h and PUL h stand for loading and unloading P − h functions. Furthermore, Sakai and Nowak derived the relationship between Ur and the applied maximum load Pmax , which in turn allows us to determine H from the plot3/2 experimental data in a relatively easy way ted Ur − Pmax [177]: √ 3/2 3/2 = C · Pmax (32) Ur = 3 · 0 · tan 3−1 · H −1/2 · Pmax Indeed, when one determines the slope C of the linear 3/2 measured for several maximum loads function Ur − Pmax 3/2 Pmax , it is possible to estimate the value of the true hardness H, given the determined shape of a sharp indenter (geometry described by the angle 0 and 3). It is worth emphasizing that the hardness H is a physically well-based parameter which appears to be load-independent, in contrast to the conventionally measured hardness H .

4.1.4. Determination of Creep, Stress Relaxation, and Other Attributes to Local Plasticity Indentation experiments can also be used to study the deformation mechanisms of nanocrystalline materials. They offer convenient means to determine, for example, the strain rate sensitivity of the material. Strain rate sensitivity m is the slope of a plot of log applied stress versus log strain rate, that is, the inverse of the stress exponent n in Eq. (4). The effective strain rate ˙eff is obtained from √ (33) ˙eff = x˙p / A where A = A xp  is projected contact area and xp is the plastic depth beneath the indenter. In order to determine the rate sensitivity of hardness (stress) by indentation tests, various approaches can be used, for example, indentation creep, rate change, or load relaxation experiments [148, 196]. In an indentation load relaxation experiment, the indenter is pushed into the specimen surface until a predetermined load is reached; then the depth is held fixed, allowing the load to relax as elastic displacement due to the specimen and load-train is gradually traded for plastic penetration. In the indentation creep experiment, the indenter is pushed into the specimen surface at a fixed rate of displacement until a predetermined load is reached; then the load is held constant, allowing the penetration depth to increase with time while the penetration is monitored. In an indentation creep test, the load slightly decreases as the projected area increases during the test, in contrast to a tensile creep test with a constant load, where the stress gradually increases with decreasing cross-sectional area of the test specimen. In the indentation rate change experiments, the indenter is pushed into the sample surface at a fixed rate of displacement until a predetermined load,

upon which the indenter is partially unloaded, then reloaded at a second rate of displacement.

4.2. Atomic Force Microscopy and Measurement of Mechanical Properties In the previous section we elaborated about the nanoindentation technique being frequently the most suitable tool to examine mechanical properties of multilayered and nanostructured materials. The method proved effective independent of crystallinity of the probed material; that is, it works equally well for crystalline structures [197–199] and amorphized [200, 201] surfaces. Another powerful tool to study nanostructured materials is the atomic force microscope (AFM), which can be used both to image the details of the structure and to determine the mechanical properties of the investigated surface. The crucial part of the AFM is a cantilever with the microfabricated tip which remains in contact with the investigated surface. The deflection of the tip, which is made of silicon or silicon nitride, may be very precisely measured by using optical lever, interferometric, or electronic tunneling method [202]. Consequently, one may acquire force-distance curves that are analogous to the discussed P − h indentation curves with accuracy as high as 2.5 nm and 0.01 nm for lateral and vertical dimensions, respectively. The contact force can be estimated with a resolution of 1 pN [202]. It is worth emphasizing here, after an excellent review of the subject by Cappella and Dieter [202], that AFM forcedisplacement curve is not recording of tip-sample interaction, contrary to nanoindentation plots. However, this curve results from tip-surface interaction and the elastic force of cantilever. The measurement allows us to determine the elastoplastic properties. One should keep in mind, however, that the AFM experiment is in a much finer scale than the nanoindentation method. The AFM evaluation of elastoplastic response of the surface is continuously improving. A proper example could be here a new scanning Moiré method, which allowed to determine in-plane deformation by AFM [203], while the detailed thermal fluctuation measurement allowed Catlege et al. [204] to conclude on the spring constant of cantilevers used in AFM. Furthermore, Kracke and Damaschke [205] recently used a scanning force microscope to measure nanohardness and nanoelasticity of thin gold films. Due to advantages offered by this particular method, the authors were able to estimate properties of single gold island formed during film formation. In sum, the AFM measurement of mechanical properties of nanostructured materials must be considered as one of the most powerful methods available nowadays for investigating the nanomaterials.

4.3. Methods for Exploring Nanotribological Properties Most tribological contacts occur at the asperities of the surface. The nanoscale tribological events have been investigated successfully with the help of the recent development

Mechanical Properties of Nanostructured Materials

of proximity probes and tip-based microscopes and surface force apparatus with the help of computational techniques simulating the tip contact. The concept of nanotribology has been introduced in association with experimental and theoretical investigations of interfacial processes on atomic and molecular scales, which occur during adhesion, friction, scratching, wear, nanoindentation, and thin-film lubrication at sliding surfaces [206]. The main tools at present are surface force apparatus (SFA), scanning tunneling microscope (STM), atomic force microscope (AFM), and friction force microscope (FFM). The comparison of the operating parameters of these methods is shown in Table 1.

4.3.1. Wear Tests for Nanostructured Materials The magnetic media are constantly in development of higher data storage capacity which demands the reduction of the coating thickness on the media [207]. Of importance in terms of the tribological properties are the 5- to 10-nmthick protective layer of diamond-like carbon (DLC) and the 0.5- to 2-nm thick perfluoropolyether lubricant layer. As an example, AFM has been used to investigate the wear evolution of a magnetic disc coated with DLC. On nanoscale it was observed that the wear is not uniform and initiates at nanoscratches [208]. AFM wear tests have been used to evaluate the wear resistance of the ultrathin DLC coatings prepared by varying the deposition parameters [207]. The surface defects present at the nanoscratches act as initiation sites for wear. FFM has been used to indicate any imperfections and variation of the coating thickness on the magnetic disk. AFM has also been used to compare the tribological properties of DLC coatings by varying the deposition method and coating thickness (from 2.5 to 20 nm). The 20-nm-thick coatings had the highest wear resistance [209].

4.3.2. Determination of Friction in Nanostructured Materials FFM provides the means to map the surface of material on nanoscale. FFM method has been used to investigate the properties of nanostructured carbon coatings (ns-C) [210]. It was found that the friction varied depending on the individual carbon nanocluster and the overall friction behavior was dependent on the parameters of the cluster beam.

145

5. MECHANICAL PROPERTIES OF NANOSTRUCTURED MATERIALS 5.1. Nanoparticles, Nanotubes, and Nanofibers 5.1.1. Nanoparticles with Various Aspect Ratios Nanoscale particles (spheres, rods, wires) can be fabricated with a variety of different methods and the methods have been applied to a multitude of materials. Generally, mechanical properties of individual nanoparticles, irrespective of their morphology, become near to ideal properties of flawless single crystals. This is due to the size effects associated to characteristic lengths of mechanical properties of materials as discussed previously. However, the large proportional number of surface atoms has an additional effect. Proportion of surface atoms to bulk atoms has been suggested to produce size dependency in elastic properties of nanosized particles. The size dependency has been modeled using continuum mechanics [132]. An important length scale in the phenomena was identified to be the ratio of the surface elastic modulus to the elastic modulus of the bulk of the material. Typically, the size dependency starts to be significant in particle sizes of a few nanometers depending on material. The strength of small wires (whiskers) has been observed to approach the theoretical cohesive strength of solid matter already in submicrometer size range [211]. The theoretical cohesive strength lies in the range of 0.03 to 0.17 times the modulus of elasticity. In case of metallic nanowires, the exceptionally high strength has been confirmed experimentally in studies of nanometer-size gold contacts using scanning tunneling microscope [212, 213]. For comparison, gold is the softest of all metals in larger dimensions. Mechanical properties of nanoparticles have been contrasted here with bulk properties of materials. However, structural forms of nanoparticles that are characteristic of the nanometer scale only, such as fullerenes and nanotubes, are also observed.

5.1.2. Nanotubes Nanotubes are large macromolecules similar to a sheet of graphite rolled into a cylinder and capped with half fullerene at both ends. Essentially, they are one-dimensional

Table 1. Comparison of typical operating parameters in SFA, STM, and AFM/FFM used for micro/nanotribological studies [206]. Operating parameter

SFA

STMa

AFM/FFM

Radius of mating surface/tip Radius of contact area Normal load Sliding velocity

∼10 mm 10–40 m 10–100 mN 0.001–100 m/s

Sample limitations

Typically atomically smooth, optically transparent mica; opaque ceramic, smooth surfaces can also be used

5–100 nm N/A N/A 0.02–2 m/s (scan size ∼ 1 nm × 1 nm to 125 m × 125 m; scan rate < 1–122 Hz) Electrically conducting samples

5–100 nm 0.05–0.5 nm 1 / cos >2 . In case of a steep wall, the ratio can be 10 or more. The thinner section t2 is susceptible to cracking at the extreme ends of the interval. Rotating the wafers in a planetary motion does help to widen the range of arrival angles but shadowing still occurs. To overcome the nonconformal deposition, the substrate can be heated during deposition (300 to 400 C) to increase the surface mobility of the arriving atoms or the wafers can be rotated individually so that the angle > varies during deposition. Nevertheless, a nonconformal step coverage is beneficial when considering the so-called lift-off technique (see Section on lithography). Laser Ablation PVD Laser ablation deposition uses intense laser radiation to erode a target and deposit the eroded material onto a substrate. A high-energy focused laser beam avoids the X-ray damage to the substrate encountered with e-beam evaporation. A high-energy excimer laser pulse coming from, for example, a KrF laser at 248 nm with a pulse energy in the focus of 2 J/cm2 is directed onto the material to be deposited. The energy of the very short wavelength radiation is absorbed in the upper surface of the target, resulting in an extreme temperature flash, evaporating a small amount of material. This material, partially ionized in the laser-induced plasma, is deposited onto a substrate almost without decomposition. This technique is particularly useful when dealing with complex compounds, as in the case of the deposition of high temperature superconductor films, for example, YBa2 Cu3 O7−x . Pulsed laser deposition faithfully replicates the atomic ratios present in the hot isostatically pressed target disc onto the thin film coating. Achieving complex stoichiometries presents more difficulties than with any other deposition technology. Approximately 10,000 pulses (pulse length of 20 ns and a repetition rate of 15 pulses per second) are needed to achieve a film thickness of 100 nm (i.e., approximately 10 nm/min). Normally, the laser deposited films are amorphous. The energy necessary

Sputter PVD Sputtering is preferred over evaporation in many applications due to a wider choice of materials to work with, better step coverage, and better adhesion to the substrate. Several sputter systems exist such as dc, reactive, rf, and magnetron sputtering as will be explained next. Figure 60 illustrates schematically a dc sputter deposition system. In the sputter system an inert gas is fed into the reactor at low pressure. A voltage is applied across two electrodes and plasma is created. The top electrode, the cathode or “target” where a negative dc voltage is applied, is actually the source material to be deposited, a plate of aluminum for example. The bottom electrode—the anode where the wafers are located—is another metal plate and is grounded. The positive ions from the plasma source, usually Ar+ , are accelerated through the potential gradient where they bombard the target. Through momentum transfer, atoms near the surface of the target material become volatile and are transported as a vapor to the substrate. At the substrate the film forms through deposition (the vapor condenses). Since the target acts as an electrode in the dc mode of sputter deposition, the target of source material must be conductive. Therefore, Al, W, Ti, silicides and other metallic components can be sputtered this way. Sometimes sputtering of the wafer is desirable—for example to improve adhesion. In such cases, a negative bias is applied to the wafer electrode. Positive argon ions from the plasma will now be accelerated to the wafer and sputter off atoms, thus removing any contaminants or native oxides. In addition it will improve adhesion due to the creation of surface dangling bonds by the ion impact. In reactive sputtering, a reactive gas is introduced in the reactor in addition to the argon plasma, and the compound is formed by the elements of that gas combining with the sputtered material. For example, TiN can be deposited by sputtering Ti in the presence of nitrogen. dc sputtering is not suitable for insulator deposition. Therefore, in radio frequency sputtering an rf voltage source is used to couple capacitively through the insulating target, so that conducting electrodes are not necessary. In magnetron sputtering, magnets are used to increase the ionization efficiency of the plasma. Electrons originating at the cathode are trapped in a

Ar

–DC

Cathode / target Plasma Anode

Vacuum

Figure 60. Thin film deposition by dc sputtering.

Ground

198 spiral motion and confined by the magnetic fields until they collide with an argon atom. This can speed up the deposition 10 to 100 times faster than without magnets. Having a larger target and higher gas phase pressure than evaporation means that the arrival angles of the atoms at the wafer surface are more widely distributed which generally improves step coverage. Also, the number of resputtered atoms on the wafer surface is higher for sputtering due to the bombardment of energetic particles, which increases the arrival angle distribution even more. In some cases, though, we actually want to narrow the arrival distribution—for example when filling a deep via with metal. This can be achieved using collimated and ionized sputtering systems. In collimated sputtering, a plate with holes is placed between the target and the wafer. The collimator acts as a physical filter to low-angle sputtered atoms. In ionized sputtering an rf antenna is used instead to direct ionized atoms toward the substrate and increasing directionality. Another way is applying bias to the substrate, which allows a minimal sputter etching concurrently with the deposition. In this way, sharp edges of the deposit are reduced during the sputter deposition due to the angle-dependent sputter yield. Surfaces with pointed and sloped features are removed more easily than horizontal or vertical surfaces. Not only does this help planarize the film, but overhang that can develop when depositing into a trench or hole is preferentially sputtered away, allowing for a better filling of the hole. Another factor may be that the resputtered atoms allow for some redeposition on sidewalls. By increasing the ion energy, the resputtering and redeposition of the atoms can be increased, resulting in better sidewall coverage. Another option for improved hole filling is to do the deposition and etching sequentially, as opposed to simultaneously. This can be done in a cluster tool with separate chambers for each process or using a plasma system, which allows both sputter deposition and etching such as in downstream cascade arc plasma (Section 5.3). Deposition rates depend on source-to-substrate distance and can be as high as 1
m/min for aluminum and its alloys. A typical sputter yield (i.e., ejected atoms per incident ion) is between 0.1 and 10 atoms/ion and is a function of ion energy and their direction. Below the so-called threshold energy, the ions have not enough energy to break the metallic bonds and subsequently the sputter yield is very low. The yield increases rapidly from the threshold energy level, which is usually in the range of 10 to 100 eV for common metals (e.g., 13 eV for Al, 15 eV for Pd, and 34 eV for Pt). To minimize the energy required to eject an atom from the target, the process uses ion energy within the range for which the sputter yield is about one atom per ion. Ion energies in the range of 0.5 to 3 keV typically are used for dc sputter deposition as nuclear collisions are predominant in this range. At ion bombardment energies in the range of 10 keV to 1 MeV, the sputter yield reaches a maximum and then gradually declines in value as a result of deep ion implantation. Average ejection energies of ions from the target range between 10 and 100 eV. At those energies, the incident ion can penetrate a substrate one to two atomic layers into the surface on which it lands. As a result, the adhesion of sputtered films is superior to films deposited by other methods. An ion coming in at low, glancing angle will not be as successful at dislodging an atom, with the ion itself being

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reflected off the surface (specular reflection). At the other extreme, ions arriving normal to the surface will push a surface atom further into the target but not necessary sputter it off. The sputter yield peaks at some angles less than 90 , just as is the case in ion beam etching (Section 5.3). The angles that the sputtered atoms leave the surface of the targets are usually found to be diffusely distributed, with an ideal cosine-emitted angle distribution. Molecular-Beam PVD (Epitaxial Crystal Deposition) Molecular-beam epitaxy is a PVD epitaxial process involving the reaction under ultrahigh vacuum conditions ( 111 > 311 > 511 > 100 , which resembles the surface atom concentration orientation dependency. For example, after 16 hours of oxidation at 800 C of 011-, 111-, and 100-oriented wafers, 300 nm oxide grows on the 011wafer, 280 nm Oxide on the 111-wafer, and 200 nm oxide on the 100-wafer, revealing a ratio of {011}:{111}:{100} = 1 5 ( 1 4 ( 1. So, because the density of silicon atoms on the {011}-plane is larger than that on the {111} and {100}plane, the linear rate constant for 011-silicon is also larger and oxidation proceeds faster in the initial growing process where the growing proceeds still linearly with time. The parabolic rate constant is independent of crystal orientation. This independence is expected, because it is a measure of the diffusion process of the oxidizing species through a random network layer of amorphous silica. Addition of chlorine-containing chemicals during oxidation increases the dielectric breakdown strength and the rate of oxidation and improves the threshold voltage of many electronic devices However, too high concentrations of halogens at high temperatures can pit the silicon surface. In general, the quality of the silicon–silica interface fails to be of importance in the MEMS field unlike the IC industry. One notable exception being the ion sensitive field effect transistor (ISFET). Understanding the stress associated with a film is important because high stress levels can contribute to wafer warpage, film cracking, and defect formation in the underlying silicon. Room temperature measurements following thermal oxidation of silicon show the film to be in a state of compression on the surface. Film stress values of 700 MPa are reported, with the stress attributed to the difference in thermal expansion for Si and SiO2 (thermal stress) and stress resulting from the change in volume between silicon and its oxide (intrinsic oxidation stress). For more details on all the subjects described above, see [1]. Evidently, such stresses are of prime concern when dealing with extremely small structures as found in nanotechnology where natural oxides are major contributions to the total thickness of structures such as nanocantilevers. Diffusion Until the early 1970s, selective doping was done mainly by diffusion at elevated temperatures. In this method the dopant atoms are placed on or near the surface of the semiconductor wafer by deposition from gas phase of the dopant or by using doped-oxide sources. The dopant distribution is determined mainly by the temperature and diffusion time. Diffusion of impurities is typically done by placing semiconductor wafers in a furnace and passing an inert gas that contains the desired dopant through it. The furnace and gas flow arrangements are similar to those used in thermal oxidation. The temperature usually ranges between 800 and

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1200 C for silicon. For diffusion in silicon, boron is the most popular dopant introducing a p-type impurity, while arsenic and phosphorous are used extensively as n-type dopants. These three elements are highly soluble in silicon as they have solubilities above 5 × 1020 /cm3 (i.e., 1% of the silicon density!) in the diffusion temperature range. These dopants can be introduced in several ways, including solid sources (e.g., BN for boron, As2 O3 for arsenic, and P2 O5 for phosphorous), liquid sources (BBr3 , AsCl3 , and POCl3 ), and gaseous sources (B2 H6 , AsH3 , and PH3 ). Usually, the source material is transported to the semiconductor surface by an inert carrier gas (e.g., nitrogen) and is then reduced at the surface. The diffusitivities of commonly used doping impurities (e.g., As, B, and P) are considerably smaller in silicon dioxide and silicon nitride than in silicon. Therefore silicon dioxide can be used as an effective mask against impurities. If we etch windows in the oxide and use the remaining oxide as a mask, we can incorporate dopant impurities into a silicon substrate in selective areas. For silicon dioxide, the diffusion process can be described as occurring in two steps. During the first step, the dopant impurities react with silicon dioxide to form a silicate glass. As the process continues, the thickness of the silicate glass increases until the entire silicon dioxide layer is converted into a silicate glass (e.g., phosphosilicate glass). After the glass forms, the second step begins. The dopant impurity diffuses through the glass; upon reaching the glass–silicon interface, it enters and diffuses into the silicon. During the first step, silicon dioxide is completely effective in masking the silicon against dopant impurities in the gas phase. Therefore, the thickness of silicon dioxide required for masking is determined by the rate of formation of the glass, which in turn is determined by the diffusion of the diffusant into the silicon dioxide. Because it has a higher diffusitivity in silicon dioxide, phosphorous requires thicker masking layers (between 20 and 80 times thicker) than boron. Silicon nitride is even more effective as a diffusion barrier than silicon dioxide. Therefore much thinner layers of silicon nitride are sufficient to effectively block dopants. Dopant impurities near the silicon surface will be redistributed during thermal oxidation. The redistribution depends on several factors. When two solid phases are brought together, an impurity in one solid will redistribute between the two solids until it reaches equilibrium. The ratio of the equilibrium concentration of the impurity in the silicon to that in the silicon dioxide is called the segregation coefficient k. For k < 1, the oxide takes up the impurity and for k > 1 it rejects the impurity. An example is phosphororus, with k approximately equal to 10.

3.7.4. Physical Vapor Growth Ion implantation is the introduction of energetic, charged particles into a substrate such as silicon. The practical use of ion implantation in semiconductor technology has been mainly to change the electrical properties of the substrate or to form a buried oxide layer for SIMOX wafers (see Section 2.3.11). Ion Implantation Since the early 1970s, many doping operations have been performed by ion implantation. In this process the dopant ions (e.g., B+ and As+ ) are implanted

201 into the semiconductor by means of a high-energy ion beam. Typical ion energies are between 30 and 300 keV, and typical ion doses vary from 1011 to 1016 ions/cm2 . The high-energy ion beam passes through vertical and horizontal scanners and is implanted into the semiconductor substrate. The energetic ions lose their energy through collisions with electrons and nuclei in the substrate and finally come to rest. Due to the kinetic energy of the impinging ions, the doping concentration has a peak inside the semiconductor and the profile of the dopant distribution is determined mainly by the ion mass and the implanted-ion energy. The advantages of the ion implantation process are precise control of the total amount of dopants, improved reproducibility of impurity levels, and lower temperature processing. For heavy ions, the energy loss is primarily due to nuclear collisions; therefore substantial lattice disorder (damage) occurs. When the displaced atoms per unit volume approach the atomic density of the semiconductor, the material becomes amorphous. For 100-keV arsenic ions, the dose required to make amorphous silicon is 6 × 1013 /cm2 . Much of the energy loss for light ions (e.g., B+ in silicon) is due to electronic collisions, which do not cause lattice damage. The ions lose their energies as they penetrate deeper into the substrate. Eventually, the ion energy is reduced sufficiently for nuclear stopping to become dominant. Therefore, most of the lattice disorder occurs near the final ion position at a depth up to a few hundreds of nm. Solid-Phase Epitaxy Because of the damaged region that results from ion implantation, semiconductor parameters such as mobility and lifetime are severely degraded. In addition, most of the ions implanted are not located in substitutional sites. To activate the implanted ions and to restore mobility and other material parameters, we must anneal the semiconductor at an appropriate combination of time and temperature in a furnace. For boron implantation, higher annealing temperatures are needed for higher doses. For phosphorus at lower doses, the annealing behavior is similar to that for boron. However, when the dose is greater than 1015 /cm2 , the annealing temperature drops to about 600 C. This phenomenon is related to the solidphase epitaxy process. At such high doses, the silicon surface layer becomes amorphous. The single-crystal semiconductor underneath the amorphous layer serves as a seeding area for recrystallization of the amorphous layer. The epitaxialgrowth rate along the 100-direction is 10 nm/min at 500 C and 50 nm/min at 600 C, with activation energy at 2.4 eV. Therefore, a 500 nm amorphous layer can be restored in a few minutes. During the solid-phase epitaxial process, the impurity dopant atoms are incorporated into the lattice sites along with the host atoms; thus, full activation can be obtained at relatively low temperatures. Note that a thin layer of damaged silicon on top of a silicon dioxide layer will not be repaired due to the missing subsurface single-crystal seeding area. In order to achieve low temperature recrystallization for boron implantation, we can implant inert ions into silicon to form an amorphous layer. The silicon can then be annealed at low temperatures (600 C) by the solid-phase epitaxy process to remove the implanted damage from the dopant ions. Another possibility to restore the crystal lattice without the

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202 need of a furnace is to use electron-beam annealing or laserbeam annealing. With low-temperature e-beam annealing we can activate the dopant fully with minimal redistribution, while the high-temperature furnace annealing substantially broadens the profile.

3.7.5. Chemical Liquid Deposition In the IC industry one tends to avoid wet chemistry when a dry deposition method presents itself, but MEMS needs are forcing reconsideration of electrochemical techniques as a viable solution. In micromachining, electrochemical liquid deposition (ECLD) is used to make structural microelements from a wide variety of metals, metal alloys, and even composite materials. Moreover, ECLD enables the metal replication of high-aspect-ratio resist molds while maintaining the highest fidelity. A chemical liquid deposition method that has been developed for copper is electrolytic plating. This can be done with the use of external electrodes and applied current. Applying an external voltage is generally referred to as electroplating. Deposition without an applied field is called electrodeless or electroless deposition and, when the substrate surface is replaced by a deposit, the process is called immersion plating. These processes are used commonly in printed circuit board manufacturing and onchip interconnect fabrication. While the electroless method has received a lot of attention in recent years, mostly due to its selectivity deposition capabilities, the electroplating method has become the current method of choice for copper deposition in integrated circuits. Electroplating In electroplating, the wafers are mounted on a cathode and immersed into a plating solution that contains metallic ions (M2+ such as Ni2+ or Cu2+  as shown in Figure 62. An inert anode, made of graphite (or platinum), for example, is also immersed into the solution. A voltage is applied between the two electrodes and the current drives the metal ions (or cations) toward the wafer at the cathode, forming, for example, nickel on the surface. The negative anions are attracted to the positive anode, which picks up electrons forming Cl2 , according to the electrochemical reaction Red: M2+ + 2e− → M (reduction at cathode)

Ox:

2Cl− → Cl2 + 2e−

–

(oxidation at anode)

+

Cathode

Anode

Cl–

M

(52)

Immersion Plating Simple metal displacement reactions where the surface of a less noble metal such as zinc immersed in a copper sulphate solution gets replaced by a copper surface feature the simplest example of electrochemical deposition, known as immersion plating. No external potential is applied, and both anodic and cathodic partial reactions occur on the same electrode surface. Zinc gives off two electrons and goes into solution while copper ions receive two electrons and deposit as a metal: Red: Ox:

Cu2+ + 2e− → Cu 2+

Zn → Zn

+ 2e

−

NiCl2/KCl/H2O

(53) (54)

The surface of the zinc substrate becomes a mosaic of anodic (zinc) and cathodic (copper) sites, which could have nanoapplications. The displacement process is continuous until the entire surface is covered with copper. At this point, oxidation (dissolution) of the zinc anode virtually stops and copper deposition ceases. The process only proceeds slowly by way of diffusion of copper and zinc ions through the copper deposit and is quite identical in time-dependent growth behavior with the thermal oxidation process. Deposits range up to 3 micrometers thick. Electroless Plating Electroless deposition involves the formation of thick metallic films from electrolytic solution without the use of external electrodes (as in electroplating) and without the dissolution of the substrate (as in immersion plating). In order to achieve this, it is essential that a sustainable oxidation reaction be employed. Simultaneous oxidation–reduction reactions between two half-reactions occur to deposit the film from solution. By this method, both blanket and selective films of good quality, low resistivity, and good filling properties can be obtained. In a typical process, the solution contains formaldehyde (HCOH) as a reducing agent and CuEDTA as the oxidizing agent and source of copper. The two half-reactions with their redox potentials in this pH = 12 solution are: Red: [CuEDTA]2− + 2e− → Cu + EDTA4−

2+

Figure 62. Electroplating set-up.

(51)

A thin seed layer, Au (or Cu), is often deposited first over the wafer so that electrical contacts can be made to the surface of the wafer and so that nickel is electroplated over the entire wafer surface. This seed layer formation can be done by PVD or CVD techniques. Excellent filling can be achieved with electroplating and is enhanced by using “leveling” agents or additives into the solution. These chemicals inhibit the deposition. They preferentially adsorb on the top surfaces of the topography rather than on the bottom of trenches or vias due to diffusion limitations. The top surfaces and corners then receive less deposition than the bottoms of trenches, resulting in excellent filling ability. Low resistivity and high deposition rate can be achieved with electroplating. Important process parameters are pH, current density, temperature, agitation, and solution composition.

Ox:

V = −0 26 (55)

2HCOH + 4OH− → 2HCOO− + 2H2 O + H2 + 2e− V = 0 32

(56)

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The hydroxide ion is commonly produced from sodium or potassium hydroxide. The net potential is positive so that the combined reaction to deposit copper is thermodynamically favorable. In parallel to the oxidation reaction, more or less severe hydrogen reduction goes on, which might upset the quality of the deposit. Stabilizers (i.e., catalytic poisons such as thiourea and Pb2+ ) are needed as the solutions are thermodynamically unstable; deposition might start spontaneously onto the container walls. In addition, buffers, accelerators (exaltants), and complexing and surfactant agents are commonly added to the solution. In order for the copper to be deposited, a thin seeding layer is required to catalyze the electroless process. These are often Pd, Au, or Cu layers, CVD or PVD deposited. Alternatively, the wafer surface is activated by dipping it into SnCl2 /HCl or PdCl2 /HCl. For selective electroless deposition, the seed layers should only be in the locations where the copper deposit is desired. This can be done by selectively etching the seed layer itself or using lift-off techniques. A problem with the electroless method has to do with contamination. The seed layer materials can all act as deep-level traps in underlying silicon. Of more concern are the alkali ions needed for the highly basic solution. Sodium and potassium ions can drift in silica and alter the electrical properties of the device; therefore tetra-methyl-ammonium-hydroxide [NC2 H5 4 OH], or TMAH, is often used instead. Electroless plating is an inexpensive technique enabling plating of conductors (such as nickel, copper, cobalt, platinum, or gold). Metal alloys, such as nickel–boron or palladium–nickel, can be produced by co-deposition. Liquid Phase Epitaxy This is the growth of epitaxial layers on crystalline substrates by direct precipitation from the liquid phase. LPE is suited only to deposit thin epi layers because it has a slow deposition rate. It is also found to be useful to grow multilayered structures in which precise doping and composition controls are required. SAM Self-assembled monolayers are indispensable for many nanoprocesses. SAMs are close-packed monolayers of molecules—just like a soap molecule—with a head attached to the underlying substrate and a tail pointing upward. The composition of the head depends on the substrate it has to be connected with: typically a silane head (SiOH or SiCl) for silicon substrates and a thiol head (SH) for gold substrates. The tail can have a varying composition and functionality and is typically between 4 and 10 carbon atoms in length (i.e., a few nm). Deposition of SAMs is a simple method to modify surface wetting properties of a variety of substrate materials. Because SAMs are close-packed, they are virtually pinhole free. Moreover, they are self-assembled and thus the thickness is highly controllable. Finally, due to the “free-tochoose” tail composition, the properties of a surface can be varied almost without any constriction. For example, hexamethyl disiloxane is a SAM used as an intermediate layer to promote adhesion of resist film to silicon-based substrates. Another example, by controlling the water content in the solvent, SAMs of trichlorosilanes can be formed on silica substrates in a short period of time. The photochemistry of the 2-nitrobenzyl group can be used for photocleavable SAMs. Ultraviolet irradiation through masks placed on top of SAM-modified surfaces

203 leads to the production of hydrophilic carboxylate groups in the irradiated regions leaving the nonirradiated regions hydrophobic. Once photopatterned, aqueous solutions can be confined to the irradiated hydrophilic regions, which results in surface-directed flow devices. Another important group has applications in biochemistry. These are SAMs having a “proteinphilic,” which can be very specific for certain enzymes. SAMs are also found in lithographs as seen in Section 4.2.3.

3.7.6. Physical Liquid Deposition In physical liquid deposition, an amount of liquid is deposited (coated) first on a substrate and then it is hardened to form a solid film. Several methods exist such as dipping, spraying, painting, casting, or melting as will be treated in this section. Spinning Spin coating has been optimized for deposition of thin layers of polymer on round and nearly ideally flat surface silicon wafers. For example in photoresist spinning, the wafer is held on a vacuum spindle, and ∼1 cm3 of liquid resist is applied to the center of the wafer. The wafer is then rapidly accelerated up to a constant rotational speed (generally in the range 1000 to 10,000 rpm), which is maintained for about 30 s to give a uniform film. During spinning, the centrifugal forces push the excess solution over the edge of the wafer, and the residue on the wafer remains due to surface tension. The√thickness of the resulting resist film is given by tRes ∼ %/ B with % the liquid viscosity,  the percent solid content in the resist, and B the spin speed. In this way films down to 10 nm and up to several tens of micrometer can be formed. Dipping In dip coating, a substrate is dipped into a solution containing a polymer and a solvent. After evaporation of the solvent, a thin layer forms on the surface. To obtain pinhole-free layers, the dipping is repeated several times interspersed with drying periods. Unlike spin coating, dip coating allows us to coat 3D surfaces such as wires uniformly. Thermoplastic and thermosetting coatings are formed by dipping a heated part into a container of resin particles set in motion by a stream of low-pressure air (fluidized-solid bed). Dip coating of a substrate in a dissolved polymer typifies the simplest method to apply an organic layer to a substrate. Spraying Spray coating may involve liquids, gases, or solids. Spray coating of a liquid involves pressurization by compressed air or pushing liquid mechanically through tiny orifices. Vapors are carried in an inert dry vapor carrier. In the case of a solid, a powdered plastic resin is melted and blown through a flame-shrouded nozzle. In electrostatic spraying a negatively charged plastic powder is spray gunned onto grounded conductive parts. Painting In some applications, it can be practical to introduce a given amount of material using a brush. Clearly, this technique is not microsystem-compatible and therefore only seldom used. Nevertheless, this process is suited in packaging where sometimes only very specific spots should be covered by a film.

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204 Casting Casting is based on the application of a given amount of dissolved material on a surface and letting the solvent evaporate. A rim structure is fashioned around the substrate, providing a “flat beaker” for the solution. This method provides a more uniform and a more reproducible layer than dip coating. Melting Melting is a technique similar to casting. Identically, it uses a dummy container to confine a liquid. The liquid is formed by melting granules of material, often a metal or polymer, in a nitrogen-purged furnace. In the liquid phase, a layer forms having a very high degree of planarization. After cooling down, the container is removed leaving a metallic layer on top of the substrate. Clearly, when using metal melting, the container should withstand the temperature. Alloying of the metallic layer with the container material (contamination) is a factor of concern.

10H+ + 10e− → 5H2

Red:

3.7.7. Chemical Liquid Growth In order to avoid the necessity of heating substrates to high temperatures as in the case for chemical vapor growth, it is possible to enhance oxidation by immersing parent metals in a chemical oxidizing liquid medium. In most cases this is the oxidation of a metal film in an electrolytic cell. The medium may be aqueous, nonaqueous, or a fused salt. Anodization Anodization is a widely used technique for obtaining amorphous, highly insulating, pinhole-free, and low-stress (due to the low temperature film growth) films and there is a very large commercial usage of these in electronic capacitors. Anodization is an oxidation process performed in an electrolytic cell as schematically shown in Figure 63 with an applied voltage ranging from 20 to 600 V. The material to be anodized becomes the anode (+) while a noble metal or graphite is made the cathode (−). When electric current is passed, the surface of the anode material is converted to an oxide having protective, insulating, or other properties. (At the cathode, the only important reaction is H2 evolution.) The oxygen required originates from the electrolyte used and the coating progresses from the solution side inward, toward the metal, so that the last-formed oxide is adjacent to the metal. Depending on the solubility of the anodic reaction products, an insoluble layer (e.g., an oxide film) results or in the case of a soluble reaction product, the electrode etches. For example, if the primary oxidizing agent is water, the resulting oxides generally are porous, whereas organic electrolytes may lead to very dense oxides providing excellent passivation.

–

So anodic oxide coatings may be of two main types. One is the so-called barrier layer, which forms when the anodizing electrolyte has little capacity for dissolving the oxide. These coatings are essentially nonporous and their thickness is limited to about 1–2 nm/V applied. This thickness represents the distance through which ions can penetrate the oxide under the influence of the applied potential. Once this limiting thickness is reached, it is an effective barrier to further ionic or electronic flow. The current drops from a typical few tens of mA/cm2 to a low leakage value and oxide formation stops. Scanning electron microscope (SEM) studies reveal the presence of close-packed cells of amorphous oxide. Their size is a function of the anodizing voltage and is typically around 100 nm. The oxide film, which forms on, for example, tantalum during anodic oxidation, is a product of the following electrochemical reaction.

Ox:

(57)

2Ta + 10OH → Ta2 O5 + 5H2 O + 10e −

−

(58)

The rate-controlling process is the ion migration within the oxide film. At high fields the current density during the anodization depends exponentially on the field strength, and the rate of oxide growth is proportional to the density of the current. Since the current efficiency is about 100%, Faraday’s law can be used for determining the amount of oxide formed from the quantity of electricity passed through the electrolytic cell. Figure 64 shows the behavior of voltage and current with time during anodization. The oxide formation usually consists of a constant current phase until a preselected voltage is reached. During this phase the oxide increases at a constant rate, according to the increase in potential, necessary to maintain the current. After the requested voltage is reached, the anodization continues until the ion current has decreased to a sufficiently low level of about 1% of its original value. This is to increase film uniformity and to remove pinholes. For example, at a current density of 1 mA/cm2 , the growth rate of tantalum pentoxide is about 0.57 nm/s. At this current density the measured voltage rise is 0.33 V/s, resulting in a growth constant of 1.73 nm/V for the formation. If this process continues until the voltage has risen to, for example, 100 V, the oxide thickness will be 173 nm.

V

Voltage

80

+

Cathode

Anode

Current

40

OH–

H+ H2SO4/H2O

Figure 63. Anodization setup.

10

20

Time [min]

Figure 64. Anodization steps: constant current-constant voltage.

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When the electrolyte has appreciable solvent action on the oxide, the barrier layer does not reach its limiting thickness; current continues to flow, resulting in a porous oxide structure. Porous coatings may be quite thick—up to several tens of micrometers—but a thin barrier oxide layer always remains at the metal–oxide interface. As in the case of thermal growth, only a limited number of materials form coherent oxides in anodization. These include the valve metals (Al, Ta, Nb, Zr, and Hf), either alone or as alloys within the group, Group IV and Group III–V semiconductors, and materials such as Bi, W, TaN, SiC, Sb, Y, Ti, Mg, Zn, Cu, Ag, Cd, and steel. The rate of formation of the oxide is a function of the current density and the final oxide thickness is limited to the voltage applied to the electrolytic cell. Asymptotic growth curves are obtained, as was the case for thermal growth. For the case of aluminum an anodization constant of approximately 1.3 nm/V and for tantalum 1.7 nm/V is found. The disadvantage of using a constant voltage approach is that the initial growth stages of anodization require very high current densities, and one way around this difficulty is to anodize initially using a constant current rather than a constant voltage. The limiting condition of the thickness of the film is the breakdown under high voltages, and in the case of aluminum and tantalum this occurs at oxide thicknesses of 1.5 and 1.1
m respectively. Other factors can, however, limit the thickness to values less than those quoted, and in particular the purity of the substrate and composition of the electrolyte are important. Although anodizing processes are used for many metals, aluminum is by far the most important. The mechanism of anodic oxidation is not completely understood. Faraday’s law predicts that for each Faraday of electricity passed, ca. 9 grams of aluminum would react, forming 17 grams of alumna, for a “coating ratio” [Al2 O3 ]/2[Al] = 1.89. This ratio is never observed; it seldom exceeds about 1.60. Although many electrolytes have been suggested and used for anodization of aluminum, H2 SO4 is the most widely employed. Concentrations are from 12 to 25 wt%. For special effects or attainment of special properties, chromic acid anodic coatings are opaque, limited to about 10 micrometers in thickness. They are used as a base for paints or adhesive bonding. Phosphoric acid anodizing has been used as a basis for plating on aluminum, though it has been superseded by zincate. Tantalum pentoxide films have been extensively studied for use in electronic devices. The high dielectric constants of these films make them very attractive as storage capacitors. Studies of tantalum films doped with 2–7 at% nitrogen demonstrated that the reliability and leak current characteristics of tantalum pentoxide capacitors obtained by anodization can be improved. The anodic oxidation of titanium is important in the use of platinum-plated titanium anodes, because even through pores in the platinum coating, the titanium oxidizes anodically and resists the action of the electrolyte involved. Oxidation of silicon never led to a commercially acceptable process, mainly because the interface state density at the SiO2 /Si interface is prohibitively high for semiconductor applications. Instead, anodization of silicon in a highly concentrated HF solution (excellent etchant for the anodic oxidation product SiO2 ) may lead to porous silicon and very

205 high aspect ratio pores, with diameters ranging from 2 nm to several micrometers. The growth rate and degree of porosity of the silicon can be controlled by the current density. More on this subject is found in Section 5.3.3.

3.7.8. Physical Liquid Growth There is no practical process known.

3.7.9. Chemical Solid Deposition There is no practical process known.

3.7.10. Physical Solid Deposition Wafer bonding has been a subject of interest for many years and a wide variety of bonding techniques have been reported, such as direct, plasma, anodic, adhesive (polymer, glass, or solder), eutectic, and compression bonding (thermocompression or ultrasonic). The basic principle of bonding is that two solid materials fuse and adhere to each other if they are brought in sufficiently close contact. The cohesion of atoms and molecules in a solid material as well as those between two different solid materials is ensured by a number of basic bond types, which are covalent, metallic, ionic, or van der Waals. All these are bond types and based on Coulombic forces resulting from the attraction of opposing electrical charges. Covalent and van der Waals bonds are the dominating bonding mechanisms and the atoms of two opposing surfaces must be less than 0.5 nm apart because these forces do not extend further than this distance. On the other hand, direct Coulombic forces can reach up to a distance of several micrometers and are dominant whenever charging occurs. This charging is due to macroscopically adsorbing or desorbing electrons. These direct Coulombic forces become negligible when water molecules are present at the interface, which partly neutralizes the charge on the surface. This overview is taken from the thesis of Frank Niklaus, “Adhesive Wafer Bonding for Microelectronic and Microelectromechanical Systems.” In this section, we are mainly concerned with wafer bonding in which two full wafers should join. Two other applications, wire bonding and bump bonding, are mostly found in packaging applications and are not treated here. Bonding can be performed between two identical wafers or two dissimilar wafers. In the latter case, high bonding temperatures might cause pronounced shear stresses at the bonding interface preventing a correct bond. In such cases, the composition of one of the wafer materials is often adapted for thermal matching. For example, materials which are fit to become bondable with silicon are Pyrex glass and Kovar steel. Direct Bonding Direct bonding is also referred to as fusion bonding or thermal bonding. In direct bonding two wafers are contacted without the assistance of any significant pressure, electrical fields, or intermediate layers. It relies on the tendency for very smooth and flat surfaces to adhere to each other. It typically involves wafer surface preparation and cleaning, room temperature contacting of the wafers, and an annealing step to increase the bond strength. Direct bonding can be applied to identical wafers (e.g., silicon-tosilicon annealing between 600 and 1200 C) and even dissimilar materials such as silicon-to-glass (annealing between 400

206 and 600 C). Direct bonding usually leads to strong bonds and is widely used in SOI technology. Plasma Bonding In this technique, the surfaces to be bonded are exposed to (oxygen) plasma for, for example, 30 seconds, dipped in deionized water, and then placed together. After 24 hr at room temperature, the surface energy is deemed sufficiently high (>1 J/m2 ) to establish a bond. Anodic Bonding The terms electrostatic bonding and field assisted bonding are also commonly used for this bonding technique. Anodic bonding is based on joining conducting material (e.g., silicon) and a material with ion conductivity (e.g., alkali-containing glass such as Pyrex). Two contacted wafers are heated to 180–500 C to mobilize the ions while a voltage of 200–1500 V is applied. The voltage creates a large electric field that pulls the wafer surfaces into intimate contact and fuses them together. Due to the high force of attraction that is created by the electric field, anodic bonding is more tolerant to surface roughness than direct bonding. It is also possible to anodically bond two wafers with intermediate layers like glass, aluminum, silicon nitride or polysilicon. Anodic bonding usually leads to strong and hermetic bonds and is widely used for microsensor fabrication and for hermetic sealing of micromachined devices. Adhesive Bonding Adhesive bonding uses organic (polymer) or inorganic (ceramics or solders) intermediate layers to create a bond between two wafers. The adhesive material deforms and flows so it can make sufficiently close contact with the wafer surface to create a bond. The adhesive layer is deposited on one or both of the wafers, for example, by spin coating, spraying, screen-printing, extrusion, sedimentation, PVD, CVD, plating, or laminating. The wafers are brought into intimate contact and the intermediate adhesive layer is cured, typically by applying heat or UV radiation and pressure. The exact bonding procedure depends very much on the adhesive material used. The advantage of adhesive bonding, as compared to anodic and direct bonding, is the ability to join various wafer materials. It does not require assisting electric fields, the intermediate bonding material is not very susceptible to particles and structure at the wafer surfaces, and, moreover, it is carried out at moderate temperatures, which minimizes bond interface shear stresses. Adhesive wafer bonding requires no special wafer surface treatments such as planarization making it a lowcost bonding process. The process and materials employed determine the hermeticity and controllability of the cavity ambient. A huge variety of organic adhesives (mainly polymers) with different chemistries and material properties are available. The bonding temperatures for polymer adhesives vary between room temperature and 450 C making the process CMOS compatible. However, hermetical sealing is limited due to the intermediate polymer material used. A typical polymer bonding is using benzocyclobutene (BCB), a commercially available polymer from Dow Chemical. BCB is selected for its minimal outgassing, low moisture uptake, liquidlike behavior during bonding, high resistivity, chemical resistance, low processing temperatures (RQ ). The best fitting gives the RL of 450 k and the Re[Zt ] with mostly the same order value as RL . This impedance of 450 k mainly corresponds to the impedance of MWNT (RN T ) in our system, because the MWNT was directly connected to the single junction and the resistance of the gold contact layer including the gold/MWNT interface was at most on the order of 100 . We cannot find the impedance of 450 k in any parts of the system other than the MWNT. The value of 450 k as the resistance of MWNT is also in good agreement with that in a previous report [31]. In addition, note that this 450 k is actually larger than RQ . Therefore, we conclude that our Coulomb blockade is consistent with phase correlation theory, and that the MWNT acts as both a high Zt  for transferring charging energy and a high RL for avoiding external environment fluctuation, because the MWNT is closely connected to the single junction. The origin of this high impedance of carbon nanotubes is the key point for this work. As we expected, it can be qualitatively understood as a result of weak localization from the curve fitting shown in Figure 10c. As shown by the solid line, the G0 vs temperature characteristic is in nice agreement with the formula of 2D WL of MWNT [28], except for the Coulomb blockade temperature region,   p  e2 n9d T G T  = G 0 + ln 1 + (18) 29 2
L Tc B 0s  where n, d, L, and 0s are the number of shells, the diameter of the inner shell of the MWNT, the length of the MWNT, and the relaxation time of spin-flip scattering, respectively. The contribution of number of MWNTs and Rt were taken into account by the term of G 0. The best fitting gives n = 18, p = 21, and Tc = 10 K. Here, a main difference from the past reports [31] is the Tc as high as 10 K. This high Tc is understandable by the presence of magnetic impurities (cobalt), which was deposited into the nanopores as a reactant for carbon nanotube growth, in the MWNT with a very small volume [29]. In addition, the localization length 2loc can be estimated to be on the order of 1 .m (< the MWNT length of 10 .m) from the carbon nanotube impedance of 450 k . It also supports that our MWNT is in the weak localization regime. Based on these confirmations [i.e., (1) Coulomb blockade following phase correlation theory with near 450 k of the external impedance, (2) the impedance of 450 k existing only in the MWNT in our system, (3) the origin of the highly resistive MWNT being weak localization], we finally conclude that the weak localization in the multiwalled carbon nanotube plays the roles of both high Zt  and high RL for the Coulomb blockade. This conclusion is controversial to our hypothesis mentioned in the Introduction. The reason may be interpreted as follows at this stage. Of course, even apart from this interpretation, observed facts and analyses strongly support our conclusion.

Mesoscopic Phenomena in Nanotubes

Unless the tunneling electrons cannot transfer their energy to the environment, a tunneling event is allowed and, hence, Coulomb blockade cannot be caused in any case, if one follows PC theory [i.e., Eqs. (4)–(6)]. This is of core importance also for MQC (MQT) following the spirit of Caldeira and Leggett. MQT is much smeared by energy dissipation in its external environment. There may exist, however, the following two exceptions [30]; (1) the Debye– Waller factor exp −  in Mössbauer effect in LC mode and (2) infrared divergence in RC mode at finite temperature. The latter comes from the analogy between the motion of free Brownian particle and the RC environmental effect with the impedance Zt  = R and is relevant for the RC environment with the impedance much larger than RQ . With Zt  = R, Re[Zt ] is given by R/ 1 + RC2  and then

9/C  for very large R at finite temperature. Hence, energy transfer is carried out only around  = 0 in accordance with P E =  E − Ec . This is the so-called infrared divergence. In this case, only thermal fluctuation yields a time evolution of phase J t (i.e., diffuse the free Brownian particles), leading to J t ∝ t for long time, because the RC mode at very low frequency has basically no time-fluctuated electromagnetic factor. Therefore, the tunneling electrons can have a chance to transfer the charging energy Ec by exciting the RC mode through thermal fluctuation even in the nondissipative electromagnetic environment, particularly in the environment sensitive to electron phase fluctuations like localization. This new interpretation means a possibility that thermal environment is taken into account as P E in Eq. (4), if it is coupled with the electromagnetic environment. Our result may be qualitatively interpreted by this case at least from the following three points, (1) Re[Zt ] of about 450 k is much larger than RQ , (2) Resistance of MWNT is basically frequency independent. (3) The measurement temperature is 2 K. Otherwise, P E in Eqs. (4) and (5) may have to be reinterpreted as “the other probability,” not associated with the energy transfer probability of the tunneling electrons to the EME. Here, P E is the Fourier transform of J T  = ˜ ˜ ˜ ) t −  0  t , a time evolution of phase fluctuation ˜ in the EME, and the origin of the phase was defined  as  t = e/
dtV t, where V t = Q t/Cj is the voltage across the tunnel junction. The phase interference effect in localization also originates from this definition. Hence, J t is a time evolution of ˜ but should be attached to the localization effect so as not to destroy phase coherence in the MWNT. In this sense, P E may be reinterpreted as a transmission probability of electrons, associated with J t in the localization regime, in the MWNT. This does not deny the energy dissipation in external environment. In this case, energy transfer may take place in the contact metal electrodes with lower impedances. In addition, we may have to perform more careful data fitting from the following points. (1) Junction capacitance C: We used C obtained in our past report [28]. Since the C was estimated from data fitting by Nazarov’s theory, it is not yet experimentally confirmed. (2) Parasitic capacitance Cp : We did not take into consideration the influence of the Cp of MWNT. When we

305

Mesoscopic Phenomena in Nanotubes

define L = 0 × c (where 0 ∼ h/eV , c is the velocity of light in vacuum) as the geometry for an effective Cp based on the horizontal model [33] and included the Cp in the data fitting, it does not exhibit perfect agreement. Cp for better agreement should be smaller than that calculated from L = 0 × c. To explain this difference, a smaller velocity instead of c may have to be employed, because our MWNT has very disordered surface. (3) LCR model: We also have employed the RC mode as a lumped circuit model in PC theory here. Since, however, MWT has distributed L, R, and C including this Cp in the actual system, the LCR transmission line model will have to be introduced.

G0 (arb. unit)

Zero-bias Conductance : G0 [arb. unit]

However, even apart from these data fitting problems, the linear G0 vs temperature dependence, the high impedance EME only in the MWNT directly connected to the junction, and its dependence on the localization effect will support our conclusion. Here, why Coulomb blockade disappears near 5 K in Figure 10c is also not obvious with the G0 discontinuity. In the Ni-nanowire system shown in Figure 10c, inset, Coulomb blockade also disappeared around 6 K due to the phase fluctuation caused by mutual Coulomb interaction in the Ni-wire [29]. Based on this result, we modulate the phase of electron waves in the MWNT by applying a magnetic field also in this case and observe its influence on the Coulomb blockade. As shown in Figure 11, the G0 vs magnetic field (B) relation exhibits oscillation. Such oscillation

T=3 K

6

0

1

2

3

B (T)

5

4

3 0

1

2

3

4

Magnetic Field : B [T] Figure 11. Magnetic field (B) dependence of G0 in the CB temperature regime. Magnetic field was applied parallel to the tube axis within a few degrees as shown in Figure 1a. The radius of the AAS cylinder calculated from the first oscillation peak (B = 22 T) is in excellent agreement with the mean radius of the actual MWNT, although we did not take into account the contribution of the tube length, the misalignment angle of B to the tube axis, and the number of many MWNTs for the oscillation magnitude. It also indicates that the electron wave flows either in all of the shells or only in the midshells. Reprinted with permission from [40], J. Haruyama et al., Phys. Rev. B 63, 073406 (2001). © 2001, American Physical Society.

in MWNT has been understood as the Altshuler–Aronov– Spivak (AAS) effect in a graphite cylinder [32], which originates from phase interference of the electron waves encircling the cylinder in opposite directions and modulated by magnetic flux enclosed, with an oscillation period B =

h/2e/ 9r 2  where r is the radius of the cylinder. Here, the radius can be estimated to be 17.3 nm from the first oscillation peak. This radius is in excellent agreement with the mean radius of our actual MWNT of 17.5 nm. It is a straightforward indication that this conductance oscillation originates from AAS effect. This result implies that the Coulomb blockade is very sensitive to the electron phase fluctuation of the MWNT even under a high RL (>RQ ) directly connected to a single junction. Since the high RL is caused by weak localization in the MWNT, this result may be relevant. It also suggests the possibility that the elimination of Coulomb blockade near T = 5 K in Figure 10c may be attributed to the dephasing process by strong spin-flip scattering in the MWNT, as well as that in the Ni-nanowire system.

4. MULTIWALLED CARBON NANOTUBES 4.1. Spintronics 4.1.1. Antilocalization Due to Spin–Orbit Interaction in Metal-Doped Nanotubes Introduction Electrode atoms are slightly diffused, with only about 5% volume-ratio, into the top end of MWNTs, standing in nanopores of porous alumina membranes. Diffusion of light-mass materials (carbon and aluminum) leads to weak localization in the AAS oscillations, which is qualitatively consistent with previous works on MWNTs. In contrast, we find that diffusion of heavy materials (gold and platinum) changes this weak localization into an antilocalization in the MWNT bulk. This effect is only observable when electrons are injected through the diffusion region and undergo a 9-phase shift in their electron waves, caused by polarized injection of spin-flipped electrons due to spin– orbit interaction in the diffusion region of the MWNT bulk. Single-walled carbon nanotubes are conducting molecular nanowires that exhibit a variety of mesoscopic phenomena. There is a renewed interest in these nanostructures because their characteristics are very sensitive to materials deposited onto the tube inner space [34]. In contrast, the physical properties of MWNTs have been interpreted only in terms of quantum phase interference effects of electron waves in the diffusive regime at the single-molecular level (e.g., WL [35–37], AAS oscillations [38–42], universal conductance fluctuation [35], possible metal–insulator transition [43], and strong spin coherence [44]). The investigation of correlation of such interference phenomena with dopant materials in the tube inner space or the MWNT itself has so far received no attention. AAS oscillations and WL are the typical phase interference effects of electron waves observed in MWNTs. Constructive phase interference in current paths encircling MWNTs with time-reversal symmetry leads to WL, when the sample size is smaller than both the phase coherence length and the localization length [45–47]. The presence

306

Experiments and Discussion In electrical measurements of MWNTs performed in previous works, an individual MWNT was deposited on a substrate [38, 39], and gold (Au) fingerlike electrodes were fabricated by lithography over the MWNT. Only the upper half-part of the MWNT that did not face the substrate, had an interface with the electrodes. Hence, it was difficult to diffuse by annealing the electrode-atoms into one entire end of the MWNT along the circumference of the NT (including the lower half-part facing the substrate). In contrast, we reported earlier on a different method to obtain the characteristics of MWNT arrays standing in nanosized diameter pores of porous Alumina membranes [40–42]. In this method, after the deposition of MWNTs into the nanopores (Fig. 12e), the top ends of the standing MWNTs were exposed from the surface of alumina membranes (Fig. 12a–d) and, then, a thick electrode was directly deposited on all of the top ends (Fig. 12f). Hence, diffusion of electrode-atoms takes places into the entire end of the standing MWNTs. For this reason, the diffusion region of the electrode-atoms forms the other nanotubelike structure on the top end of MWNTs (Fig. 12f). In fact, we confirmed that our sample clearly exhibited the diffusion of Au atoms, deposited as an electrode material, into the top end of MWNT, in [81]. Figure 13 shows typical MR oscillation characteristics observed in the samples with four different electrode materials. In this work, we measured a large number of MWNTs in one array sample at the same time. However, although this smears MR oscillation in some cases, we assumed that the observed characteristics were the simple superposition of the characteristic of each MWNT from the following three reasons: (1) The uniformity of the tube diameter was extremely high (e.g., half-width of distribution was less than 13). (2) The spacing between the MWNTs was relatively large. (3) According to [53], the characteristics of the individual MWNTs and the MWNT arrays fabricated by this method were basically consistent.

(a)

SE

(b)

25–Nov–02

WD 4.9 mm 15.0 kV x35 k

1 µm

25–Nov–02

WD 4.9 mm 15.0 kV x80 k 500 nm

(c) (d)

SE 19–Nov–02 WD 4.6 mm 15.0 kV x100 k 500 nm SE

25–Nov–02

WD 4.9 mm 15.0 kV x45 k

1 µm

(e) Ferromagnetic catalysts (cobalt, nickel)

C2H2+N2

alumina membrane

Al

MWNT

(f) Each pore

Electrode

Diffusion region Multiwalled Carbon nanotube

B Porous Alumina membrane V 10 µm 60 nm

(g)

Number of the MWNTs

of a resistance maximum and a negative magnetoresistance (MR) around zero-magnetic field reflect WL in the AAS oscillations [48]. Previous works on MWNTs reported only this type of AAS oscillation. On the other hand, the presence of a strong spin–orbit interaction (SOI) in thin metallic cylinders formed by heavy mass atoms leads to antilocalization (AL), reflected by a resistance minimum and a positive MR around zero-magnetic field, in the AAS oscillations [49]. This is because the SOI causes electron-spin flipping, thereby leading to change of the electron phase by 9 [50– 52]. No group, however, has yet successfully observed this electron-spin flipping and AL in the AAS oscillations in MWNTs. In this chapter we find that diffusion of heavy-mass atoms, deposited onto the top end of MWNT electrodes with only about 5% in volume-ratio drastically changes this WL to AL in the bulk of the MWNTs. Based on a revised Altshuler’s theory, we show that SOI, depending on the diffused atom mass and the diffusion volume-ratio, is the key for understanding the WL to AL change. We find that this phenomenon is observable only when electrons are injected through the diffusion region and is understood as spin flipping of electron waves (i.e., phase shift by 9), caused by SOI in the diffusion region of the bulk of MWNTs.

Mesoscopic Phenomena in Nanotubes

18 16 14 12 10 8 6 4 2 0

4

5

Al Substrate

6

7

Diffusion volume-ratio(%) Figure 12. (a) SEM overview image of the exposed top part of a MWNT array, exhibiting a high regularity like a honeycomb. (b) High resolution image of (a). (c) SEM top view of (b), implying the opened top portion. (d) SEM image of one MWNT. (e) How to synthesize MWNTs in nanopores of alumina membrane by chemical vapor deposition. (f) Schematic cross-section of the MWNT array sample for this section. Thin tunnel barriers attached to the bottom end of MWNTs, used for Section 3, were basically deleted in the experiments of this section. Hence, MWNTs have direct contact to Al substrate. (g) Distribution of the diffusion volume ratio of Au electrode, obtained from CSTEM images of one array. The total number of MWNTs investigated is 41. Reprinted with permission from [81], J. Haruyama et al., Phys. Rev. B 65, 33402 (2002). © 2002, American Physical Society.

307

(a) 80

(b) 66

Carbon electrode

R0 [arb.unit]

R0 [arb.unit]

78 76 74

70 0.0

0.5

1.0

62 60

56 0.0

1.5

0 .5

1.0

(d)

A

48

56 A 54 52 0

Au electrode

R0 [arb.unit]

R0 [arb.unit]

B

B

B

46

Magnetic field : B [T]

0

Normalized L / L′

(a) (a)

1

(b) 0 2

0

1 2 3 r –2 (10–3 × nm–2)

Diffusion ratio 10%

0.0

6

8

10

12

Diffusion ratio 3% Au

R0 [arb. unit] Au

4

Diffusion volume-ratio (%)

(d)

(c)

0.5 Magnetic field : B [T]

1.0

0.0

0.5

1.0

Magnetic field : B [T]

Figure 14. (a) MR oscillation period vs square of mean tube radii. Mean tube radii of the array samples are confirmed by TEM and SEM images. (b) Normalized L /L′ vs diffusion volume ratio of Au atom to the MWNT. Each L /L′ was obtained from the best data fitting to Figure 3c and d by Eqs. (15)–(18) and then normalized by that for line A of the Figure 2c sample with 5% ratio. (c) MR oscillation in the sample with the diffusion volume ratio two times higher than the Figure 2c sample. Dotted line means the calculation result from Eqs. (15)–(18). (d) That with the diffusion volume ratio 0.6 times smaller than the Figure 2c sample. The smaller oscillation period is due to the larger tube radius caused by the fabrication process to get the longer tune length. Reprinted with permission from [81], J. Haruyama et al., Phys. Rev. B 65, 33402 (2002). © 2002, American Physical Society.

diffusion region of our electrode materials is only about 5% of the volume-ratio in our MWNTs. Hence, one deals with a qualitatively different phenomenon from any previous observations in thin metallic film systems, although nothing of this kind has been reported in MWNT systems. In order to resolve this issue, we carry out a data fitting procedure based on Altshuler’s equations for AAS oscillations [48]. In [48], the equations for AAS oscillations including the contribution of SOI can be rewritten as

− 3/2Z% L′ H  + $ H  Z% L H  = ln L /ℓ + 2

A

42 A

2

1

44

40

1

2

Au contact

2

G = − e2 /9h 29r/Ls ) 1/2 + :Z% L H 

B

60 58

1.5

Magnetic field : B [T]

Magnetic field : B [T] (c) 62

Au contact

3

Al electrode

64

58

72

4

R0 [arb. unit]

Since Figure 13a exhibits the MR maximum at B = 0 T and negative MR, the localization type is WL. This is qualitatively consistent with the previous works on AAS oscillations in MWNTs. Figure 13b also exhibits a MR oscillation with WL, although the decrease of MR saturates around B = 05 T. On the contrary, the MR oscillations shown in Figure 13c and d clearly reveal the MR minimums at B = 0 T and positive MRs which imply the presence of AL, although the oscillations themselves are not clear in comparison with (a) and (b). The positive MR is in contradiction with previous works [38–42]. In order to confirm the correlation between the observed MR oscillations and the AAS effect, we investigated the dependence of the oscillation period, B, on the MWNT radius, r. Figure 14a shows the result, which is a linear B vs r −2 relation with the slope value of 25 × 10−16 (J S/C). This is quantitatively in good agreement with the relation B = h/2e/ 9r 2  given by the AAS oscillation theory, with h/2e/9 ∼ 65 × 10−16 . Next, we discuss the influence of the electrode materials on the type of localization observed in the AAS oscillations as suggested by the results in Figure 13. The atomic numbers of Pt and Au are 78 and 79, respectively, whereas those of C and Al are 6 and 13. This indicates that the emergence of WL or AL strongly depends on the mass of the electrode-material atoms. Since AL is observable only in the samples with heavy-mass electrode materials (Pt and Au), this is qualitatively consistent with the previous works on thin Mg and Li cylinders [48, 49], which emphasizes the contribution of SOI. However, it should be noticed that the

Oscillation period : δB [T]

Mesoscopic Phenomena in Nanotubes

0

 

(19)

k0 n 29r/L 

n=1

Pt electrode 1

× cos)29n @/ hc/2e 2

Magnetic field :B [T]

Figure 13. Dependence of magnetoresistance oscillations on the top electrode materials. Four samples with different electrode materials [i.e., (a) carbon, (b) aluminum, (c) gold, and (d) platinum] were measured. Magnetic field was applied parallel to the tube axis. We basically plot the three times measurement results at each magnetic field. Dashed and dotted lines are the calculation results by Eqs. (15)–(18). Reprinted with permission from [81], J. Haruyama et al., Phys. Rev. B 65, 33402 (2002). © 2002, American Physical Society.

(20)

1/L2 = 1/D0

(21)

2 1/L′2  = 1/L + 2/D0so

(22)

where Ls , :, L , and L′ in Eq. (19) are the tube length, the constant depending on electron–electron interaction, and the phase coherent length without and with SOI, respectively. ℓ k0 , and @ in Eq. (21) are the mean free path, the Macdonald function, and the magnetic flux (9r 2 H ), respectively. D 0 , and 0so in Eqs. (21) and (22) are the diffusion constant,

308 the relaxation time for inelastic scattering, and the relaxation time for SOI, respectively. Here, $ H  in Eq. (19) represents the increase or decrease of the mean value of conductance, depending on magnetic field H. We also neglected the contribution of magnetic field on L in Eq. (21). Equation (19) has very simple physical meaning: The first term related to Z% L H  basically represents the AAS oscillations without SOI (i.e., WL), whereas the second term with Z% L′ H  reveals the influence of SOI (i.e., AL) on the AAS oscillations, using Eq. (22). Equation (22) includes the term 1/D0so as the contribution of SOI. If SOI is very weak, 0so diverges to an infinite value and, hence, L /L′ becomes “1” because of (L /L′ 2 = 1 + 2 L2 /D0so , leading to WL. On the contrary, if 0so has a finite value, L /L′ becomes larger than “1” because of 2 L2 D0so > 0, leading to the increase of the oscillation amplitude of the second term of Eq. (19) and thus AL. Therefore, the contribution of 0so can be represented by L /L′ . We selected this L /L′ as the fitting parameter. As shown by the dashed line in Figure 13, the measurement and calculation results are in good agreement in all the samples. This is interpreted as strong evidence for AAS oscillations. The best fittings to Figure 13a and b give L /L′ = 1, assuming L = 10−5 m and : = 2. This strongly supports the absence of SOI and the presence of WL for the reason mentioned previously. In particular, the measurement and calculation results are in excellent agreement in Figure 13a. On the other hand, both Figure 13c and d are fitted by two independent oscillation modes depending on magnetic field (i.e., bimodal behavior) as shown by lines A and B, assuming finite values for 0so . Compared with the value of L /L′ of the carbon electrode sample, the best fittings give L /L′ = 918 and L /L′ = 93 for lines A and B in Figure 13c and L /L′ = 928 and L /L′ = 94 for lines A and B in Figure 13d, respectively. These values of L /L′ ∼ 9 (>1) are strong evidence for the contribution of SOI and, hence, the emergence of AL, also for the reason explained. The comment for the bimodal behavior is mentioned in the later part of this chapter. The central issue of this chapter is the physical relevance of L /L′ , as obtained from the best fit shown in Figure 13, because Eqs. (19)–(22) do not relate to actual material parameters. Two facts make it possible to physically identify this L /L′ : There is a correlation (1) with the atomic numbers of the electrode materials (i.e., mass of the atoms) and (2) also with the volume-ratio of the diffusion region to the MWNT. From the viewpoint of correlation (1), the atomic numbers (Z) of C and Pt are 6 and 78. Reference [48] indicates that 0 /0so is given by 3L2 /ℓa aZ4 , where a is the fine structure constant (≈1/137). In the case of carbon, 0 /0so can be estimated to be on the order of 10−6 in our system from this equation. This is nearly consistent with 0so =  (i.e., L /L′ = 1) obtained from the best fits in Figure 13a and b. In contrast, in the case of Pt, 0 /0so can be estimated to be on the order of 10−2 . This does not quantitatively agree with 0 /0so ≈ 5 estimated from L /L′ ≈ 10 obtained from the data fitting. In this case, only the increase of 0 /0so with the atomic number is in qualitative agreement. Hence, based only on [48], the physical meanings of L /L′ cannot be quantitatively identified from the atomic numbers.

Mesoscopic Phenomena in Nanotubes

In order to clarify correlation (2), we varied the diffusion volume-ratio by changing the MWNT length with a constant diffusion length in the same electrode-material samples. L /L′ was obtained from the best fit of the experimental data in Figure 14c and d by Eqs. (19)–(22) by identifying each MWNT length with LS in Eq. (19). As shown in Figure 14b, the relation between the L /L′ values and the diffusion volume-ratio is mostly linear. This is the strong evidence that factor (2) is the key to determine L /L′ (i.e., the contribution of SOI) and L /L′ has a correlation with actual systems. It implies that the contribution of SOI to AL is linearly proportional to the volume-ratio of the diffused Au atom. Consequently, the diffusion of heavy-mass atoms, deposited as the electrode materials on MWNTs, at only about 5% in volume-ratio can drastically change WL to AL in the bulk of NTs. This can be shown by a phase shift of the electron waves by 9, caused by spin flipping due to SOI in the diffusion region of MWNT bulk. However, which conjugated conditions are formed between the atom of Au or Pt and the carbon nanotube by annealing and how it leads to SOI is still an open question. Further investigation is indispensable to clarify this issue. Based on the linear relation mentioned, the bimodal behaviors and the two different L /L′ values obtained in Figure 13c and d suggest the presence of two different distribution peaks in the diffusion volume of Au and Pt atoms in one array sample. The equal ratio of L /L′ from line B to line A (∼1013) in both (c) and (d) also supports this conclusion. As a confirmation, we exactly investigated the distribution of diffusion volume-ratio in an array. As shown in Figure 12d, we could actually find two peaks at 4.9% and 5.1% of the volume-ratio. Since the ratio of 5.1%/4.9% is 1.041, this is nearly consistent with the L /L′ ratio between lines A and B (∼1013). However, the reason they independently emerge in the different magnetic-field regions is still unclear. Finally, we show why such a small diffusion region only at the one end of MWNT drastically changes the phase interference in the bulk of MWNT. Figure 15a shows MR oscillations when electrons are injected into the MWNTs from either the Au electrode or Al substrate. It reveals a polarity of AL and WL; that is, only when electrons are injected through the Au diffusion region does a positive MR (i.e., AL) emerge. This strongly supports the contribution of SOI caused in the diffusion region. As shown in Figure 15b, when the electrons are injected through the Au diffusion region, the electron phases are spin-flipped by the strong SOI right after the injection, and then they cause phase interference. Since the spin coherence is strongly conserved in all the phase interference paths of electron waves encircling the MWNT [44], it leads to the AL in the bulk of the MWNTs. In contrast, when the electrons are injected from the Al substrate, they are spin-flipped in the diffusion region, after most of the interference procedure is completed (i.e., after the interference paths were already closed) as shown in (b). Such electrons no longer contribute to the phase interference. These phenomena are the direct evidence of the important role played by the small diffusion region in the phase interference in the bulk of the MWNTs. For the application of this effect, we propose a phase switching device like a CMOS circuit, as shown in Figure 16.

309

Mesoscopic Phenomena in Nanotubes (a)

VDD

VDD

from Au-diffusion region

Magnetic Resistance [aub. unit]

field

NT1

ON

current

OFF

Vout

Vout NT2

0

1 from Al substrate 0

1

OFF 2

Magnetic field [T] (b)

Electron injection

Au diffusion

current

ON

Au diffusion region

Phase interference path

Al substrate

Figure 15. (a) MR features when electrons are injected from different electrode sides. Open and filled symbols are the MRs for the electron injection from the Al substrate and the Au electrode, respectively. (b) Schematic figures of MWNTs with the phase interference path, encircling the MWNT, for AAS oscillations and the direction of electron injection. Left and right figures mean the electron injections from the Au diffusion region and Al substrate sides, respectively.

When magnetic field is applied, WL is destroyed in the MWNT1 leading to high conductance, whereas AL is destroyed in the MWNT2 leading to low conductance. Hence, the current flows from VDD to Vout and, hence, Vout becomes “1” as shown in the left figure. In contrast, when magnetic field is not applied, MWNT1 and MWNT2 show WL and AL, respectively. Hence, no current flows between VDD and Vout . It makes the potential difference between earth and Vout equal and, hence, Vout becomes “0.” This is a quite novel electron-phase switching device, although detailed adjustment of the resistances of MWNTs is of course required.

4.1.2. Anomalous Spin Interference Due to Excess Cobalt Catalyst and Strong Spin Coherence Introduction We report on the sensitivity of localization effects, identified in conductance (G) versus logarithmic temperature (log [T ]) relations (G vs log [T ] relations) and

With magnetic field

No magnetic field

Figure 16. Novel electron-phase switching device utilizing the effect found here. MWNT1 is a general MWNT, exhibiting WL under no magnetic field. MWNT2 is our MWNT with an Au diffusion region, exhibiting AL under no magnetic field. Reprinted with permission from [81], J. Haruyama et al., Phys. Rev. B 65, 33402 (2002). © 2002, American Physical Society.

in MR oscillations, to excess volume of a cobalt catalyst in MWNTs synthesized in nanoporous alumina membranes. These localization effects bring about the following anomalies in bulk MWNTs. (1) A slight increase in the volume of excess cobalt changes AL to WL both in MR oscillations and in the G vs log [T ] relation. (2) A further increase in excess changes this WL back to the AL, but only in MR oscillation. (3) Even under this AL in MR, neither AL nor WL can be observed in the G vs log [T ] relation. We carry out data fitting to the MR oscillations by a revised formula for Altshuler–Aronov–Spivak oscillation and find a drastic change of phase coherence length depending on the excess cobalt deposition time. We also carefully observe each MWNT by high resolution cross-sectional transmission electron microscopy and find unique MWNT structures with cobalt particles and wire. Based on these, we propose interpretation for the anomalies. We interpret the first anomaly by the odd-time spin flip due to the cobalt particles remaining in MWNTs and spin polarization due to the short cobalt wires formed at the bottoms of MWNTs; these particles and wires are yielded by the slight increase in excess cobalt. The second and third anomalies are also interpreted by thick and highly disordered MWNT shells, which surround cobalt particle arrays. This is yielded by a further increase of the amount of cobalt. These phenomena can be basically universal in MWNTs that are synthesized by excess ferromagnetic catalysts, by virtue of the strong spin coherence. Carbon nanotubes (CN), single-level molecular conductors, are attracting much attention, because they exhibit

310 unique quantum-mesoscopic phenomena and provide a variety of applications to novel molecular-quantum devices. It is well known that such quantum phenomena are very sensitive to the presence of impurities and defects in CNs. Here, one method of synthesizing CNs is a catalytic process of chemical vapor deposition using ferromagnetic catalysts (e.g., cobalt, nickel, and iron) [54]. Because these ferromagnetic catalysts remain in CNs even after synthesis under excess catalyst volume, it is of core importance to clarify how the excess volume of ferromagnetic catalysts contributes to changes in the physical characteristics of CNs. Excess volume of the ferromagnetic catalysts affects CNs in at least two aspects: (1) During synthesis, excess volume changes CN structures, leading to changes in their physical characteristics, (2). After synthesis, excess volumes remaining in CNs are magnetic impurities, which change the physical characteristics of CNs. No work has been reported on the first of these aspects, whereas the second aspect, the influence of magnetic impurities, has been studied in both single-walled CNs and multiwalled CNs, as follows. The influence of magnetic impurities in SWNTs has been studied mainly through electron spin resonance [55, 56]. Even a small concentration of magnetic impurities can relax the conducting electrons very efficiently [55], because SWNTs have a large carrier mean free path and a large spin diffusion length, like one-dimensional conductors. Spins and phases of electron waves in this ballistic regime are very sensitive to magnetic impurities. In addition, recently even a novel Kondo effect was reported, in which a SWNT serves as a one-dimensional host for conducting electrons, with magnetic clusters including a localized spin [56]. In contrast, the influence of magnetic impurities in MWNTs has been interpreted to be the origin of dephasing for quantum electron waves, as follows. The electrical properties of MWNTs are basically understood by the phase interference of quantum electron waves in the diffusive regime [54]. A typical example of such a phenomenon is a 2D WL, a constructive phase interference of electron waves. In thin metallic film and 2D electron gas systems, the conductance of 2D WL exhibits linearly logarithmic temperature (log[T ]) dependence with a saturation region forming at low temperatures. The Log [T ]-dependent region is a manifestation of decoherence by electron–phonon scattering, whereas the saturation region implies decoherence by spin-flip scattering due to magnetic impurities. Also in MWNTs, the conductance (G) vs log [T ] relation has exhibited such 2D WL behavior [57, 59–61], although the linear G vs log [T ] relation survived at higher temperatures. The influence of magnetic impurities on the electrical properties of MWNTs has been reported in regards only to this decoherence for spin relaxation. For our MWNTs utilizing cobalt catalysts, we also reported previously that the transition temperature, Tc , between the linear G vs log [T ] and its saturation regions was higher than the transition temperatures, Tc′ , in thin metallic-film samples: about Tc ∼ 6 K versus, for example, Tc′ ∼ 1 K [59–61]. However, no researchers have clarified how increases in the volume of excess cobalt change such phase interference phenomena in MWNTs. In this work, we reveal for the first time that phase interference, identified by G vs log[T ] relations and magnetoresistance oscillations, is very sensitive to

Mesoscopic Phenomena in Nanotubes

increases in excess cobalt catalysts, based on our previous discovery of antilocalization in our MWNTs [64]. We find three anomalies in this sensitivity, and we interpret them in terms of correlation of AL and WL with complicated MWNT structures, observed by TEM (e.g., cobalt particles remaining in the MWNTs, short cobalt nanowires at the bottoms of the MWNTs, and thick and highly disordered MWNT shells), yielded by the excess cobalt catalyst. Experimental Results and Discussion Sample Structures and Measurement Methods Figure 17a shows the schematic cross section of our MWNT array synthesized into nanopores of an alumina membrane. After the membrane was formed by anodizing an aluminum substrate, a cobalt catalyst was electrochemically deposited (a)

Each pore

Diffusion region

Au electrode

Multi-walled Carbon nanotube

B

Porous Alumina membrane

Cobalt catalyst

V 10 µm

(b)

Spin flow

60 nm

Au diffusion (SOI) region

Al Substrate

(c) Current flow

SOI-flipped spins Spins flipped by cobalt particles

Cobalt particle AAS interference

Cobalt wire Polarized spins

Cobalt particle array

L

Thick and disordered MWNT shells

Figure 17. (a) Schematic cross-section of an MWNT array synthesized into nanopores of porous alumina membranes. We prepared three samples with three different times for cobalt deposition (i.e., 30, 120, and 360 seconds for samples 1, 2, and 3, respectively). The deposition time of 30 seconds corresponds to the optimal cobalt volume, whereas 120 and 360 seconds lead to the slightly and highly excess cobalt volumes, respectively. (b) Schematic cross-sectional model of the MWNT with the cobalt particles and the short cobalt nanowire accumulated at the bottom of the MWNT. This explains the first anomaly in this work. This model was obtained from the observation of high resolution cross-sectional TEM images (Fig. 20a–c), and the increase of spin scattering due to magnetic impurities obtained from the drastic decrease in L (change from Figure 19a to b in Table 1). Slight increase of excess cobalt catalyst yields this original structure. (c) Schematic cross-sectional model of the MWNT with thick and disordered shells surrounding a cobalt particle array. This explains the second and third anomalies. This model was obtained from a TEM image (Fig. 20c), the increase in L (change from Fig. 19b to c in Table 1), and the decrease in Tc (change from Figs. 18b to c). High increase of excess cobalt catalyst leads to this original structure. Reprinted with permission from [81], J. Haruyama et al., Phys. Rev. B 65, 33402 (2002). © 2002, American Physical Society.

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into the bottom of the nanopores at three different times. As we explain later, the deposition time of 30 seconds is around the optimal point for our parameters of alumina membranes. Hence, 120 and 360 seconds led to the excess deposition times. With this cobalt catalyst, MWNTs were synthesized by chemical vapor deposition of C2 H2 and N2 gases. Although we measured the physical properties of MWNTs as averaging about 103 in the array, it was already confirmed in [65] that the averaged properties of such arrays were mostly the same as those of individual MWNTs because of the extremely high uniformity of the nanostructure parameters of this alumina membrane. It also turned out that even averaged measurement results could exhibit unique quantum-mesoscopic phenomena (see [59, 61–64]).

G0 40

40

30

30

#2 3

2

Log [T]

20

#1 t = 30 S

10

G0 [K Ohm]

zero-bias conductance : G0 [K Ohm]

Relationship between Conductance vs log [T ] and Excess Cobalt Volume Figure 18 shows the dependence of the zero-bias conductance (G0 vs log [T ] relation on the volume of cobalt catalyst in the samples with three different cobalt deposition times. The data reveal drastic changes in the G0 vs log [T ] relation, depending strongly on the deposition time. Figure 18a and its inset exhibit a slight decrease of G0 as the temperature increases (i.e., negative G0 behavior) up to T = 2 K. In contrast, Figure 18b, in which the cobalt deposition time was slightly increased, surprisingly implies that this decrease of G0 disappears and only a saturation region (flatness) emerges at the lowest temperatures. The further increase of the cobalt deposition time interestingly leads to the elimination of this saturation region (Fig. 18c). Even negative G0 behavior, like that shown in

t = 120 S

20 10

(b)

(a) 0

0 1

10

Log [T] (K)

1

10

Log [T] (K)

40

G0 [K Ohm]

#3 30

t = 360 S

20 10

(c) 0 1

10

Log [T] (K) Figure 18. Dependence of zero-bias conductance (G0 ) vs logarithmic temperature (log[T ]) relation on the three different cobalt deposition times. (a), (b), and (c) correspond to the optimized cobalt volume, the slightly excess cobalt volume, and the highly excess cobalt volume, respectively. Solid lines are the calculation results by 2D weaklocalization formula for MWNTs [Eq. (19)]. Reprinted with permission from [81], J. Haruyama et al., Phys. Rev. B 65, 33402 (2002). © 2002, American Physical Society.

Figure 18a, is unobservable. At almost all of the temperatures measured, only a linear and positive G0 vs log [T ] relation appears. The characteristics in Figure 18 can be understood as follows. Figure 18a results from the presence of AL, a destructive phase interference phenomenon, which we reported previously [64]. In that study, we revealed that the golddiffusion region at the top end of our MWNTs had SOI and the spins flipped by this SOI were injected into the bulk MWNT (Figs. 17a and b), leading to the phase shift by 9 and, hence, the AL [64]. In this AL regime, decoherence due to the increased temperature leads to a negative G0 vs log [T ] relation because the destructive interference is eliminated. In contrast, qualitatively Figure 18b means the emergence of 2D WL, consistent with previous reports on MWNTs [57], with magnetic-impurity (spin-flip) scattering at low temperatures as mentioned in the Introduction. Quantitatively, the relation was well fitted by the formula of 2D WL, as shown by the solid line in Figure 18b [59], G T  = G 0 + e2 /9h n9d/L ln)1 + T /Tc B 0s p  (23) where n, p, d, L, and 0s are the number of shells, the parameter for dominant inelastic scattering, the diameter of the inner shell of the MWNT, the length of the MWNT, and the relaxation time of spin-flip scattering due to magnetic impurities, respectively. The contribution of the number of MWNTs is taken into account by the term G 0. The good agreement between the data and calculation in Figure 18b supports presence of 2D WL. The best fitting to the experimental result gives Tc = 54 K, using n = 18, p = 21, d = 50 nm, and L = 10 mm. This Tc as high as 5.4 K actually implies the presence of strong spin-flip scattering by magnetic impurities. In contrast, the best fitting to Figure 18c gives Tc as low as 1.7 K, which actually emphasizes a mostly linear G0 vs log[T ] relation in the measured temperature range down to T = 15 K. Relationship between Magnetoresistance Oscillations and Volume of Excess Cobalt In order to confirm these AL and 2D WL, we measured the MRs in the sample in each figure. Figure 19 shows the results. Figure 19a exhibits a positive MR around B = 0 T. This is actually consistent with decoherence in the AL regime shown in Figure 18a, with the bimodal oscillations (i.e., large- and small-magnitude oscillations, depending on the magnetic fields), as we already reported in [64]. In contrast, a negative MR surprisingly emerges around B = 0 T in Figure 19b. This is also consistent with the 2D WL regime shown in Figure 18b. We performed data-fitting for Figure 19a and b by the revised Altshuler’s formula for AAS oscillation [64], G = − e2 /9h 29r/Ls ) 1/2 + :Z% L H  − 3/2Z% L′ H  + $ H  Z% L H  = ln L /ℓ + 2

 

(24)

k0 n 29r/L 

n=1

× cos)29n @/ hc/2e

(25)

1/L2 = 1/D0

(26)

1/L2

(27)

1/L′2 

=

+ 2/D0so

Mesoscopic Phenomena in Nanotubes

(a)

(b)

A

t = 120 S

#1 #2

R0 [a.u.]

Zero-bias resistance : R0 [a.u.]

312

B

B

A t = 30 S 0

1

2

0.0

Magnetic field : B [T]

0.5

1.0

Magnetic field: B [T]

(c)

B #3

R0 [a.u.]

AL or WL. Since this is represented by L /L′ , we selected this L /L′ as the fitting parameter. The results are shown in each figure by the solid and dotted lines. The agreement between data and theory is good in each figure also for the bimodal oscillation modes (i.e., large- and small-magnitude oscillations, depending on the magnetic fields, as we reported in [11]). This bimodal behavior means the presence of two different L /L′ . Because L /L′ depended on the diffusion volume of gold atoms (Figure 20a), we clarified that this bimodal behavior was attributable to the presence of two distribution peak of this gold diffusion volume in one array. The best fitting to the

Cobalt particles B

B A A A

0.0

t = 360 S 0.5

Cobalt wires

1.0

Magnetic field: B [T] Figure 19. Dependence of magnetoresistance features, corresponding to each figure in Figure 18. A magnetic field was applied in parallel with the tube axis. Lines A and B in (a) and (c) and the dotted line in (b) are the calculation results by the revised formula of Altshuler–Aronov– Spivak oscillation with and without spin–orbit interaction, respectively [Eqs. (20)–(23)]. Different oscillation periods in (a), (b), and (c) are due to the different tube diameters caused during the anodization procedure. They were also taken into account for the data fitting. Reprinted with permission from [81], J. Haruyama et al., Phys. Rev. B 65, 33402 (2002). © 2002, American Physical Society.

10 nm

(a)

150 nm

(b)

Cobalt particles

Shells

where Ls : L , and L′ in Eq. (24) are the tube length, the constant depending on electron–electron interaction, and the phase coherent length without and with SOI, respectively. ℓ, k0 , and @ in Eq. (25) are the mean free path, the Macdonald function, the magnetic flux (9r 2 H ), respectively. D 0 , and 0so in Eqs. (26) and (27) are the diffusion constant, the relaxation time for inelastic scattering, and the relaxation time for SOI, respectively. Here, $ H  in Eq. (24) represents the increase or decrease of the mean value of conductance, depending on magnetic field H . We also neglected the contribution of magnetic field on L in Eq. (26). Equation (24) has a very simple physical meaning: The first term related to Z% L H  basically represents the AAS oscillations without SOI (i.e., WL), whereas the second term with Z% L′ H  reveals the influence of SOI (i.e., AL) on the AAS oscillations, using eq. (27). Equation (27) includes the term 1/D0so as the contribution of SOI. If SOI is very weak, 0so diverges to an infinite value and, hence, L /L′ becomes “1” because of (L /L′ 2 = 1 + 2 L2 /D0so , leading to WL. On the contrary, if 0so has a finite value, L /L′ becomes larger than “1” because of 2 L2 /D0so > 0, leading to the increase of the oscillation amplitude of the second term of Eq. (24) and thus AL. Therefore, whether 0so has infinite or finite values can decide emergence of either

20 nm

(c)

Figure 20. Typical high-resolution cross-sectional TEM images of each MWNT. (a) Example of a cobalt particle, without any shells, included in the MWNTs of the samples in Figures 18b and 19b. This sample includes high density of such particles. (b) Short cobalt wires formed at the bottom of MWNTs of the samples in Figures 18b and 19b. This is formed by accumulation of cobalt catalyst at the bottom of a nanopore of alumina membrane and has no diffusion during the synthesis. (c) Cobalt particle arrays surrounded by the disordered and thick shells in the samples in Figures 18c and 19c. Highly disordered shell structures (i.e., coffee-cup structures), which originated from the cobalt particle array, are also observable. Highly excess cobalt catalyst leads to this unique structure. (d) General shell structures of our MWNT, with about 36 shells, observable in the samples in Figures 18b and 19b. Reprinted with permission from [81], J. Haruyama et al., Phys. Rev. B 65, 33402 (2002). © 2002, American Physical Society.

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Mesoscopic Phenomena in Nanotubes

line A in Figure 19a gives “L = 102 .m” and L′ = 11 .m, respectively. Because L /L′ > 1, this means the finite value of 0so and hence quantitatively supports the presence of strong SOI and AL in Figure 18a. In contrast, the best fitting to Figure 19b actually gives “L = 013 .m” and “L′ = 102 .m.” In this case, L drastically decreases for reasons explained in the next section (d), whereas L′ (i.e., the strength of the SOI) is nearly equal to that of Figure 19a. This decrease of L leads to L /L′ ∼ 1 under a constant 0so , because (L /L′ 2 = 1 + 2 L2 /D0so . This L /L′ ∼ 1 is also consistent with the presence of 2D WL. In Figure 19c, a positive MR emerges again with the bimodal oscillations. The best fitting to line A gives “L = 82 .m” and L′ = 075 .m, implying the presence of AL, similar to Figure 19a. L increased again nearly up to the value found in Figure 19a under mostly the same L′ as that in Figure 19b and we explain why in the next section. It should be noticed, however, that this is not consistent with the linear G0 vs log[T ] relation shown in Figure 18c, because AL should exhibit a negative G0 vs log [T ] relation like Figure 18a. Consequently, Figure 18 and 19 imply that G0 vs log [T ] relations and MRs (i.e., AL and WL) are very sensitive to the excess cobalt-deposition time (i.e., the volume of excess cobalt). We find the following three anomalies in these results. (1) A slight increase in the excess cobalt volume causes a transition from the AL to the 2D WL, in both the G0 vs log [T ] relations and the MRs [i.e., from (a) to (b) in Figure 18 and 19]. (2) A further increase changes this WL back to the AL only in the MRs (Fig. 19c). (3) Despite that, AL is unobservable in the G0 vs log [T ] dependence (Fig. 18c), exhibiting only the linear log [T ] relation. Proposal of the Models for the Three Anomalies What is the origin for these anomalies? In Table 1, we show the summary of the fitting parameters obtained from the best fit to each of Figure 19 and the density of cobalt particles, confirmed by high resolution cross sectional TEM (HRCSTEM) images, in each MWNT corresponding to Figure 19. As we explained, we note that only L changes drastically depending on the deposition time of cobalt catalyst, whereas L′ is mostly constant. In general, 1/L2 is given by 1/D0in + 2/D0s = 1/L2in + 2/L2s , where 0in is the relaxation times for inelastic scattering, when decoherence due to electron– electron interaction is neglected (e.g., at temperatures above T = 15 K). We can propose models as the origins for the anomalies, based on these. In the first anomaly, L decreased drastically and we confirmed the increase of cobalt density in the MWNT by the HRCSTEM image (Fig. 20a). Because no change was

found in the MWNT shell structure at least by the HRCSTEM image (Fig. 20d, i.e., no change in disorder of the MWNT), we have no reason for the change in Lin . Hence, the decrease of L can be due to the decrease of Ls . This Ls decrease and the increased density of cobalt particles strongly suggest that the spin-flip scattering by the cobalt particles is the main reason for the first anomaly. Based on this, we propose a model representable by Figure 17b. In the second anomaly, L increased drastically, whereas we found that the density of cobalt particles also increased further, leading to the arrays of cobalt particles (Fig. 20c), by HRCSTEM. These are not consistent. Besides, we also found the highly disordered shells of the MWNT by the HRTEM (Fig. 20c). This can bring strong electron–phonon interaction and hence decrease of Lin . This is also not consistent with the increase of L . We found, however, that the cobalt particle arrays were surprisingly surrounded by the thick shells, by the HRCSTEM (Fig. 20c). If the current flows along the outer part of these thick MWNT shells, this large thickness reduces the influence of the spin scattering due to the cobalt particles, leading to the increase of L . We propose a model explainable by Figure 17c, based on this. The third anomaly is at least strongly associated with the strong disorder of the thick MWNT shells mentioned (Fig. 20c), because the linear G0 vs log [T ] relation implies the presence of strong electron–phonon interaction caused by the disordered structure. We also propose an interpretation based on Figure 17c. Relationship among the First Anomaly, Cobalt Particles, and Short Cobalt Wires The AL observable in Figures 18a and 19a was attributed to the polarized injection of the spins, flipped by SOI in the gold-diffusion region at the top end of the MWNTs, into the bulk of MWNTs as we reported in [64]. Since the flipped spins led to the phase shift of electron waves by 9 in the bulk MWNTs, the WL in the bulk MWNTs changed to the AL. This phase shift and AL are well represented by the negative G0 vs log [T ] regime at low temperatures and the positive MR in Figures 18a and 19a, respectively. This AL was caused when the volume of the cobalt catalyst was optimal, because no cobalt particles could be detected in the bulk MWNTs. However, when the volume of excess cobalt is increased slightly, the cobalt particles easily remain in the bulk MWNT even after the synthesis. We explain the first anomaly, based on Figure 17b, taking into consideration these cobalt particles, as we implied. In general, this influence may lead to simply random flipping and the decoherence of these spins and hence to the elimination of both the negative G0 vs log [T ] relation and

Table 1. Relation of deposition time of the cobalt catalyst vs magnetoresistance oscillation behavior, confirmed from Figure 19, around zero magnetic field. Phase coherence length without (L ) and with (L′ ) spin–orbit interaction obtained from the best fit in Figure 19. Those ratios and density of cobalt particles confirmed by high resolution cross-sectional TEM image of each sample for Figure 3 (see Fig. 20), in MWNT after the synthesis. Cobalt deposition time 30 S (Fig. 3a) 120 S (Fig. 3b) 360 S (Fig. 3c)

MR (at B = 0)

L

L′

L /L′ )

Averaged density of cobalt particles in a MWNT

positive [AL] negative [WL] positive [AL]

102 013 82

11 102 075

927 013 109

∼0 27 55 [particle array]

Source: Reprinted with permission from [81], J. Haruyama et al., Phys. Rev. B 65, 33402 (2002). © 2002, American Physical Society.

314 the positive MR (i.e., elimination of the AL). This scenario does not agree with Figures 18b and 19b. Here, if the spin, flipped by the SOI at the top of MWNT, is flipped by these cobalt particles in the nth time (here, n should be the odd integer) during flowing through the MWNT before AAS interference occurs, the interference is caused by this flipped spin with opposite moment (Fig. 17b). Because this leads to phase shift by 9 in the AAS interference, this changes the AL to the WL. These flipped spins, however, have fluctuation. Here, HRCSTEM detected the presence of cobalt wire as short as about 300 nm at the bottom end of the MWNTs in sample 2 (Fig. 20b). This wire was yielded by an accumulation of excess cobalt catalyst at the bottom part of the nanopores of the alumina membrane due to the excess deposition time, because such excess cobalt can no longer contribute to the growth of the MWNTs and no longer diffuse into the MWNTs as particles. After the AAS interference took place, such spins with fluctuation are injected into the short cobalt wire at the bottom end of the MWNT (Fig. 17b). If this cobalt nanowire plays a role of spin polarization for these spins, all such spins will be aligned reducing the fluctuation as they flow through the cobalt nanowire. This makes the magnitude of the WL increase. Consequently, the WL appears in Figures 18b and 19b, when the magnitude of this WL becomes dominant compared with that for the AL. In fact, it was reported that MWNTs connected to ferromagnetic electrodes exhibited strong spin polarization, characterized by strong spin coherence [63]. Besides, we confirmed that these phenomena could not be observed when electrons were injected from the Al substrate. Quantitatively, in this case, SOI length (Lso  ≥ spin scattering length (Ls ) must be satisfied, because the spin-flip scattering due to the cobalt particles has to beat the spin flipping by the SOI. Here, L in Figure 19b decreased remarkably from that in Figure 19a under the mostly constant L′ (see Table 1). This led to (L /L′ 2 = 1 + 2 L2 /D0so ∼ 1 and hence this WL. This change means (L2 / D0so  =

L /Lso 2 ∼ 0 and hence Lso ≥ L . As explained, this L decrease is due to the decrease of Ls . Therefore, Lso ≥ L implies presence of Lso ≥ Ls . This quantitatively supports our argument discussed. The high Tc of 5.4 K in Figure 18b supports this explanation, because Tc is the transition temperature for decoherence from the spin-flip scattering to the inelastic scattering regimes with increasing temperature. These structures, that is, the presence of ferromagnetic particles remaining in the MWNTs and ferromagnetic electrodes formed at the bottom ends of MWNTs, can be yielded in any MWNTs, when excess volume of a ferromagnetic catalyst is used. Therefore, this phenomenon can be universal in such MWNTs. The strong spin coherence, which cannot surprisingly be dephased even after the nth time flipping, of the MWNTs makes this spin interference phenomenon possible. Relationship between the Second and Third Anomalies and Thick and Disordered Shells of MWNTs The second anomaly is more complicated, because a further increase in excess of the cobalt volume seems merely to induce further spin-flip scattering, leading to stronger decoherence of the 2D WL and hence the destruction of MR

Mesoscopic Phenomena in Nanotubes

oscillation in Figure 19b. We also explain this anomaly based on Figure 16c, as we mentioned. In order to clarify the reason for this anomaly, we carefully observed, by HRCSTEM, the shell structures of the MWNTs around cobalt particles. In Figure 20c, we found the following. (1) There is a larger density of cobalt particles in the Figure 18c sample than in Figure 18b, and such cobalt particles were combined, in most cases, to cobaltparticle arrays. (2) Such cobalt-particle arrays were surrounded by the disordered and thick shells of the MWNTs. These structures can be yielded by a high increase in the excess volume of the cobalt catalyst, far from the optimal condition, because the growth of the MWNTs is very sensitive to the catalyst, especially in chemical vapor deposition. Here, quantum electron waves in our MWNTs flow along the outer portions of the shells [64]. Hence, these thick shells increase the distance (L) between the cobalt particles and the wave flow, reducing the influence of spin-flip scattering by the cobalt particle on phase coherence (Fig. 17c). This leads to the elimination of the 2D WL, because the origin for the 2D WL in Figure 19b was this spin-flip scattering. This in turn changes the WL back to the AL, similar to Figure 19a. This phenomenon can be also universal in MWNTs, when the excess volume of a catalyst is too high. Such unoptimized conditions easily lead to MWNTs with thick shells surrounding ferromagnetic catalysts. One should note that even such thick MWNTs can conserve strong spin coherence. In this case, L increased up to about 8.2 .m with mostly constant L′ , leading to L > L′ again (Table 1). This quantitatively supports the explanation mentioned, because only Ls can increase in this structure, along with decreased Lin as will be mentioned. In contrast, the third anomaly stresses decoherence by only strong electron–phonon scattering. The highly disordered shell structure observed in Figure 20c emphasizes the possible presence of strong electron–phonon scattering in this MWNT (i.e., a decrease in Lin ), leading to the elimination of AL. Besides, dephasing by the cobalt particles leading to the low temperature saturation in the WL is also reduced by the thick shells as mentioned. Therefore, only the lineal and positive G0 vs log [T ] relation can emerge (Fig. 18c). This behavior, however, can be consistent with the AL in MR (Fig. 19c) because of the following: (1) The positive MR in Figure 19c was yielded by decoherence of SOI due to the increase of magnetic field at the fixed temperature (T = 15 K), whereas the third anomaly is caused by decoherence of electron–phonon interaction due to the increase of temperature at the fixed magnetic field (B = 0). (2) Decoherence of SOI and electron–phonon scattering are very sensitive only to magnetic field and temperature, respectively. These second and third anomalies stress that the thick shell of MWNTs reduces the influence of spin-flip scattering due to the cobalt particles under the magneticfield change, but its disorder enhances the electron–phonon interaction under the temperature change. The coexistence of the second and third anomalies may be not universal, because it can be constructed only when there is a highly optimized balance among the thickness of MWNT shells, the strength of their disorder, and the location of

315

Mesoscopic Phenomena in Nanotubes

the cobalt particles in the MWNTs. Our system seems to occasionally have included such an optimized structure. Conclusion In conclusion, we found for the first time that the G0 vs log[T ] relation and MRs were very sensitive to the excess increase of cobalt-catalyst volume in MWNT arrays, synthesized in nanoporous alumina membranes. We found the following three anomalies in these results. (1) A slight increase in the excess cobalt volume caused a transition from the AL to the 2D WL, in both the G0 vs log[T ] relations and the MRs. (2) A further increase changed this WL back to the AL only in the MRs. (3) Despite that, AL was unobservable in the G0 vs log[T ] dependence, exhibiting only the linear log[T ] relation. We found drastic change of L in each anomaly, from the data fitting to the MR oscillations by revised AAS oscillation theory. We also performed careful observation of each MWNT by HRCSTEM and found the unique MWNT structures with the cobalt particles. We proposed interpretations for the anomalies, based on those. Based on the drastic decrease of L and the increased density of cobalt particles, we qualitatively attributed the first anomaly to the odd-time flipping of electron spins by the cobalt particles remaining in the MWNTs, leading to the phase shift by 9 and, hence, the change from AL to 2D WL. The polarization of those spins by the short cobalt wires, formed at the bottoms of the MWNTs, induced this. These structures resulted from the slightly excess cobalt volume. Quantitative comparison of change of Lso and Ls also supported this interpretation. We explained the second anomaly by the thick shell structures of the MWNTs, based on the increase of L . The thick shells eliminated the 2D WL by surrounding the cobalt particle array and reducing the spin scattering due to the cobalt particles by detaching the current flow along the outer portion of MWNTs from the cobalt particles. This led to the re-emergence of AL. In contrast, the disordered shells strongly enhanced the decoherence by electron–phonon scattering, leading to the linear G0 vs log[T ] down to T = 17 K. We qualitatively attributed this third anomaly to the different sensitivity of decoherence between magnetic field increases and temperature increases. For further quantitative confirmation, estimation of Ls from the G0 vs log[T ] relations will be at least indispensable. It has been already reported that diffusive SWNT rings can, interestingly, exhibit WL and AL together with strong localization, depending on the temperature[66]. We also reported that 2D WL in the bulk MWNT was changed to AL by doping gold and platinum on the top end of the MWNT[64]. On the other hand, this chapter implies the possibility that bulk MWNTs themselves can provide AL, 2D WL, and the switching between them. In any case, it is important to note that we can control these by changing the volume of excess ferromagnetic catalyst. We believe that these phenomena are basically universal in MWNTs with excess volume of ferromagnetic catalysts, because these are reproducible. Only the strong spin coherence of MWNTs can make these anomalous spin interference phenomena possible. These phenomena will be also very useful to realize novel spintronics and phase interference devices that utilize MWNT networks synthesized by ferromagnetic catalysts networks.

4.2. Superconductivity Proximity-Induced Superconductivity and Its Reentrance Effect in Niobium/Multiwalled Carbon Nanotube Junctions

4.2.1. Introduction We report on an experimental study of the diffusive transport near interface of niobium(Nb)/multiwalled carbon nanotube junctions. Utilizing MWNTs synthesized in nanopores of alumina membranes makes a highly transparent interface possible. On the magnetic-field dependence of observed conductance increase and the transition temperatures versus nanotube length diagram, we observe proximityinduced superconductivity with an onset temperature of T = 9 K at the highest case. We reveal that this conductance decreases due to its reentrance effect at low temperature. These phenomena are the manifestation of the extremely large diffusion constant of Cooper pairs in the MWNTs. The drastic magnetic-field dependence of the reentrant conductance supports the presence of a reentrance effect associated with the Altshuler-Aronov-Spivak effect. Superconductivity of carbon nanotube, a molecular conductor, is currently of great interest, because it was recently found that hole-doped C60 and magnesium diboride that have structures similar to CNs, exhibit hightemperature superconductivity. Until recently, only two groups had reported superconductivity in single-walled carbon nanotubes [67–69]. The first group claimed to have observed superconductivity at T = 15 K only from the Meissner effect without actually showing vanishing resistance [67]. The other group reported a transition temperature as low as T < 1 K in both proximity-induced and intrinsic superconductivity [68, 69]. However, no other group has been able to reproduce successfully these results. In fact, Morpurgo et al. attribute the absence of proximity-induced superconductivity in niobium(Nb)/SWNT/Nb junctions [70] to the following two reasons: (1) Because charge carriers in SWNTs behave as a Luttinger liquid due to the strong one-dimensional repulsive electron interaction, unusual phonon modes would be capable of producing Cooper pairs with attractive electron interaction [69, 70, 78–80]. (2) High transparency of the metal electrode/CNs interface is hard to achieve because of the misalignment between Fermi levels. Only electrodes made of titanium(Ti), carbide(C), silicon(Si)C, or NbC by a special technique [68, 69] meet this criterion, but Ti and Si are not superconductors. Consequently, only NbC is a suitable candidate for highly transparent superconductor/CN interfaces. In contrast, nobody has successfully reported superconductivity in multiwalled carbon nanotubes. Because MWNTs exclude the existence of Luttinger liquid (although this issue is debatable, we could not actually find any power law dependence in the conductance versus temperature and voltage characteristics of our samples), one can at least avoid the former handicap of SWNTs. In addition, it is well known that two-dimensional quantum electron waves generated from the molecular band in MWNTs have the longest phase coherence among many materials in the diffusive regime; therefore, it is crucial to show that Cooper pairs can exist with such strong phase coherence.

316 In this work, we for the first time, investigate “PIS” in Nb/MWNTs junctions. When the superconductor (S)/ normal conductor (N) interface is highly transparent, leakage of the Cooper pair wave function from the S into the N leads to PIS in the N. Recent experimental transport studies near a mesoscopic S/N interface (e.g., S/2D electron gas (2DEG)[71–73] and thin metal S/N junctions [74–77]), have revealed the presence of subtle physics implying the coexistence of Cooper pair wave functions with the 2D electron waves. In particular, the “reentrance effect” has attracted much attention. This effect emerges when the conductance enhancement due to PIS suddenly decreases at energy below the “Thouless energy (ETh )” that arises from the uncertainty between the diffusion time of Cooper pair and its energy fluctuation [76]. Furthermore, when an Aharonov– Bohm (AB) ring is inserted on the N channel of such S/N junctions, the AB flux causes drastic changes in the reentrance effect, simultaneously with modifications of the effective channel length and the Andreev reflection at the S/N mirrors [73–77]. How can such phenomena take place in S-electrode/ MWNT junction systems? In this chapter, we report the existence of PIS at a temperature of T = 9 K at the highest case and its reentrant effect from the magnetic-field dependence of conductance behaviors and the dependence of the transition temperatures on the nanotube length in a hightransparency Nb/MWNT junctions. This junction is realized by utilizing MWNTs synthesized into the nanopores of alumina membranes. Next, we show that two magnetic-field dependences strongly support the “reentrance effect connected to the AB trajectory,” with two anomalous behaviors.

4.2.2. Experiments and Discussion Here, in any case, the low-transparency interface of S/N junctions prevents PIS from occurring. Figure 21a and b shows the schematic views of an array of Nb/MWNTs (S/N) junctions and a single Nb/MWNT junction, respectively. After the synthesis of MWNTs into the nanopores of alumina membranes [81–83], we performed the preannealing. Then, the surface of alumina membrane was etched out so that the top portion of the MWNTs was exposed. Right after we evaporated Nb/gold film (in high vacuum with each 1 .m thickness, superconducting transition temperature of about 8.1–9 K, and critical magnetic field of about 1500 Gauss) on these top ends of MWNTs, we carried out the annealing in vacuum, again. Hence, the annealing changes only the boundary conditions of the Nb/MWNT interface. We found that annealing at 650  C for this structure led to high diffusion of Nb atoms into the top ends of all shells in MWNTs, due to the interface area being large enough for diffusion along the circumferential direction (Fig. 21b and d). Because this process leads to the generation of NbC (right panel of Fig. 21d), the interface became highly transparent. In contrast, we could not find any diffusion of Nb and the presence of NbC in the samples annealed at lower temperatures [150 (e) and 400  C]. The end-bonded MWNT also contributes to the high transparency [85]. We also showed that even the normal metal electrodes, slightly diffusing into the top ends of MWNTs, actually led to a drastic change of phase interference in the bulk of our MWNTs [81].

Mesoscopic Phenomena in Nanotubes

Nb

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Figure 21. The schematic cross-sections of (a) an array of Nb/MWNT junctions and (b) one Nb/MWNT (S/N) junction, synthesized into the nanopores of alumina membranes by chemical vapor deposition. The mean outer and inner diameters of MWNT are 100 and 60 nm, respectively, with the shell thickness of 20 nm. The half width of the distribution of the outer diameter is as small as about 15%. The shell structure proving the MWNT was already reported in [82]. Because this system is not a S/N/S junction, there is no Josephson contribution in the measurement results. Although we measured the average characteristics of Nb/MWNTs junctions with about 104 in one array, it was already confirmed that they could exhibit approximately the same quantum phenomena as those of an individual MWNT [81–83], due to the extremely high uniformity. (c) One of the general methods, much different from ours (b), used to provide electrical contact with the nanotube. It is difficult to provide high-transparency interface by this, because only half of the most outer shell along the circumferential direction has the interface with the electrode. (d) Left: High angle annular dark field image of cross-sectional TEM around the Nb/MWNT junction array [see (a)] annealed at 650  C, implying the high diffusion of Nb atoms. Right: High resolution CSTEM image of an Nb/MWNT interface. The gray regions blended by the white (MWNTs) and black (Nb) regions are clearly visible at the boundary, implying the presence of NbC with the lattice constant of 0.35 nm. (e) High resolution CSTEM image of an Nb/MWNTs interface annealed at 150  C, implying no gray region at the border between the MWNTs and Nb and hence the absence of NbC.

In the main panel of Figure 22a, we show the temperature dependences of zero-bias conductance (G0 ) in an Nb/MWNT array annealed at TAn = 650  C. We successfully find the gradual but obvious conductance increases with the onset transition temperature (Tpx of Tpx = 54 K under zero magnetic field (H = 0). In contrast, we note that this conductance starts to drop from T = 34 K (i.e, transition temperature for the conductance decrease, Tre = 34 K). The Tpx was shifted to lower temperature when a magnetic field (H ) was applied in the Nb electrode (i.e., perpendicular to the tube axis). The critical magnetic field (Hc ) for the disappearance of the conductance increase was about 1400 Gauss, which is mostly the same as Hc for the vanishing

317

Mesoscopic Phenomena in Nanotubes

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Figure 22. (a) Temperature dependences of zero-bias conductance (G0 ), in an Nb/MWNT array annealed at TAn = 650  C, measured for different values of the magnetic fields perpendicular to the MWNT axis. The labels on the curves correspond to the value of magnetic field in Gauss. The resistance of one MWNT with the interface resistance is around 100 K to 1 M at H = 0 Gauss, which is consistent with that of MWNTs with weak localization [81, 82]. Inset: The averaged tube length (Ltube  vs Tpx−1/2 relation obtained from the measurements of 10 samples, with different Ltube annealed at TAn = 650  C. The dotted linear line was obtained from the minimum square method. (b) Temperature dependences of conductance vs voltage relation, around the superconducting transition temperature of our Nb film, in an Nb/MWNTs array with Tpx = 35 K. Conductance dip is observable above T = 84 K, whereas this abruptly changes to the conductance peak at T = 82 K in a decrease of temperature. We qualitatively confirm that this conductance peak originates from the emerging Andreev reflection, due to the superconducting transition of Nb film, at the Nb/MWNT junction, because (1) T = 82 K mentioned previously is approximately near Tc of our Nb-film and (2) the voltage width of the conductance peak (∼12 meV) is nearly equal to the  of Nb (i.e., Nb ∼14 meV). (c) Transition temperature for reentrant conductance (Tre ) vs L−2 tube relation obtained from the six samples in the inset of (a). We could not find reentrant conductance in other four samples in (a). The dot and solid lines are calculation results from TTh =
D/kL2 = A/:2 /L2 with L = Ltube , A∼19 × 10−6 , and : as a fitting parameter.

superconducting transition of our Nb electrode film, in contradiction to [3]. The Tre also moved to lower temperature in H = 400 Gauss, and the conductance drop vanished above H = 800 Gauss. The conductance increase observable

mainly in the change from H = 0 to H = 400 Gauss at all the temperatures above T = 54 K is due to destruction of weak localization in the MWNTs [81], because this increase exhibited a linear and positive G0 vs log(H ) relation. We do not discuss this phenomenon in this chapter. These characteristics for the conductance increase and its H dependence are similar to the behavior of superconducting transition. However, conductance does not increase up to infinite value like in general superconducting transition, due to the conductance drop. Besides, each curve in Figure 22a is inhomogeneous on temperature change unlike in general conductance vs temperature relations. Hence, in order to confirm the correlation of this conductance increase with superconducting transition, we investigated dependence of Tpx on the MWNT length. We found that Tpx decreased with increasing the averaged MWNT length (Ltube ), following the linear Ltube vs Tpx−1/2 relation (i.e., “Ltube = A · Tpx−1/2 ,” where A is a coefficient constant) (inset of Fig. 22a). Besides, we found even Tpx as high as T = 9 K in the junction of Nb/MWNTs with Ltube = 06 .m. Importantly, this relation qualitatively agrees with the temperature dependence of LT [i.e., “LT =
D/kT 1/2 ,” where D is the diffusion constant]. This effect stresses that the “LT =
D/kT 1/2 ” relation becomes dominant in the MWNTs below Tpx . This is the straightforward evidence that the conductance increase below Tpx is strongly associated with the PIS caused by the Nb electrode. The conductance mechanism follows the smallest of the two parameters, LT or the phase coherence length (L% ). Because L% in our MWNTs is on the order of a few .m [81] around about T = 10 K, thereby implying L% > LT below about T = 10 K, we believe that this discussion is relevant. We understand that such a conductance increase was never observed in any of our MWNTs without superconductor electrodes, despite the fact that we measured over 300 samples. They just exhibited monotonic conductance decreases due to weak localization. Besides, one should note that even the highest Tpx ∼ 9 K observed is below the superconducting transition temperature (∼9.1 K) of our Nb film. This suggests a strong relation between the conductance increase with superconducting transition of Nb electrode and PIS. PIS can occur even at the N-channel length ≫ LT , leading only to the shrinkage of the normal conducting state length (e.g., by Maki–Thompson–Larkin fluctuations of the order parameters)[72]. However, this is not the case because the conductance increase does not exhibit strong dependence on the N-channel length. We already mentioned that (high-temperature) PIS requires high-transparency interface of S/N junction (see Fig. 21). In fact, we confirmed that the conductance increase in the main panel of Figure 22a is also very sensitive to the interface transparency of Nb/MWNT junctions, as follows. An Nb/MWNT array annealed at TAn = 150  C exhibited no conductance increase. This low-temperature annealing results in the low-transparency Nb/MWNTs interface due to absence of NbC by the poor diffusion of Nb into the MWNTs (see Fig. 21d and e). The interface resistance of the 150  C-annealed Nb/MWNT junction can be estimated to be at least 10 times larger than that in the 650  C-annealed sample. In addition, no current could be detected in the sample without annealing, indicating zero

318

MWNTs with lengths as short as 0.6 .m. We speculate that the high-transparency MWNTs/Al (N/N’) interface, the key for this reentrance effect, was also realized with the 650  C annealing, because this temperature is near both the melting point of Al and the synthesis temperature of MWNT. The Al atoms and MWNT are actively connected in such conditions. Nevertheless, the instability and reproducibility of this junction lead to the reproducibility of the reentrant conductance with 60% probability. The highest Tre = 45 K of the reentrance effect observed in this work is much higher than reported in the Nb/2DEG (Tre = 05 K) [72] and in the Al/Cu junctions (Tre = 60 mK)[74]. This is a manifestation of the extremely large diffusivity D = 037 m2 /s, estimated from the parameters A ∼ 19 × 10−6 and :2 = 135, in our MWNTs (e.g., D = 008 m2 /s at most, in the case of 2DEG and D = 0007 m2 /s in the Cu film), resulting in the strong phase coherence. The discovery of the reentrance effect surprisingly implies that the diffusion of Cooper pair even into MWNTs, consisting of 9 and 3 bands formed by sp2 - and sp3 -mixed orbitals, can lead to the reduction of NN E, which is qualitatively similar to that in Nb/2DEG and metal S/N junctions. We put emphasis on this reentrant conductance as the other evidence for PIS. However, it is interesting to notice that the strong phase coherence did not enhance the critical magnetic field for the vanishing PIS in our MWNTs (main panel in Fig. 22a). This is in contradiction to that in SWNT, which reported the 10 times larger critical field [69]. The magnetic-field dependence [the inset of Fig. 23a and the relation at @/@0′ = 1/2 (where @0′ = @0 /80 and @0 is 4

47

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transparency. Here, the abrupt onset of a conductance peak, which can be due to Andreev reflection (in which an incident electron coming from the N is converted into the Cooper pair in the S, leaving a reflected hole in the N, at the S/N junction [67, 84]), with decreasing temperature from T = 82 K (Fig. 22b) also supports the presence of this high-transparency interface in the 650  C-annealed sample, because Andreev reflection can only take place at a highly transparent S/N interface. We still need to establish evidence for the existence of PIS. Unlike in general superconductivity, the junction conductance does not reach infinite value but rather starts to drop at Tre = 34 K as temperature decreases. We argue that this is due to the “reentrance effect,” which is critical for the manifestation of the PIS regime. The N-channel/N-reservoir (N/N′ ) junction attached to the other end of the N-channel plays an important role in this context. When the N/N′ interface is highly transparent, the proximity-induced Cooper pair amplitude is suppressed near the N/N′ junction because the Cooper pairs diffuse out of the N-channel, where they feel the ETh =
D/L2  gap rather than . Here  and L are the bulk superconducting gap and the N-channel length, respectively, there. This leads to “the spatially averaged normalized density of state (NN E) in the N-channel < its normal state value,” at E ≤ ETh . Consequently, the conductance decreases at E ≤ ETh (i.e., reentrance effect), whereas the PIS can survive only at E ≥ ETh . In Figure 22c, we show the Tre vs L−2 tube relation obtained from the measurement results for Figure 22b samples. Interestingly, this relation is mostly linear except at Ltube = 06 .m. This result agrees qualitatively with the Thouless temperature (TTh ) dependence on the N-channel length, L (i.e., TTh =
D/kL2 , and is the first evidence that the conductance decrease from Tre is due to the reentrance effect. We show the second evidence for PIS as follows. As explained, because the “Ltube = A · Tpx−1/2 ” relation in the inset of Figure 22a was qualitatively equivalent to “LT =


D/kT 1/2 ,“ we define A = :
D/k1/2 , where : is a constant coefficient. Hence, from the asymptotic value of Ltube vs Tpx−1/2 (A = 19 × 10−6 ) and the value at which the dotted line crosses to the Y -axis (004 × 10−6 , the data obtained in Figure 22b can be fitted by the expression Ltube = 19 × 10−6  · Tpx−1/2 + 004 × 10−6 . With TTh =
D/kL2 = A/:2 /L2 , we can derive the TTh vs L−2 tube relation, by using A ∼ 19 × 10−6 , L = Ltube , and : as a fitting parameter. From the data shown in Figure 22c, the value :2 = 135 gives the best fit to the measurements in the linear regime. This :2 = 135 value establishes the relation Tre = 074 × TTh .” In fact, similar relations were reported in the reentrance effect observed in the Nb/2DEG junction (“Tre = 04 × TTh ”)[72] and in the Al/Cu junction (“Tre = 05 × TTh ”)[70]. Our coefficient value of 0.74 approximately agrees with those. From this discussion, we conclude that the conductance drop at Tre = 34 K in the main panel of Figure 22a is attributed to the “reentrance effect.” The particular “0.74” value is discussed. The Ltube = 06 .m value for the departure from the linear regime shown in Figure 22c is associated with a weakening of the reentrance effect due to the decrease of Cooper pair diffusion in the MWNT. Indeed, the density of Cooper pairs is very high even around the MWNT/Al interface in

Mesoscopic Phenomena in Nanotubes

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Figure 23. (a) Periodic magnetoconductance oscillation (solid line) observed in the reentrant regime. Magnetic flux was applied along the MWNT axis. This can be fitted by the formula of Altshuler-AronovSpivak oscillations (dotted line)[81], assuming the anomalous period of @ = @0 /80 = @0′ = 25 Gauss and the presence of spin-orbit interaction for the negative MC around zero magnetic field. This period of 25 Gauss corresponds to the magnetic flux @ = @0 /80 = @0′ , based on the best fit (dotted line) with the mean MWNT radius of 40 nm[81]. Inset: Power-law relation of the normalized magnitude of this MC oscillation (G/GN ) vs 1/T above Tre = 45 K and its saturation below Tre . GN is the normal state conductance. The solid line is a guide for the eyes. (b) Magnetic field dependence of the G0 vs temperature relations around Tre at the fields shown by the arrows in (a) (i.e., @/@0′ = 1/2 and @/@0′ = 1, respectively). At @/@0′ = 1/2, the G0 maximum shifts up to about T = 6 K (enhancement of the reentrance regime). In contrast, at @/@0′ = 1, G0 exhibited a monotonic increase (its shrinkage).

319

Mesoscopic Phenomena in Nanotubes

the superconducting quantum flux) in Fig. 23b] also supports the presence of reentrance effect, if we assume our Nb/MWNT structure is equivalent to an S/N junction connected to AAS trajectory, like a S/N junction connected to an AB ring [8] (Fig. 24a and b). The reentrance effect in this system has been successfully studied [73–76]. Reference [74] showed the power-law decay of G/GN on temperature increase with the ratio between 2.5% and 0.5% and its saturation below the Tre (= 50 mK). These are quantitatively in precise agreement with the inset of Figure 23a. Besides, the enhancement of reentrance effect at the magnetic flux in the bottom of oscillation (@/@0′ = 1/2) in Figure 23b also qualitatively agrees, when we neglect that the magnetic flux was @/@0 = 1/2 in [74]. These two results strongly support the presence of a reentrance effect associated with the AAS effect in our Nb/MWNT system. The enhancement of the reentrance effect at @/@0 = 1/2 is qualitatively explained by the decrease of the effective Nchannel length (L), due to the destructive phase interference in the AB ring, for ETh =
D/L2 in [74] (Fig. 24b). The L for ETh consists of the L′ and L′′ regions. Because the destructive phase interference at @/@0 = 1/2 enhances the zero electron–hole pair amplitude at the C point and the L′′ region, this effect leads to the reduction of L down to L′ . Consequently the conductance-maximum temperature shifts to higher temperatures. Our results are consistent with this interpretation (Fig. 24). In the following, we explain the “Tre = 074 × TTh ” relation. We point out that in the data fitting for the TTh vs L−2 tube relation, we did not include the length of AAS trajectory. By using : = 1 and assuming a length of 500 nm for this AAS trajectory, we confirmed that it gave the best fit to the measured Tre vs L−2 tube relation. Hence, the conductance-maximum temperature shifts to Tre = 6 K, indicating L = 740 nm, at @/@0′ = 1/2. For a AAS trajectory length of 500 nm, this means L′ = 240 nm, based on the previous fitting. Interestingly, this implies that the main AAS trajectory is located at a distance of 240 nm from the Nb/MWNT interface (Fig. 24a). However, (1) the AAS oscillations assuming @ = @0 /80 = @0′ and influence of spin–orbit interaction (SOI) and (2) the “shrinkage” of the reentrance effect at @/@0′ = 1 are very anomalous. In (1), SOI is not required if one follows the aforementioned explanation. The negative MC around zero magnetic field in the MC oscillations can be qualitatively understood by the enhancement of the reentrant con(a)

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Figure 24. (a) An Nb/MWNT junction with a trajectory for AAS oscillation. (c) An S/N junction with the AB ring in its N-region [74]. This structure is assumed to be equivalent to (a) just by replacing the AB ring to the AAS trajectory.

ductance (Fig. 23b) due to the destructive phase interference at @/@0′ = 1/2. When this conductance decrease due to the reentrance effect overcomes the conductance increase due to the destructive phase interference in the AAS effect, the negative MC can emerge However, the MC oscillation with “the period ≪ the quantum flux” has never been observed in our N electrode/MWNT junctions before [81]. Besides, only quantum flux should penetrate into the Nb electrode that exists on the inner space of MWNTs in Figure 24a, because the tops of the inner space of MWNTs are capped by the Nb film. In this sense, the small period may indicate that MC oscillations may be not associated with AAS oscillations. This is still in contradiction to the explanation supporting the reentrance effect. For a possible interpretation, we may have to take into consideration (1) the contribution of the trajectory, which encircles a MWNT in the nth time, where n is the integer, which leads to @ = @0 /n, (2) the contribution of extra phases resulting from Andreev reflection, which takes place in AAS trajectories facing the Nb/MWNT interface, which leads to @ = @0 /2 [75], and (3) multiple Andreev reflections due to the strong electron interaction [67, 77], which may lead to @ = @0 /2n . Finally, we tried to eliminate the reentrance effect by reducing the interface transparency of the MWNT/Al substrate junction. In order to realize this, a thin tunnel barrier with a thickness of a few nanometers was formed at the bottom end of the pores (i.e., MWNTs) by optimizing the anodization condition of the alumina membrane. Annealing this sample after the synthesis of MWNTs leads to diffusion of this tunnel barrier and the bottom part of the MWNT (we confirmed this by TEM), yielding a lower transparency interface of the MWNT/Al-substrate junction. As explained, because this low transparency reduces diffusion out of Cooper pairs from the MWNT to the Al substrate, the reentrance effect must disappear. The result is shown in the inset of Figure 25. In fact, the G0 increase is only observable from T = 6 K down to T = 15 K as temperature decreases. Because this T = 6 K approximately corresponds to Tpx of MWNTs with Ltube = 08 .m, this conductance increase can be due to PIS. The main panel of Figure 25 also shows the temperature dependence of its G0 vs voltage relationship. A conductance peak around zero voltage starts to grow in the region between −065 and +065 mV (i.e.,  = 13 meV) from T = 6 K corresponding to Tpx = 6 K, whereas two conductance dips appear between the voltage regions of ±06 and ± 2mV also at T = 6 K. This conductance peak monotonically reduces to T = 15 K with decreasing temperature, while the conductance dips also monotonically deepen. In addition, the very sharp conductance valley observable at a voltage of +02 mV disappears as the temperature decreases. This disappearance of reentrant conductance strongly supports the claim that the highly transparent interface of the MWNT/Al substrate junction is the key factor in the reentrance effect. This growth in the conductance peak is also evidence of the high-transparency interface of the Nb/MWNT junction and the consequent PIS. It is already known that Andreev reflection (in which an incident electron coming from the N is converted into a Cooper pair in the S, leaving a reflected hole in the N, at the S/N junction)

320 Zer-bias conductance (mS)

Mesoscopic Phenomena in Nanotubes 0.082 1.5 K 2K 3K 4K 5K 6K 7K

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with a highly transparent S/N interface leads to a conductance peak, particularly in one-dimensional N/S junctions [70, 84]. Our Nb/MWNT junction mostly corresponds to this case, because: (1) T = 6 K, at which the conductance peak emerges, agrees with Tpx as mentioned and is below Tc of our Nb film. (2) The value of  = 13 meV is approximately equal to the  of Nb (i.e., Nb ∼14 meV). (3) The phase coherence length, estimated from D = 037 m2 /s as 523 nm, is larger than the circumferential length of the MWNT which is about 250 nm, so that our MWNT can be a one-dimensional conductor in the diffusive regime.

4.2.3. Conclusion In conclusion, we reported a conductance increase with the onset temperature of Tpx = 9 K as the highest case and its decreasing with decreasing temperature in Nb/MWNTs junctions with high-transparency interface. The junctions have been achieved by utilizing MWNTs synthesized in nanopores of alumina membranes. We argued that the former and the latter originated from the PIS and its reentrance effect, respectively. The estimated large diffusion constant of Cooper pairs in the MWNTs strongly contributed to these two effects, whereas it did not enhance the critical magnetic field for the vanishing PIS. The observed drastic magnetic-field dependences were also consistent with previous works but some questions remain open. Because of the high reproducibility, MWNTs must be a molecular material relevant for the investigation of superconductivity related phenomena.

4.3. Y-Junction Carbon Nanotubes Self-gate Suppressed Rectification Property in Y-Junction Carbon Nanotube with a Large Diameter and Acute Angle of Two Branches.

We successfully synthesize a variety of Y-junction multiwalled carbon nanotubes with different diameters and angles of two branches by utilizing porous alumina membranes realized by a two-step anodization method and investigate those electrical properties. We find here that even a Y-junction MWNT with a diameter as large as 50 nm in its stem can show a stable rectification property following the Anderson mode for macroscopic heteroband junction with 20 meV of built-in potential, when the two branches form acute angle. In contrast, we clarify the presence of a currentsuppression mechanism deviating from the Anderson model, in the forward voltage region. We argue that this is due to a self-gating effect, caused by difference in an electrochemical potential between the two branches. A carbon nanotube, a molecular conductor, is a strong candidate for nanoelectronics devices. It is theoretically known that the junction at which a larger diameter “stem” of a single-walled carbon nanotubes is divided into two smaller diameter“branches” (Y-junction or T-junction SWNTs) exhibits interesting electrical properties (such as nano-hetero-junctions of different bandgap semiconductors and nano-Schottky junctions) representing a rectifying nanodiode [86–88]. This is because SWNTs can be either metal or semiconductor with different bandgaps, depending on the diameter, chirality, and defects. Multiple connection of such SWNTs with differences in chiralities, diameters, and defects leads to the properties mentioned at the Y-junction [89]. In addition, the presence of the Y-junction implies the connection of one more SWNT to this two-terminal junction as the third terminal. This third terminal can act as a gate electrode which can control the electric features of two-terminal SWNT devices. A three-terminal operation of quantum conductivity, like a metal–oxide–semiconductor transistor, has also been predicted only theoretically [86]. Hence, Y- and T-junction SWNTs are expected to become a key component of carbon nanotube integration circuits, but synthesizing them with high reproducibility has proved to be very difficult. Only recently have some experiments [90–92] reported successful synthesis of Y-junction nanotubes and the presence of asymmetric current versus voltage features only at room temperature, possibly resulting from heteroband junctions. The details of the electrical properties are still ambiguous. Even apart from carbon nanotube systems, the Y-branch nano-electron-wave guide is attracting large attention as a novel switching device in nanoelectronic junctions [93, 94]. It has been reported that capacitive coupled two branches led to switching of electron-wave flow between the branches up into THz range due to a self-gating effect in new class of gateless mesoscopic devices [93] and to switching gain increasing superlinearly with source–drain voltages due to side-gate voltages applied [94]. Both reports implied that even very small voltages applied on both sides of the branches (i.e., lateral electric field) efficiently switched flow of electron waves between the two branches. A Y-junction carbon nanotube can be a good candidate for such novel nano-electron-wave guides. Here, in this work, we successfully synthesize a variety of Y-junction multiwalled carbon nanotubes with different

321

Mesoscopic Phenomena in Nanotubes

diameters and branch angles by utilizing Y-shaped nanopores of alumina membranes [95, 96] realized by a twostep anodization method. We clarify that even a Y-junction MWNT with a large diameter stem can lead to macroscopic heteroband junction representable by the Anderson model at the Y-junction, when the two branches form an “acute angle.” We also find a deviation from the model, implying a self-gating effect due to capacitive coupling of the two branches.

(a) pore

alumina membranes

Al stem

3C2H2+N2

4.3.2. Experimental Results and Discussion We show the structural information of Y-shaped pores, in which Y-junction MWNTs were synthesized, in Figure 26. We have already confirmed that our carbon nanotubes synthesized in porous alumina membrane by chemical vapor deposition were MWNTs, which exhibited diffusive electron-wave transport at low temperature [95, 96]. Besides, nanotubes synthesized by similar methods showed semiconducting behavior at room temperature [91]. Hence, our MWNTs can have semiconducting characteristics in the diffusive regime. We prepared three different types of Y-junction MWNTs with one straight MWNT as a reference for this experiment, and their features are described in Table 2. SEM images of those pores are shown in Figure 26c. These imply that only type B1 has an acute angle between the two branches. In contrast, there is a spacing of 20–30 nm between two branches in types A and B2, due to the large diameter stems. Figure 27 shows the current versus voltage (J vs V ) characteristics of each type of MWNT at room temperature. First, we find that only type B1 exhibits a strong asymmetry and rectification property similar to that noted in past reports (Fig. 27b). Because type C, which is not a Y-junction MWNT, exhibited a symmetric J vs V curve (Fig. 27d), we conclude that not the interface of electrode/MWNT junctions but the Y-junction is the origin for this asymmetric J vs V property of type B1. In contrast, second, we note that the J vs V feature of type A is mostly symmetric and shows poor reproducibility (Fig. 27a). Because the ratio of diameters between the stem and branches is the same as that of type B1, the very large diameter around 90 nm in the stem of type A can be the origin for the instability and elimination of the rectification property in Figure 27a. Third, we find that the J vs V feature of type B2 (Fig. 27c) even with a high diameter ratio (above 4) of the stem and branch is also symmetric. This also implies that a large diameter around 70 nm in the stem of type B2 eliminates the rectification property, even under such a high diameter ratio. Why do the large diameter stems in types A and B2 eliminate the rectification property? Why can only type B1 have the rectification property? One main reason can be the angle between the two branches (i.e., whether the angle is obtuse or acute) as mentioned for Figure 27c, because only type B1 has the acute angle between the two branches. Reference [86] theoretically reported a rectification property in a (14,0) SWNT branching two (7,0) SWNTs with acute angle. The acute angle led to the presence of six heptagons clustered at the Y-junction, leading to the rectification property. In contrast, [86] also showed that a Y-junction SWNT, consisting of three (8,0) SWNTs, with an obtuse angle led

branch

nickel Au

V

Y-junction MWNT

(c) Type A

Type B1

Type B2

(b) stem spacing

Fig.1(b)

Acute angle spacing

200 nm branch 50 nm

(d) branch stem

200 nm

Figure 26. Schematic cross-section of alumina membrane with Yshaped nanopores and its synthesis method. First, aluminum substrate, with applied positive bias voltage (50 V for type A and B1, 60 V for type B2), is anodized in H2 C2 O4 under a current density and temperature of 10  C (left upper). This leads to large-diameter pores for the stem in the alumina membrane. After this anodization is stopped, second, anodization with reduced bias voltage of 35 V was continuously performed under the same conditions, leading to smaller diameter pores for the branch (right upper). The total thickness of the alumina membrane is 5 .m in each sample. Y-shaped pores were synthesized by automatic alignment of the interface of the upper and lower membranes, due to self-organization (left lower). We also realized smaller diameter pores in type B by reducing current density for anodization, compared with type A. Consequently, we successfully prepared three types of Y-shaped pores for this experiment (Table 2). After the synthesis of the Y-shaped pores, nickel was electrochemically deposited into the bottom ends of the branch pores and then, Y-junction MWNTs were synthesized by chemical vapor deposition using the nickel as a catalyst (right lower and the lowest). Although we measured the averaged characteristics of Y-junction MWNTs with the number of about 104 , it was already confirmed that even this was mostly the same as those in an individual Y-junction nanotube [91]. (b) Cross-sectional TEM image of Y-shaped pore array for type B1 in an alumina membrane. (c) Cross-sectional SEM images of Y-shaped pores, for types A, B1, and B2 (see Table 2), in alumina membranes. (d) SEM overview image of a Y-junction nanotube (shown by an arrow) of type B1.

322

Mesoscopic Phenomena in Nanotubes

Table 2. Structure parameters for types A, B1, B2, and C of Y-shaped pores. Type B1

Type B2

Type C

90 26 27 3.5 obtuse

50 15 16 3.3 acute

69 17 19 4.1 obtuse

80 — — 1 —

φ1

φ3 θ

Note: The diameter corresponds to most outer diameters of MWNTs. We measured about 30 pores in each array to confirm these averaged structure parameters. Types A and B1 have mostly the same ratio of the stem and branch in diameter, but each pore diameter in type A is approximately two times larger than that in type B1. Types B1 and B2 have mostly the same diameter in the branch, but the ratios of the stem and branch in diameter in type B2 were increased from that of type B1 by increasing the stem diameter. These lead to acute angle of two branches only in type B1. Type C has just a straight shape like a general MWNT with a large diameter.

to only two heptagonal defects. These calculation results imply the presence of heptagon defects at the Y-junction parts with the acute angle in our nanotubes (i.e., in type B1), although we failed to observe actual chilarity of our 15

–4 –8

2nd time 3rd time Type A (a)

of current:J [µA]

1st time

0

Absolute value

Current: J [µA]

8 4

Measurement

T = 300 K

T = 300 K 10

Calculation 1 Calculation 2

5

0.40

(b)

0 –10 –8 –6 –4 –2 0 2 4 6 8 10

–10 –10 –8 –6 –4 –2 0 2 4 6 8 10

Voltage [V]

Voltage [V] 8

T = 300 K

0

–15

Type B2

(c) Voltage [V]

V = +1 V

0.28

T285 K

4

1st time

0.36

T = 300 K

2nd time Current: J [µA]

Current: J [µA]

15

Type B1

0.5

(a) Log [G] (µS)

10

Log [G] (µS)

φ2

Log [J] (µA)

%1 (nm) %2 (nm) %3 (nm) %1/%2 D

Type A

Y-junction MWNTs here. Besides, because one MWNT consists of many SWNTs, rolled up coaxially, with different chiralities and diameters, the acute angle between the branches in our Y-junction MWNT will introduce defects with the number larger than that of one Y-junction SWNT, at some of shells. Reference [86] implied that heptagonal defect had a positive charge and, hence, asymmetric locations of such defects in Y-junction tube easily led to the rectification property. Y-junction MWNTs can also easily introduce such asymmetric location of defects near the Y-junction parts at some of shells, due to the structural reasons mentioned with a larger number of defects. Therefore, we speculate that the presence of heptagon defects introduced by the acute angle of two branches and the asymmetric location yielded the rectification property in our Y-junction MWNTs. Anyway, these experimental results revealed that even a Y-junction MWNT with diameter as large as 50 nm in its stem could show a stable rectification property when the two branches formed the acute angle. In contrast, the Y-junction MWNTs including the diameters larger than 50 nm with obtuse angle between two branches could not show any rectification properties even if they had the high diameter ratio of the stem and branches. Based on this result, we focus on detailed features of type B1. Figure 28 shows the logarithmic conductance (log[G]) versus the inverse of temperature (1/T ) relation, which are the so-called thermal-activation-type characteristics representing the semiconductor-like features, in type B1. We found that the log[G] vs 1/T relationships were very different between the positive (Fig. 28a and b) and negative (Fig. 28c) bias voltage regions. The log[G] vs 1/T relation in the negative bias voltages is linear and hence follows the thermal-activation type at high temperatures (Fig. 28c),

T 80000) were obtained [370]. Studies on the catalytic properties of colloidal bimetallic catalysts, a promising new kind of material, started about 10 years ago [90, 91, 371]. PVP-protected Pt/Rh and Pt/Pd bimetallic colloids with small metal particles exhibit much better activities than those of the corresponding monometallic colloids. The preparation, characterization, and application to catalysis of some polymer- or ligand-stabilized bimetallic nanoparticles have been reviewed by Toshima and Yonezawa [372]. The structure of the bimetallic nanoclusters has a significant influence on their catalytic properties. The catalytic properties of our Cu/Pd alloy nanocluster protected by PVP for the selective hydrogenation of 1,3-cyclooctadine to corresponding monoene and selective hydration of acrylonitrile to acrylamide (see Scheme 1), an important industrial process, have been intensively studied. In the hydrogenation reaction, both the coexisting Cu in the alloy nanoclusters and PVP can improve the selectivity to the formation of monoene by several times; however, cooperation of both effects causes an extreme increase in the selectivity. An industrial process of producing acrylamide from acrylonitrile needs a very high selectivity, because a small amount of cyanohydrine in the product will cause a big problem in the following process of polymerization of acrylamide. Our Cu/Pd alloy nanoclusters not only exhibit a much higher activity than usual Cu-supported catalyst but also give rise to a selectivity near 100% to acrylamide and no cyanohydrine can be detected during the reaction. Both the catalytic selectivity and activity of the Cu/Pd alloy nanocluster catalysts for the aforementioned two reactions are sensitive to the Cu/Pd ratio in the alloy nanoclusters [111]. The selective hydrogenation of ,-unsaturated aldehydes to the corresponding unsaturated alcohols is an important step for the preparation of various fine chemicals (see Scheme 2). It is a challenging task to reduce the C O group while leaving the C C double bond since usual metal catalysts do in the reverse. The PVP-Pt/Co (3/1) alloy nanoclusters, narrowly distributed in a size range from 1 to 2.7 nm with an average diameter of 1.7 nm, prepared by the “cold alloying process” exhibit quite excellent catalytic properties for the selective hydrogenation of cinnamaldehyde to cinnamyl alcohol. The average activity of 114 mol CAL/mol

CH CH CHO

Selectivity: 99.8% Conversion: 92.8%

Scheme 2

metal per hr and a selectivity of 99.8% at a conversion of 96.2% could be easily achieved [113, 373]. PVP-protected Ni/Pd bimetallic colloids with narrow particle size distribution prepared by a similar method show high catalytic activity in the hydrogenation of nitrobenzene. The highest activity can be achieved for a bimetallic nanocluster with a molar ratio of Ni:Pd = 2:3, which exhibits 3.5 times greater activity than that of a typical colloidal palladium catalyst [374]. Monometallic, bimetallic, trimetallic, and tetrametallic nanoclusters, average size ranging 1.6–2.1 nm, containing Cu, Pd, Pt, and Ru have been prepared by reduction of corresponding metal chlorides with tetraoctylammonium formate in dimethylformamide. Catalytic properties of these colloidal catalysts for the coupling reaction of phenylboronic acid and iodobenzene to give biphenyl (see Scheme 3) have been investigated. Pd and Pd/Cu nanoclusters are more active than the others, and the Pd/Cu nanoclusters exhibit better activity at higher conversions. Ru and, surprisingly, Cu nanoclusters were found to be both active and stable for this reaction [375]. Catalyst modification is a widely applied strategy in heterogeneous hydrogenation. The chiral modification of metal nanoparticles in metal-supported catalysts has been a wellknown strategy providing a high enantioselectivity in the hydrogenation of some organic compounds having potential to generate chiral center during the reactions. Heterogeneous Ni catalyst modified with tartaric acid and Pt catalyst modified with cinchona alkaloids are the most successful catalytic systems in enantioselective heterogeneous catalysts, which have been intensively studied in the field of heterogeneous catalyst. It has been concluded that supported Pt catalysts with relatively low dispersion (particle diameter larger than 2 nm) are preferred for the hydrogenation of -ketoester derivatives [376–382]. A platinum colloid prepared using the alkaloid dihydrocinchonidine was found to catalyze the hydrogenation of -ketoester pyruvates with a good enantioselectivity and high catalytic activity [383, 384]. A very interesting result was reported by Zuo et al. that an enantiomeric excess in favor of R-(+)-methyl lactate up to 97.6% could be obtained in the hydrogenation of pyruvate over a PVP-stabilized platinum colloidal catalyst with an average Pt particle size of only 1.4 nm (see Scheme 4) [385]. Molecular mechanics calculations of the modifier–reactant interaction on the I

B(OH)2

Pd or Cu/Pd or Pd/Ru colloid

(Selectiveity > 99.6%)

+

HOCH2 CH CN

Scheme 1

CH CH CH2OH H2, 4 MPa, C2H5OH

H2C CH CONH2 H2C CH CN + H2O

PVP/Pt-Co (3:1) nanocusters

DMF, K2CO3, 110˚ C Yield: near 100%

Scheme 3

Metal Nanoclusters

352

HO

O C

H2, PVP-Pt

H

OH C

O

CH3

CH3 O

H

N Cinchonidine

O

CH3

N H

CH3 O

+

OH C

O

CH3

CH3 O

(R)-(+)-methyl lactate

(S)-(-)-methyl lactate

(major)

(minor)

Scheme 4

platinum surface suggest that it is possible to obtain good enantioselectivity on the small clusters [386]. Metal cations can have significant modifying effects on the catalytic properties of metal nanoclusters. An acceleration effect of lanthanoid ions on the catalytic activity of Pd nanoparticles protected by lanthanoid polyacrylate (PAAPd-Ln) was observed in the hydrogenation of acrylic acid. However, Ln3+ ions do not influence the catalytic activity of PVP-protected Pd colloid. On the other hand, the promotion effect of Nd3+ ions on the PAA-Pd-catalyzed hydrogenation of methyl acrylate and allyl amine was observed, but not of 1-hexene. It was believed that the observed promotion effect stemmed from the following factors: Ln3+ ions were concentrated around the Pd nanoparticles; the coordination of Ln3+ ions to the substrates containing an oxygen or a nitrogen atom is an important factor for the promotion; and the dissociative hydrogen adsorption on the surface of Pd nanoparticles can be accelerated by the presence of Ln3+ ions [387]. Selective hydrogenation of citronellal to citronellol was conducted over PVP-stabilized Pt and Ru colloids; metal cations were found to increase both the activity and the selectivity. The modification was assumed to be due to the adsorbed metal cations activating the C O double bonds, resulting in accelerating the reaction rate and increasing the selectivity to unsaturated alcohols [388]. A similar positive influence of the metal cations was also observed in the hydrogenation of cinnamaldehyde to cinnamyl alcohol and of crotonaldehyde to crotyl alcohol over a polymerprotected Pt colloid catalyst [389]. The amazing promotion effect of metal cations appears again in the selective hydrogenation of o-chloronitrobenzene (o-CNB) to o-chloroaniline (o-CAN), in which eliminating chlorin is an obstacle to be overcome. The reaction was carried out in methanol at 303 K under 0.1 MPa of hydrogen over PVP-protected Ru–Pd and Ru–Pt bimetallic colloids [390] prepared by NaBH4 reduction of the corresponding mixed-metal salts at room temperature. In the presence of cobalt ion, nearly 100% selectivity to (o-CAN) was achieved over PVP-Ru/Pt colloids at 100% conversion of o-CNB, with an activity two orders of magnitude higher than that of monometallic PVP-Ru colloid [391]. Besides simple metal cations, metal complexes were also found to enable an obvious improvement on the catalytic performance of metal nanoclusters dispersed in liquid [392], which revealed a new possibility to modify the surface of

metal nanocluster catalysts with organometallic complexes of designed structures. The size effect of Pd particles on the catalytic Suzuki reactions between phenylboronic acid and iodobenzene was investigated using catalysts of PVP-protected Pd colloids with varying particle size prepared by the stepwise growth reaction. The catalytic activity of the Pd nanoparticles was found to be in the order of Pd (3.9 nm) > Pd (3.0 nm) approximate to Pd (5.2 nm) > Pd (6.6 nm). The trend of increased catalytic activity with the decrease in particle size was believed to reflect the fact that the vertex and edge atoms of the particles are active sites for the Suzuki reaction. The lower catalytic activity for the smallest Pd nanoparticles might stem from a strong adsorption of the reaction intermediates on the particle surface [393]. The influence of protective agents, poly(amido-amine) dendrimers, block copolymer of polystyrene-b-poly(sodium acrylate), and PVP, on the catalytic properties of Pd nanoparticles in this reaction was also investigated [394]. Catalytic properties of colloidal Pt as electrocatalysts for the electrochemical oxidation of methanol were studied. Current efficiencies of CO2 during methanol oxidation were determined by differential electrochemical mass spectrometry. It was observed that CO2 formed via COad oxidation in a serial reaction, while formaldehyde and formic acid also formed in a parallel reaction. The further oxidation of these intermediates depends on the diffusion and convection conditions in connection with the surface structure of the Pt electrode. Ru promotes methanol oxidation to CO2 via COad , leading to a higher current efficiency of CO2 [395]. Catalytic activities of palladium, platinum, rhodium, and Pd/Pt nanoclusters stabilized by various ligands with average sizes ranging from 1.3 to 3.2 nm and from 2.2 to 4.0 nm were evaluated by hydrogenation of 1,3-cyclooctadiene and methyl acrylate. The activities depend upon the particle size. The activities of heterogeneous catalysts prepared from supporting the metal nanoclusters on charcoal depend strongly on the covering strength of the stabilizer [396]. The catalytic properties of Pd∼561 phen∼60 (OAC)∼180 and Pd∼561 phen∼60 O∼60 (PF6 ∼60 nanoclusters (where phen = phenanthroline) dispersed in water for several organic reactions have been studied by Vargaftik and co-workers [397–399]. Rh colloids stabilized with cationic surfactant have been demonstrated to be effective catalysts for the hydrogenation of arene derivatives such as anisole, toluene, and p-xylene in liquid–liquid biphasic systems in which the rhodium nanoparticles are suspended in an aqueous phase. A maximum TOF is obtained when the surfactant concentration is near the critical micellar concentration [400]. Microemulsion could be used as a microreactor for organic reaction catalyzed by metal nanoclusters. For example, in a water/AOT/n-heptane microemulsion, the reactions between p-Me2 NC6 H4 NH2 and Co(NH3 5 Cl2+ forming N ,N -dimethyl-p-semiquinonediimine, a process of relevance in color photography, over colloidal palladium catalysts with average diameter of 2.5 nm have been studied by Spiro and de Jesus. The palladium colloids were prepared by mixing microemulsions containing K2 PdCl4 with ones containing 10 times this concentration of hydrazine, followed

Metal Nanoclusters

by sonication. It was observed that the activation energies increased as the temperature fell [401]. The electrochemical mechanism in which electrons are transferred from reductant to oxidant through the nanoparticles of gold and other noble metals has been accepted to explain the catalytic functions of metal nanoclusters for many redox reactions occurring on the surface of metal nanoclusters, such as the reaction between N ,N -dimethylp-phenylenediamine (p-Me2 NC6 H4 NH2  and Co(NH3 5 Cl2+ forming N ,N -dimethyl-p-semi-quinonediimine [401–404], 4− 2− the reduction of Fe(CN)3− 6 to Fe(CN)6 by S2 O3 [405–407], or the reduction of water by reduced methyl viologen [408]. Usually when metal nanoclusters stabilized with surfactants or simple anions are used as catalysts, especially in the hydrogenation of organic compounds, a decrease in catalytic activity will soon be observed due to the easy aggregation of small metal nanoparticles under hydrogen, which should have relation to the adsorption of H2 on the metal nanoparticles. Therefore, the lifetimes of these catalysts in a colloidal solution are usually not long enough for real applications, different from that of PVP-protected metal nanocluster catalysts. Aiken and Finke reported that the catalytic lifetime of a Rh nanocluster, particle size 2–4 nm, stabilized with polyoxoanion and tetrabutylammonium achieved a number ≥193000, which is near that of a heterogeneous catalyst, 5% Rh/Al2 O3 , and much higher than those of homogenous complex catalysts such as RhCl(PPh3 )3 (Wilkinson’s catalyst) or [(1,5-COD)Rh(CH3 CN)2 ]BF4 . The Rh nanoclusters are prepared by the hydrogen reduction of [(nC4 H9 4 N]5 Na3 [(1,5-COD)-Rh2 ·W15 Nb3 O62 ] [366, 409].

3.2. Immobilized Metal Nanocluster Catalysts Research on adsorbing metal colloidal particles on a support could be traced back to before the 1970s. One example is the adsorption of Pd colloidal particles on Al2 O3 contributed by Turkevich and Kim in 1970 [410]. Before 1990, the catalyst preparation procedure by immobilizing colloidal metal particles had not attracted reasonable attention, due to the lack of exciting results on the improvement of catalytic properties achieved in an unusual way, which seems a little complex compared with the traditional impregnation method in heterogeneous catalyst preparation. In 1989, Wang et al. prepared very active Rh and Pt nanocluster supported catalysts via coordination capturing Rh (3.5 nm) and Pt (1.6 nm) nanoclusters in PVP-protected metal colloids with mercapto group anchored on a silica support [123]. In the hydrogenation of hex-1-ene and cyclohexene, the catalytic activities of these mercaptan-fixed Rh and Pt nanoparticle catalysts are 100 to 300 times higher than those of commercial Rh/C and Pt/C catalysts at the same conditions. This is the first example of a mercapto-containing (which have been generally regarded as poisons for platinum metal catalysts) supported metallic catalyst with high activity for hydrogenation of alkenes. The as-prepared immobilized Pt and Rh nanoclusters are very stable during the reactions and can be reused many times. We have pointed out that the extremely high activities derived from the immobilization of metal nanoclusters via coordination capture can create favorable conditions for the substrates to easily access

353 the catalytic active sites in the catalyst and prevent the small colloidal particles from aggregating. With thioether group anchored on silica such as -Si(CH2 3 -S(CH2 2 CH3 , Pd nanoclusters in PVP-protected Pd colloid can easily be immobilized. This catalyst shows a selectivity of 99% in the partial hydrogenation of cyclopentadiene (COD) to cyclopentene (COE) with an initial rate of 2.7 (mol H2 /s mol Pd) at room temperature and atmosphere pressure (unpublished data). Immobilization of polymer (PVP)-stabilized metal colloids on different supports has also been realized by a modified coordination capture method in which the supports were pretreated with an ethanol solution of triphenylphosphine (TPP) and then were led to reaction with the PVPprotective metal colloidal solutions. TPP adsorbed on the surface of support captured the metal nanoparticles in colloidal solution. PVP and TPP in the solid products then were removed by washing with water and ethanol/toluene, resulting in a supported metal nanocluster catalyst having a similar size and size distribution of metal particles as their precursor. Platinum catalysts prepared in this way exhibited superior catalytic properties to their precursors in colloidal solution for the selective hydrogenations of o-chloronitrobenzene to o-chloroaniline and citronellal to citronellol. This revealed the great potential of nanoscale metal colloidal particles in catalysis [411]. Modification effects of metal cations on the catalytic properties of a Pt nanocluster supported catalyst, prepared by the modified coordination capture method, were investigated for the selective hydrogenation of o-chloronitrobenzene to o-chloroaniline, cinnamaldehyde to cinnamyl alcohol, and citronellal to citronellol. It was found that Ni2+ and Co2+ cations increased both the activity and the selectivity at the same time [412]. The immobilized polymer-protected metal colloid catalysts Wang et al. prepared in 1995 by the formation of polymer hydrogen bond complexes on inorganic support such as silica, like a skin of cross-linked polymer embedded with small metal nanoparticles, exhibit very high selectivity in the selective hydrogenation of COD to COE. The PVPPAA-Pd catalyst supported on silica prepared by forming hydrogen bond complex between polyacrylic acid and PVP in a PVP-protected Pd colloid in the presence of a silica support can catalyze the reaction in a selectivity of 98% to COE at a COD conversion of 100% with a TOF of 2.25 mol H2 /mol Pd s. The catalytic selectivity of PVA-PAAPd catalysts prepared by the same is better than the PVPPAA-Pd catalyst, although its catalytic activity is much lower than PVP-PAA-Pd catalyst, partly due to the large Pd particle size in the PAA-Pd colloid. PVP-Rh and PVP-Pt colloid catalysts can also be easily immobilized by this method and the obtained skin catalysts covered on silica support exhibit good activities in this hydrogenation reaction [139]. The selective partial hydrogenation of 3-hexyn-1-ol giving leaf alcohol, a valuable fragrance, and the selective oxidation of glucose giving sodium gluconate over supported nanosized metal colloidal particles originally stabilized with surfactant were examined by Bonnemann and co-workers. It has been described that independent of the support, the performance of these nanoparticle precursors may be optimized dependent on the size, composition, and structure of

354 the particles. Furthermore, the protective agents can shield the catalytic active surface of metal nanoclusters against poisons and addition of doping agents can enhance the catalytic properties [413, 414]. In 1999, Lange et al. reported a convenient method for preparing embedded polymer-protected metal nanocluster catalysts. The PVP-protected Pt nanoclusters with size of 1.4 nm embedded in amorphous microporous titania–silica mixed oxide by a sol–gel procedure exhibited a quite good selectivity to the formation of hexene in the hydrogenation of 2-hexyne. A 2-hexene selectivity of >94% was obtained at hexyne conversion up to 50%, and at complete conversion a selectivity to 2-hexenes of 88% (cis-2-hexene selectivity of 91%) was achieved. In colloidal dispersions of the PVPstabilized catalyst in propanol, however, the initial hexene selectivity of 80% at a conversion less than 10% fell to ca. 45% at 100% conversion [140]. The obvious increases in the selectivity may be derived from the configuration confinement of PVP by the matrix of inorganic nanoparticles. This success showed an interesting variant procedure for developing new hybrid catalyst with some special catalytic properties. SiO2 -embedded nanoscopic Pd/Au alloy colloids were prepared by embedding the alloy particles of 3 nm in size stabilized with tetraalkylammonium in a silica matrix using a sol–gel process with THF as the solvent. Removing the protecting agent could lead to a mesoporous texture with a comparatively narrow pore distribution and the SiO2 -embedded Pd/Au colloid preserves the size and the structural characteristics of the colloidal metal precursor. The new material exhibits good catalytic properties in selective hydrogenation of 3-hexyn-1-ol to the corresponding cis-hexanol derivatives [142]. Recently Niederer and co-workers reported the synthesis of metal nanoparticle containing [Me](x)-MCM-41 heterogeneous catalyst using surfactant stabilized palladium, iridium, and rhodium nanoparticles in the synthesis gel. Characterization results using XRD, inductively coupled plasma-atomic emission spectrometry (ICP-AES), thermogravimetric analysis (TA), TEM, and nitrogen sorption techniques on this catalyst revealed that the nanoparticles were present inside the pores of MCM-41. Catalytic properties for the hydrogenation of cyclohexene, cyclooctene, cyclododecene, and norbornene over these catalysts were examined [415]. Dendrimer-encapsulated Pd and Pt nanoparticles with narrow particle size distribution dispersed in supercritical CO2 have been used as effective catalysts for the hydrogenation of styrene and Heck heterocoupling of iodobenzene and methacrylate [416]. Metal nanoclusters stabilized by surfactants can be easily adsorbed on supports to prepare metal supported heterogeneous catalysts. Mono- and bimetallic nanoparticles stabilized by lipophilic or hydrophilic surfactants of the cationic, anionic, or nonionic type have been used as precursors for preparing heterogeneous metal nanocluster catalysts, which are effective for the hydrogenation and oxidation of organic substrates. A comparison of catalytic results and CO chemisorption experiments revealed that the protecting surfactants still covered the nanoparticle surface after

Metal Nanoclusters

adsorption on supports, which markedly improved the lifetime of the catalysts [205]. A lanthanium oxide supported Ru colloid was used as the catalyst for the hydrogenation of benzene in an aqueous solution of sodium hydroxide. Selectivity to cyclohexene of higher than 50% at 50% conversion was achieved [417]. Frelink et al. reported in 1995 that the catalytic activities for oxidation of methanol of carbon-supported catalysts derived from colloidal techniques are 2–3 times higher than those prepared using either impregnation or ion-exchange methods [418]. Metal particle size would have an influence on the catalytic activity of a supported metal nanocluster electrocatalytic catalyst. Large particles are accompanied by a loss in specific area of the metal particles; however, if the small particles are entrapped in micropores of the support, an obvious decrease in the apparent catalytic activity may also be observed. It has been demonstrated that the optimal Pt particle size for reactions in a H2 /O2 fuel cell is ∼3 nm [419]. The microwave-assisted synthesis method has been used to prepare well-dispersed Pt nanoparticles, average size in 3.5–4 nm, supported on carbon for the application of fuel cells. This catalyst exhibits high electrocatalytic activity in the room-temperature oxidation of liquid methanol [420]. Highly active electrocatalytic electrodes of carbon–silica composites containing Pt nanoparticles of about 2 nm have been prepared by Anderson and co-workers [421] by embedding Vulcan carbon XC-72 carbon-supported Pt nanoparticles in a silica gel followed by a CO2 supercritical drying process. The electrocatalytic activity for methanol oxidation over the colloidal-Pt-modified carbon–silica composite aerogels was reported to be 4 orders of magnitude higher than that over the native Pt-modified carbon powder. A further improvement in the activity was achieved by appropriately annealing the electrodes to increase the size of Pt nanoparticles to 3–4 nm. Bimetallic colloidal nanoparticles containing Pt, especially the Pt/Ru nanoclusters with particle sizes of 1–2 nm stabilized by organoaluminum, were reported to be suitable for preparing fuel cell anode catalysts with an improved CO tolerance. The colloid precursors were supported and activated by thermal conditioning to remove the organic stabilizer [422–426]. It was also found that the size of organoaluminum-stabilized metal particles did not change during the thermal conditioning even at high metal loadings (20 wt% metal). A Pt–Ru/graphitic carbon nanofibers nanocomposite containing Pt–Ru alloy nanoclusters having 6 nm average diameter and 1:1 bulk Pt/Ru ratio with a total metal content of 42 wt% has been prepared and used as an anode catalyst in a direct-methanol fuel cell. An average current density at 0.4 V of 0.21 A/cm2 for the fuel cell was achieved [427]. Bimetallic Pt–Sn nanoclusters, PtSn (niggliite), and Pt3 Sn, with an average diameter of 5–8 nm, highly dispersed on a carbon powder support at a total metal loading of ca. 15 wt%, have been prepared and their electrocatalytic properties have also been investigated. It is observed that both the Pt–Sn/C nanocomposites as electrooxidation catalysts in a direct methanol fuel cell give fuel cell performances comparable to that expected for Pt–Sn catalysts prepared by more conventional methods [428].

Metal Nanoclusters

Pt–Co bimetallic nanoclusters of 3–4 nm diameter prepared by Zhang and Chan using a water-in-oil reverse microemulsion of water-Triton X-100-propan-2-ol-cyclohexane were supported on a carbon electrode which has a high catalytic activity for methanol oxidation at room temperature [429]. Hydrogenation of butyronitrile and the adsorption of CO over Pt/Rh bimetallic nanoparticles supported on activated charcoal have been studied. The Pt/Rh ratio at the surface has an important influence on the catalytic activity and CO chemisorption ability. Maximum activity in this hydrogenation reaction and CO adsorption ability were observed at a Pt/Rh atomic ratio of 0.1. Detection of the different types of CO bonding at the surface by IR and the EXAFS characterization results revealed that Rh was enriched in the surface [430]. Catalytic properties for the selective hydrogenation of 3,4dichloronitrobenzene to corresponding aniline under high pressure over a supported Pt catalyst prepared by immobilizing nanoparticles in surfactant-protected Pt hydrosols have been examined in batchwise and continuous manners [431]. R4 N+ Br-stabilized Pd colloids were embedded in inorganic matrix by an in-situ fluoride-catalyzed hydrolysis of CH3 Si(OCH3 )3 and Mg(OC2 H5 )3 , resulting in micro/mesoporous hydrophobic sol–gel materials entrapped with individual Pd nanoclusters, which are active catalysts in the hydrogenation of 1,5-cyclooctadiene [141]. Multilayered polyelectrolyte films containing silver metal nanoparticles of 4–30 nm in average diameter were prepared by reducing silver ions in the films by heating or NaBH4 . These metal nanocluster embedded polyelectrolyte films exhibit obvious electrochemical catalytic properties and can be used as antimicrobial coatings [432]. Ag nanoparticles in a composite of organosulfur containing a conducting polymer (DMcT-PAn) component were found to have the capacity to improve the charge–discharge performance of the composite as a cathode material for lithium rechargeable batteries. Ag nanoparticles were bound to DMcT with a silver–sulfur bond in this composite system. The observed enhancement in the battery performance was attributed to the electrocatalytic activity of the metal nanoparticles and the increased conductivity of the composite films [433].

4. METAL NANOCLUSTER MAGNETIC MATERIALS AND DEVICES Magnetism related to metal nanoclusters and clusterassembled thin films has been reviewed recently [434]. In this section, we will give a brief description of metal nanoclusters and their assemblies as promising magnetic materials in order to make up for the lack of reviews in this aspect at present [435]. Nanoscale magnetic particles have attracted considerable growing interest [434–436], both theoretical and experimental, in recent years, because of their unique size-dependent magnetic properties and their potential in advanced magnetic functional materials. Both magnetic particles and their assemblies have attractive and extensive applications in various fields of materials science. Isolated magnetic particles can be used as magnetic fluid for magnetic separation

355 and magnetic sealing devices [437, 438]. Controlled assemblies of magnetic particles with other stuff will find their applications in smart AFM tips [439, 440], magnetic forceenhanced biomolecule recognition [441, 442], and magnetic field-assisted drug delivery [443–445]. Furthermore, selfassembly of magnetic nanoparticles as building blocks in chemically controllable manners can be used to build up novel magnetic nanostructures [446]. Due to collective physical phenomena of many elementary particulates magnetic properties of a nanostructured assembly are dominated by the interaction of its building blocks besides the nature of the blocks. This kind of nanoparticle-based self-assembly, which is governed by particle–particle and particle–substrate interactions, is extremely important in fabricating unique nanocomposite functional magnetic materials with potential in strong permanent magnets [447, 448], ultrahigh density data storage media [251, 449–451], and spintronic devices, including spin valves [452, 453] and spin-dependent tunneling junctions [454–456] based on the giant magnetoresistance (GMR) effect [457], for ultrasensitive magnetic heads [458, 459], and for nonvolatile magnetic random access memory (MRAM) [460–462]. In the design and preparation of nanostructured magnetic materials, controlled self-assembly of magnetic nanoparticles is an exciting and promising area and has stimulated great recent interest as it may offer a convenient tool for magnetic nanodevice fabrication [446]. Generally speaking, only the uniform nanoparticles as building blocks are, in principle, easy to self-assemble into well-defined 2D patterns and 3D architectures, which are considerably important in nanodevice fabrication. Recently developed solution-phase synthetic approaches (including the pyrolysis of organometallic compounds [463, 464], thermal [465, 466] or sonochemical decomposition of metal carbonyl compounds [467], and the reduction of metal salts by borohydride [468, 469], triethylborohydride [470, 471] or diols [251, 373], for preparing highly well-monodispersed elemental Fe [467, 472] and Co [465, 466, 468–471, 473–477], binary Fe– Pt [251, 478], Co–Pt [373, 464, 479–481], and Co–Ag [214], and ternary Fe–Co–Pt [482] and Fe–Pt–Ag [483] magnetic nanocrystals with narrow size distribution of standard deviation  within about 10%) have given scientists the chance to construct novel self-assembled magnetic nanostructures based on magnetic metal nanoclusters. Chemical synthesis [484] and ordered assembly [485] of magnetic metal nanoparticles have just been reviewed. Electronic and magnetic properties of monodispersed FePt nanoparticles [486], arrays of ferromagnetic iron and cobalt nanoclusters wires along lines of magnetic flux of the applied field [487], control of the magnetic anisotropy of a Co/Pt nanomultilayer with embedded particles [488], and granular GMR sensors of Co/Cu and Co/Ag nanoparticles [489] have been reported recently. In the following examples of this section, we will focus on the potential applications of self-assembled nanostructures from magnetic metal nanoclusters.

4.1. Ultrahigh Density Data Storage Media Magnetic data storage has been playing a key role in the development of audio, video facilities, and computers since its invention more than 100 years ago by Poulsen [490].

356 In 1956, the first hard disk drive was made by IBM and had a total storage capacity of 5 MB at a recording density of 2 kb/in2 . Since then the principle of magnetic data storage has been based on writing magnetic bits in plane on magnetic layers, which is the so-called longitudinal recording. In pursuit of lowering the cost and improving the performance, the areal density (i.e., the number of bits per unit area on a disk surface) has increased nearly 20 million-fold to more than 40 Gb/in2 in modern disk drives and currently doubles every year. Recently, recording densities beyond 100 Gb/ in2 have been reached in two laboratory demonstrations [491, 492]. This continued growth in areal density was achieved by scaling the critical physical dimensions of the constituted magnetic grains; however, there is a limit to this scaling that will be approached within the next few years [493]. One of these limits (i.e., thermal limits [494–496]) lies in the reduction in magnetic grain size, where due to enhanced thermal effects the onset of superparamagnetism at room temperature for small particles will define the size of the smallest possible particles to keep one from losing recording data. The size of a grain to block superparamagnetism is related to the thermal stability of the grain magnetization, which can be described by the stability ratio, C = E/kB T , where E stands for the magnetic anisotropy energy of the grain in question, kB is Boltzman’s constant, and T is the temperature. The magnetic anisotropy energy E per grain is dependent on the grain volume Vg and the anisotropy energy density Ku , and defined as E = Ku Vg . To store information reliably for 10 years, it requires C = 60 [494, 495]. If one assumes cylindrical particles with a height of the typical disk film thickness of 20 nm and Ku of current media (about 3 × 105 J/m3 ), this implies a minimum stable particle diameter of no less than about 7 nm for monodispersed particles. To increase the storage density, however, the size of the grains needs to be reduced. This together with increasing magnetic isolation is the conventional way taken to scale media. Since ultimately the transition width is governed by the size of the grains, higher densities require smaller grains. Also, to maintain a satisfactory signal-to-noise ratio, it is imperative to keep the number of grains per bit constant, and thus the grain size is reduced as the density is increased. The anisotropy energy density Ku can only be increased to some extent to uphold the thermal stability as the grain size is reduced, since the media switching field increases with Ku and cannot go beyond the write field available from the head [493]. Various alternative routes to postpone perceived thermal limits [494–496] for acquiring higher recording densities have been proposed in recent years [493, 495–498]. One of the most promising ways is to use a nanoparticle medium, which is a magnetic film fabricated with metal nanoparticles. The present candidates for nanoparticle media are FePt [251] and CoPt [451] binary alloy with face-centered tetragonal structure, since they have high uniaxial magnetocrystalline anisotropy (Ku ≈ 7 × 106 and 5 × 106 J/m3 for FePt and CoPt, respectively) and good chemical stability and show excellent hard magnetic properties [495, 499, 500]. Self-assembled FePt nanoparticulate film has been successfully used in preliminary longitudinal contact recording studies [251]. Earlier attempts to make FePt [501–503] and CoPt particle thin films [504, 505] have mainly relied upon sputter deposition or other vacuum techniques. But those methods

Metal Nanoclusters

result in chemically disordered crystallites of face-centered cubic structure, which require high-temperature annealing to encourage the alloy films to adopt the magnetically advantageous face-centered tetragonal phase. A shortcoming of vacuum-deposition/annealing procedures is that they commonly lead to products characterized by a broad distribution of grain sizes, with a typical standard deviation of about  = 30–35% [493], due to random nucleation in the initial stages of growth and subsequent agglomeration during annealing. The broad distribution of grain sizes in a magnetic film is undesirable, because uniformity of grain size can help maintain a high signal-to-noise ratio in magnetic recording applications. In a recording medium with widely varying grain sizes, the smallest grains are most susceptible to demagnetization and losing their stored data, or they are superparamagnetic and not useful for magnetic storage, while the large grains contribute disproportionately to the noise. That is less of a problem when all grains are approximately the same size. In addition, today’s magnetic reading heads detect signals from very small data bits most accurately when the bits are made up of grains with uniform size distribution. To produce high performance recording media with good thermal stability, large storage density, and low noise, one needs naturally to increase the number of grains of median size in a magnetic film with a simultaneous narrowing of their size distribution. The keys to making nanoparticle media are controlling the size of magnetic grains and controlling their array from agglomeration in the films. In a recent report by Sun et al. [251], both problems have been solved primarily, using controllable solution-phase chemistry. The strategy adopted by Sun et al. is to make tiny bimetallic nanoparticles from iron and platinum compounds which as prepared are magnetically weak, allowing them to form self-assembled layers, followed by annealing at about 500
C, and transforming them into stronger magnets at the end. In this controllable procedure, monodisperse FePt nanoclusters, with a very narrow size distribution of standard deviation  < 5%, is first synthesized by reduction of platinum acetylacetonate with 1,2-hexadecanediol, and simultaneously thermal decomposition of iron pentacarbonyl in dioctylether, in the presence of oleic acid and oleyl amine stabilizers (see Fig. 20). The size and composition of these FePt nanoclusters can be readily controlled. Their composition is adjusted by controlling the molar ratio of iron carbonyl to the platinum salt. The size of FePt nanoclusters can be tuned from 3 to 10 nm by first growing 3nm monodisperse seed nanoclusters in-situ and then adding more reagents to enlarge the existing seeds to the desired size. These nanoparticles are well isolated and purified easily by centrifugation after the addition of a precipitant such as ethanol and can be redispersed in a variety of nonpolar solvents. To make a film, the resulting FePt nanoclusters are spread on a substrate. As the solvent is slowly evaporated, the weakly magnetic nanoparticles nestle down by self-assembly into a regular array. Within an array, the interparticle distance may be adjusted by replacing oleic acid and oleyl amine with shorter chain alkyl group via ligand exchange, and correspondingly the symmetry of the array can be controlled.

Metal Nanoclusters

Figure 20. TEM micrograph of arrays of nanosized FePt particles (at right) that are smaller and more uniform in size than those obtained from a CoPtCrB material (left) that was used recently in a very high density data-storage demonstration. Reprinted with permission from [449], M. Jacoby, C&E News 78, 37 (2000). © 2000, Shouheng Sun.

Next, the films are annealed at 560
C, for about half an hour, to convert the internal particle structure from a chemically disordered face-centered cubic phase to the chemically ordered, ferromagnetic face-centered tetragonal phase. During the annealing, no agglomeration occurs and the organic stabilizers are fused into a hard coat surrounding each magnetic nanoparticle. The resulting magnetic films are chemically and mechanically robust. Sun et al. have shown that these materials can store data faithfully at a density equivalent to that of CoCr-based alloy hard disks on the market today (see Fig. 20 for the film structure). On the basis of conventional grain size scaling arguments, these materials may even allow one to boost that density 10-fold using current read and write heads. This strategy, developed by Sun et al. as well as by workers at IBM, to fabricate nanoparticle media is an important milestone for ultrahigh density magnetic data storage, which also bring forth the fascination of magnetic nanoclusters in the process of self-assembly chemistry. Now, more effort is still needed for future practical applications. For instance, the biggest problem is that it is necessary to find a way to orient the particle easy magnetization axes all perpendicularly to the film, since the tiny FePt nanoclusters can freeze in place facing any direction and conventional recording heads work only if all the magnetic particles on a disk have their crystalline axes aligned with the disk’s surface. Ultimately, if one would like to record one bit per nanoparticle for patterned media using magnetic metal nanoclusters, which would correspond to higher recording densities of about 10–20 Tb/in2 , it requires one to make a long-range regular array of the nanoclusters—this will be a formidable challenge to future self-assembly chemistry.

4.2. Exchange-Spring Strong Magnets Permanent magnets are one of the most technologically important magnetic functional materials in science and technology and in our everyday life. The performance of

357 permanent-magnet materials is evaluated by their maximum magnetic energy product—this figure of merit is a measure of the maximum magnetostatic energy that would be stored in free space between the pole pieces of a magnet made from the material in question [506]. The larger its magnetic energy product, the greater the performance of a permanent magnet, and hence it is called a strong magnet. The maximum magnetic energy product is proportional to the area closed in the saturated hysteresis loop of a magnet, which arises from plotting the magnetization of the material as the applied magnetic field is cycled under its saturation field. This hysteresis loop is characterized by the saturation magnetization, that is, maximum magnetization and the coercivity of the material, which is the reverse applied field strength to reduce the magnetization to zero. The larger the coercivity of a magnet, the harder it is, whereas the smaller the coercivity of a magnet, the softer it is. To gain a strong magnet with a large magnetic energy product, it requires that there are both lager magnetization and lager coercivity in the material. Progress in making strong permanent magnets has been limited by the difficulty of finding new compounds with these two necessary properties. For instance, Fe65 Co35 alloy, a material with the largest room-temperature saturation magnetization of 24 kG, should have a theoretical maximum magnetic energy product of 144 MG Oe—the upper bound on the magnetic energy product for strong magnets. But in practice this material does not have such a large magnetic energy product because it is a soft magnet (i.e., its coercivity is actually fairly low and a small reverse field is sufficient to reduce the magnetization to zero). About a decade ago, the idea of exchange coupling between a hard material and a soft material with a large magnetization occurred to physicists [507–509], which brought a new hope of producing magnets with their maximum magnetic energy product approaching the upper bound of 144 MG Oe. These kinds of exchange-spring magnets are nanocomposites that are composed of magnetically hard and soft nanophases that interact by magnetic exchange coupling. In a two-nanophase mixture of such materials, exchange forces between the phases mean that the resulting magnetization and coercivity of the material will be some average of the properties of the two constituent phases [508]. In order to realize the effective exchange coupling, the relative sizes of the grains of the two nanophases must be chosen carefully [507]: In general, the characteristic dimensions of the soft magnetic phase cannot exceed about twice the wall thickness of magnetic domains in the hard one. Typically, this limits the soft magnetic phase to be about 10 nm in diameter. Correspondingly, the hard one must have dimensions of this order too, or the volume fraction of the soft magnetic phase will be rather low, thus reducing the magnetization of the composite. Following the concept of magnetic exchange coupling, a lot of techniques, including melt-spinning [510–512], mechanical milling [513–515], and sputtering [516–518], have been exploited to prepare exchange-spring magnets. However, all of these techniques have had only limited success in fabricating two-phase nanostructures with a high magnetic energy product, as they could not afford

358 to effectively control the so-required nanostructures for exchange coupling. Recently, Zen and co-workers [448] reported on how to use self-assembly of magnetic nanoparticles as building blocks to fabricate novel exchange-spring magnets. Their method of chemical synthesis under controlled self-assembly is attractive potentially in making three-dimensional bulk magnets with high magnetic energy product. When monodispersed 4 nm Fe58 Pt42 and 4 nm Fe3 O4 nanoclusters are mixed in hexane under ultrasonic agitation and allowed to self-assemble three-dimensionally by either evaporation of the hexane or addition of ethanol, they form nanoscale structures which, when heated and chemically reduced by H2 under Ar gas at 650
C for one hour, form homogeneous mixtures, at 5-nm scale, of a hard tetragonal FePt phase and a high-magnetization soft Fe3 Pt phase. The admixture of Pt in the Fe3 Pt nanograins results from sintering at a temperature of 650
C, which is used to induce the phase transition from disordered FePt to ordered tetragonal FePt. The magnetic energy product of this two-nanophase material is 20.1 MG Oe, which considerably exceeds the theoretical limit of 13 MG Oe for non-exchange-coupled isotropic FePt magnet by over 50%. This self-assembly protocol opens the door to make strong magnets for practical applications [447], since the size and composition of the individual building blocks can be independently tuned, and the self-assembly results in homogeneous mixtures, at the nanosacle, to effective exchange coupling of the hard and soft magnetic nanophases. However, there are still many practical challenges to be faced when producing magnets with their magnetic energy products approaching the magic number of 144 MG Oe. For example, ways of compressing the two-nanophase material into a high-density compact must be explored, as well as improved alignment of the axes of the hard particles to exploit the full magnetic potential of the nanocomposite system [447]. Nevertheless, it could be expected that highly monodispersed magnetic metal nanoclusters, especially the uniform nanoparticles with zero distribution, will play an important role in making superstrong magnets in the future.

4.3. Metal Spintronic Devices Since the discovery of the GMR effect [457] in 1988, spintronics [519–521], an innovative emerging electronics based on electron spin as well as charge, has made great progress in information science and technology for outstripping the performance of traditional electronics devices. Spintronic devices use magnetic moment to carry information and can combine the performance of standard microelectronics with spin-dependent effects that arise from the interaction between spin of the carrier and the magnetic properties of the material. Introduction of the electron spin degree of freedom to such devices gives them various advantages, including low electric power consumption, nonvolatile data retention, excellent radiation protection, superfast data processing speed, and high integration densities. At present, spintronic hard disk drive read-heads are well established commercially [458], MRAMs appear to be set to follow suit [519], and an all-metallic magnetic logic NOT gate [522] has just been achieved in a laboratory demonstration. In the

Metal Nanoclusters

future, spintronics will lead to very rapid quantum computers [523]. One of the promising applications of ferromagnetic metals or alloys materials is to make spintronic devices that stand for information by the magnetization direction of the ferromagnetic metal components. Spin valves and spindependent tunneling junctions are fundamentally metallic spintronic devices developed currently in the world for hard disk drive read-heads and MRAM [521]. Both devices are based on the giant magnetoresistive effect of thin-film materials composed of alternate ferromagnetic and nonmagnetic layers. A spin valve has two ferromagnetic layers (alloys of nickel, iron, and cobalt) sandwiching a thin nonmagnetic metal (usually copper), with one of the two magnetic layers being “pinned” (i.e., the magnetization in that layer is relatively insensitive to moderate magnetic fields, and the other being “free”; i.e., its magnetization can be changed by a relatively small applied magnetic field). A spin-dependent tunnel junction (SDTJ) is a device in which a pinned layer and a free layer are separated by a very thin insulating layer, commonly aluminum oxide. As the magnetizations in the two layers change from parallel to antiparallel alignment, the magnetoresistance of them rises typically from 5 to 10% for spin valves and 20 to 40% for SDTJ, respectively. Pinning is usually accomplished by using an antiferromagnetic layer that is in intimate contact with the pinned magnetic layer. The two films form an interface that acts to resist changes to the pinned magnetic layer’s magnetization. To date, all the metallic films for these devices, including the recent magnetic logic gates under development [522], are fabricated with vacuum techniques of metal vapor deposition such as sputter. The fundamental developing work exploiting the self-assembly technique of metal nanoparticles has just begun at IBM. In a recent report [226], using monodisperse Co nanoclusters with  = 5%, Black and co-workers have self-assembled nanoscale ordered arrays of 10-nm ferromagnetic Co nanoclusters between lithographically patterned metal contacts spaced about 100 nm apart, for the study of SDTJ devices. After annealing under Ar with 5% H2 at 400
C for about one hour, to strip off the organic ligands protecting the clusters, the arrays convert into films displaying spin-dependent electron transport. At low temperatures, the current–voltage characteristics of the junction reflect single-electron tunneling through the array, and the observed magnetoresistance is on the order of 10% ratio, approaching the maximum predicted theoretically for ensembles of cobalt islands with randomly oriented easy magnetic axes. This work demonstrates that self-assembled Co-nanocrystal superlattices are excellent model experimental systems for studying magnetotransport in nanostructured materials. The observed spin-dependent tunneling in such nanoscale devices of highly uniform magnetic-nanocrystal arrays implies that magnetic metal nanoclusters have vast potential in making advanced spintronic devices. It is reasonable to believe that novel spin valves, spin-dependent tunneling junctions, and magnetic logic elements made from metal nanoclusters might become realized in the future, if the spin-dependent electron transport within an array of metal nanoclusters takes place at room temperature. From these examples, we can see that, in various potential applications of magnetic metal nanoclusters for fabricating

Metal Nanoclusters

advanced magnetical materials and devices, self-assembly has played a key role. This technique is an attractive tool in future nanofabrication because it provides the way to precisely engineer structures on the nanometer scale over large sample areas. However, there is still a long and hard road to the well-developed self-assembly chemistry. It requires more convenient routines to largely prepare size-, shape-, and composition-controllable, even uniform nanoclusters, and easily controlled processes to assemble the nanoclusters into regular arrays or patterns with different symmetry at will.

5. SUMMARY Nanoclusters with small particle sizes and narrow size distributions of noble metals such as Au, Pt, Pd, Rh, Ru, and Ir, light transition metals such as Cu, Co, and Ni, early transition metals such as Zr and Ti, and some alloys of these elements are available from chemical preparations. The structure and composition of them are usually characterized using techniques of TEM, HRTEM, EDX, XPS and Auger Spectroscopy, EELS, XRD, EXAFS, IR-CO probe, STM, AFM, etc. Current interests in metal nanocluster preparation are control of the size, shape, composition, and core–shell structures, especially tailoring the physical and chemical properties by alloying different metals. The so-called “unprotected” metal nanoclusters stabilized with organic solvent and simple anions are tractable building blocks in nanochemistry and nanomaterial science because they can be easily prepared in large scale, modified with various preferred ligands and embedded in a functional or matrix materials with high loading. Self-assembly of narrowly distributed metal nanoclusters into an ordered superlattice pattern of large area has been intensively studied and some promising progress has been achieved based on narrowly distributed metal nanoclusters stabilized by ligands or surfactants during last decade. However, obstacles still need to be overcome before this technique can be put into real applications. It requires more convenient routines to largely prepare size- and shapecontrollable, even uniform, nanoclusters, and easily controlled processes to assemble the nanoclusters into regular arrays and patterns with different symmetry at will. Electron beam lithography and especially the conductiveAFM-tip-induced nanolithography technique have highlighted the generic, controllable, and realizable assembly methodologies to the nanoarchitectures. More realistic possibilities for wide applications of metal nanocluster building blocks are catalysts, nanostructured magnets, and chemical or biochemical sensors. Polymer-protective metal nanoclusters are suitable candidates for quasi-homogeneous catalysts due to their high stability in the conditions of many organic reactions and the weak interaction between the metal surface atoms and residue groups in usual adopted polymer protective agents. PVP is still the most preferred polymer protective agent for such a purpose. Immobilization of preformed structure-controllable metal and alloy nanoclusters originally stabilized with various protective agents provides a promising new concept and practice to generate heterogeneous catalyst for various

359 applications. The “coordination capture method,” which fixes individual nanoparticles on the outer surface of a support via anchored ligands, not only contributes the most active catalysts for hydrogenation of organic compounds because of the easy access of the substrates to the small metal and alloy nanoclusters but also has been adopted in the meaningful exploration of the specific properties of small metal nanoclusters and their self-assemblies. Embedding metal nanoclusters in porous inorganic oxide matrixes by stacking metal oxide nanoparticles around the various preformed metal nanoclusters or the adsorbing metal nanoclusters on supports could produce a new type of catalyst that should find real applications in many catalytic reactions and in the fuel cells operated at a relatively low temperature. Modifying the catalytically active metal nanocluster surfaces with chiral ligands, metal cations, or metal complexes can greatly improve their catalytic selectivities in many reactions. The combination of metal nanoclusters with biomolecules is a very challenging approach to assemble nanoclusters in a designed pattern that would find applications in developing new biomaterials or biosensors, nanoelectronics, and evaluating the superstructures and functions of boimolecules or organisms. Syntheses and assemblies of bimetallic magnetic nanoclusters with narrowly distributed sizes and shapes would produce promising magnetic media of the highest recording density. Self-assembly of different magnetic metal and alloy nanoclusters using a wet chemical process, followed by suitable chemical and physical treatment, is a very promising and realistic approach to create new magnetic materials and devices with superior properties that are difficult to be realize through other routes so far.

GLOSSARY Alcohol refluxing method A method for reducing metal cations with refluxed alcohol. AOT bis(2-ethylhexyl)sulfosuccinate, a surfactant with two alkyl chains. Catalyst modification Optimizing the catalytic property of the active sites in a catalytic system by adding additives or changing its support structure. Coordination capture method A strategy for immobilizing metal nanoparticles characterized by the coordination action or specific reaction between ligands anchored on a support and surface atoms of the metal nanoparticles. Dendrimer A polymer with star-shaped or tree-like structure. Deoxyribonucleic acid (DNA) A naturally occurring polymer usually has a double-stranded structure and plays an important role in heredity of life. Electrocatalytic electrode An electrode having an ability to catalyze an electrochemical reaction occurring on it, which is useful in electrochemical devices such as a full cell sensor or detector. Electron beam lithography A process for fabricating a designed pattern on a material by destroying the structure at irradiated positions with high-energy electron beams.

Metal Nanoclusters

360 Electrophoretic deposition Deposition of charged colloidal particles or molecules on electrodes immersed in a colloidal solution under the influence of an applied electric field. Exchange-spring magnet A nanocomposite magnet composed of magnetically hard and soft nanophases that interact by magnetic exchange coupling. Fuel cell An electrochemical cell in which the energy of a reaction between a fuel and an oxidant is converted directly and continuously into electrical energy. Giant magnetoresistance effect (GMR) A physical phenomenon characterized by a dramatic increase in the electric resistance of a material under an applied magnetic field. Infrared carbon monoxide probe An IR analysis method for species or structures based on the vibration of adsorbed carbon monoxide. Ionic liquids Salts, typically possessing at least one organic ion, with low melting-points in a liquid state within a wide temperature range including room temperature. Ionic liquids are becoming widely recognized as solvents for “green” chemical synthesis because they have no measurable vapor pressure, are nonflammable, and show dramatic enhancements in reaction rate, yield, and selectivity. Magnetic random access memory (MRAM) A novel nonvolatile random access memory based on magnetic moment to carry information, it still keeps the recorded information in the memory when the power is off. Micelle A submicroscopic or nanoscopic aggregation of molecules, as a droplet in a colloidal system. Polymer hydrogen bond complex An complex derived from different polymers with hydrogen bonds between them. Polyoxometallates A large family of metal-oxygen clusters of the early transition metals in high oxidation states, most commonly VV , MoVI , and WVI . Their diversity in composition and molecular structure allows a wide versatility in terms of shape, polarity, redox potentials, surface charge distribution, and acidity. Schlenck technique A method for handling oxygen- or moisture-sensitive compounds under inert atmosphere. Sol–gel procedure A wet chemical technique for fabricating nanostructured materials via hydrolysis and condensation processes in a suitable solvent with metal salts, silicon chloride and metal or non-metal alkoxides as the precursors. Solvated metal atom dispersion technique (SMAD) A method for preparing metal nanoclusters or colloids involving vaporization of a metal under vacuum and codeposition of the atoms with the vapors of a solvent on cooled walls of a reactor. During a warming up process, metal nanoparticles formed, are stabilized both by solvation and negative charge. Spin-dependent tunnel junction (SDTJ) A spintronic device in which a pinned and a free magnetic metallic layer is separated by a very thin insulating layer, commonly aluminum oxide. As the magnetization in the two layers changes from parallel to antiparallel alignment, the magnetoresistance of such a device rises typically from 20 to 40%. Spintronics An innovative branch emerging in electronics based on not only the charge but also the spin of an electron.

Spintronic device A device based on spintronics, which carries information exploiting the charge and spin of an electron. Spin valve A spintronic device composed of two ferromagnetic metal layers (alloys of nickel, iron, or cobalt) sandwiching a thin nonmagnetic metal (usually copper). Under a moderately applied magnetic field, the magnetization of one layer, called “pinned” layer, is relatively insensitive to the field, whereas the applied field can change that of the other layer, called “free” layer. As the magnetization in the two layers changes from parallel to antiparallel alignment, the magnetoresistance of such a device rises typically from 5 to 10%. Triton X-100 Polyethylene glycol mono [4-(1,1,3,3,tetramethylbutyl)phenyl]ether. Ultraviolet photolysis Inducing a chemical reaction by ultraviolet light irradiation.

ACKNOWLEDGMENTS The authors thank the NSFC and the Chinese Ministry of Science and Technology for financial support (projects 29925308 and TG2000077503).

REFERENCES 1. M. Faraday, Philos. Trans. Roy. Soc. London 147, 145 (1857). 2. G. Schmid, Chem. Rev. 92, 1709 (1992). 3. G. Schmid, M. Baumle, M. Geerkens, I. Heim, C. Osemann, and T. Sawitowski, Chem. Soc. Rev. 28, 179 (1999). 4. G. Schmid and L. F. Chi, Adv. Mater. 10, 515 (1998). 5. G. Schmid and G. L. Hornyak, Curr. Opin. Solid State Mater. Sci. 2, 204 (1997). 6. G. Schmid, J. Chem. Soc. Dalton Trans. 7, 1077 (1998). 7. G. Schmid, Adv. Eng. Mater. 3, 737 (2001). 8. G. Schmid, J. Mater. Chem. 12, 1231 (2002). 9. G. Schmid, V. Maihack, F. Lantermann, and S. Peschel, J. Chem. Soc. Dalton Trans. 5, 589 (1996) 10. “Cluster and Colloids” (G. Schmid, Ed.). VCH, Weinheim, 1994. 11. “Metal Nanoparticles: Synthesis, Characterization, and Applications” (D. L. Feldheim and C. A. Foss, Eds.). Dekker, New York/Basel, 2002. 12. “Nanosale Materials in Chemistry” (K. J. Klabunde, Ed.). Wiley, New York, 2001. 13. N. Toshima, in “Nanoscale Materials” (L. M. Liz-Marzán and P. Kamat, Eds.). Kluwer, New York, 2002. 14. T. Teranishi and N. Toshima, Preparation, characterization and properties of bimetallic nanoparticles, in “Catalysis and Electrocatalysis at Nanoparticle Surfaces” (A. Wieckowski, E. R. Savinova, and C. G. Vayenas, Eds.), Ch. 11, p. 379. Dekker, New York, 2002. 15. N. Toshima and Y. Shiraishi, in “Encyclopedia of Surface and Colloid Science” (A. T. Hubbard, Ed.), p. 879. Dekker, New York, 2002. 16. T. Yonezawa and N. Toshima, in “Advanced Functional Molecules and Polymers” (H. S. Nalwa, Ed.), Vol. 2, Ch. 3, p. 65. Gordon & Breach, New York, 2000. 17. N. Toshima, Macromol. Symp. 156, 45 (2000). 18. N. Toshima, in “Fine Particles: Synthesis, Characterization, and Mechanism of Growth” (T. Sugimoto, Ed.), Ch. 9, p. 430. Dekker, New York, 2000. 19. N. Toshima, Pure Appl. Chem. 72, 317 (2000).

Metal Nanoclusters 20. N. Toshima, in “Nanostructured Materials in Biological and Artificial Systems” (A. Yamagishi and Y. Fukushima, Eds.), p. 395. Elsevier, Oxford, 1998. 21. N. Toshima and T. Yonezawa, New J. Chem. 22, 1179 (1998). 22. A. C. Templeton, W. P. Wuelfing, and R. W. Murray, Acc. Chem. Res. 33, 27 (2000). 23. C. N. R. Rao, G. U. Kulkarni, P. J. Thomas, and P. Edwards, Chem. Soc. Rev. 29, 27 (2000). 24. L. N. Lewis, Chem. Rev. 93, 2693 (1993). 25. G. Schon and U. Simon, Colloid Polym. Sci. 273, 101 (1995). 26. G. Schon and U. Simon, Colloid Polym. Sci. 273, 202 (1995). 27. J. D. Aiken III and R. G. Finke, J. Mol. Catal. A 145, 1 (1999). 28. H. Bonnemann, Preparation Catalysts VI 91, 185 (1995). 29. H. Bonnemann and R. M. Richards, Eur. J. Inorg. Chem. 10, 2455 (2001). 30. S. R. Liu, H. J. Zhai, and L. S. Wang, Phys. Rev. B 65, 113397 (2002). 31. S. R. Liu, H. J. Zhai, and L. S. Wang, J. Chem. Phys. 117, 9758 (2002). 32. S. R. Liu, H. J. Zhai, and L. S. Wang, Phys. Rev. B 64, 153398 (2001). 33. M. Takagi, J. Phys. Soc. Jpn. 9, 359 (1954). 34. J. E. Martin, J. Odinek, J. P. Wilcoxon, R. A. Anderson, and P. Provencio, J. Phys. Chem. B 107, 430 (2003). 35. M. A. El-Sayed, Acc. Chem. Res. 34, 257 (2001). 36. M. Valden, X. Lai, and D. W. Goodman, Science 281, 1647 (1998). 37. H. G. Boyen, G. Kastle, F. Weigl, B. Koslowski, C. Dietrich, P. Ziemann, J. P. Spatz, S. Riethmuller, C. Hartmann, M. Moller, G. Schmid, M. G. Garnier, and P. Oelhafen, Science 297, 1533 (2002). 38. T. V. Choudhary and D. W. Goodman, Top. Catal. 21, 25 (2002) and references therein. 39. For examples: K. Bromann, C. Félix, H. Brune, W. Harbich, R. Monot, J. Buttet, and K. Kern, Science 274, 956 (1996). 40. H. Hirai, Y. Nakao, and N. Toshima, J. Macromol. Sci. Chem. A 12, 1117 (1978). 41. H. Hirai, Y. Nakao, and N. Toshima, J. Macromol. Sci. Chem. A 13, 727 (1979). 42. T. Teranishi and M. Miyake, Adv. Mater. 10, 594 (1998). 43. X. Yan, H. Liu, and K. Y. Liew, J. Mater. Chem. 3387 (2001). 44. H. P. Choo, K. Y. Liew, and H. Liu, J. Mater. Chem. 934 (2002). 45. T. Teranishi, I. Kiyokawa, and M. Miyake, Adv. Mater. 10, 596 (1998). 46. A. B. R. Mayer, Polym. Adv. Tech. 12, 96 (2001). 47. Y. Zhou, H. Itoh, T. Uemura, K. Naka, and Y. Chujo, Chem. Commun. 613 (2001). 48. M. Zhao, L. Sun, and R. M. Crooks, J. Am. Chem. Soc. 120, 4877 (1998). 49. L. Balogh and D. A. Tomalia, J. Am. Chem. Soc. 120, 7355 (1998). 50. K. Esumi, A. Suzuki, N. Aihara, K. Usui, and K. Torigoe, Langmuir 14, 3157 (1998). 51. M. Zhao and R. M. Crooks, Angew. Chem. Int. Ed. 38, 364 (1999). 52. M. Zhao and R. M. Crooks, Adv. Mater. 11, 217 (1999). 53. V. Chechik, M. Zhao, and R. M. Crooks, J. Am. Chem. Soc. 121, 4910 (1999). 54. M. Zhao and R. M. Crooks, Chem. Mater. 11, 3379 (1999). 55. L. K. Yeung and R. M. Crooks, Nano Lett. 1, 14 (2001). 56. K. Esumi, A. Kameo, A. Suzuki, and K. Torigoe, Colloid Surf. A 189, 155 (2001). 57. E. H. Rahim, F. S. Kamounah, J. Frederiksen, and J. B. Christensen, Nano Lett. 1, 499 (2001). 58. F. Grohn, G. Kim, B. J. Bauer, and E. J. Amis, Macromolecules 34, 2179 (2001). 59. M.-C. Daniel, J. Ruiz, S. Nlate, J. Palumbo, J.-C. Blais, and D. Astruc, Chem. Commun. 2000 (2001). 60. M.-K. Kim, Y.-M. Jeon, W. S. Jeon, H.-J. Kim, S. G. Hong, C. G. Park, and K. Kim, Chem. Commun. 667 (2001).

361 61. T. Vossmeyer, B. Guse, I. Besnard, R. E. Bauer, K. Müllen, and A. Yasuda, Adv. Mater. 14, 238 (2002). 62. M. Ooe, M. Murata, T. M., K. Ebitani, and K. Kaneda, Nano Lett. 2, 999 (2002). 63. C. Aymonier, U. Schlotterbeck, L. Antonietti, P. Zacharias, R. Thomann, J. C. Tiller, and S. Mecking, Chem. Commun. 3018 (2002). 64. J. J. L. M. Cornelissen, R. van Heerbeek, P. C. J. Kamer, J. N. H. Reek, N. A. J. M. Sommerdijk, and R. J. M. Nolte, Adv. Mater. 14, 489 (2002). 65. J. P. Spatz, A. Roescher, and M. Moller, Adv. Mater. 8, 337 (1996). 66. J. P. Spatz, S. Mossmer, C. Hartmann, M. Moller, T. Herzog, M. Krieger, H. G. Boyen, P. Ziemann, and B. Kabius, Langmuir 16, 407 (2000). 67. M. Moffitt, L. McMahon, V. Pessel, and A. Eisenberg, Chem. Mater. 7, 1185 (1995). 68. Y. Boontongkong and R. E. Cohen, Macromolecules 35, 3647 (2002). 69. S. Bharathi, N. Fishelson, and O. Lev, Langmuir 15, 1929 (1999). 70. S. Bharathi and O. Lev, J. Chem. Soc. Chem. Commun. 2303 (1997). 71. Y. Zhang, F. Chen, J. Zhuang, Y. Tang, D. Wang, Y. Wang, A. Dong, and N. Ren, Chem. Commun. 2814 (2002). 72. K. S. Morley, P. C. Marr, P. B. Webb, A. R. Berry, F. J. Allison, G. Moldovan, P. D. Brown, and S. M. Howdle, J. Mater. Chem. 1898 (2002). 73. L. Armelao, R. Bertoncello, E. Cattaruzza, S. Gialanella, S. Gross, G. Mattei, P. Mazzoldi, and E. Tondello, J. Mater. Chem. 2401 (2002). 74. S. Besson, T. Gacoin, C. Ricolleau, and J.-P. Boilot, Chem. Commun. (2003). 75. Y. Guari, C. Thieuleux, A. Mehdi, C. Reye, R. J. P. Corriu, S. Gomez-Gallardo, K. Philippot, B. Chaudret, and R. Dutartre, Chem. Commun. 1374 (2001). 76. A. Fukuoka, H. Araki, Y. Sakamoto, N. Sugimoto, H. Tsukada, Y. Kumai, Y. Akimoto, and M. Ichikawa, Nano Lett. 2, 793 (2002). 77. L.-X. Zhang, J.-L. Shi, J. Yu, Z.-L. Hua, X.-G. Zhao, and M.-L. Ruan, Adv. Mater. 14, 1510 (2002). 78. F. Schweyer, P. Braunstein, C. Estournès, J. Guille, H. Kessler, J.-L. Paillaud, and J. Rosé, Chem. Commun. 1271 (2000). 79. H.-Q. Wu, X.-W. Wei, M.-W. Shao, J.-S. Gu, and M.-Z. Qu, J. Mater. Chem. 1919 (2002). 80. B. Xue, P. Chen, Q. Hong, J. Lin, and K. L. Tan, J. Mater. Chem. 2378 (2001). 81. N. Toshima, T. Takahashi, and H. Hirai, Chem. Lett. 1245 (1985). 82. M. Ohtaki, N. Toshima, M. Komiyama, and H. Hirai, Bull. Chem. Soc. Jpn. 63, 1433 (1990). 83. K. Esumi, M. Wakabayashi, and K. Torigoe, Colloid Surf. A 109, 55 (1996). 84. M. Y. Han and C. H. Quek, Langmuir 16, 362 (2000). 85. W. Yu, W. Tu, and H. Liu, Langmuir 15, 6 (1999). 86. K. S. Morley, P. C. Marr, P. B. Webb, A. R. Berry, F. J. Allison, G. Moldovan, P. D. Brown, and S. M. Howdle, J. Mater. Chem. 1898 (2002). 87. A. I. Cooper, Adv. Mater. 13, 1111 (2001). 88. Y. Wang, J. Ren, K. Deng, L. Gui, and Y. Tang, Chem. Mater. 12, 1622 (2000). 89. N. Toshima, K. Kushihashi, T. Yonezawa, and H. Hirai, Chem. Lett. 1769 (1989). 90. Y. Wang and H. Liu, Polymer Bull. 25, 139 (1991). 91. N. Toshima, M. Harada, T. Yonezawa, K. Kushibashi, and K. Asakura, J. Phys. Chem. 95, 7448 (1991). 92. Y. Wang and N. Toshima, J. Phys. Chem. B 101, 5301 (1997). 93. L. M. Liz-Marzan and A. Philipse, J. Phys. Chem. 99, 15120 (1995). 94. S. Link, Z. L. Wang, and M. A. El-Sayed, J. Phys. Chem. B 103, 3529 (1999).

362 95. L. Rivas, S. Sanchez-Cortea, J. V. Garcia-Ramos, and G. Morcillo, Langmuir 16, 9722 (2000). 96. I. Srnova-Sloufova, F. Lednicky, A. Gemperle, and J. Gemperlova, Langmuir 16, 9928 (2000). 97. I. Lee, S. Han, and K. Kim, Chem. Commun. 1782 (2001). 98. K. Mallik, M. Mandal, N. Pradhan, and T. Pal, Nano Lett. 1, 319 (2001). 99. N. Kometani, M. Tsubonishi, T. Fujita, K. Asami, and Y. Yonezawa, Langmuir 17, 578 (2001). 100. C. S. Ah, S. D. Hong, and D. Jang, J. Phys. Chem. B 105, 7871 (2001). 101. M. P. Mallin and C. J. Murphy, Nano Lett. 2, 1235 (2002). 102. D. Chen and C. Chen, J. Mater. Chem. 12, 1557 (2002). 103. L. Lu, H. Wang, Y. Zhou, S. Xi, H. Zhang, J. Hu, and B. Zhao, Chem. Commun. 144 (2002). 104. K. L. Kelly, T. R. Jensen, A. A. Lazarides, and G. C. Schatz, in “Metal Nanoparticles: Synthesis, Characterization and Applications” (D. L. Feldheim and C. A. Foss, Jr., Ed.). Dekker, New York, 2002. 105. Y. Wang, L. Gui, and Y. Tang, Chin. J. Chem. 12, 11 (1994). 106. Y. Wang, L. Gui, and Y. Tang, “Abstract of Materials Research Society 1992 Spring Meeting, Symposium O,” O3.8, San Francisco, 1992. 107. J. S. Bradley, E. W. Hill, C. Klein, B. Chaudret, and A. Duteil, Chem. Mater. 5, 254 (1993). 108. J. S. Bradley, G. H. Via, L. Bonnevio, and E. W. Hill, Chem. Mater. 8, 1895 (1996). 109. N. Toshima and Y. Wang, Adv. Mater. 6, 245 (1994). 110. N. Toshima and Y. Wang, Chem. Lett. 1611 (1993). 111. N. Toshima and Y. Wang, Langmuir 10, 4574 (1994). 112. C.-R. Bian, S. Suzuki, K. Asakura, P. Lu, and N. Toshima, J. Phys. Chem. B 106, 8587 (2002). 113. W. Yu, Y. Wang, H. Liu, and W. Zheng, Polym. Adv. Tech. 7, 719 (1996). 114. T. S. Ahmadi, Z. L. Wang, T. C. Green, A. Henglein, and M. A. El-Sayed, Science 272, 1924 (1996). 115. T. S. Ahmadi, Z. L. Wang, A. Henglein, and M. A. El-Sayed, Chem. Mater. 8, 1161 (1996). 116. J. M. Petroski, Z. L. Wang, T. C. Green, and M. A. El-Sayed, J. Phys. Chem. B 102, 3316 (1998). 117. T. Teranishi, R. Kurita, and M. Miyake, J. Inorg. Organomet. Polym. 10, 145 (2000). 118. A. Miyazaki and Y. Nakano, Langmuir 16, 7109 (2000). 119. H. P. Choo, K. Y. Liew, W. A. K. Mahmood, and H. Liu, J. Mater. Chem. 2906 (2001). 120. R. He, X. Qian, J. Yin, and Z. Zhu, J. Mater. Chem. 3783 (2002). 121. H. Hirai, M. Ohtaki, and M. Komiyama, Chem. Lett. 149 (1987). 122. H. Hirai, M. Ohtaki, and M. Komiyama, Chem. Lett. 269 (1986). 123. Y. Wang, H. Liu, and Y. Jiang, J. Chem. Soc. Chem. Commun. 1878 (1989). 124. R. G. Freeman, K. C. Grabar, K. J. Allison, R. M Bright, J. A. Davis, A. P. Guthrie, M. B. Hommer, M. A. Jackson, P. C. Smith, D. G. Walter, and M. J. Natan, Science 267, 1629 (1995). 125. K. C. Grabar, K. J. Allison, B. E. Baker, R. M. Bright, K. R. Brown, R. G. Freeman, A. P. Fox, C. D. Keating, M. D. Musick, and M. J. Natan, Langmuir 12, 2353 (1996). 126. M. Brust, D. Bethell, D. Schiffrin, and C. Kiely, Adv. Mater. 7, 795 (1995). 127. R. Andres, S. Datta, M. Dorongi, J. Gomez, J. I. Henderson, D. B. Janes, V. R. Kolagunta, C. P. Kubiak, W. Mahoney, R. F. Osifchin, R. Reifenberger, M. P. Samanta, and W. Tian, J. Vac. Sci. Technol. A 14, 1178 (1996). 128. J. I. Henderson, S. Feng, G. Ferrence, T. Bein, and C. Kubiak, Inorg. Chim. Acta 242, 115 (1996). 129. D. Bethell, M. Brust, D. J. Schiffrin, and C. Kiely, J. Electroanal. Chem. 409, 137 (1996).

Metal Nanoclusters 130. K. V. Sarathy, P. J. Thomas, G. U. Kulkarni, and C. N. R. Rao, J. Phys. Chem. B 103, 399 (1999). 131. S. W. Chen, J. Phys. Chem. B 104, 663 (2000). 132. N. Fishelson, I. Shkrob, O. Lev, J. Gun, and A. D. Modestov, Langmuir 17, 403 (2001). 133. M. Aslam, I. Mulla, and K. Vijayamohanan, Langmuir 17, 7487 (2001). 134. M. Brust and C. Kiely, Coll. Surf. A 202, 175 (2002). 135. M. Dorogi, J. Gomez, R. Osifchin, R. Andres, and R. Reifenberger, Phys. Rev. B 52, 9071 (1995). 136. R. P. Andres, T. Bein, M. Dorogi, S. Feng, J. I. Henderson, C. P. Kubiak, W. Mahoney, R. G. Osifchin, and R. Reifenberger, Science 272, 1323 (1996). 137. D. I. Gittins, D. Bethell, D. J. Schiffrin, and R. J. Nichols, Nature 408, 67 (2000). 138. Y. Nakamura and H. Hirai, Chem. Lett. 1197 (1976). 139. Y. Wang, H. Liu, and Y. Huang, Polym. Adv. Tech. 7, 634 (1996). 140. C. Lange, D. De Caro, A. Gamez, S. Storck, J. S. Bradley, and W. F. Maier, Langmuir 15, 5333 (1999). 141. M. T. Reetz and M. Dugal, Catal. Lett. 58, 207 (1999). 142. H. Bonnemann, U. Endruschat, B. Tesche, A. Rufinska, C. W. Lehmann, F. E. Wagner, G. Filoti, V. Parvulescu, and V. I. Parvulescu, Eur. J. Inorg. Chem. 5, 819 (2000). 143. T. Teranishi, M. Hosoe, and M. Miyake, Adv. Mater. 9, 65 (1997). 144. “Single-Charge Tunneling” (H. Grabert and M. H. Devoret, Eds.). Plenum, New York, 1992. 145. M. Kastner, Nature 389, 667 (1997). 146. H. Liu and N. Toshima, J. Chem. Soc. Chem. Commun. 1095 (1992). 147. X. Fu, Y. Wang, N. Wu, L. Gui, and Y. Tang, J. Colloid Interf. Sci. 243, 326 (2001). 148. G. Schmid, B. Morun, and J.-O. Malm, Angew. Chem. Int. Ed. Engl. 28, 778 (1989). 149. G. Schmid, Inorg. Synth. 7, 214 (1990). 150. G. Schmid, M. Hams, J.-O. Malm, J.-O. Bovin, J. v. Ruitenbeck, H. W. Zandbergen, and W. T. Fu, J. Am. Chem. Soc. 115, 2046 (1993). 151. G. Schmid, S. Emde, V. Maihack, W. Meyer-Zaika, and St. Peschel, J. Mol. Catal. A 107, 95 (1996). 152. G. Schmid, R. Pugin, J.-O. Malm, and J.-O. Bovin, Eur. J. Inorg. Chem. 813 (1998). 153. M. Green and P. O’Brien, Chem. Commun. 1912 (2001). 154. N. T. Tran, D. R. Powell, and L. F. Dahl, Angew. Chem. Int. Ed. 39, 4121 (2000). 155. A. L. Mackay, Acta Crstallogr. 15, 916 (1962). 156. M. Brust, M. Walker, D. Bethell, D. J. Schiffrin, and R. Whyman, J. Chem. Soc., Chem. Commun. 801 (1994). 157. M. Brust, J. Fink, D. Bethell, D. J. Schiffrin, and C. Kiely, J. Chem. Soc., Chem. Commun. 1655 (1995). 158. C. K. Yee, R. Jordan, A.Ulman, H. White, A. King, M. Rafailivich, and J. Sokolov, Langmuir 15, 3486 (1999). 159. C. K. Yee, M. Scotti, A. Ulman, H. White, A. King, M. Rafailivich, and J. Sokolov, Langmuir 15, 4314 (1999). 160. N. Sandhyarani, M. R. Resmi, R. Unnikrishnan, K. Vidyasagar, S. G. Ma, M. P. Antony, G. P. Selvam, V. Visalakshi, N. Chandrakumar, K. Pandian, Y. T. Tao, and T. Pradeep, Chem. Mater. 12, 104 (2000). 161. N. K. Chaki, S. G. Sudrik, H. R. Sonawane, and K. Vijayamohanan, Chem. Commun. 76 (2002). 162. S. L. Horswell, C. J. Kiely, I. A. O’Neil, and D. J. Schiffrin, J. Am. Chem. Soc. 121, 5573 (1999). 163. M. J. Hostetler, C.-J. Zhong, B. K. H. Yen, J. Anderegg, S. M. Gross, N. D. Evans, M. Porter, and R. W. Murray, J. Am. Chem. Soc. 120, 9396 (1998). 164. S. R. Johnson, S. D. Evans, S. W. Mahon, and A. Ulman, Langmuir 13, 51 (1997). 165. S. Chen and R. W. Murray, Langmuir 15, 682 (1999).

Metal Nanoclusters 166. R. H. Terrill, T. A. Postlethwaite, C.-H. Chen, C.-D. Poon, A. Terzis, A. Chen, J. E. Hutchison, M. R. Clark, G. Wignall, J. D. Londono, R. Superfine, M. Falve, C. S. Johnson, E. T. Samulski, and R. W. Murray, J. Am. Chem. Soc. 117, 12537 (1995). 167. M. J. Hostetler, J. E. Wingate, C.-J. Zhong, J. E. Harris, R. W. Vachet, M. R. Clark, J. D. Londono, S. J. Green, J. J. Stokes, G. D. Wignall, G. L. Glish, M. D. Porter, N. D. Evans, and R. W. Murray, Langmuir 14, 17 (1998). 168. S. Chen and K. Kimura, Langmuir 15, 1075 (1999). 169. J. Hu, J. Zhang, F. Liu, K. Kittredge, J. K. Whitesell, and M. A. Fox, J. Am. Chem. Soc. 123, 1464 (2001). 170. J. Zhang, J. K. Whitesell, and M. A. Fox, Chem. Mater. 13, 2323 (2001). 171. M. Yamada, I. Quiros, J. Mizutani, K. Kubo, and H. Nishihara, Phys. Chem. Chem. Phys. 3377 (2001). 172. N. Kanayama, O. Tsutsumi, A. Kanazawa, and T. Ikeda, Chem. Commun. 2604 (2001). 173. S. Watanabe, M. Sonobe, M. Arai, Y. Tazume, T. Matsuo, T. Nakamura, and K. Yoshida, Chem. Commun. 2866 (2002). 174. G. Wang, J. Zhang, and R. W. Murray, Anal. Chem. 74, 4320 (2002). 175. D. V. Leff, P. C. Ohara, J. R. Heath, and W. M. Gelbart, J. Phys. Chem. 99, 7036 (1995). 176. K. Hata and H. Fujihara, Chem. Commun. 2714 (2002). 177. D. V. Leff, L. Brandt, and J. R. Heath, Langmuir 12, 4723 (1996). 178. S. Gomez, K. Philippot, V. Collière, B. Chaudret, F. Senocq, and P. Lecante, Chem. Commun. 1945 (2000). 179. S. Mandal, P. R. Selvakannan, D. Roy, R. V. Chaudhari, and M. Sastry, Chem. Commun. 3002 (2002). 180. P. R. Selvakannan, S. Mandal, R. Pasricha, S. D. Adyanthaya, and M. Sastry, Chem. Commun. 1334 (2002). 181. J. Hambrock, R. Becker, A. Birkner, J. Weiss, and R. A. Fischer, Chem. Commun. 68 (2002). 182. C. Damle and M. Sastry, J. Mater. Chem. 1860 (2002). 183. C.-J. Zhong, W.-X. Zhang, F. L. Leibowitz, and H. H. Eichelberger, Chem. Commun. 1211 (1999). 184. T. Yonezawa, K. Yasui, and N. Kimizuka, Langmuir 17, 271 (2001). 185. J. Liu, S. Mendoza, E. Roman, M. J. Lynn, R. L. Xu, and A. E. Kaifer, J. Am. Chem. Soc. 121, 4304 (1999). 186. J. Liu, J. Alvarez, and A. E. Kaifer, Adv. Mater. 12, 1381 (2000). 187. J. Alvarez, J. Liu, E. Roman, and A. E. Kaifer, Chem. Commun. 1151 (2000). 188. J. Liu, W. Ong, E. Roman, M. J. Lynn, and A. E. Kaifer, Langmuir 16, 3000 (2000). 189. J. Liu, J. Alvarez, W. Ong, E. Roman, and A. E. Kaifer, J. Am. Chem. Soc. 123, 11148 (2001). 190. J. Liu, J. Alvarez, W. Ong, E. Roman, and A. E. Kaifer, Langmuir 17, 6762 (2001). 191. J. Liu, J. Alvarez, W. Ong, and A. E. Kaifer, Nano Lett. 1, 27 (2001). 192. J. Alvarez, J. Liu, E. Román, and A. E. Kaifer, Chem. Commun. 2000, 1151 (2002). 193. J. Liu, W. Ong, A. E. Kaifer, and C. Peinador, Langmuir 18, 5981 (2002). 194. R. L. Whetten, J. T. Khoury, M. M. Alvarez, S. Murthy, I. Vezmar, Z. L. Wang, P. W. Stephens, C. L. Cleveland, W. D. Luedtke, and U. Landman, Adv. Mater. 8, 428 (1996). 195. X. M. Lin and C. M. Sorensen, Chem. Mater. 11, 198 (1999). 196. T. G. Schaaff, M. N. Shafigullin, J. T. Khoury, I. Vezmar, R. L. Wherren, W. G. Cullen, P. N. First, C. Gutiérrrez, J. Ascensio, and M. J. Jose-Yacamán, J. Phys. Chem. B 101, 7885 (1997). 197. T. G. Schaaff, G. Knight, M. N. Shafigulin, R. F. Borkman, and R. L. Whetten, J. Phys. Chem. B 102, 10643 (1998). 198. T. T. P Cheung, Surf. Sci. 140, 151 (1984). 199. W. Ederhardt, P. Fayet, D. M. Cox, Z. Fu, A. Kaldor, R. Sherwood, and D. Sondericker, Phys. Rev. Lett. 64, 780 (1990).

363 200. G. K. Wertheim, S. B. Dicenzo, and S. E. Young, Phys. Rev. Lett. 51, 2310 (1983). 201. S. Link, M. A. El-Sayed, T. G. Schaaff, and R. L. Whetten, Chem. Phys. Lett. 356, 240 (2002). 202. S. Link, A. Beeby, S. FitzGerald, M. A. El-Sayed, T. G. Schaaff, and R. L. Whetten, J. Phys. Chem. B 106, 3410 (2002). 203. D. V. Goia and E. Matijevic, New J. Chem. 1203 (1998). 204. T. Yonezawa, K. Imamura, and N. Kimizuka, Langmuir 17, 4701 (2001). 205. H. Bonnemann, G. Braun, W. Brijoux, R. Brinkmann, A. Tilling, K. Seevogel, and K. Siepen, J. Organomet. Chem. 520, 143 (1996). 206. H. Bonnemann, P. Britz, and W. Vogel, Langmuir 14, 6654 (1998). 207. J. Rothe, J. Hormes, H. Bönnemann, W. Brijoux, and K. Siepen, J. Am. Chem. Soc. 120, 6019 (1998). 208. J. P. Abid, A. W. Wark, P. F. Brevet, and H. H. Girault, Chem. Commun. 792 (2002). 209. N. Kometani, H. Doi, K. Asami, and Y. Yonezawa, Phys. Chem. Chem. Phys. 5142 (2002). 210. C.-L. Lee, C.-C. Wan, and Y.-Y. Wang, Adv. Funct. Mater. 11, 344 (2000). 211. S. J. Lee, S. W. Han, and K. Kim, Chem. Commun. 442 (2002). 212. M. Moreno-Manas, R. Pleixats, and S. Villarroya, Chem. Commun. 60 (2002). 213. M. T. Reetz, M. Winter, R. Breinbauer, T. Thurn-Albrecht, and W. Vogel, Chem.-Eur. J. 7, 1084 (2001). 214. N. S. Sobal, M. Hilgendorff, H. Möhwald, and M. Giersig, Nano Lett. 2, 621 (2002). 215. M. Mandal, S. K. Ghosh, S. Kundu, K. Esumi, and T. Pal, Langmuir 18, 7792 (2002). 216. J. S. Bradley, B. Tesche, W. Busser, M. Masse, and R. T. Reetz, J. Am. Chem. Soc. 122, 4631 (2000). 217. D. V. Averin and K. K. Likaharev, J. Low Temp. Phys. 62, 345 (1986). 218. A. Kumar and G. M. Whitesides, Science 263, 60 (1994). 219. R. H. Terrill, T. A. Postlethwaite, C. Chen, C.-D. Poon, A. Terzis, A. Chen, J. E. Hutchison, M. R. Clark, G. Wignall, J. D. Londono, R. Superfine, M. Falvo, C. S. Johnson, Jr., E. T. Samulski, and R. W. Murray, J. Am. Chem. Soc. 117, 12537 (1995). 220. A. P. Alivisatos, Science 271, 933 (1996). 221. R. P. Andres, J. D. Bielefeld, J. I. Henderson, D. B. Janes, V. R. Kolagunta, C. P. Kubiak, W. J. Mahoney, and R. G. Osifchin, Science 273, 1690 (1996). 222. D. L. Feldheim, K. C. Grabar, M. J. Natan, and T. E. Mallouk, J. Am. Chem. Soc. 118, 7640 (1996). 223. Y. Xia, E. Kim, M. Mrksich, and G. M.Whitesides, Chem. Mater. 8, 601 (1996). 224. G. Hornyak, M. Kroll, R. Pugin, T. Sawitowski, G. Schmid, J. O. Bovin, G. Karsson, H. Hofmeister, and S. Hopfe, Chem.-Eur. J. 3, 1951 (1997). 225. Z.-L. Wang, Adv. Mater. 10, 13 (1998). 226. C. T. Black, C. B. Murry, R. L. Sandstrom, and S. Sun, Science 290, 1131 (2000). 227. T. Teranishi, M. Haga, Y. Shiozawa, and M. Miyake, J. Am. Chem. Soc. 122, 4237 (2000). 228. J. Liu, T. Lee, D. B. Janes, B. L. Walsh, M. R. Melloch, J. M. Woodall, R. Reifenberger, and R. P. Andres, Appl. Phys. Lett. 77, 373 (2000). 229. D. B. Janes, T. Lee, J. Liu, M. Batistuta, N. P. Chen, B. L. Walsh, R. P. Andres, E. H. Chen, M. R. Melloch, J. M. Woodall, and R. Reifenberger, J. Electron. Mater. 29, 565 (2000). 230. V. Torma, T. Reuter, O. Vidoni, M. Schumann, C. Radehaus, and G. Schmid, Chem. Phys. Chem. 2, 546 (2001). 231. D. Wyrwa, N. Beyer, and G. Schmid, Nano Lett. 2, 419 (2002). 232. B. A. Korgel and D. Fitzmaurice, Phys. Rev. Lett. 80, 3531 (1998). 233. D. I. Gittins, A. S. Susha, B. Schoeler, and F. Caruso, Adv. Mater. 14, 508 (2002).

364 234. T. C. Rojas, J. M. de la Fuente, A. G. Barrientos, S. Penadés, L. Ponsonnet, and A. Fernández, Adv. Mater. 14, 585 (2002). 235. C. R. Mayer, S. Neveu, and V. Cabuil, Adv. Mater. 14, 595 (2002). 236. T. Hassenkam, K. Nˇrrgaard, L. Iversen, C. J. Kiely, M. Brust, and T. Bjˇrrnholm, Adv. Mater. 14, 1126 (2002). 237. J. Fink, C. J. Kiely, D. Bethell, and D. J. Schiffrin, Chem. Mater. 10, 922 (1998). 238. S. T. Liu, T. Zhu, R. S. Hu, and Z. F. Liu, Phys. Chem. Chem. Phys. 4, 6059 (2002). 239. I. Sloufova-Srnova and B. Vlckova, Nano Lett. 2, 121 (2002). 240. G. Schmid, M. Bäumle, and N. Beyer, Angew. Chem. Int. Ed. 39, 181 (2000). 241. S. A. Harfenist, Z.-L. Wang, M. M. Alvarez, I. Vezmar, and R. L. Whetten, J. Phys. Chem. 100, 13904 (1996). 242. B. A. Korgel and D. Fitzmaurice, Adv. Mater. 10, 661 (1998). 243. B. A. Korgel, S. Fullam, S. Connolly, and D. Fitzmaurice, J. Phys. Chem. B 102, 8379 (1998). 244. Z. L. Wang, S. A. Harfenist, R. L. Whetten, J. Bebtley, and N. D. Evans, J. Phys. Chem. B 102, 3068 (1998). 245. B. A. Korgel, N. Zaccheroni, and D. Fitzmaurice, J. Am. Chem. Soc. 121, 3533 (1999). 246. B. A. Korgel and D. Fitzmanurice, Phys. Rev. B 59, 14191 (1999). 247. H. I. S. Nogueira, P. C. R. Soares-Santos, S. M. G. Cruz, and T. Trindade, J. Mater. Chem. 2339 (2002). 248. K. V. Sarathy, G. Raina, R. T. Yadav, G. U. Kulkarni, and C. N. R. Rao, J. Phys. Chem. B 101, 9876 (1997). 249. M. T. Reetz, M. W. Winter, and B. Tesche, Chem. Commun. 147 (1997). 250. Z.- L. Wang, Z.-R. Dai, and S.-H. Sun, Adv. Mater. 12, 1944 (2000). 251. S. Sun, C. B. Murray, D. Weller, L. Folks, and A. Moser, Science 287, 1989 (2000). 252. S. A. Harfenist, Z.-L. Wang, M. M. Alvarez, I. Vezmar, and R. L. Whetten, J. Phys. Chem. 100, 13904 (1996). 253. W. D. Luedtke and U. Landman, J. Phys. Chem. 100, 13323 (1996). 254. Z. L. Wang, S. A. Harfenist, I. Vezmar, R. L. Whetten, J. Bentley, N. D. Evans, and K. B. Alexander, Adv. Mater. 10, 808 (1998). 255. J. R. Heath, C. M. Knobler, and D. V. Leff, J. Phys. Chem. B 101, 189 (1998). 256. E. Shevchenko, D. Talapin, A. Kornowski, F. Wiekhorst, J. Kötzler, M. Haase, A. Rogach, and H. Weller. Adv. Mater. 14, 287 (2002). 257. T. Yonezawa, S. Onoue, and N. Kimizuka, Langmuir 17, 2291 (2001). 258. T. Yonezawa, S. Onoue, and N. Kimizuka, Adv. Mater. 13, 140 (2001). 259. T. Yonezawa and T. Kunitake, Colloid Surf. A 149, 193 (1999). 260. J. Simard, C. Briggs, A. K. Boal, and V. M. Rotello, Chem. Commun. 1943 (2000). 261. T. Yonezawa, H. Matsune, and T. Kunitake, Chem. Mater. 11, 33 (1999). 262. W. Cheng, J. Jiang, S. Dong, and E. Wang, Chem. Commun. 1706 (2002). 263. R. I. Nooney, T. Dhanasekaran, Y. Chen, R. Josephs, and A. E. Ostafin, Adv. Mater. 14, 529 (2002). 264. H. Rensmo, A. Ongaro, D. Ryan, and D. Fitzmaurice, J. Mater. Chem. 2762 (2002). 265. H. Y. Y. Ko, M. Mizuhata, A. Kajinami, and S. Deki, J. Mater. Chem. 1495 (2002). 266. Y.-S. Shon and H. Choo, Chem. Commun. 2560 (2002). 267. K. i Uosaki, T. Kondo, M. Okamura, and W. Song, Faraday Discuss. 373 (2002). 268. A. W. Snow, M. G. Ancona, W. Kruppa, G. G. Jernigan, E. E. Foos, and D. Park, J. Mater. Chem. 1222 (2002). 269. S. D. Jhaveri, D. A. Lowy, E. E. Foos, A. W. Snow, M. G. Ancona, and L. M. Tender, Chem. Commun. 1544 (2002). 270. M. Yamada and H. Nishihara, Chem. Commun. 2578 (2002). 271. M. Yamada, A. Kuzume, M. Kurihara, K. Kubo, and H. Nishihara, Chem. Commun. 2476 (2001).

Metal Nanoclusters 272. H. Bonnemann, N. Waldofner, H. G. Haubold, and T. Vad, Chem. Mater. 14, 1115 (2002). 273. M. Kogiso, K. Yoshida, K. Yase, and T. Shimizu, Chem. Commun. 2492 (2002). 274. T. Cassagneau and F. Caruso, Adv. Mater. 14, 732 (2002). 275. E. Hutter and J. H. Fendler, Chem. Commun. 378 (2002). 276. J. B. Carroll, B. L. Frankamp, and V. M. Rotello, Chem. Commun. 1892 (2002). 277. N. Lu, J. Zheng, M. Gleiche, H. Fuchs, L. Chi, O. Vidoni, T. Reuter, and G. Schmid, Nano Lett. 2, 1097 (2002). 278. S. Hoeppener, L. Chi, and H. Fuchs, Nano Lett. 2, 459 (2002). 279. D. Wyrwa, N. Beyer, and G. Schmid, Nano Lett. 2, 419 (2002). 280. T. Reuter, O. Vidoni, V. Torma, and G. Schmid, Nano Lett. 2, 709 (2002). 281. G. Dumpich, E. F. Wassermann, M. Winter, and M. T. Reetz, Mater. Sci. Forum 287, 413 (1998). 282. L. Clarke, M. N. Wybourne, M. D. Yan, S. X. Cai, and J. F. W. Keana, Appl. Phys. Lett. 71, 617 (1997). 283. X. M. Lin, R. Parthasarathy, and H. M. Jaeger, Appl. Phys. Lett. 78, 1915 (2001). 284. T. R. Bedson, R. E. Palmer, T. E. Jenkins, D. J. Hayton, and J. P. Wilcoxon, Appl. Phys. Lett. 78, 1921 (2001). 285. T. R. Bedson, R. E. Palmer, and J. P. Wilcoxon, Appl. Phys. Lett. 78, 2061 (2001). 286. M. H. V. Werts, L. Mathieu, J. Bourgoin, and M. Brust, Nano Lett. 2, 43 (2002). 287. B. F. G. Johnson, K. M. Sanderson, D. S. Shephard, D. Ozkaya, W. Zhou, H. Ahmed, M. D. R. Thomas, L. Gladden, and M. Mantle, Chem. Commun. 1317 (2000). 288. F. Stellacci, C. A. Bauer, T. Meyer-Friedrichsen, W. Wenseleers, V. Alain, S. M. Kuebler, S. J. K. Pond, Y. Zhang, S. R. Marder, and J. W. Perry, Adv. Mater. 14, 194 (2002). 289. R. Maoz, S. R. Cohen, and J. Sagiv, Adv. Mater. 11, 55 (1999). 290. R. Maoz, E. Frydman, S. R. Cohen, and J. Sagiv, Adv. Mater. 12, 424 (2000). 291. R. Maoz, E. Frydman, S. R. Cohen, and J. Sagiv, Adv. Mater. 12, 725 (2000). 292. S. Hoeppener, R. Maoz, S. R. Cohen, L. F. Chi, H. Fuchs, and J. Sagiv, Adv. Mater. 14, 1036 (2002). 293. S. Liu, R. Maoz, G. Schmid, and J. Sagiv, Nano Lett. 2, 1055 (2002). 294. C. M. Niemeyer, Angew. Chem. Int. Ed. 40, 4128 (2001). 295. S. Behrens, K. Rahn, W. Habicht, K.-J. Böhm, H. Rösner, E. Dinjus, and E. Unger, Adv. Mater. 14, 1621 (2002). 296. M. Mertig, R. Kirsch, W. Pompe, and H. Engelhardt, Eur. Phys. J. D 9, 45 (1999). 297. U. B. Slytr, P. Messner, D. Pum, and M. Sara, Angew. Chem. Int. Ed. 38, 1034 (1999). 298. W. Shenton, D. Pum, U. B. Sleytr, and S. Mann, Nature 389, 585 (1997). 299. W. Shenton, T. Douglas, M. Young, G. Stubbs, and S. Mann, Adv. Mater. 11, 253 (1999). 300. T. A. Taton, R. C. Mucic, C. A. Mirkin, and R. L. Letsinger, J. Am. Chem. Soc. 122, 6305 (2000). 301. L. M. Demers, S. J. Park, T. A. Taton, Z. Li, and C. A. Mirkin, Angew. Chem. Int. Ed. 40, 3071 (2001). 302. M. Sastry, A. Kumar, S. Datar, C. V. Dharmadhikari, and K. N. Ganesh, Appl. Phys. Lett. 78, 2943 (2001). 303. Y. Maeda, H. Tabata, and T. Kawai, Appl. Phys. Lett. 79, 1181 (2001). 304. S. J. Lin, M. Satjapipat, A. J. Baca, and F. Zhou, Chem. Commun. 609 (2001). 305. E. Dujardin, L. B. Hsin, C. R. C. Wang, and S. Mann, Chem. Commun. 1264 (2001). 306. A. N. Shipway and I. Willner, Chem. Commun. 2035 (2001). 307. E. Braun, Y. Eichen, U. Sivan, and G. Ben-Yoseph, Nature 391, 775 (1998).

Metal Nanoclusters 308. J. Richter, R. Seidel, R. Kirsch, M. Mertig, W. Pomp, J. Plaschke, and H. K. Schackert, Adv. Mater. 12, 507 (2000). 309. J. Richter, M. Mertig, M. I. Pomp, and H. K. Schackert, Appl. Phys. Lett. 78, 536 (2001). 310. O. Harnack, W. E. Ford, A. Yasuda, and J. M. Wessels, Nano Lett. 2, 919 (2002). 311. R. Elghanian, J. J. Storhoff, R. C. Mucic, R. L. Letsinger, and C. A. Mirkin, Science 277, 1078 (1997). 312. A. P. F. Turner, Science 290, 1315 (2000). 313. B. H. Schneider, F. D. Quinn, and D. A. Shafer, ACS Symp. Ser. 815, 107 (2002). 314. I. M. Klotz, “Ligand–Receptor Energetics: A Guide for the Perplexed.” Wiley, New York, 1997. 315. A. J. Haes and R. P. Van Duyne, J. Am. Chem. Soc. 124, 10596 (2002). 316. D. J. Maxwell, J. R. Taylor, and S. M. Nie, J. Am. Chem. Soc. 124, 9606 (2002). 317. J. J. Storhoff, R. Elghanian, R. C. Mucic, C. A. Mirkin, and R. L. Letsinger, J. Am. Chem. Soc. 120, 1959 (1998). 318. T. A. Taton, C. A. Mirkin, and R. L. Letsinger, Science 289, 1757 (2000). 319. R. A. Reynolds III, C. A. Mirkin, and R. L. Letsinger, J. Am. Chem. Soc. 122, 3795 (2000). 320. L. M. Demers, C. A. Mirkin, R. C. Mucic, R. A. Reynolds, R. L. Letsinger, R. Elghanian, and Viswanadham, Anal. Chem. 72, 5535 (2000). 321. R. A. Reynolds III, C. A. Mirkin, and R. L. Letsinger, Pure Appl. Chem. 72, 229 (2000). 322. T. A. Taton, G. Lu, and C. A. Mirkin, J. Am. Chem. Soc. 123, 5164 (2001). 323. S.-J. Park, T. A. Taton, and C. A. Mirkin, Science 295, 1503 (2002). 324. Y. W. C. Cao, R. C. Jin, and C. A. Mirkin, Science 297, 1536 (2002). 325. R. C. Jin, G. S. Wu, Z. Li, C. A. Mirkin, and G. C. Schatz, J. Am. Chem. Soc. 125, 1643 (2003). 326. K. T. Ranjit, A. Lichtenstein, F. Patolsky, and I. Willner, Chem. Commun. 1025 (2000). 327. O. Lioubashevski, F. Patolsky, and I. Willner, Langmuir 17, 5134 (2001). 328. Y. Weimann, F. Patolsky, and I. Willner, Analyst 126, 1502 (2001). 329. I. Willner, F. Patolsky, Y. Weimann, and B. Willner, Talanta 56, 847 (2002). 330. J. Wang, D. K. Xu, A. N. Kawde, and R. Polsky, Anal. Chem. 73, 5576 (2001). 331. J. Wang, R. Polsky, and D. K. Xu, Langmuir 17, 5739 (2001). 332. J. Wang, Anal. Chim. Acta 469, 63 (2002). 333. L. He, M. D. Musick, S. R. Nicewarner, F. G. Salinas, S. J. Benkovic, M. J. Natan, and C. D. Keating, J. Am. Chem. Soc. 122, 9071 (2000). 334. X. C. Zhou, S. J. O’Shea, and S. F. Y. Li, Chem. Commun. 953 (2000). 335. N. Stich, A. Gandhum, V. Matushin, C. Mayer, G. Bauer, and T. Schalkhammer, J. Nanosci. Nanotech. 1, 397 (2001). 336. J. H. Xu, J. J. Zhu, Y. L. Zhu, K. Gu, and H. Y. Chen, Anal. Lett. 34, 503 (2001). 337. H. Q. Zhao, L. Lin, J. R. Li, J. A. Tang, M. X. Duan, and L. Jiang, J. Nanopart. Res. 3, 321 (2001). 338. H. Q. Zhao, L. Lin, J. Tang, M. X. Duan, and L. Jiang, Chin. Sci. Bull. 46, 1074 (2001). 339. H. Cai, Y. Q. Wang, P. G. He, and Y. H. Fang, Anal. Chim. Acta. 469, 165 (2002). 340. H. Cai, Y. Xu, N. N. Zhu, P. G. He, and Y. Z. Fang, Analyst 127, 803 (2002). 341. S. Sampath and O. Lev, Adv. Mater. 9, 410 (1997). 342. S. Bharathi and O. Lev, Anal. Commun. 35, 29 (1998). 343. S. Bharathi, M. Nogami, and O. Lev, Langmuir 17, 2602 (2001). 344. S. Bharathi and M. Nogami, Analyst 126, 1919 (2001).

365 345. F. Q. Tang and L. Jiang, Ann. NY Acad. Sci. 864, 538 (1998). 346. F. Q. Tang, J. F. Shen, J. F. Zhang, and G. L. Zhang, Chem. J. Chin. Univ. 20, 634 (1999). 347. F. Q. Tang, Z. Wei, D. Chen, X. W. Meng, L. Gou, and J. G. Ran, Chem. J. Chin. Univ. 21, 91 (2000). 348. F. Q. Tang, X. W. Meng, D. Chen, J. G. Ran, and C. Q. Zheng, Sci. Chin.: Chem. B 43, 268 (2000). 349. F. Q. Tang and X. L. Ren, Acta Chim. Sinica 60, 393 (2002). 350. X. Su, S. F. Y. Li, and S. J. O’Shea, Chem. Commun. 755 (2001). 351. J. B. Jia, B. Q. Wang, A. G. Wu, G. J. Cheng, Z. Li, and S. J. Dong, Anal. Chem. 74, 2217 (2002). 352. R. Wilson, Chem. Commun. 108 (2003). 353. N. Stich, A. Gandhum, V. Matushin, J. Raats, C. Mayer, Y. Alguel, and T. Schalkhammer, J. Nanosci. Nanotech. 2, 375 (2002). 354. G. Cardenas-Trivino, K. Klabunde, and D. E. Brock, Langmuir 3, 986 (1987). 355. F. Tian and K. J. Klabunde, New J. Chem. 22, 1275 (1998). 356. S. Stoeva, K. J. Klabunde, C. M. Sorensen, and I. Dragieva, J. Am. Chem. Soc. 124, 2305 (2002). 357. X. Du, Y. Wang, Y. Mu, L. Gui, P. Wang, and Y. Tang, Chem. Mater. 14, 3953 (2002). 358. T. Tano, K. Esumi, and K. Meguro, J. Colloid Interf. Sci. 133, 530 (1999). 359. F. Endres, Chem. Phys. Chem. 3, 144 (2002). 360. F. Endres and S. Z. El Abedin, Chem. Commun. 892 (2002). 361. H. Bonnemann and W. Brijoux, Nanostruct. Mater. 5, 135 (1995). 362. R. Pranke, J. Rothe, J. Pollmann, J. Hormes, H. Bonnemann, W. Brijoux, and T. Hindenburg, J. Am. Chem. Soc. 118, 12090 (1996). 363. X. Fu, Y. Wang, N. Wu, L. Gui, and Y. Tang, Langmuir 18, 4619 (2002). 364. K. Torigoe and K. Esumi, J. Phys. Chem. B 103, 2862 (1999). 365. Y. Lin and R. G. Finke, J. Am. Chem. Soc. 116, 8335 (1994). 366. J. D. Aiken III and R. G. Finke, J. Am. Chem. Soc. 121, 8803 (1999). 367. A. Troupis, A. Hiskia, and E. Papaconstantinou, Angew. Chem. Int. Ed. 41, 1911 (2002). 368. L. D. Rampino and F. F. Nord, J. Am. Chem. Soc. 63, 2745 (1941). 369. C. Sachs, A. Pundt, R. Kirchheim, R, M. Winter, M. T. Reetz, and D. Fritsch, Phys. Rev. B 6407, 075408 (2001). 370. J. Le Bars, U. Specht, J. S. Bradley, and D. G. Blackmond, Langmuir 15, 7621 (1999). 371. Toshima, N., Yonezawa, T. Harada, M. Asakura, and K. Iwasawa, Chem. Lett. 815 (1990). 372. N. Toshima and T. Yonezawa, New J. Chem. 22, 1179 (1998). 373. W. Yu, Y. Wang, and H. Liu, J. Mol. Catal. A 112, 105 (1996). 374. P. Lu, T. Teranishi, K. Asakura, M. Miyake, and N. Toshima, J. Phys. Chem. B 103, 9673 (1999). 375. M. B. Thathagar, J. Beckers, and G. Rothenberg, J. Am. Chem. Soc. 124 11858 (2002). 376. Y. Izumi, Adv. Catal. 32, 2151 (1983). 377. A. Tai and T. Harada, in “Tailored Metal Catalysts” (Y. Iwasawa, Ed.), p. 265. Kluwer, Dordrecht, 1986. 378. A. F. Carley, M. K. Rajurnon, M. W. Roberts, and P. B. Wells, J. Chem. Soc., Faraday Trans. 91, 2176 (1995). 379. H. Blaser, H. Jalett, M. Muller, and M. Studer, Catal. Today 37, 441 (1997). 380. M. O. Lorenzo, C. J. Baddeley, and R. Muryn, Nature 404, 376 (2000). 381. L. A. M. M. Barbosa and P. Sautet, J. Am. Chem. Soc. 123, 6639 (2001). 382. V. Hurnhlot, S. Haq, C. Muryn, W. A. Hofer, and R. Raval, J. Am. Chem. Soc. 124, 503 (2002). 383. H. Bonnemann and G. A. Braun, Chem.- Eur. J. 3, 1200 (1997). 384. H. Bonnemann and G. A. Braun, Angew. Chem. Int. Ed. Engl. 35, 1992 (1996).

366 385. X. B. Zuo, H. F. Liu, and M. H. Liu, Tetrahedron Lett. 39, 1941 (1998). 386. X. B. Zuo, H. F. Liu, D. W. Guo, and X. Z. Yang, Tetrahedron 55, 7787 (1999). 387. T. Teranishi, K. Nakata, M. Iwamoto, M. Miyake, and N. Toshima, React. Funct. Polym. 37, 111 (1998). 388. W. Yu, H. Liu, M. Liu, and Z. Liu, React. Funct. Polym. 44, 21 (2000). 389. W. Yu, H. Liu, M. Liu, and Q. Tao, J. Mol. Catal. A 138, 273 (1999). 390. M. Liu, W. Yu, H. Liu, and J. Zheng, J. Colloid Interf. Sci. 214, 231 (1999). 391. M. Liu, W. Yu, and H. Liu, J. Mol. Catal. A 138, 295 (1999). 392. H. Feng and H. Liu, J. Mol. Catal. A 126, L5 (1997). 393. Y. Li, E. Boone, and M. A. El-Sayed, Langmuir 18, 4921 (2002). 394. Y. Li and M. A. El-Sayed, J. Phys. Chem. B 105, 8938 (2001). 395. H. S. Wang, C. Wingender, H. Baltruschat, M. Lopez, and M. T. Reetz, J. Electroanal. Chem. 509, 163 (2001). 396. N. Toshima, Y. Shiraishi, T. Teranishi, M. Miyake, T. Tominaga, H. Watanabe, W. Brijoux, H. Bonnemann, and G. Schmid, Appl. Organomet. Chem. 15, 178 (2001). 397. M. N. Vargaftik, V. P. Zargorodnikov, I. P. Stolarov, and I. I. Moiseev, J. Chem. Soc. Chem. Commun. 937 (1985). 398. I. I. Moiseev, M. N. Vargaftik, T. V. Chernysheva, T. A. Stromnova, A. E. Gekhman, G. A. Tsirkov, and A. M. Makhlina, J. Mol. Catal. A 108, 77 (1996). 399. M. N. Vargaftik, N. Y. Kozitsyna, N. V. Cherkashina, R. I. Rudyi, D. I. Kochubei, and B. N. Novgorodov, Kinet. Catal. 39, 740 (1998). 400. J. Schulz, S. Levigne, A. Roucoux, and H. Patin, Adv. Syn. Catal. 334, 266 (2002). 401. M. Spiro and D. M. de Jesus, Langmuir 16, 2464 (2000). 402. U. Nickel, C. Liu, P. Lachenmayr, and M. Schneider, Bull. Soc. Chim. Fr. 308 (1988). 403. U. Nickel and C.-Y. Liu, J. Imaging Sci. 34, 8 (1990). 404. Y.-H. Chen, U. Nickel, and M. Spiro, J. Chem. Soc., Faraday Trans. 90, 617 (1994). 405. P. L. Freund and M. Spiro, J. Phys. Chem. 89, 1074 (1985). 406. P. L. Freund and M. Spiro, J. Chem. Soc., Faraday Trans. 82, 2277 (1986). 407. M. Spiro, Catal. Today 17, 517 (1993). 408. A. Mills, P. Douglas, and T. Russell, J. Chem. Soc., Faraday Trans. 86, 1417 (1990). 409. J. D. Aiken III and R. G. Finke, Chem. Mater. 11, 1035 (1999). 410. J. Turkevich and G. Kim, Science 169, 873 (1970). 411. W. Yu, M. Liu, H. Liu, X. An, Z. Liu, and X. Ma, J. Mol. Catal. A 142, 201 (1999). 412. W. Yu, H. Liu, X. An, X. Ma, Z. Liu, and L. Qiang, J. Mol. Catal. A 147, 73 (1999). 413. H. Bonnemann, W. Brijoux, A. S. Tilling, and K. Siepen, Top. Catal. 4, 217 (1997). 414. H. Bonnemann, W. Brijoux, K. Siepen, J. Hormes, R. Franke, J. Pollmann, and J. Rothe, Appl. Organomet. Chem. 11, 783 (1997). 415. J. P. M. Niederer, A. B. J. Arnold, W. F. Holderich, B. Spliethof, B. Tesche, M. Reetz, and H. Bonnemann, Top. Catal. 18, 265 (2002). 416. Mi. Zhao and R. M. Crooks, Angew. Chem. Inter. Ed. 38, 364 (1999). 417. H. Bonnemann, P. Britz, and H. Ehwald, Chem. Tech. 49, 189 (1997). 418. T. Frelink, W. Visscher, and J. A. R. van Veen, J. Electroanal. Chem. 382, 65 (1995). 419. K. Kinoshita, J. Electrochem. Soc. 137, 845 (1990). 420. W. Chen, J. Lee, and Z. Liu, Chem. Commun. 2588 (2002). 421. M. L. Anderson, R. M. Stroud, and D. R. Rolison, Nano Lett. 2, 235 (2002).

Metal Nanoclusters 422. T. J. Schmidt, M. Noeske, H. A. Gasteiger, R. J. Behm, P. Britz, W. Brijoux, and H. Bonnemann, Langmuir 13, 2591 (1997). 423. T. J. Schmidt, M. Noeske, H. A. Gasteiger, R. J. Behm, P. Britz, and H. Bonnemann, J. Electrochem. Soc. 145, 925 (1998). 424. T. J. Schmidt, M. Noeske, H. A. Gasteiger, R. J. Behm, P. Britz, and H. Bonnemann, J. Electrochem. Soc. 145, 3697 (1998). 425. U. A. Paulus, U. Endruschat, G. J. Feldmeyer, T. J. Schmidt, H. Bonnemann, and R. J. Behm, J. Catal. 195, 383 (2000). 426. H. Bonnemann, R. Brinkmann, P. Britz, U. Endruschat, R. Mortel, U. A. Paulus, G. J. Feldmeyer, T. J. Schmidt, H. A. Gasteiger, and R. J. Behm, J. New Mat. Electrochem. Syst. 3, 199 (2000). 427. E. S. Steigerwalt, G. A. Deluga, D. E. Cliffel, and C. M. Lukehart, J. Phys. Chem. B 105, 8097 (2001). 428. F. E. Jones, S. B. Milne, B. Gurau, E. S. Smotkin, S. R. Stock, and C. M. Lukehart, J. Nanosci. Nanotech. 2, 81 (2002). 429. X. Zhang and K. Chan, J. Mater. Chem. 1203 (2002). 430. K. Siepen, H. Bonnemann, W. Brijoux, J. Rothe, and J. Hormes, Appl. Organomet. Chem. 14, 549 (2000). 431. H. Bonnemann, W. Wittholt, J. D. Jentsch, and A. S. Tilling, New J. Chem. 22, 713 (1998). 432. J. Dai and M. L. Bruening, Nano Lett. 2, 497 (2002). 433. J. E. Park, S. Kim, S. Mihashi, O. Hatozaki, and N. Oyama, Macromol. Symp. 168, 35 (2002). 434. C. Binns, J. Nanosci. Nanotech. 1, 243 (2001). 435. D. L. Leslie-Pelecky and R. D. Rieke, Chem. Mater. 8, 1770 (1996). 436. J. L. Dormann, D. Fiorani, and E. Tronc, Adv. Chem. Phys. 98, 283 (1997). 437. K. Satoh, J. Jpn. Soc. Tribol. 41, 458 (1996). 438. G. D. Li, Rare Metal Mat. Eng. 31, 1 (2002). 439. S. H. Liou, IEEE Trans. Mag. 35, 3989 (1999). 440. O. Sqalli, M. P. Bernal, P. Hoffmann, and F. Marquis-Weible, Appl. Phys. Lett. 76, 2134 (2000). 441. D. R. Baselt, G. U. Lee, K. M. Hansen, L. A. Chrisey, and R. J. Colton, Proc. IEEE 85, 672 (1997). 442. D. K. Kim, Y. Zhang, J. Kehr, T. Klason, D. Bjelke, and M. Muhammed, J. Magn. Magn. Mater. 225, 256 (2001). 443. A. N. Rusetski and E. K. Ruuge, J. Magn. Magn. Mater. 85, 299 (1990). 444. A. Jordan, R. Scholz, P. Wust, H. Fahling, and R. Felix, J. Magn. Magn. Mater. 201, 413 (1999). 445. E. E. Carpenter, J. Magn. Magn. Mater. 225, 17 (2001). 446. S. Sun, S. Anders, H. F. Hamann, Jan-U. Thiele, J. E. E. Baglin, T. Thomson, E. E. Fullerton, C. B. Murray, and B. D. Terris, J. Am. Chem. Soc. 124, 2884 (2002). 447. D. J. Sellmyer, Nature 420, 374 (2002). 448. H. Zeng, J. Li, J. P. Liu, Z. L. Wang, and S. Sun, Nature 420, 395 (2002). 449. M. Jacoby, C&E News 78, 37 (2000). 450. R. F. Service, Science 287, 1902 (2000). 451. B. Warne, O. I. Kasyutich, E. L. Mayes, J. A. L. Wiggins, and K. K. W. Wong, IEEE Trans. Mag. 36, 3009 (2000). 452. B. Dieny, V. S. Speriosu, S. Metin, S. S. P. Parkin, B. A. Gurney, P. Baumgart, and D. R. Wilhoit, J. Appl. Phys. 69, 4774 (1991). 453. S. S. P. Parkin and D. Mauri, Phys. Rev. B 44, 7131 (1991). 454. J. S. Moodera, L. R. Kinder, T. M. Wong, and R. Meservey, Phys. Rev. Lett. 74, 3273 (1995). 455. T. Miyazaki and N. Tezuka, J. Magn. Magn. Mater. 139, L231 (1995). 456. T. Miyazaki and N. Tezuka, J. Magn. Magn. Mater. 151, 403 (1995). 457. M. N. Baibich, J. M. Broto, A. Fert, F. N. Van Dau, F. Petroff, P. Eitenne, G. Creuzet, A. Friederich, and J. Chazelas, Phys. Rev. Lett. 61, 2472 (1988). 458. C. Tsang, R. E. Fontana, B. A. Gurney, D. E. Heim, V. S. Speriosu, T. Lin, and M. L. Williams, IEEE Trans. Magn. 30, 3801 (1994). 459. J. C. Mallinson, “Magneto-Resitive Heads: Fundamentals and Applications,” p. 103. Academic Press, New York, 1996.

Metal Nanoclusters 460. S. S. P. Parkin, K. P. Roche, M. G. Samant, P. M. Rice, R.B. Beyers, R. E. Scheuerlein, E. J. Sullivan, S. L. Brown, J. Bucchigano, D. W. Abraham, Y. Lu, M. Rooks, P. L. Trouilloud, R. A. Wanner, and W. J. Gallagher, J. Appl. Phys. 85, 5828 (1999). 461. S. Tehrani, E. Chen, M. Durlam, M. DeHerrera, J. M. Slaughter, J. Shi, and G. Kerszykowski, J. Appl. Phys. 85, 5822 (1999). 462. S. Tehrani, B. Engel, J. M. Slaughter, E. Chen, M. DeHerrera, M. Durlam, P. Naji, R. Whig, J. Janesky, and J. Cader, IEEE Trans. Mag. 36, 2752 (2000). 463. J. Osuna, D. de Caro, C. Amiens, B. Chaudret, E. Snoeck, M. Respaud, J.-M. Broto, and A. Fert, J. Phys. Chem. 100, 14571 (1996). 464. T. O. Ely, C. Pan, C. Amiens, B. Chaudret, F. Dassenoy, P. Lecante, M.-J. Casanove, A. Mosset, M. Respaud, and J.-M. Broto, J. Phys. Chem. B 104, 695 (2000). 465. S.-J. Park, S. Kim, S. Lee, Z. G. Khim, K. Char, and T. Hyeon, J. Am. Chem. Soc. 122, 8581 (2000). 466. V. F. Puntes, K. M. Krishnan, and A. P. Alivisatos, Science 291, 2115 (2001). 467. K. S. Suslick, M. M. Fang, and T. Hyeon, J. Am. Chem. Soc. 118, 11960 (1996). 468. C. Petit, A. Taleb, and M. P. Pileni, Adv. Mater. 10, 259 (1998). 469. C. Petit, A. Taleb, and M. P. Pileni, J. Phys. Chem. B 103, 1805 (1999). 470. S. Sun and C. B. Murry, J. Appl. Phys. 85, 4325 (1999). 471. S. Sun, C. B. Murry, and H. Doyle, Mater. Res. Soc. Symp. Proc. 577, 395 (1999). 472. S.-J. Park, S. Kim, S. Lee, Z. G. Khim, K. Char, and T. Hyeon, J. Am. Chem. Soc. 122, 8581 (2000). 473. D. P. Dinega and M. G. Bawendi, Angew. Chem., Int. Ed. Engl. 38, 1788 (1999). 474. M. Giersig and M. Hilgendorff, J. Phys. D 32, L111 (1999). 475. U. Wiedwald, M. Spasova, and M. Farle, J. Vac. Sci. Technol. A 19, 1773 (2001). 476. S. I. Woods, J. R., Kirtley, S. Sun, and R. H. Koch, Phys. Rev. Lett. 87, 137205 (2001). 477. V. F. Puntes, K. M. Krishnan, and A. P. Alivisatos, Appl. Phys. Lett. 78, 2187 (2001). 478. S. Sun, E. E. Fullerton, D. Weller, and C. B. Murry, IEEE Trans. Mag. 37, 1239 (2001). 479. J.-I. Park and J. Cheon, J. Am. Chem. Soc. 123, 5743 (2001). 480. E. V. Shevchenko, D. V. Talapin, A. L. Rogach, A. Kornowski, M. Haase, and H. Weller, J. Am. Chem. Soc. 124, 11480 (2002). 481. C. Frommen, H. Rosner, and D. Fenske, J. Nanosci. Nanotech. 2, 509 (2002). 482. M. Chen and D. E. Nikles, Nano Lett. 2, 211 (2002). 483. S. Kang, J. W. Harrell, and D. E. Nikles, Nano Lett. 2, 1033 (2002). 484. T. Hyeon, Chem. Commun. in press. 485. A. L. Rogach, D. V. Talapin, E. V. Shevchenko, A. Kornowski, M. Haase, and H. Weller, Adv. Funct. Mater. 12, 653 (2002). 486. B. Stahl, N. S. Gajbhiye, G. Wilde, D. Kramer, J. Ellrich, M. Ghafari, H. Hahn, H. Gleiter, J. Weißmüller, R. Würschum, and P. Schlossmacher, Adv. Mater. 14, 24 (2002). 487. G. H. Lee, S. H. Huh, J. W. Park, H.-C. Ri, and J. W. Jeong, Phys. Chem. B 106, 2123 (2002). 488. I.-J. Jeon, D.-W. Kang, D.-E. Kim, D.-H. Kim, S.-B. Choe, and S.-C. Shin, Adv. Mater. 14, 1116 (2002). 489. S. Ram and P. S. Frankwicz, Physica Status Solidi A 188, 1129 (2001). 490. “Magnetic Recording: The First 100 Years” (E. D. Daniel, M. C. Denis, and M. H. Clark, Eds.). IEEE Press, New York, 1998.

367 491. J. Hong, J. Kane, J. Hashimoto, M. Yamagishi, K. Noma, and H. Kanai, presented at the 12th Magnetic Recording Conf., TMRC2001, Minneapolis, MN, 20–22 August 2001. 492. Z. Zhang, presented at Intermag Europe 2002, Amsterdam, The Netherlands, 28 April–May 2002. 493. S. Anders, S. Sun, C. B. Murray, C. T. Rettner, M. E. Best, T. Thomson, M. Albrecht, J.-U. Thiele, E. E. Fullerton, and B. D. Terris, Microelectron. Eng. 61-2, 569 (2002). 494. S. H. Charap, P.-L. Lu, and Y.-J. He, IEEE Trans. Magn. 33, 978 (1997). 495. D. Weller and A. Moser, IEEE Trans. Magn. 35, 4423 (1999). 496. R. L. White, J. Magn. Mag. Mater. 209, 1 (2000). 497. A. Moser, K. Takano, D. T. Margulies, M. Albrecht, Y. Sonobe, Y. Ikeda, S. Sun, and E. E. Fullerton, J. Phys. D 35, R157 (2002). 498. R. L. Comstock, J. Mater. Sci. 13, 509 (2002). 499. K. Inomata, T. Sawa, and S. Hashimoto, J. Appl. Phys. 64, 2537 (1988). 500. S. H. Liou, S. Huang, E. Klimek, R. D. Kirby, and Y. D. Yao, J. Appl. Phys. 85, 4334 (1999). 501. K. R. Coffey, M. A. Parker, and J. K. Howard, IEEE Trans. Magn. 31, 2737 (1995). 502. N. Li and B. M. Lairson, IEEE Trans. Magn. 35, 1077 (1999). 503. R. A. Ristau, K. Barmak, L. H. Lewis, K. R. Coffey, and J. K. Howard, J. Appl. Phys. 86, 4527 (1999). 504. C. Chen, O. Kitakami, S. Okamoto, Y. Shimada, K. Shibata, and M. Tanaka, IEEE Trans. Magn. 35, 3466 (1999). 505. M. Yu, Y. Liu, A. Moser, D.Weller, and D. J. Sellmyer, Appl. Phys. Lett. 75, 3992 (1999). 506. S. Chikazumi and C. D. Graham, Jr., “Physics of Ferromagnetism,” 2nd ed. Oxford Univ. Press, New York, 1997. 507. E. F. Kneller and R. Hawig, IEEE Trans. Magn. 27, 3588 (1991). 508. R. Skomski and J. M. D. Coey, Phys. Rev. B 48, 15812 (1993). 509. T. Schrefl, H. Kronmüller, and J. Fidler, J. Magn. Magn. Mater. 127, L273 (1993). 510. D. H. Ping, K. Hono, and S. Hirosawa, J. Appl. Phys. 83, 7769 (1998). 511. R. Coehoorn, D. B. De Mooij, and C. De Waard, J. Magn. Magn. Mater. 80, 101 (1989). 512. T. Kobayashi, M. Yamasaki, and M. Hamano, J. Appl. Phys. 87, 6579 (2000). 513. W. Gong, G. C. Hadjipanayis, and R. F. Krause, J. Appl. Phys. 75, 6649 (1994). 514. P. G. McCormick, W. F. Miao, P. A. I. Smith, J. Ding, and R. Street, J. Appl. Phys. 83, 6256 (1998). 515. J. Zhang, S.-Y. Zhang, H.-W. Zhang, B.-G. Shen, and B.-H. Li, J. Appl. Phys. 89, 2857 (2001). 516. J. P. Liu, Y. Liu, R. Skomski, and D. J. Sellmyer, J. Appl. Phys. 85, 4812 (1995). 517. E. E. Fullerton, J. S. Jiang, C. H. Sowers, J. E. Pearson, and S. D. Bader, Appl. Phys. Lett. 72, 380 (1998). 518. J. P. Liu, C. P. Luo, Y. Liu, and D. J. Sellmyer, Appl. Phys. Lett. 72, 483 (1998). 519. G. Prinz, Science 282, 1660 (1998). 520. S. A. Wolf and D. M. Treger, IEEE Trans. Magn. 36, 2748 (2000). 521. S. A. Wolf, D. D. Awschalom, R. A. Buhrman, J. M. Daughton, S. von Molnár, M. L. Roukes, A. Y. Chtchelkanova, and D. M. Treger, Science 294, 1488 (2001). 522. D. A. Allwood, G. Xiong, M. D. Cooke, C. C. Faulkner, D. Atkinson, N. Vernier, and R. P. Cowburn, Science 296, 2003 (2002). 523. D. P. DiVincenzo, Science 270, 255 (1995). 524. X. Fu, Y. Wang, L. Huang, Y. Sha, L. Gui, L. Lai and Y. Tang, Adv. Mater. 15, 902 (2003). 525. X. Fu, Y. Wang, N. Wu, L. Gui and Y. Tang, J. Mater. Chem. 13, 1192 (2003).

Encyclopedia of Nanoscience and Nanotechnology

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Metal Nanoclusters by Ion Implantation Elti Cattaruzza, Francesco Gonella Università Ca’ Foscari di Venezia, Venezia, Italy

CONTENTS 1. Introduction 2. Metal Nanoclusters in Silica Glass 3. Ion Implantation in Silica Glass 4. Single Implantation: The Case of Copper 5. Double Implantation: The Case of Gold + Copper 6. Conclusions Glossary References

1. INTRODUCTION One of the interesting suitable methods to modify the structure and properties of a near-surface region of a material along selected patterns is to implant accelerated ions at high velocity into the solid matrix. By ion implantation, the features of the host material may be dramatically changed, depending on the host matrix as well as on the ion-implanted species and the process parameters, namely, fluence, energy, temperature, and current density. The use of ion implantation to modify a solid matrix starts from the determination of the chemical, mechanical, optical, or magnetic properties required for achieving prescribed material properties. By ion implantation, very large dopant concentration values can be obtained in the ion-irradiated region, thus inducing important effects on the chemical and physical properties near the surface. A proper choice of implantation energies and fluences allows the implanted atoms to pre-determine the composition, the depth, and the spatial shape of the modified layers as desired. The implanted layer can then be considered as a new material, interconnected with the host one in a prescribed region under the surface of the original solid. This region has thickness values ranging from tens of nanometers to several microns, depending mainly on the implanted species and on the energy of implantation. Furthermore, the use of accelerators and mass separators of ISBN: 1-58883-061-6/$35.00 Copyright © 2004 by American Scientific Publishers All rights of reproduction in any form reserved.

high resolution makes the ion implantation a synthesis technique with an intrinsic high level of cleanness, even permitting to implant a single isotope. Taking a general look at the advantages of introducing fast atoms in a solid matrix, it is worth remarking that the new material is not formed under a thermodynamic equilibrium process. This is of crucial importance, because the usual solubility limits can be largely overcome, thus opening the possibility to achieve impurity local concentrations inaccessible by conventional synthesis routes. Moreover, the possibility to control the temperature of the solid during implantation allows in many cases the formation of chemical phases in the implanted layers which could not be synthesized by adding the dopant to the unmodified material in a conventional melting procedure. As far as the ion track inside the solid is concerned, the random nature of the energy loss and of the scattering processes during the slowing down of the implanted atoms results in a dispersed distribution of dopant, also for large concentrations of the implanted element. By selecting the temperature at which the implantation process is carried out, one can favor either the aggregation of the dopants or their diffusion into the solid. Actually, the diffusion coefficients of the different species can be enhanced by the production of defects due to ion irradiation, thus completely changing the diffusion rates inside the matrix. Moreover, enhanced diffusion in certain regions of a solid can be produced by implanting one ion species, and then exploited for enhancing the diffusion of a second ion species owing to enhanced mobility along the radiation damage pattern already formed. The radiation damage may be reduced or removed by an appropriate annealing of the solid during and/or after the ion implantation. In many situations, the radiation damage is not an undesired effect: the passage of fast atoms inside a solid can produce some desired property changes, such as the variation of the local density, or the creation of aggregation and precipitation centers for the implanted atoms. The literature about ion implantation as a tool to modify the physical properties of semiconductors is enormous, with the first implantation experiments all devoted to the semiconductor physics. However, in the last ten years experiments of ion implantation in insulators have largely taken

Encyclopedia of Nanoscience and Nanotechnology Edited by H. S. Nalwa Volume 5: Pages (369–385)

370 place, mainly as a consequence of the rising technological interest in new optical materials. In this chapter, we describe the present grasp of the processes involved in ion implantation of metal atoms in a dielectric matrix, exploring the representative and largely investigated case of silica glass. Depending on the reactivity of the implanted metal atoms with the host matrix, formation of compounds or metal particles in the nanometer range of size takes place. The composite materials formed by metal nanoparticles embedded in glasses are shortly indicated with the acronym MNCGs, standing for metal nanocluster composite glasses. The main physical properties which make technologically interesting the MNCGs will be described, with particular emphasis to the linear and nonlinear optical properties. The relevant effects of the radiation damage in the case of ion implantation in silica glass will be also summarized. The processes governing the chemical and physical interaction between the implanted atoms and the atoms in the host matrix have not been fully understood nor phenomenologically described, so a comparison will be given among the different existing approaches to the comprehension of the chemical interaction in these systems. Two case studies of MNCGs will be presented, namely, copper nanoclusters obtained by copper ion implantation in fused silica, and copper-gold alloy nanoclusters obtained by sequential implantation of copper and gold in fused silica. The preparation protocols for the formation of single and binary alloy nanoparticles will be reported, together with the linear and nonlinear optical figures of merit interesting for technological applications of these MNCGs.

2. METAL NANOCLUSTERS IN SILICA GLASS Composite materials formed by transition-metal clusters embedded in glass matrices (metal nanocluster composite glasses, MNCGs) have been used for artistic purposes since the fourth century A.D. by Roman glass-makers. Architects exploited their peculiar optical properties for the medieval cathedral windows through several European countries. These glasses exhibit a great variety of beautiful colors owing to the nanosized metal particles embedded in the matrix. Since Michael Faraday first gave a scientific description of the effects inducing the coloration in MNCGs [1], much attention has been continuously dedicated to study their physical and chemical properties, and to the development of fabrication methods. Physical properties of metal aggregates as well as of nanocomposites may change dramatically in the transition from atom to molecule to cluster to solid. In this chapter, some aspects will be presented and discussed, particularly related to situations in which cluster concentration is below percolation limit, and where cluster radius is much smaller than the wavelength
of the light used to probe its response (quasi-static regime, valid for clusters with size R such that R/
≤ 001, in which retardation effects of the electromagnetic field over the cluster diameter are negligible). Moreover, clusters larger than 1 nm diameter exhibit electronic behavior features of the metal, but are small enough (up to tens of nanometers diameter) to exhibit strong confinement effects.

Metal Nanoclusters by Ion Implantation

As concerns the application aspects connected to MNCGs, the interest in these systems regards several different fields. Dielectric matrices containing dispersed nanoclusters may exhibit enhanced coercivity, shift of the hysteresis loop, superparamagnetic and large magnetotransport properties [2]. Nanostructured materials are studied also for catalysis, where high surface-to-volume ratios are required [3]. Glass-based composites are in general expected to play an important role as materials for various nanotechnology applications, due to the low cost, ease of processing, high durability and resistance, and high transparency, with the possibility of tailoring the behavior of the glass-based structures. Much attention has been dedicated to MNCGs in the last decade in the field of nonlinear integrated optics and photonics, where photons are used instead of electrons to acquire, store, process, and transmit information [4–8]. All-optical switching devices may be designed in which the intensity-dependent refractive index of the material, owing to the third-order electric susceptibility,  3 , is strongly enhanced. Nonlinear switching devices are based on optical waveguiding structures that provide strong beam confinement in prescribed patterns. In these devices, the intensity of an optical signal is used as the parameter that causes switching between two output channels that perform logic operations [9]. The main properties of MNCGs for applications in optoelectronics devices are short response times (ps or lower), low power switching threshold, wavelength tunability, thermal stability, low two-photon absorption, high threshold for laser-induced damage, and THz recycling frequency. In general, the optical properties of MNCGs are strongly dependent on several factors, among which are the nature and the chemical composition of the nanocrystals in the host matrix; the size and the shape of the clusters; the concentration of clusters and its gradient across the sample; the interaction of the cluster with the host matrix. Besides the interest for their technological application, MNCGs are studied from several points of view, including the dynamics of cluster nucleation and growth, the stability of the clusters, as well as the conditions that determine the cluster structure in terms of composition, crystalline phase, size, and size distribution. MNCGs present also interesting peculiar properties related to the thermodynamics of cluster formation, as well as to the chemical and physical aspects of the composite structure in terms of reactivity, stability, transport phenomena, magnetic properties, and so on [10]. A great effort has been made to develop new preparation methods, among which are those based on ion implantation techniques, irradiation techniques of metal-doped glass matrices, deposition techniques, and chemical routes such as sol–gel. In the literature, several updated reviews may be found on the technology of MNCGs. A very broad review on nanotechnology may be found in [11], in which a specific chapter is dedicated to MNCGs [12], while for example the Materials Research Society has dedicated one of the latest issues of its Bulletin to the topic of nanocrystals research [13]. Reference [14] specifically introduces quantum dot materials, including MNCGs. Glasses for optoelectronic devices, particularly MNCGs, are treated in [15] as well as in [16]. Concerning the theoretical aspects of MNCG properties, the literature offers a great variety of approaches. Reference

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371

[17] extensively deals with the electronic properties of metal clusters, while [18] focuses on quantum size effect. Optical properties of small metal particles are treated in detail in [19] and [20], which present extended reviews on theoretical and experimental aspects of the optical response of metal clusters. Recent aspects concerning the interface properties of MNCGs are in [21], while [22] presents a review of alloptical switching via nonlinear optical materials. In the following, we are going to treat in some detail the aspects concerning the optical response of MNCGs, since optical properties are the most appealing features of these materials. The first theoretical approach for describing the interaction of light with metal aggregates is due to Maxwell– Garnett, who in 1904 [23, 24] developed a model that is still used in some circumstances. Some years later, Gustav Mie [25] observed that the Maxwell-Garnett description was suitable only for some of the studied colloidal solutions with metal particles. Mie theory starts from a phenomenological approach, without a physical description involving the electron behavior inside the clusters. Collective plasmon oscillations of different multipole order, with the aim to interpret the Mie theory, was introduced only in the 1970s by Kreibig [26, 27]. In the quasi-static regime, an electromagnetic wave propagating in the composite does not resolve the individual scattering centers, and the medium appears homogeneous and characterized by an effective complex dielectric function. Its optical response may be approached following a discrete island model, in which each scattering center is considered, or an effective medium model, in which one scattering center is considered, the rest of the surrounding medium being averaged into a homogeneous medium. Bruggeman was the first [28] to develop an effective medium theory. A composite film is regarded as an array of two components, without constraints in the volume ratio of one component with respect to the other, arbitrarily considered as the host medium. This approach is particularly effective in the vicinity of the percolation threshold for the composite, when it abruptly increases its electrical conductivity. The composites of this kind are, however, typically formed by clusters larger than the nanometer range. On the other hand, MaxwellGarnett [23, 24] considered metal clusters embedded in a surrounding medium of dielectric constant h (real), polarized by an optical field. The Lorentz local-field relationships derived in standard textbooks of electrodynamics give the effective frequency-dependent dielectric function ˜ (complex) of the composite medium: ˜ − h  − h =p m ˜ + 2h m + 2h

(1)

where p is the metal volume fraction (or filling factor), and m   = 1   + i2   is the dielectric function of the metal particle. For small p values, Eq. (1) may be expanded to the first order in the volume fraction, and recalling that the linear absorption coefficient 0 is related to the imagi˜ one finds [20] nary part of ,  = 9p

2

3/2 h c 1 + 2h 2 + 22

(2)

This expression has a maximum at a frequency for which 1 + 2h ≈ 0. This is the absorption resonance condition

known as the surface plasmon resonance (SPR). The position, width, and shape of the SPR are determined by the metal dielectric function, as well as by the size and shape of the particles, the concentration of particles, and the surrounding dielectric. This absorption feature actually plays an important role in several optical properties interesting for application aspects, as discussed later. The resonant contribution to the absorption in MNCGs disappears when the nanoparticle diameter is lowered to about 1 nm. At that dimension, quantum corrections to the classical absorption become also significant [29]. When particle volume fraction is greater than a few percent, the interaction between the particles causes a redshift of the absorption band, an effect for which the Maxwell-Garnett picture can give account. On the other hand, increasing the concentration of the particles also leads to optical broadening due to statistical effects [30]. Mie was the first to derive an exact description of optical absorption and elastic scattering by a metal spherical cluster [25]. By adding the contribution of single clusters, the theory accounts correctly for many experimental cases, provided that interaction effects among the clusters as well as multiple scattering effects are missing. This concerns, however, a large class of inhomogeneous composite glasses, where the cluster density is anyhow sufficiently low to allow a description within this regime. Data for the optical extinction in the visible range of 52 metallic nanoparticles are given in [12, 31]. The optical absorption of the glass matrix containing metal clusters is usually expressed starting from either the Mie theory or from the Maxwell-Garnett effective dielectric function model [32]. In the first case, the contribution of each cluster to the absorption is calculated, so obtaining the absorption coefficient. In the second case, an effective dielectric function is calculated for the glass-clusters composite, and the absorption coefficient is obtained from the imaginary part of this function. Comprehensive reviews of the different models describing the absorption features are in [19, 27], with several tests of the reliability of the different models. In [19], an extended bibliography on optical spectroscopy experimental data for MNCG is also given. An estimation may be given of the size at which the cluster can be considered as a small metallic particle, with electronic behavior similar to that of solid metal. In alkali-metal clusters, the transition between covalent and metallic behavior may take place even with only a few atoms forming the cluster [33]. In the case of noble metals, the optical properties are due to d and s-p (conduction) electrons. In calculating the band structure, the outermost d and s electrons must be treated together, leading to six bands, five of which are flat, lying a few electon volts below the Fermi level (d-like bands); the other one is almost free-electron-like (it is the actual conduction band or s-p band). As in the approach by [34], the metal-nonmetal transition occurs approximately at some critical size corresponding to the number of atoms
Nc ≈ 12fc + 171 − 6 (3) where fc is a temperature-dependent function that can be determined from the bulk metal properties, fc T  =

Wb2 100kB2 T 2 Zb

(4)

Metal Nanoclusters by Ion Implantation

372 where Wb and Zb are the d-band width and effective coordination number, respectively. For example, the values of Nc obtained for Fe, Co, and Ni are, respectively, of 50, 39, and 34 atoms. These values correspond to clusters of radius of about 21 nm. Schematically, the original one-electron energy levels of an atom split into two components when a dimer is formed. The levels split further for larger clusters, finally giving rise to the quasi-continuous band structure of the bulk solid, with electrons filling the bands up to the Fermi energy EF . The first ionization potential of the atoms correspondingly turns into the bulk work function. As concerns the nonlinear optical properties of MNCGs, the second-order susceptibility vanishes because of the centrosymmetric structure of these composites. Moreover, the enhancement of the third-order susceptibility due to classical and quantum confinement effects [35] may be exploited in all-optical switching technology, since its real part is related to the nonlinear refractive index n2 , defined in terms of the linear index n0 and of the light intensity, I, as n = n0 + n2 I [5, 36–38]. In a similar way, the intensity-dependent absorption coefficient can be written as  = 0 + I, where  is the nonlinear absorption coefficient. Let us take a composite consisting of small particles with a relative volume fraction p ≪ 1 in a glass host, and denote the complex dielectric function of the metal cluster as m   = 1   + i2  . For low incident intensities, only the linear response of the composite is important; however, wherever light confinement is important, such as in waveguides, and for high-power pulsed laser irradiation, higher-order effects play an important role. The linear index of refraction n0 and the linear absorption coefficient 0 are related to the real and the imaginary part of the first-order susceptibility, respectively. In an amorphous matrix such as in MNCGs composites, the third-order susceptibility of the material is related to the nonlinear index of refraction, n2 , and to the nonlinear absorption coefficient, , as follows [39]  m2 120 2 = Re  3 (electrostatic units) W cn20   m 240 2

 = Im  3 (electrostatic units) W c 2 n20 n2



(5) (6)

where c is the light velocity in vacuum. The change in the refractive index of a material with the intensity of the optical field is called the optical Kerr effect. The effects of classical confinement on third-order susceptibility of the composite medium can be derived by considering the composite medium and applying Maxwell’s equations for the case in which the susceptibility is nonlinear; the calculation is carried out to the first order in the electric field [40]. It can be shown that the effective nonlinear optical susceptibility of the composites at issue has the expression  

3 3 eff = p ·qd 

2  2 32  32 3 ≡ p ·qd fc 2 fc 2 1 +22  1 +22

(7)

where the quantity fc may be considered as a measure of the local-field enhancement of the polarization, and 3 qd is the intrinsic third-order nonlinear susceptibility of

metal nanoparticle. More rigorous, self-consistent treatments using a jellium model for the metal particle yield the same result for this special case [41]. In the specific case of metal nanoclusters embedded in silicate glasses, three kinds of transitions in the cluster may actually occur, namely, (1) intraband transitions; (2) interband transitions; and (3) the hot-electron transitions. Intraband transitions originate in the filled conductionband states near the Fermi level and terminate in other conduction-band states which satisfy the selection rules for electric-dipole transitions. Because both the initial and final states are free-electron-like, these transitions show the strongest quantum-confinement effects, since the initial and final states both “feel” the effects of the boundary surface of the quantum dot. For an absorptive nonlinearity, the result3 ing value of intra has been calculated in a phenomenological theory [42] to be proportional to 1/a3 (where a is the nanocluster radius) and to T1 and T2 , that is, the relaxation times (energy lifetime and dephasing time, respectively) [14, 18]. Attempts to observe the intraband nonlinearity are complicated by the fact that this contribution to the third-order susceptibility is typically the smallest in magnitude, although it has the fastest response time. The interband transitions are from the d-like orbitals of the valence band to the empty conduction-band states, and these transitions are the ones which produce the characteristic colors of metals. These states are only weakly dependent on quantum-size effects because the initial state is already localized in space. Finally, the hot-electron transitions are those in which an electron in the conduction band absorbs a photon and is heated, losing its energy by electron-phonon scattering or collisions with the nanoparticle walls. Indeed, when light of frequency near that of plasmon resonance is incident upon a metal cluster-doped glass, part of the energy is transferred to the metal particles. This energy partly promotes d-electrons to the conduction band, and the rest is absorbed by the conduction electrons, which have relatively weak specific heat, and thus can be raised to high temperatures. The hotelectron effect is sometimes called “Fermi smearing,” since it results in a broadening of the electron population distribution near the Fermi edge through electronic excitation. During the electron-lattice thermalization time, the Fermi– Dirac distribution is modified, part of the one-electron levels below the Fermi one being emptied and part of the levels above becoming occupied. This leads to a modification of the dielectric constant, originating a contribution to the third-order susceptibility. The hot-electron transitions can be particularly strong and can, under certain circumstances, be the dominant transitions for a metallic nanocluster in an optical field, giving positive imaginary (absorptive) contribution to the third-order susceptibility. While these transitions produce a third-order susceptibility with magnitudes 10 to 104 times as large as the intraband transitions at a given wavelength, the excited states tend to have relaxation times on the order of hundreds of picoseconds. In fact, the hot-electron system thermalizes with the lattice by electronphonon collisions and interaction with the nanoparticle surface on a time scale of a few picoseconds [43]. Then, on a typical time scale of tens of picoseconds, the excess thermal energy is removed by thermal diffusion toward the matrix [44], while on the scale of hundreds of picoseconds the

Metal Nanoclusters by Ion Implantation

373

whole system reaches the initial temperature of the sample. However, besides the nonlinear n2 coefficient, the suitability of MNCGs in the field of all-optical switching technology is also linked to other features, that is, high intensity threshold for laser-induced damage, low thermo-optic contribution to n2 , and very short response-recovery time (high recycling frequency). All these aspects concur to define some figures of merit of the material [7, 9, 38, 45], the determination of which is the basis for an effective reliable material design. The most quoted figures of merit are related to very important properties that a material must accomplish for application in ultrafast all-optical switching devices. For example, the possibility to process light signals without needing to convert them to electronic form should allow all-optical devices to operate in a frequency range inaccessible to electronics. However, high switching speeds must be coupled with low power switching threshold, to get high packing densities in optoelectronic or photonic devices. The nonlinear material must exhibit a large n2 value to operate at watt peak power in centimeter-long devices. At the same time, it must have a low optical absorption (a nonlinear phase shift of at least 2 should be possible over one attenuation distance for reasonable device throughput), a high intensity threshold for laser-induced damage, a low thermo-optic contribution to n2 , and a very short response-recovery time (i.e., a high recycling frequency). Moreover, thermal stability and wavelength tunability are important peculiarities for promising nonlinear materials. Depending on the main absorption mechanism of a given material, that is, linear or nonlinear, two figures of merit have to be satisfied for 2 phase shift [38, 45] W =

n2 Imax > 1 0


T =


1, '1  is expected to cross zero at the screened plasma frequency, p = p /(' 1/2 , where ' is the highenergy contribution to '1 [74]. This is the case for the parallel direction in the stretched sample; '1  crosses zero at 1.6 eV and goes to negative values deeper in the IR. This is supported by theoretical analysis using the LMD model [52] as shown in Figure 8. The fits to the data yield p ≈ 23 eV and ! ≈ 12 × 10−15 sec for the parallel polarization. Using these values, we obtain p ≈ 16 eV with ' ≈ 2 and p ! ≈ 42 > 1. However, in contrast to simple Drude behavior, weak localization [53] causes '1  cross zero again at 0.24 eV and remain positive down to ≈50 cm−1 (our low frequency measurement limit). Although one hopes to obtain information on the parallel and perpendicular charge dynamics from the data, the samples are only partially oriented. In such partially aligned 1D systems, both  for polarization parallel [// ] and perpendicular [⊥ ] to the draw axis are given by a combination of intrinsic intrachain part, 0// , and interchain component, 0⊥ , in the context of effective mediumlike approach. Using the degree of chain orientation for those samples as obtained from independent experiment, 0//  and 0⊥  are obtained from the analysis of //  and ⊥  as displayed in Figure 9. The 0//  spectrum is typical of a disordered Drude metal [52] with a dominant response in the low energy for
 ≤ 05 eV. On the other hand, 0⊥  exhibits spectral features of strongly localized conductors with 0⊥  ≈ 0 for
 ≤ 03 eV and a peak around 1.4 eV. These imply the interchain charge dynamics is incoherent and severely limits the charge transport process in conducting polymers. This is attributed to the weak interchain coupling as compared with the intrachain scattering rate; when estimated to be
/! ≈ 05 eV from the spectral shape of 0// , it is larger than the usual value of t⊥ (≈0.01–0.2 eV) for conducting polymers; hence t⊥ <
/!. In such a case, theories [79] predict that the interchain charge motion is incoherent with a strong localization, as consistent with the experimental observation. Finally, the value 0//  → 0 ≈ 2 × 103 S/cm is considerably larger than the experimentally measured conductivity (//dc ≈ 800 S/cm). This suggests that significant

Figure 9. Intrachain [0// ] and interchain optical conductivity [0⊥ ] for PPy-PF6 . Reprinted with permission from [81], K. Lee and A. J. Heeger, Synth. Met. 128, 279 (2002). © 2002, Elsevier Science.

546 improvement in the performance of conducting polymers can be achieved by better control of morphology and by improving chain alignment.

7. CONDUCTING POLYMERS AS NANOTECHNOLOGY MATERIALS According to Moore’s law, it is expected that the dimensions of integrated circuit components will be reduced to approximately 10 nm by the year 2020. In such a case the interconnecting wires within such circuits would approach the ultimate limit: so-called “molecular wires” in which a linear array of single atoms just provides building blocks of the components. One of the potential candidates for such semiconductive and/or metallic “molecular wires” is the
conjugated polymer system [8 86]. Another promising aspect for conducting polymers as nanotechnology materials is the “molecular electronics” [9 87 88]. Recently molecular-scale electronics have received much attention because of their promise of future electronic devices, which operate at nanometer size and also at THz speeds. Such a molecular-scale electronic concept also requires use of single or few molecules as major electronic components such as diodes, transistors, and laser diodes. For the realization of such nanometer scale devices, therefore, it is crucial to control the synthesis of a conducting polymer in a nanometer scale and to evaluate the performance and mechanism of molecular conduction. In recent years there have been several pioneering works focusing on those subjects, and some examples are introduced here. Grozema and co-workers [89] measured hole mobility along isolated chains of
-conjugated polymers after irradiating polymer solutions with Van de Graaff accelerator. Pulsed irradiation produces radical cations and excess electrons in the solutions. Then, the change in the conductivity of a solution was monitored using the time-resolved microwave conductivity technique at a frequency of 30 GHz. They showed that mobilities well in excess of 0.1 cm2 /Vs are possible for hole transport along isolated chains. They conclude that conformational disorder and/or structural defects in the backbone plays a decisive role in determining the magnitude of the mobility and that values in excess of 1 cm2 /Vs would be realizable, if the disorder can be reduced by either chemical or physical means. Nonresonant tunnel conduction through a self-assembled monolayer of conjugated molecules fabricated on gold (111) was reported by Sakaguchi and co-workers [90]. In their experiment, conjugated molecules with different numbers of oligothiphene rings were fabricated on gold to form the selfassembled monolayer (SAM), which was covalently bonded to the metal surface. Nanometer-scale electrical measurements were performed in a manner of contacting the Ptcoated cantilever having a 20 nm sphere radius with the SAM surface using a conductive atomic force microscope. The sample current image was obtained by monitoring the current with a two-dimensional scan of metal-coated cantilever on the sample surface. This work proved that the electrical measurements with nanometer spatial resolution enable mapping of tunnel current as well as efficiency of tunnel conduction through molecular wire by analyzing length

Metallic State in Conducting Polymers

dependence on current; a series of conjugated molecules with different numbers of oligothiphene rings possess a high tunnel-conduction efficiency. Boggild et al. [91] also reported the direct measurements of the microscale conductivity on thin polymer films by mapping the conductivity of single uniaxially ordered domains and surrounding disordered areas. This was possible due to a novel scanning micro four-point probe that allows the source, drain, and voltage electrodes to be positioned within the same domain. Exceptionally high conductivities were observed on the single domain level, while the disordered regions exhibited much poorer conduction. This indicates that the in-plane alignment of polymer molecules in a monolayer is a crucial parameter for the electrical properties. Devices based on conjugated polymers usually make use of the polymers as solution cast thin films. Since the electronic and optical properties of the films are inherently related to their local structure, it is important to achieve a greater control of the self-assembly process that takes the polymers from a disordered state in solution into a semi ordered solid state. The desire to make nanometer scale devices for future electronic applications further emphasizes the need for such nanoscale control. In an effort to achieve such a purpose, Bjornholm and co-workers [92] reported on the formation of conjugated polymer nanowires by collapsing a monolayer of amphiphilic polythiophene on a Langmuir–Blodgett trough. Isothermic compression leads to dense packed monolayers in which the polythiophene backbones are
-stacked parallel to the water surface as shown in Figure 10. The stacking of the polymers is highly ordered. From X-ray diffraction data, the domain size of the highly ordered
-stacked polymer has been estimated to be 6 nm in the stacking direction. The average length of the polymers is ≤40 nm (i.e., ≤50 repeat units). The room temperature conductivity of the undoped wires is less than 10−5 S/cm, while the iodine-doped sample reaches a value of  ≈ 40 S/cm. Since application of conducting polymers in molecular sensors or electronic devices requires nanosized polymer dots or wires, nanosized conducting polymer fibers have been prepared electrochemically using hollowed templates made from polycarbonates with neutron beams [93] or chemically using zeolites with linear pores [94]. However, for practical applications in electronic circuits of nanometer size, preparation of nanosized conducting polymer

Figure 10. Molecular structure of the amphiphilic polythiophene derivative. Reprinted with permission from Ref. [92], T. Bjornholm et al., Adv. Mater 11, 1218 (1999). © 1999, Wiley-VCH.

Metallic State in Conducting Polymers

dots and/or wires needs to be simplified. Nanowires prepared inside zeolite pores or polycarbonate templates could eventually be used for electronic circuits; however, it would not be trivial to separate them from the template materials although the nanowires thus prepared may be manipulated with nanotweezers [95]. Recently Choi and Park [96] have developed a new concept to grow nanosized conducting polymer wires and rings by in situ electrochemical techniques. Conducting polymer nanowires and nanorings were synthesized using electrochemical growth on gold electrodes modified with SAMs of well-separated thioated cyclodextrins in an alkanethiol “forest.” Thiolated aniline monomer is anchored to the surface within the cyclodextrin cavity and forms an initiation point for polymer wire growth. The polymer wires appear to be made of numerous single strands several tens of nanometers thick and a few micrometers long. They claimed that a single nanowire thread of a conducting polymer has been isolated for the first time [96]. In addition to the fields of electronics and optics, conducting polymers are also promising candidate materials for biomedical applications [97–101]. As a next generation of implantable biomaterials, the capability of communication with surrounding tissues would be essential; those materials should incorporate stimulatory cues (such as electrical signals) directly into tissues for regulating cell attachment, proliferation, and differentiation. Moreover, the use of electroactive materials would allow one to locally deliver an electrical stimulus at the site of damage, while also providing a physical template for cell growth and tissue repair. Therefore conducting polymers, such as polypyrrole and polythiophene, are expected to play a crucial role in such biomedical applications [97–101]. In fact, in vitro enhancement of nerve cell axonal extension has been reported using polypyrrole with application of either constant current or constant voltage [97–99]. Polypyrrole has also been used as a substrate to increase electronic interfacing between neurons and micromachined microelectrodes for potential applications in neural probes and prosthetic devices [100]. Recently Rivers and co-workers [101] reported the synthesis and characterization of a novel biodegradable, electrically conducting polymer that demonstrates good tissue compatibility. The polymer was synthesized from conducting oligomers of pyrrole and thiophene that are connected together via degradable ester linkages. They addressed that the material has broad potential for tissue engineering applications as a temporary scaffold for cell attachment and as a source of electrical signals to stimulate tissue regeneration. They also expect that the material will be useful to some bioelectronic application in which a transient electronic–tissue interface is desired.

8. CONCLUDING REMARKS As a new class of materials which exhibit the electrical and optical properties of semiconductors or metals together with the processing advantages of typical polymers, conjugated polymers provide a route to “plastic electronic” devices, including polymer LEDs, polymer lasers, high-sensitivity polymer photodiodes and photovoltaic cells, thin-film transistors, and all-polymer integrated circuits. In addition to

547 such polymer electronics and optoelectronics, conjugated polymers also emerge as promising candidate materials for nanotechnology materials in the form of “molecular wires” for molecular electronics. For the realization of such novel devices using conjugated polymers, it is crucial to understand the mechanism of charge conduction and to evaluate the physical properties of those materials on a nanometer scale. However, although the electrical and optical properties of conducting polymers have been investigated for over a decade, the nature of the metallic states and the corresponding metal–insulator transition are not still fully understood. This mainly originates from their complex morphologies inherent to typical polymer systems and also from their novel reduced dimensionality. Although the structural mesoscopic inhomogeneities have strongly dominated the physical properties of earlier conducting polymers, recent progress in the processing has significantly improved the quality of the materials with corresponding improvements in the physical properties. The transport and optical measurements on the improved materials have proved that the relevant electronic length scales are larger than the characteristic size of structural inhomogeneities, and the conventional localization theory is a good description for the physical properties of the improved systems. In such a case the intrachain charge dynamics is typical of a disordered Drude metal with a weak interchain coupling, while the interchain responses are dominated by spectral features of strongly localized conductors. This suggests that significant improvement in the performance of conducting polymers can be achieved by better control of morphology and by improving chain alignment. The desire to make nanometer scale devices using these materials further emphasizes the need for such nanoscale control and improvement.

GLOSSARY
–
∗ Transition An electronic transition described approximately as a promotion of an electron from a “bonding” orbital to an “antibonding” orbital (designated as ∗ ) generally in the conjugated polymer systems. Hagen–Rubens approximation The approximate relation for infrared reflectivity of typical metals at low frequencies. Ioffe–Regel limit A limit to conventional metallic behaviors as the extent of disorder increases in a metallic system. Infrared active vibrational modes (IRAV) Molecular vibration modes originating from a local symmetry breaking by introducing doping charges to the backbone of conjugated polymers. These modes are optically observed in the infrared region. Kramers–Kronig relation Dispersion relation between the real part and imaginary part of the response function of a linear passive system, such as complex dielectric constant, complex refractive index, and reflectivity. Langmuir–Blodgett (LB) films A set of monolayers, or layers of organic material one molecule thick, deposited on a solid substrate. An LB film can consist of a single layer or many, up to a depth of several visible-light wavelengths.

548 Molecular electronics Research and development of electronic devices at a molecular level of miniaturization with electrons as signal carriers. Peierls instability The phenomenon of opening bandgap by lattice distortion due to the modulation of the charge density wave with wave vector 2kF in one-dimensional materials.

ACKNOWLEDGMENTS It is a pleasure to acknowledge Professor A. J. Heeger for valuable discussions on this subject. This work was supported by the National Program for Nanoscience and Technology of the Ministry of Science and Technology of Korea (M1-0214-00-0077).

REFERENCES 1. C. K. Chiang, C. R. Fincher, Y. W. Park, A. J. Heeger, H. Shirakawa, and E. J. Louis, Phys. Rev. Lett. 39, 1098 (1977). 2. A. J. Heeger, S. Kivelson, J. R. Schrieffer, and W. P. Su, Rev. Mod. Phys. 60, 781 (1988). 3. See, for example, “Handbook of Conducting Polymers,” 2nd ed. (T. A. Skotheim, R. L. Elsenbaumer, and J. R. Reynolds, Eds.), Dekker, New York, 1998. 4. A. J. Heeger, Rev. Mod. Phys. 73, 681 (2001). 5. J. H. Burroughes, D. D. C. Bradley, A. R. Brown, R. N. Marks, R. H. Friend, P. L. Burns, and A. B. Holmes, Nature 335, 539 (1990). 6. R. H. Friend, R. W. Gymer, A. B. Holmes, J. H. Burroughes, R. N. Marks, C. Taliani, D. D. C. Bradley, D. A. Dos Santos, J. L. Bredas, M. Logdlund, and W. R. Salaneck, Nature 397, 121 (1999). 7. See, for example, “Semiconducting Polymers” (G. Hadziioannou and P. F. van Hutten, Eds.), Wiley–VCH, Weinheim, 2000. 8. B. Wessling, in “Handbook of Nanostructured Materials and Nanotechnology”(H. S. Nalwa, Ed.), Vol. 5, p. 501. Academic Press, San Diego, 2000. 9. C. Joachim, J. K. Gimzewski, and A. Aviram, Nature 408, 541 (2000). 10. W. P. Su, J. R. Schrieffer, and A. J. Heeger, Phys. Rev. Lett. 42, 1698 (1979). 11. Y. Lu, “Solitons and Polarons in Conducting Polymers.” World Scientific, Singapore, 1988. 12. J. Chen, T.-C. Chung, F. Moraes, and A. J. Heeger, Solid State Commun. 53, 757 (1985). 13. Y. H. Kim and A. J. Heeger, Phys. Rev. B 40, 8393 (1989). 14. B. Horovitz, Solid State Commun. 41, 729 (1982). 15. E. Ehrenfrund, E. Vardeny, O. Brafman, and B. Horovitz, Phys. Rev. B 36, 1535 (1987). 16. E. M. Conwell, H. A. Mizes, and S. Jeyadev, Phys. Rev. B 40, 1630 (1989). 17. E. M. Conwell and H. A. Mizes, Phys. Rev. B 44, 937 (1985). 18. S. Kivelson and A .J. Heeger, Phys. Rev. Lett. 55, 308 (1985). 19. H. Y. Choi and E. J. Mele, Phys. Rev. B 34, 8750 (1986). 20. S. Stafstrom and J. L. Bredas, Phys. Rev. B 38, 4180 (1988). 21. C. K. Chiang, S. C. Gau, C. R. Fincher, Y. W. Park, and A. G. MacDiarmid, Appl. Phys. Lett. 33, 18 (1978). 22. H. Shirakawa, E. J. Louis, A. G. MacDiarmid, C. K. Chiang, and A. J. Heeger, Chem. Commun. 578 (1977). 23. C. K. Chiang, C. R. Fincher, Y. W. Park, A. J. Heeger, H. Shirakawa, and E. J. Louis, Phys. Rev. Lett. 39, 1098 (1977). 24. J. Tsukamoto, Adv. Phys. 41, 509 (1992). 25. N. Basescu, Z.-N.X. Liu, D. Moses, A. J. Heeger, H. Naarmann, and N. Theophilou, Nature 327, 403 (1987).

Metallic State in Conducting Polymers 26. H. Shirakawa, Y.-X. Zhang, T. Okuda, K. Sakamaki, and K. Akagi, Synth. Met. 65, 14 (1994). 27. Y. Cao, P. Smith, and A. J. Heeger, Synth. Met. 48, 91 (1992). 28. K. Sato, M. Yamaura, T. Hagiwara, K. Murata, and M. Tokumoto, Synth. Met. 40, 35 (1991). 29. T. Ohnishi, T. Noguchi, T. Nakano, M. Hirooka, and I. Murase, Synth. Met. 41–43, 309 (1991). 30. W. R. Salaneck, I. Lundstrom, W. S. Haung, and A. G. MacDiarmid, Synth. Met. 13, 291 (1986). 31. F. Wudl, R. O. Angus, F. L. Lu, P. M. Allemand, D. J. Vachon, M. Nowak, Z. X. Liu, and A. J. Heeger, J. Am. Chem. Soc. 109, 3677 (1987). 32. Y. Cao, P. Smith, and A. J. Heeger, U.S. Patent 5, 232, 631. 33. P. J. Nigrey, A. G. MacDiarmid, and A. J. Heeger, Chem. Commun. 96, 594 (1979). 34. R. Kiebooms, A. Aleshin, K. Hutchison, and F. Wudl, J. Phys. Chem. 101, 11037 (1997). 35. J. H. Edwards and E. J. Feast, Polym. Commun. 21, 595 (1980). 36. D. R. Gagnon, J. D. Capistran, F. E. Karasz, and R. W. Lenz, Polym. Bull. 12, 93 (1984). 37. I. Murasi, T. Ohnishi, and M. Hirooka, Polym. Commun. 25, 327 (1984). 38. R. Menon, Y. Cao, D. Moses, and A. J. Heeger, Phys. Rev. B 497, 1758 (1993). 39. L. Sun and S. C. Yang, Polym. Prepr. 33, 379 (1992). 40. G. Heywang and F. Jonas, Adv. Mater. 4, 116 (1992). 41. J. Friedrich and K. Werner, U.S. Patent 5, 300, 575. 42. M. Yamaura, K. Sato, T. Hagiwara, and K. Ieata, Synth. Met. 48, 337 (1992). 43. Y. Nogami, J.-P. Pouget, and T. Ishiguro, Synth. Met. 62, 257 (1994). 44. J. Joo, Z. Oblakowski, G. Du, J. P. Pouget, E. J. Oh, J. M. Weisinger, Y. G. Min, A. G. MacDiarmid, and A. J. Epstein, Phys. Rev. B 49, 2977 (1994). 45. J. P. Pouget, Z. Oblakowski, Y. Nogami, P. A. Albouy, M. Laridjani, E. J. Oh, Y. Min, A. G. MacDiarmid, J. Tsukamoto, T. Ishiguro, and A. J. Epstein, Synth. Met. 65, 131 (1994). 46. Z. H. Wang, E. M. Scherr, A. G. MacDiarmid, and A. J. Epstein, Phys. Rev. B 45, 4190 (1992). 47. R. S. Kohlman, J. Joo, and A. J. Epstein, in “Physical Properties of Polymers Handbook” (J. E. Mark, Ed.), Am. Inst. of Phys., New York, 1996. 48. R. S. Kohlman, J. Joo, Y. Z. Wang, J. P. Pouget, H. Kaneko, T. Ishiguro, and A. J. Epstein, Phys. Rev. Lett. 74, 773 (1995). 49. R. S. Kohlman, J. Joo, Y. G. Min, A. G. MacDiarmid, and A. J. Epstein, Phys. Rev. Lett. 77, 2766 (1996). 50. R. S. Kohlman, A. Zibold, D. B. Tanner, G. G. Ihas, T. Ishiguro, Y. G. Min, A. G. MacDiarmid, and A. J. Epstein, Phys. Rev. Lett. 78, 3915 (1997). 51. R. Menon, C. O. Yoon, D. Moses, and A. J. Heeger, in “Handbook of Conducting Polymers,” 2nd ed. (T. A. Skotheim, R. L. Elsenbaumer, and J. R. Reynolds, Eds.), Dekker, New York, 1998. 52. R. Kiebooms, R. Menon, and K. Lee, in “Handbook of Advanced Electronic and Photonic Materials and Devices” (H. S. Nalwa, Ed.), Vol. 8. Academic Press, San Diego, 2001. 53. K. Lee, E. K. Miller, A. N. Aleshin, R. Menon, A. J. Heeger, J. H. Kim, C. O. Yoon, and H. Lee, Adv. Mater. 10, 456 (1998). 54. K. Lee, A. J. Heeger, and Y. Cao, Phys. Rev. B 48, 14884 (1993). 55. C. O. Yoon, R. Menon, D. Moses, and A. J. Heeger, Phys. Rev. B 49, 10851 (1994). 56. K. Lee, R. Menon, C. O. Yoon, and A. J. Heeger, Phys. Rev. B 52, 4779 (1995). 57. A. Aleshin, R. Kiebooms, R. Menon, and A. J. Heeger, Phys. Rev. B 56, 3659 (1997). 58. Y. Chang, K. Lee, R. Kiebooms, A. Aleshin, and A. J. Heeger, Synth. Met. 105, 203 (1999).

Metallic State in Conducting Polymers 59. N. F. Mott, “Metal–Insulator Transitions.” Taylor and Francis, New York, 1990. 60. T. G. Castner, in “Hopping Transport in Solids” (M. Pollak and B. I. Shklovskii, Ed.). North-Holland, Amsterdam, 1990. 61. P. A. Lee and T. V. Ramakrishnan, Rev. Mod. Phys. 57, 287 (1985). 62. N. F. Mott and E. A. Davis, “Electronic Processes in Noncrystalline Materials.” Oxford Univ. Press, Oxford, 1979. 63. A. F. Ioffe and A. R. Regel, Progr. Semicond. 4, 237 (1960). 64. P. W. Anderson, Phys. Rev. 109, 1492 (1958). 65. P. W. Anderson, Comments Solid State Phys. 2, 193 (1970). 66. E. Abrahams, P. W. Anderson, D. C. Licciardello, and T. V. Ramakrishnan, Phys. Rev. Lett. 42, 695 (1979). 67. W. L. McMillan, Phys. Rev. B 24, 2739 (1981). 68. A. I. Larkin and D. E. Khmelnitskii, Sov. Phys. JETP 56, 647 (1982). 69. M. Reghu, K. Vakiparta, Y. Cao, and D. Moses, Phys. Rev. B 49, 16162 (1994). 70. M. Ahlskog, M. Reghu, A. J. Heeger, T. Noguchi, and T. Ohnishi, Phys. Rev. B 53, 15529 (1996). 71. M. Ahlskog, M. Reghu, A. J. Heeger, T. Noguchi, and T. Ohnishi, Phys. Rev. B 55, 6777 (1997). 72. A. G. Zabrodskii and K. N. Zinovjeva, Zh. Eksp. Teor. Fiz. 86, 727 (1984). 73. B. I. Shklovskii and A. L. Efros, “Electronic Processes in Doped Semiconductors.” Springer, Heidelberg, 1984. 74. F. Wooten, “Optical Properties of Solids.” Academic Press, New York, 1972. 75. K. Lee, A. J. Heeger, and Y. Cao, Synth. Met. 72, 25 (1995). 76. E. Hagen and H. Rubens, Ann. Phys. 11, 873 (1903). 77. N. F. Mott and M. Kaveh, Adv. Phys. 34, 329 (1985). 78. Y. Cao, P. Smith, and A. J. Heeger, Polymer 32, 1210 (1991). 79. Y. A. Firsov, in “Localization and Metal–Insulator Transition” (H. Fritzsche and D. Adler, Ed.), Plenum Press, New York, 1985. 80. A. J. Heeger, Faraday Discuss. Chem. Soc. 88, 1 (1989). 81. K. Lee and A. J. Heeger, Synth. Met. 128, 279 (2002). 82. J. Joo, S. M. Long, J. P. Pouget, E. J. Oh, A. G. MacDiarmid, and A. J. Epstein, Phys. Rev. B 57, 9567 (1998).

549 83. C. O. Yoon, H. K. Sung, J. H. Kim, E. Barsoukov, J. H. Kim, and Hosull Lee, Synth. Met. 99, 201 (1999). 84. J. A. Reedijk, H. C. F. Martens, H. B. Brom, and M. A. J. Michels, Phys. Rev. Lett. 83, 3904 (1999). 85. G. Leising, Phys. Rev. B 38, 10313 (1988). 86. See, for example, “Nanostructure Physics and Fabrication” (M. A. Reed and W. P. Kirk, Eds.), Academic Press, New York, 1989; “Nanostructures and Mesoscopic Systems” (M. A. Reed and W. P. Kirk, Eds.), Academic Press, New York, 1992. 87. M. Pope and C. Swenberg, “Electronic Processes in Organic Crystals and Polymers,” 2nd ed., p. 1172. Oxford Univ. Press, Oxford, 1999. 88. See, for example, “Molecular Electronics: Science and Technology Conference Proceedings No. 262.” Am. Inst. of Physics, New York, 1992. 89. F. C. Grozema, L. D. A. Siebbeles, J. M. Warman, S. Seki, S. Tagawa, and U. Scherf, Adv. Mater. 14, 228 (2002). 90. H. Sakaguchi, A. Hirai, F. Iwata, A. Sasaki, and T. Nagamura, Appl. Phys. Lett. 79, 3708 (2001). 91. P. Boggild, F. Grey, T. Hassenkam, D. R. Greve, and T. Bjornholm, Adv. Mater. 12, 947 (2000). 92. T. Bjornholm, T. Hassenkam, D. R. Greve, R. D. McCullough, M. Jayaraman, S. M. Savoy, C. E. Jones, and J. T. McDevitt, Adv. Mater. 11, 1218 (1999). 93. C. R. Martin, Acc. Chem. Res. 28, 61 (1995). 94. C. G. Wu and T. Bein, Science 264, 1757 (1994). 95. P. Kim and C. M. Lieber, Science 286, 2148 (1999). 96. S.-J. Choi and S.-M. Park, Adv. Mater. 12, 1547 (2000). 97. C. E. Schmidt, V. R. Shastri, J. P. Vacanti, and R. Langer, Proc. Nat. Acad. Sci. USA 94, 8948 (1997). 98. A. Kotwal and C. E. Schmidt, Biomaterials 22, 1055 (2001). 99. J. H. Collier, J. P. Camp, T. W. Hudson, and C. E. Schmidt, J. Biomed. Mater. Res. 50, 574 (2000). 100. X. Cui, V. A. Lee, Y. Raphael, J. A. Wiler, J. F. Hetke, D. J. Anderson, and D. C. Martin, J. Biomed. Mater. Res. 56, 261 (2001). 101. T. J. Rivers, T. W. Hudson, and C. E. Schmidt, Adv. Funct. Mater. 12, 33 (2002).

Encyclopedia of Nanoscience and Nanotechnology

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Micro and Nanocantilever Sensors P. G. Datskos, T. Thundat, Nickolay V. Lavrik Oak Ridge National Laboratory, Oak Ridge, Tennesee, USA

CONTENTS 1. 2. 3. 4. 5.

Introduction Cantilever Sensors Cantilever Sensor Characteristics Nanocantilevers Conclusions Glossary References

1. INTRODUCTION Cantilever structures are the simplest micro-electro-mechanical systems (MEMS) that can be easily micromachined and mass produced. The ability to detect extremely small displacements make the cantilever beams ideal for detection of extremely small forces and stresses. Here we assume that the displacement is directly proportional to the force acting on the cantilever beam. In general, small cantilever beams execute thermal motion (Brownian motion) with amplitudes proportional to the square root of the thermal energy. Measuring the thermal motion amplitude as a function of frequency enables the determination of resonance frequency of the cantilever beam. Adsorption of molecules on the surface of a cantilever changes the total mass and, consequently, the resonance frequency of the cantilever. The resonance frequency of a microcantilever varies sensitively as a function of mass loading due to molecular adsorption [1–7]. The resonance frequency of a cantilever beam depends on its dimensions, elastic modulus, and density. By changing the dimensions, the resonance frequency can be varied from hundreds of Hz to hundreds of MHz. In fact, depending on the material when the cantilever is of nanoscale dimensions, GHz frequencies can be expected. For a given thickness, shorter cantilevers have higher resonance frequency than longer cantilevers. For a cantilever of given mass, higher resonance frequency implies a larger spring constant. The effect of damping due to medium density is higher for higher resonance frequencies. Although many cantilever sensors take advantage of adsorption-induced bending as the transduction method, an

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approach based on resonance frequency shifts can potentially provide ultimate sensitivity for detection of a single molecule. If molecular adsorption is confined to one side of the cantilever, the cantilever undergoes bending due to adsorptioninduced variation in surface stress [1–4, 8]. Molecular adsorption onto cantilevers that have two chemically different surfaces results in a differential stress between the top and bottom surfaces of the cantilever. The differential stress produces microcantilever bending. Generally, adsorption decreases the surface energy. For small bending of a cantilever, the surface stress variation can be equated to the variation of surface-free energy. The extent of cantilever bending is often directly proportional to the surface-free energy variation due to molecular adsorption. Therefore, the cantilever bending due to molecular adsorption depends on the change in free energy per adsorbate and the total number of molecules taking part in the adsorption process. The extent of bending depends on the spring constant of the cantilever. In fact, for smaller spring constant cantilevers, the deflection of the cantilever will be larger.

2. CANTILEVER SENSORS The typical thickness of commonly used microcantilevers is approximately 1
m. The length of the cantilever can vary from tens of
m to a few hundred
m. The spring constants of the cantilevers are typically in the range of 0.01– 1 N/m. Microcantilevers are usually fabricated from silicon or silicon nitride using standard photolithographic and etching techniques. A silicon nitride or a silicon dioxide film is deposited on a single-crystal silicon wafer by a low-pressure chemical vapor deposition (LPCVD) process. By varying the conditions of LPCVD, efforts are made to reduce the stress and stress gradient in the film so that the cantilevers are flat and undeformed when fabricated. The nitride or oxide films are then patterned by photolithography, and the cantilever shapes are defined on the top surface and the etch masks on the bottom surface. The silicon substrate is then etched away to produce free-standing cantilevers. A metal layer such as gold can be coated onto either side of the cantilever, either to provide a surface for chemical modification

Encyclopedia of Nanoscience and Nanotechnology Edited by H. S. Nalwa Volume 5: Pages (551–560)

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through alkanethiol linkers or to make the surface nonreactive for silane-amino linkages of molecules that bind to the oxide surface. Adsorption-induced cantilever deflection and resonance frequency variation can form the basis of a universal platform for real-time, in-situ measurement of physical, chemical, and biochemical properties. A plethora of physical, chemical, and biological sensors, based on the micromachined cantilever platform, have already been demonstrated [1–4, 8–18]. Because cantilever bending and resonance frequency can be measured simultaneously, sensors can be based on adsorption-induced resonance frequency shifts and/or cantilever bending. The resonance frequency shifts and bending of a cantilever can be measured with very high precision using different readout techniques [19], such as optical beam deflection, variations in piezoresistivity, capacitance, and piezoelectric properties.

2.1. Thermal Motions of a Cantilever The resonance frequency of a cantilever, f , is given by
K 1 (1) f = 2 m∗ where K is the spring constant and m is the effective mass of the cantilever. The effective mass can be related to the mass of the beam, m, through the relation m∗ = nm, where n is a unitless geometric parameter. For a rectangular cantilever, n has a typical value of 0.24 [20]. For a rectangular cantilever sensor, the spring constant for vertical deflection is given by [19]: K=

Ewt 3 4L3

(2)

where E is the modulus of elasticity for the composing material and w, t, L are the width, thickness, and length of the beam, respectively. From eq. (1), it is clear that longer cantilevers have smaller spring constants. Therefore, longer cantilevers are more sensitive for measuring surface stresses. However, increasing the length also increases the thermal vibrational noise of the cantilever [19], which from statistical physics, is  2KB T B (3) n = kf0 Q −23

Here, kB is the Boltzmann constant (1.38 × 10 J/K), T is the absolute temperature (300 K at room temperature), B is the bandwidth of measurement (typically about 1000 Hz for dc measurement), f0 is the resonant frequency of the cantilever, and Q is the quality factor of the resonance which is related to damping. It is clear from eq. (3) that lower spring stiffness produces higher thermal noise. It is important to note that the resonance frequency f0 may undergo noticeable fluctuations, f0 , due to exchange between the mechanical and thermal energy of the cantilever [21]:  1 2kB T B (4) f0 = A KQf0

where T is the absolute temperature, Q is the quality factor of the cantilever oscillator, A is the oscillation amplitude, and B is the measurements bandwidth. Although eq. (4) predicts increased absolute fluctuations of the resonance frequency, f0 , as the resonance frequency f0 increases, relative frequency instability, f0 /f0 , decreases in the case of higher frequency oscillators  1 2kB T B f0 = (5) f0 A KQf0

2.2. Q-Factor The quality factor, or Q-factor, of a resonator is a measure of the spread of the resonance peak, f0 , and is thus related to energy loss due to damping (Q = f0 /f0 . The lower the Q-factor, the more damped the oscillator. The Q-factor depends on parameters such as cantilever material, geometrical shape, and the viscosity of the medium. Typically, the Q-factor of a rectangular silicon cantilever in air is approximately 30. However, in liquids, the Q-factor decreases by a factor of 10. Therefore, measurements of adsorbed mass based on resonance frequency variation suffer from low resolution in liquid environment. Recently, it has been shown that the effective Q-factor can be increased by two to three orders of magnitude by a feedback mechanism [22]. In the feedback technique, the position sensitive detector (PSD) signal is fed back to a piezoelectric element that drives the cantilever into resonance. This technique also works with thermal motion of the cantilever.

2.3. Signal Transduction For a cantilever with a dimension in tens of microns, the bending and resonance frequency shifts are measured with high precision using optical reflection, piezoresistive, capacitance, and piezoelectric methods. One great advantage of the cantilever technique is that both bending and resonance frequency can be measured simultaneously. Moreover, other resonance parameters such as phase, amplitude, and Q-factor can be determined if a frequency spectrum is obtained. All the signal transduction methods are compatible with an array format.

2.3.1. Optical Beam Deflection The simplest way of measuring cantilever deflection is by using optical beam deflection [19, 23]. In optical beam deflection technique, a laser diode is focused at the free end of the cantilever. The reflected beam is monitored using a position-sensitive detector. Displacement of the order of 0.1 nm can be measured using optical beam deflection. Optical beam deflection has many advantages such as being compatible with use under liquid and lack of electrical contact to the cantilever beam.

2.3.2. Piezoresistance Method Piezoresistivity is the variation of bulk resistivity with applied stress. Doped silicon exhibits a strong piezoresistive effect [24–27]. The resistance of a doped region on a cantilever

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can change reliably when the cantilever is stressed with deflection. This deflection can be caused by changes in adsorption-induced stress or by externally applied stress, such as thermal stress. The variation in cantilever resistance can be measured using an external, dc-biased, Wheatstone bridge. Typical resistance of a silicon microcantilever with a doped boron channel is a few k. If the resistances in the Wheatstone bridge is assumed to have identical values, R, and an applied voltage V , the differential voltage across the bridge can be expressed as V = VR/4R. If the cantilever is designed to have two identical legs, the current can flow in and out of the cantilever through boron channels. Metallic interconnects can be made to the boron channels at the base of the cantilever for application of external power. The disadvantage of the piezoresistive technique is that it requires passing a current through the cantilever for displacement measurements. This results in electronic noises and thermal drift in cantilever deflection. In addition, the cantilever beam is at a higher temperature due to resistive losses in the cantilever. Since the cantilever temperature is above ambient temperature, any changes in flow rate or thermal conductivity of the ambient can cause parasitic cantilever deflection.

2.3.3. Piezoelectric Method Piezoelectric technique utilizes cantilevers with overlayers that are piezoelectric. Thin layers of piezoelectric materials such as ZnO induces transient charge due to cantilever movement [28–30]. One disadvantage of the piezoelectric technique is that it requires electrodes to the piezoelectric film. In addition, for measurable piezoelectric signals, the film needs to be thicker. Piezoelectric technique is difficult to use when static cantilever deflection measurements are needed. Piezoelectric cantilevers are ideal for resonance, frequency-based approaches.

2.3.4. Capacitance Method The capacitance variation technique of measuring cantilever deflection makes use of the variation in capacitance between cantilever and a fixed substrate [17, 31]. The capacitance varies sensitively as a function of cantilever bending. Capacitance technique, however, is not suitable for liquid environments. Also, variation in the dielectric constant of ambient can contribute to cantilever bending signal.

2.4. Advantages of Cantilever Sensors One great advantage of the cantilever-based sensors is that four resonance response parameters (resonance frequency, phase, amplitude, and Q-factor) can be measured simultaneously. Another compelling feature of microcantilever sensors is that they can be operated in air, vacuum, or liquid. The damping effect in a liquid medium, however, reduces the resonance response of a microcantilever. In most liquids, the observed resonance response is approximately an order of magnitude smaller than that in air. The bending response, however, remains unaffected by the

presence of a liquid medium. Therefore, the feasibility of operating a microcantilever in a solution with high sensitivity makes the microcantilever an ideal choice for biochemical sensors. Therefore, microfabricated cantilevers can provide the basis for a universal platform for real-time, in-situ measurement, and determination of physical, chemical, and biochemical properties. Cantilever sensors offer improved dynamic response, greatly reduced size and high precision, and increased reliability compared to conventional sensors. They are the simplest micromechanical systems that can be mass-produced with conventional micromachining techniques. They can be fabricated into multielement sensor arrays and fully integrated with on-chip electronic circuitry. Because the thermal mass of microcantilevers is extremely small, they can be heated and cooled with a thermal timeconstant of less than a millisecond. This is advantageous for rapid reversal of molecular absorption processes and regeneration purposes. Therefore, the micromechanical platform offers an unparalleled opportunity for the development and mass production of extremely sensitive, low-cost sensors for real-time in-situ sensing of many chemical and biological species. Therefore, cantilever sensors with extremely high sensitivity can be fabricated by simply reducing the cantilever dimensions. These cantilevers with reduced sizes belong to a class known as nano-electro-mechanical systems (NEMS). Reducing the dimension increases energy efficiency, time response, and sensitivity. However, decreasing the cantilever size results in increased difficulties in fabrication as well as monitoring cantilever response.

3. CANTILEVER SENSOR CHARACTERISTICS The most important aspects of any sensor are its sensitivity, selectivity, and the ability for regeneration. Cantileverbased sensors are extremely sensitive displacement sensors, but they do not offer any intrinsic chemical selectivity. For cantilever-based sensors, the chemical selectivity is obtained by utilizing chemically selective layers such as polymeric films, self-assembled monolayers, or antibody-antigen layers. Regeneration of the sensor originates from thermodynamics. If the analyte-substrate interaction energy is large, the sensor may not regenerate at room temperature. As pointed out earlier, the cantilever sensor can be operated in two modes: resonance frequency variation and adsorption-induced cantilever bending. The sensitivity of the cantilever bending increases as the spring constant of the cantilever is reduced. Therefore, longer cantilevers with very small spring constants are attractive for use with the adsorption-bending method. However, thermal motion of the cantilever severely limits the extent by which the spring constant of the cantilever can be reduced. On the other hand, the sensitivity of resonance frequency shifts based-approach increases as a function of frequency of operation. Therefore, shorter, higher frequency cantilevers are more suitable for increasing the detection limit when utilizing an approach that takes advantage of frequency shifts.

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3.1. Sensitivity of Resonance Frequency-Based Approach Assuming the contribution from variation in spring constant is small, a mass dependence of the fundamental frequency can be written by combining eqs. (1) and (2) as 
1 K E t f = = (6) ∗ 2 2 m 2098L  where  is the density of the cantilever material. The mass of the adsorbed material can be determined from the initial and final resonance frequency and the initial mass of the cantilever as f12 − f22  m = m f12

(7)

where f1 and f2 are the initial and final frequency, respectively, and m and m are adsorbed mass and initial mass of the cantilever, respectively. If the adsorption is uniform on the cantilever surface, eq. (7) needs to be modified appropriately in order to take into account the effective mass of the cantilever. The mass sensitivity of a cantilever sensor can be written as Sm = lim

m→0

1 df 1 f = f m f0 dm

(8)

where m and dm are normalized to the active sensor area of the device (m = m/A, where A is the area of the cantilever). As can be seen from the expression in eq. (8), the sensitivity is the fractional change of the resonant frequency of the structure with addition of mass to the sensor. When applying this definition to the case of the cantilever sensor, the sensitivity can be expressed as

Sm =

1 df f dt

(9)

where  and t are the density and the thickness of the adsorbate, respectively. If mass is added uniformly on a cantilever, its resonance frequency decreases as a function of adsorbed mass. Note that the sensitivity of a cantilever sensor depends only on its thickness and material density. Another characterization parameter of a cantilever sensor is its minimum detection mass density. The minimum detectable mass density can be obtained by rearranging eqs. (6) and (7) as mmin =

1 fmin Sm f

(10)

where mmin is the minimum detectable mass density and fmin is the minimum detectable frequency shift. Typically, minimum detectable mass density values are experimentally quoted results due to specifics of the sensor as well as the frequency detection limitations determining fmin . Therefore, by changing the physical dimension of a cantilever, one can increase its detection limits by many orders of magnitude.

The absolute limit of minimum detection can be derived by combining eqs. 4 and 5. The smallest (noise limited) detectable change in the resonator mass per unit area can be expressed as  2 5 KkB T B mmin = 8 (11) f05 Q

3.2. Sensitivity of Adsorption-Induced Cantilever Deflection Approach As mentioned earlier, thin microcantilevers also undergo bending due to mechanical forces generated by molecular adsorption, one of the most overlooked yet fascinating aspects of adsorption. These adsorption-induced forces can be easily detected on so-called “real surfaces” such as the surface of a microcantilever operated in air or under liquid. Adsorption-induced forces are applicable only for monolayer films and should not be confused with bending due to dimensional changes such as the swelling of thicker polymer films on cantilevers. Adsorption-induced stress sensors have sensitivities three orders of magnitude higher than frequency variation (for resonance frequencies in the range of tens of kHz) based on adsorbed mass. In addition, adsorption-induced cantilever bending is ideal for liquidbased applications. Using Stoney’s formula [32], we can express the radius of curvature of cantilever bending due to adsorption as to adsorption as 1 1 −   =6 R Et 2

(12)

where R is the cantilever’s radius of curvature;  and E are Poisson’s ratio and Young’s modulus for the substrate, respectively; t is the thickness of the cantilever; and  is the differential surface stress. The differential surface stress is the difference between the surface stress of the top and bottom surfaces of the cantilever beam in units of N/m or J/m2 . Typically, the microcantilevers have spring constants in the range of 0.1 N/m. Using geometry, a relationship between the cantilever displacement and the differential surface stress can be expressed as z=

3L2 1 −   Et 2

(13)

where L is the length and h is the deflection. Equation 13 shows a linear relation between cantilever bending and differential surface stress. Therefore, any variation in the differential surface stress can result in cantilever bending. When confined to one surface, molecular adsorption on a thin cantilever can cause large changes in surface stress. Surface stress, , and surface free energy, , can be related using the Shuttleworth eqn. [33]   ! = + (14) !" where  is the surface stress. The surface strain !" is defined as a ratio of change in surface area, !" = A/A. Since the bending of the cantilever is very small compared to the

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length of the cantilever, the strain contribution is only in the ppm (10−6  range while the surface free-energy changes are in the 10−3 range. Therefore, one can easily neglect the contribution from surface strain effects and equate the freeenergy change to surface stress variation.

4. NANOCANTILEVERS Microcantilevers designed for scanning probe microscopy (SPM) applications have a resonance frequency in the 10– 300 kHz range depending on the spring constant. The cantilevers used in SPM typically have dimensions in the 100 microns range and are fabricated by micromachining. These cantilevers demonstrated to be excellent sensors based on resonance frequency variation or cantilever bending. For a microcantilever, the sensitivity of mass detection increases with higher spring constant while bending signal sensitivity increases with lower spring constant. It has been demonstrated that a mass resolution of approximately 1 pg can be achieved for a 200-micron-long cantilever with a resonance frequency of 25 kHz. The mass sensitivity of a microcantilever sensor can be greatly increased by decreasing its dimensions [34–36]. It is conceivable that reducing the dimensions of a cantilever sensor can lead to detection of individual binding events of molecular adsorption on a cantilever. The cantilevers with reduced dimensions are called nanocantilevers. Nanocantilevers typically have a length of approximately 1
m. The thickness and width of a nanocantilever are adjusted such that the cantilever is free from size-induced deformations. One advantage of decreasing the length of the cantilever is that its resonance frequency can be increased into GHz. Higher resonance frequency implies higher spring constant. Since these cantilevers have high spring constants, they are not suitable for detecting adsorption-induced cantilever bending. Therefore, the nanocantilevers are more suited for a resonance frequency variation-based sensing approach than a bendingbased method. However, it is possible to design a nanocantilever with a spring constant around 1 N/m by adjusting the length, width, and thickness. Davis et al. calculated a resonance frequency of 179.9 MHz for a cantilever of 2.82 microns long with a spring constant of 1 N/m [37]. In the case of resonating cantilevers scaled down to the nanosize, further dramatic increases in their sensitivity to chemical or biological stimuli are expected providing an opportunity to achieve ultra-high mass sensitivity, ultimately, approaching detection to the single molecule level [38]. The minimum detectable mass strongly depends on K and Q and is given by [38]:  8G m5/4 kB T B 0 mmin = 2 1/2 3/4 (15) z  K Q where G is a geometrical factor of the cantilever, kB is the Boltzmann constant, T is the temperature of the cantilever, B is the bandwidth of the measurement, m0 is the initial cantilever mass, and z2 1/2 is the root mean-square amplitude of the cantilever motion. Therefore, both increased stiffness and the mass of the externally actuated resonator can influence the mass sensitivity. From eq. (15), however, it is clear

that there is a connection between effects of the resonator stiffness mass and the Q-factor. Obviously, accurate predictions of the mechanical quality factors are needed in order for eq. (15) to accurately predict the mass detection limit for nanocantilevers. In addition to analytical implications, single-molecule detection is also very important for many fundamental areas of physics, chemistry, and biology. Nanomechanical structures capable of detecting single-molecule interactions have the potential for providing real-time information that cannot be obtained using the currently available methods. In addition to sensing applications, nanocantilevers may also find applications in imaging such as scanning probe microscopy where fast imaging is needed. In this case, the cantilever beam is used for detecting force gradients that exists on the sample surface. The detectable force resolution of the cantilever is given by (KkB /f0 Q1/2 . By varying the dimension, the cantilevers can be made sensitive to detect force gradients or to increase the resonance frequency and thus the scanning speed. It is possible to increase the resonance frequency without significantly changing the spring constant by optimizing the dimensions. In other applications, smaller dimensions of the nanocantilever will tend to increase the spatial resolution in techniques for in-situ mapping of molecular beams [39]. It should be pointed out that many of the signal transduction techniques for cantilever deflection measurements discussed in Section 2, such as optical beam deflection, are not suitable when cantilever length is reduced below a few micrometers. Davis et al. demonstrated a cantilever signal detection based on capacitive readout [37]. In this sensor, the nanocantilever was excited into resonance electrostatically by means of a lateral electrode. The detection of oscillation amplitude of the cantilever was achieved by measuring displacement current in the capacitor formed by the cantilever and the driver electrode. The length of the cantilever was 50 microns. Kawakatsu et al. [40] fabricated nanocantilevers (nanometric oscillators) using siliconetching processes. The cantilever was a nanometric tip with an elastic neck where the tip was fabricated by anisotropic etching of silicon by KOH. Burger et al. demonstrated nanocantilever fabrication based on focused ion beam (FIB) patterning/milling and KOH etching [41]. These nanocantilevers were 30 nm thin and 100 nm wide with lengths ranging from 0.5–2 microns. As mentioned earlier, signal transduction is a formidable challenge for nanocantilevers. This challenge, however, can be overcome by utilizing a signal transduction method based on electron transfer that is ideally suited for detection of nanocantilever motion. As an electrically driven cantilever vibrates between two biased electrodes, a current flows through the system due to charge transfer between the electrodes through the floating cantilever. The basic concept of charge transport is similar to a electrostatic charge shuttle demonstrated by Tuominen et al. [42].

4.1. Nanocantilever Fabrication Single crystal and polycrystalline cantilever structures routinely fabricated by a number of conventional processes of wet or dry etching. The dry etching process involves

556 etching in inductively coupled plasma systems. Cantilevers can also be fabricated using photo-electrochemical etching using etch stops. These conventional techniques of fabricating cantilevers using micromachining techniques are ideal for cantilevers that are tens of
m in size. However, fabrication of cantilevers with dimensions of only a few
m or smaller is still a formidable task. There exist a number of ways by which nanocantilevers can be fabricated, such as FIB or a combination of FIB and etching. Abadal et al. [7] have demonstrated two different types of fabrication techniques—one based on a combination of laser and atomic force microscopy (AFM) lithography and a second one based on electron beam lithography (EBL) [43]. In AFM lithography, a cantilever is fabricated on an Al-coated SiO2 surface by oxidation. Electron beam lithography utilized a lift-off defined chrome layer as a mask for SF6 -based reactive ion etching. Cantilevers with a width of 100 nm and with varied lengths between 10
m to 40
m have been fabricated. However, none of these techniques are compatible with mass production. Nanofabrication using a FIB is more compatible with mass production [38, 44]. In the FIB technique, a focused Ga ion beam with energy in tens of KeV is used to physically cut out cantilevers from thin silicon membranes. We used this technique where the starting surfaces for fabricating cantilevers were single-crystal Si membranes having an initial thickness of 10
m. Prior to cantilever fabrication, the FIB was used to reduce the thickness of the Si membrane down to a few micrometers. Cantilevers with dimensions 0.8 to 2
m in length, 50 nm to 500 nm in width, and 25 to 100 nm in thickness, have been fabricated using FIB. The calculated resonance frequency of a rectangular Si cantilever with these dimensions is 265 MHz. The FIB technique can be used to nanofabricate devices from different materials and not limited to only Si. A different approach that involves a combination of a focused ion beam and anisotropic wet etching can also be used for single-crystal substrates [41, 43, 45]. In this case, the focused Ga ion beam is used to dope specific parts of the target, single-crystal surface. Selective Ga ion implantation and subsequent milling by FIB exposure followed by wet chemical etching can be used to fabricate nanomechanical structures in single-crystal Si. Nanobridges and nanocantilevers with around 30 nm thickness can be made by controlled selective underetching between unexposed and exposed areas. In Figure 1, we show an example of nanomechanical bridges fabricated using the FIB doping technique. The patterned Ga ion implantation was performed on a (100) Si wafer and the effective doping depth was estimated to be around 70 nm. Anisotropic etching was performed on the implanted samples at 83 C using KOH.

Micro and Nanocantilever Sensors

1 µm

Figure 1. An ion micrograph of an array of nanobridges fabricated from a single-crystal silicon using a focused ion beam doping technique.

piezoresistive techniques, are harder to implement at nanoscale. Davis et al. [37] demonstrated capacitive-based signal transduction for 30–50
m long cantilevers. However, as the cantilever dimensions are reduced, the capacitance signal will become comparable to parasitic capacitance from lead wires and bonding pads. Direct integration of CMOS circuitry on the cantilever chip can reduce the parasitic capacitance. Other techniques, such as electron tunneling and electron shuttling, can be used as signal transduction techniques for nanocantilevers since the amplitude of vibration is within nanometer range. In an electron tunneling device, the electrons tunnel between two surfaces maintained at a potential difference and separated by a few nanometers. In electron shuttling, the cantilever is vibrated between two surfaces maintained at a potential difference. Both electron tunneling and shuttling mechanisms can be used with ease when nanocantilevers are involved. In electron shuttling signal transduction, a nanocantilever is nanofabricated between two fixed electrodes using FIB. The cantilever and the associated electrode system were fabricated monolithically using an FIB from a silicon membrane. A scanning ion micrograph of the monolithic

500 nm

4.2. Nanocantilever Measurements As indicated earlier, optical detection of cantilever motion of nanocantilevers and nanocantilever arrays at their resonance frequency is extremely difficult due to the reduced reflection (scattered) signal from the cantilever surface. Other techniques, such as piezoelectric and

Figure 2. An ion micrograph of an array of nanocantilevers fabricated from commercially available microcantilevers using a focused ion beam.

557

Micro and Nanocantilever Sensors

4.3. Nanocantilever Resonance Response Characterization The motion of the nanofabricated cantilevers was studied using the experimental set-up described above [44]. When a bias voltage is applied between the source and drain electrodes, no electron current flowed through the system under d.c. voltage condition because of the air gap between the cantilever and the two electrodes. It is possible that when the system is biased with a d.c., the cantilever can bend due to applied electrostatic force. However, such cantilever bending due to electrostatic force was too small to cause the cantilever to bend enough and make contact with the electrodes. Also, since d.c. bias voltage is used, no displacement current flowed through the system. When the cantilever was excited into resonance (using an acoustic source), the oscillatory motion caused the cantilever to make electrical contact with the source and the drain electrode. Electronic charge was transferred to the electrically floating cantilever “gate” when the cantilever made contact with the source electrode. The electron charge on the cantilever was subsequently transferred to the drain electrode as the cantilever oscillated in the opposite direction and made contact with

the drain electrode. As the cantilever made alternating contact with the source and drain electrodes, electrical charge was transferred from the source to the drain electrode causing a net electron current to flow through the system. The applied bias voltage between the source and the drain electrode was 500 mV. When the cantilever was acoustically excited, the current through the circuit exhibited a peak at 5.2 MHz (see Fig. 4). At resonance, the acoustic frequency used for cantilever excitation matches with natural frequency of the cantilever. In Figure 4, we show the electron current through the system measured with a pico-ammeter as a function of the acoustic frequency that excited the cantilever into motion. From the data in Figure 4, it appears that at resonance the electron current increases to 7 pA against the noise floor of 1.7 pA. The mechanical Q-factor of the cantilever was calculated to be around 10 when the device was operated in air. The Q-factor can be increased by an order of magnitude by operating in a He gas environment; when the cantilever oscillates in a low viscosity medium such as He oscillation damping is reduced. At the resonance frequency, the measured electron current was approximately 7 pA. The flow of electron current between the source and drain electrodes, facilitated by the cantilever motion, can be understood as follows. As the cantilever comes in contact with the energized source electrode, the cantilever will pick up charge q, either by electron tunneling or by physical contact. This charge will then be transferred to the drain electrode as the cantilever oscillates and makes contact with the drain electrode. The total current due to electron transfer can be expressed as i = 2nef

(16)

where n is the number of charge quanta (electrons) transferred to the cantilever, e is the electronic charge, and 8

f0 = 5.2 MHz V = 500 mV

6

Electron Current (pA)

cantilever and detection system is shown in Figure 3. The length of the cantilever was 4.5
m and the thickness of the cantilever was 0.5
m. This type of geometry allowed in-plane motion of the cantilever. The motion of the cantilever was in the plane of the image. The micrograph shows the thickness of the cantilever. Two electrodes (labeled as source and drain) were micromachined in such a way that the cantilever can oscillate between these two structures. The source and drain electrodes were equidistant from the cantilever beam. The separation distance between the cantilever and the source and drain was approximately 50 nm. All three components—cantilever (gate), source, and drain—were electrically isolated from each other. The nanocantilever was excited into resonance using an acoustic excitation source. The source and drain electrodes were electrically biased and the current flowing through the system was measured using a pico-ammeter.

4

2

0 2

4

6

8

10

12

14

Frequency (MHz) Figure 3. An ion micrograph of a nanocantilever with a readout system fabricated from a single-crystal silicon using an FIB. The cantilever “gate” was actuated acoustically and had a resonance frequency of 5.2 MHz.

Figure 4. Electron current measured as a function of frequency. The nanocantilever gate was actuated acoustically around its first harmonic resonance and the effective electron transport was monitored for an applied bias of 500 mV.

558 f is the excitation frequency. From the data presented in Figure 4, we obtain a value of n = 5 at resonance and n = 1 at frequencies far away from resonance. These values correspond to 1.7 pA noise current and 7 pA current at resonance, respectively. From the physical dimensions of the Si nanocantilever, a cantilever mass of 10−15 g can be calculated. If the resonance frequency can be measured with a resolution of 100 Hz, the minimum detection limit for adsorbed mass can be calculated as 10−19 g at a resonance frequency of 5.2 MHz. This detection limit is ample to detect changes in adsorbed mass due to a single biomolecule of a large protein or a DNA strand of 50 nm in length. The detection limit can be further improved by increasing the Q-factor of the cantilever. The Q-factor can be possibly amplified by a feedback system, which was demonstrated for optical signal transduction.

4.4. Femtogram Mass Sensitivity Mass sensitivity of a few femtograms was demonstrated using small-size cantilevers in the air. The smaller cantilevers were fabricated from commercially available cantilevers (200
m long, 50
m wide, and 1.5
m thick) and were coated with a 35-nm gold layer on one side to increase optical reflectivity and response to photothermal actuation [38]. An FIB milling instrument (FEI 200) was used to fabricate cantilevers that measured 2 to 6
m long, 50 to 100 nm thick, and had resonance frequencies in the range of 1–6 MHz [38]. It was reported that all these fabricated resonators exhibited very similar normalized widths of the resonances in air, which was almost independent of the cantilever thicknesses and shapes. The explanation offered [38] was that for cantilevers in air, viscous damping by the medium is the predominant energy dissipation mechanism. Based on the width of the measured resonance curves, a Q-factor of 25 was estimated. At a lower air pressure, the Q-factor increased by at least five-fold. A very important conclusion that can be drawn from these observations is that minimization of intrinsic mechanical losses may not be practical in the case of nanomechanical mass-sensitive transducers operating in the air at room temperature and atmospheric pressure [38]. A rectangular, gold-coated silicon cantilever with a resonance frequency of 2.25 MHz with an approximate 2
m width and 6
m length was exposed to 11-mercaptoundecanoic acid vapor. Upon exposure of the cantilever to 11-mercaptoundecanoic acid vapors, the resonance frequency was found to decrease, which was attributed to chemisorption of the analyte molecules onto the gold-coated surface of the cantilever. The measured frequency shift of 2 KHz was found to correspond to an added mass of 55 × 10−15 g, a value that is close to a 50% coverage of a monolayer of 11-mercaptoundecanoic with a total mass of 6 × 10−15 g over the area of the cantilever which is 12
m2 .

4.5. Controlling Q-Factor of a Cantilever The Q-factor of a cantilever, defined as the ratio of resonance frequency to FWHM of a resonance curve, determines the efficiency of oscillations. The Q of a microcantilever vibrating in air is typically in the range of 30–100. In

Micro and Nanocantilever Sensors

liquids Q drops to a small value close to 1. The resolution of the resonance frequency measurement increases with Q. Therefore, techniques to improve the Q-factor of vibrating cantilevers will have important implications in imaging and sensor applications. Recently, it has been demonstrated that the Q of a cantilever vibration can be manipulated using a feedback technique [22, 46]. It is shown that the Q can be increased by a factor 10–1000 using feedback. Even Brownian motion (thermal motion) of a cantilever can be amplified. As pointed out earlier, a low Q-factor leads to a lower resolution in resonance frequency detection and thus a low sensitivity in mass detection. When the cantilever sensor is operated in a medium, the damping decreases the Q-factor leading to lower sensitivity. Therefore, despite its suitability for liquid operations resonance, frequency-based, cantilever sensors have not attracted much attention as sensitive biological and chemical sensors. The Q-factor of a cantilever can be increased by utilizing a feedback technique. For an optical beam deflection technique, the feedback can be accomplished by feeding back the output of the PSD to a piezoelectric cantilever holder. A phase shifter and a gain controller placed between the PSD and piezoelectric holder determines the feedback condition. By adjusting the phase shift and gain, the Q-factor can be manipulated in a controlled fashion. The governing equation of motion for a feedback-driven cantilever, modeled as a damped harmonic oscillator, is meff

d2 z dz + + kz = Gei' zt dt 2 dt

(17)

where, meff is the effective mass of the cantilever, is the resistance or damping force on the cantilever, k is the spring constant, G is the gain of the feedback amplifier, ' is the phase shift added by the phase shifter, and z is the vertical displacement of the cantilever. Thus the system can be thought of as a harmonic oscillator with an effective spring constant keff = k − Gei' . The general form of the solution for zt can be written as −

t

zt = C1 cos )∗ t + C2 sin )∗ te 2meff *  2 keff ∗ where ) = − meff 4m2eff

(18)

The gain of the feedback amplifier (G and phase shift (') is critical in tuning the feedback signal to achieve resonance and amplification. The magnitude of the gain and phase shift was a function of the physical dimensions and material properties of the cantilever. We have shown that the Q-factor of a silicon-nitride cantilever oscillating under a solution can be varied. In air, we were able to increase the Q from 20 to 3000 for silicon-nitride cantilevers resonating by Brownian motion. The smaller FWHM achieved with the feedback allows frequency measurements at a smaller linewidth, improving the minimum detectable frequency shift. Similar Q-factor enhancement can be achieved for other signal transduction methods [7, 22, 46].

559

Micro and Nanocantilever Sensors

5. CONCLUSIONS As the technology to fabricate nanosize mechanical structures further develops, we envision a plethora of new application where these systems can play an important role. As the frequency of these devices approaches or even exceeds GHz nanomechanical devices will be in the same time and frequency domain reserved now only for electronic devices. One very important issue that need to be addressed is the efficient readout of nanocantilevers not only because of the small size but also because of the readout of large arrays. Compared to presently used signal transduction methods, electron transfer using a cantilever system is ideally suited for NEMS nanocantilevers. Conventional techniques of measuring the resonance frequency, such as optical beam deflection, fall short when applied to micromachined nanocantilevers. For example, in optical beam deflection, the cantilever motion is measured by reflecting a laser diode off the free end of a cantilever into a position-sensitive detector. The shortcomings of optical techniques are simply due to the lack of a sufficient reflected (or scattered) optical signal from the cantilever beam. Optical beam deflection is extremely sensitive when used for cantilevers that are 5
m to a few hundreds of micrometers long while the electron transfer signal transduction is extremely sensitive for cantilevers that are a few hundred nanometers to a few microns in length. The applicability of electron transfer signal transduction for aqueous environments remains extremely challenging. Presence of electro active ions in the water can cause a large Faraday leakage current that can overwhelm electron transfer signal. The leakage current, however, can be significantly reduced using proper insulation, reduced bias voltage, and a reduced number of charge carriers in the solution. However, this technique may be applicable for biosensors that can be operated in humid atmosphere.

GLOSSARY B Bandwidth of measurements, a frequency range, within which measured signals are analyzed, a very narrow bandwidth of measurements can be achieved by collecting and averaging the data for prolonged periods of time. Cantilever Suspended beam structure with a single clamping point; suspended structures with shapes more complex than a rectangular beam and more than one (typically two) clamping points are also refereed to as cantilevers. An example of the latter is a V-shaped cantilever, often used in scanning probe microscopy. K Spring constant, can be used to quantify the elasticity of suspended beams and analogous structures; assumes linear relationship between the force exerted on the beam and its deformation (Hook’s law) and is defined as a force that would displace the reference point (usually an end of the cantilever) by 1 meter; spring constants of typical microcantilevers are in the range of 10−2 to 10 N/m. Microcantilever Cantilever with characteristic sizes on the order of microns; microcantilever devices that are widely used as force probes in scanning probe microscopy have lengths, widths and thicknesses in the range of, respectively, 50–300
m, 20–100
m, and 0.5–5
m.

Micro-electro-mechanical systems (MEMS) Term coined to denote microfabricated devices that rely on mechanical phenomena and mechanical energy, may integrate micromechanical and traditional microelectronic components. Nano-electro-mechanical-systems (NEMS) Devices that rely on mechanical phenomena and mechanical energy and has characteristic dimensions less than 1 micron. Q-factor Quality factor, parameter that quantifies energy dissipation in the resonating device, can be defined as the ratio of the average energy stored in the resonator to the energy dissipated per oscillation cycle. Thermal energy Kinetic energy of atoms, molecules and any microscopic particles at nonzero temperatures. Thermal motion Motion of microscopic objects in equilibrium with their thermal environment (“thermal bath”) due to continuous dynamic exchange of thermal energy.

REFERENCES 1. T. Thundat, R. J. Warmack, Chen, and D. P. Allison, Appl. Phys. Lett. 64, 2894 (1994). 2. T. Thundat, G. Y. Chen, R. J. Warmack, D. P. Allison, and E. A. Wachter, Anal. Chem. 67, 519 (1995). 3. T. Thundat, E. A. Wachter, S. L. Sharp, and R. J. Warmack, Appl. Phys. Lett. 66 (1995). 4. P. G. Datskos, C. M. Egert, and I. Sauers, Sensors and Actuators B 61, 75 (2000). 5. J. K. Gimzewski, C. Gerber, E. Meyer, and R. R. Schlittler, Chem. Phys. Lett. 217, 589 (1994). 6. R. Berger, C. Gerber, H. P. Lang, and J. K. Gimzewski, Microelectronic Engineering 35, 373 (1997). 7. G. Abadal, Z. J. Davis, B. Helbo, X. Borris, R. Ruiz, A. Boisen, F. Campabadal, J. Esteve, E. Figueras, F. Perez-Murano, and N. Barniol, Nanotechnology 12, 100 (2001). 8. T. Thundat, P. I. Oden, P. G. Datskos, G. Y. Chen, and R. J. Warmack, in “The 16th Warner Brandt Workshop on Charged Particle Penetration Phenomena.” Oak Ridge, TN, 1996. 9. N. V. Lavrik, C. A. Tipple, M. J. Sepaniak, and P. G. Datskos, Biomedical Microdevices 3, 33 (2001). 10. N. V. Lavrik, C. A. Tipple, M. J. Sepaniak, and P. G. Datskos, Proc. SPIE 4560, 152 (2001). 11. N. V. Lavrik, C. A. Tipple, M. J. Sepaniak, and P. G. Datskos, Chem. Phys. Lett. 336, 371 (2001). 12. H. P. Lang, R. Berger, F. Battistion, J. P. Ramseyer, E. Meyer, C. Andreoli, J. Brugger, P. Vettiger, M. Despont, T. Mezzacasa, L. Scandella, H.-J. Guntherodt, C. Gerber, and J. K. Gimzewski, Appl. Phys. A 66, S61 (1998). 13. H. P. Lang, M. K. Baller, R. Berger, C. Gerber, J. K. Gimzewski, F. M. Battison, P. Fornaro, J. P. Ramseyer, E. Meyer, and H. J. Gÿntherodt, Anal. Chim. Acta 393, 59 (1999). 14. H. P. Lang, R. Berger, C. Andreoli, J. Brugger, M. Despont, P. Vettiger, C. Gerber, J. K. Gimzewski, J. P. Ramseyer, E. Meyer, and H.-J. Güntherodt, Appl. Phys. Lett. 72, 383 (1998). 15. P. G. Datskos, M. J. Sepaniak, C. A. Tipple, and N. Lavrik, Sensors and Actuators B-Chemical 76, 393 (2001). 16. P. G. Datskos, S. Rajic, M. J. Sepaniak, N. Lavrik, C. A. Tipple, L. R. Senesac, and I. Datskou, J. Vac. Sci. Tech. B 19, 1173 (2001). 17. J. C. L. Britton, R. L. Jones, P. I. Oden, Z. Hu, R. J. Warmack, S. F. Smith, W. L. Bryan, and J. M. Rochelle, Ultramicroscopy 82, 17 (2000).

560 18. R. Berger, E. Delamarche, H. P. Lang, C. Gerber, J. K. Gimzewski, E. Meyer, and H.-J. Güntherodt, Science 276, 2021 (1997). 19. D. Sarid, “Scanning Force Microscopy with Applications to Electric, Magnetic, and Atomic Forces.” Oxford University Press, New York, 1991. 20. G. Y. Chen, T. Thundat, E. A. Wachter, and R. J. Warmack, J. Appl. Phys. 77, 3618 (1995). 21. T. R. Albrecht, P. Grutter, D. Horne, and D. Rugar, J. Appl. Phys. 69, 668 (1991). 22. A. Mehta, S. Cherian, D. Hedden, and T. Thundat, Appl. Phys. Lett. 78, 1637 (2001). 23. E. A. Wachter, T. Thundat, P. G. Datskos, P. I. Oden, R. J. Warmack, and S. L. Sharp, Rev. Sci. Instrum. 67 (1996). 24. M. Tortonese, H. Yamada, R. C. Barrett, and C. F. Quate, in “The Proceedings of Transducers ’91.” IEEE, Pennington, NJ, 1991. 25. M. Tortonese, R. C. Barrett, and C. F. Quate, Appl. Phys. Lett. 62, 834 (1996). 26. J. A. Harley and T. W. Kenny, J. Microelectromechanical Systems 9, 226 (2000). 27. P. I. Oden, E. A. Wachter, P. G. Datskos, T. Thundat, and R. J. Warmack, Infrared Technology and Applications XXII, SPIE 2744, 345 (1996). 28. D. L. DeVoe and A. P. Pisano, J. Microelectromechanical Systems 6, 266 (1997). 29. S. Zurn, M. Hseih, G. Smith, D. Markus, M. Zang, G. Hughes, Y. Nam, M. Arik, and D. Polla, Smart Materials and Structures 10, 252 (2001). 30. Q. M. Wang and L. E. Cross, Ferroelectrics 215, 187 (1998).

Micro and Nanocantilever Sensors 31. R. Amantea, C. M. Knoedler, F. P. Pantuso, V. K. Patel, D. J. Sauer, and J. R. Tower, in “SPIE,” Vol. 3061, p. 210. Orlando, FL, 1997. 32. G. G. Stoney, Proc. Royal Soc. London 82, 172 (1909). 33. R. Shuttleworth, Proc. Phys. Soc. London 63A, 444 (1950). 34. Y. T. Yang, K. L. Ekinci, X. M. H. Huang, L. M. Schiavone, and M. L. Roukes, Appl. Phys. Lett. 78, 162 (2001). 35. D. W. Carr, L. Sekaric, and H. G. Craighead, J. Vac. Sci. Tech. B 16, 3821 (1998). 36. A. Olkhovets, S. Evoy, D. W. Carr, J. M. Parpia, and H. G. Craighead, J. Vac. Sci. Tech. B18, 3549 (2000). 37. Z. J. Davis, G. Abadal, O. Kuhn, O. Hansen, F. Grey, and A. Boisen, J. Vac. Sci. Tech. B 18 (2000). 38. N. V. Lavrik and P. G. Datskos, Appl. Phys. Lett. 82, 2697 (2003). 39. U. Drodofsky, M. Drewsen, T. Pfau, S. Nowack, and J. Mlynek, Microelectronic Engineering 30, 383 (1996). 40. H. Kawakatsu, H. Toshiyoshi, D. Saya, K. Fukushima, and H. Fujita, Appl. Surf. Sci. 57, 320 (2000). 41. J. Brugger, G. Beljakovic, M. Despont, N. F. deRooij, and P. Vettiger, Microelectronic Engineering 35, 401 (1997). 42. M. T. Tuominen, R. V. Krotkov, and M. L. Breuer, Phys. Rev. Lett. 83, 3025 (1999). 43. J. Xu and A. J. Steckl, Appl. Phys. Lett. 65, 2081 (1994). 44. P. G. Datskos and T. Thundat, J. Nanosci. Nanotech. 2, 369 (2001). 45. A. J. Steckl, H. C. Mogul, and S. Mogren, Appl. Phys. Lett. 60, 1833 (1992). 46. J. Tamayo, A. D. L. Humphris, and M. J. Miles, Appl. Phys. Lett. 77, 582 (2000).

Encyclopedia of Nanoscience and Nanotechnology

www.aspbs.com/enn

Micro- and Nanomechanics Barton C. Prorok Auburn University, Auburn, Alabama, USA

˘ P. Bažant, Zaoyang Guo Yong Zhu, Horacio D. Espinosa,∗ Zdenek Northwestern University, Evanston, Illinois, USA

Yufeng Zhao, Boris I. Yakobson Rice University, Houston, Texas, USA

CONTENTS 1. Mechanics of Scale 2. Micro- and Nanoscale Measurement Techniques 3. Micro- and Nanoscale Measured Material Properties 4. Theoretical Modeling and Scaling 5. Modeling One-Dimensional Materials: Nanotubes and Nanowires Glossary References

1. MECHANICS OF SCALE It has been known for quite some time that materials and structures with small-scale dimensions do not behave in the same manner as their bulk counterparts. This aspect was first observed in thin films where certain defect structures were found to have deleterious effects on the film’s structural integrity and reliability. This became a significant concern because thin films are routinely employed as components in microelectronics and microelectromechanical systems (MEMS). Their properties frequently allow essential device functions and therefore accurate identification of these properties is key to the development of new technologies. Unfortunately, most of our knowledge is based on bulk material behavior, which many times fails to describe material response in small-scale dimensions because of the dominance of surface and interface effects, finite number ∗

Corresponding author.

ISBN: 1-58883-061-6/$35.00 Copyright © 2004 by American Scientific Publishers All rights of reproduction in any form reserved.

of grains in a given structure (e.g., through the thickness), and the role played by the manufacturing process (e.g., texture, residual stress, and dislocation structure). This last feature is particularly important since material surfaces and microstructures are the result of the process employed to deposit or remove material [1].

1.1. Thin Films As thin film dimensions begin to approach that of the films microstructural features, the material mechanical properties begin to exhibit a dependence on the specimen size. In metallic thin films this translates to plastic yielding occurring at increased stresses over their bulk counterparts. Although this phenomenon was observed as early as 1959 [2], no consensus or common basic understanding of it yet exists. In addition to plastic behavior, other mechanical properties can exhibit size effects, such as fracture toughness and fatigue resistance. Each of these properties operates on a characteristic length scale that can be compared to the physical dimensions of microelectronics, microdevices, or nanodevices. This is shown schematically in Figure 1, which utilizes a logarithmic length scale map beginning at the atomic scale and ending at the macro scale. On the left are four categories of structures and the regime where their dimensional size fits on the length scale. On the right are regimes indicating where dimensional size effects begin to affect the material mechanical properties and theories used to predict behavior. Elastic properties are dependent on the bonding nature of the material and only exhibit size effects at the atomic scale. In contrast, plastic, fatigue, and fracture toughness properties all exhibit size effects in the micrometer and submicrometer regime. These properties all depend on defect generation and evolution, which are mechanisms

Encyclopedia of Nanoscience and Nanotechnology Edited by H. S. Nalwa Volume 5: Pages (561–606)

Micro- and Nanomechanics

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10 1

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Figure 1. Illustration of length-scale effects on the mechanical properties of materials.

that operate on characteristic length scales [3]. These fundamental changes in mechanical behavior occur in the size scale of MEMS and microelectronics devices, and thus, a better understanding of inelastic mechanisms is required to better predict their limits of strength and reliability. The right side of Figure 1 also lists the theories used to predict material behavior and the length scale where they are applicable. These include classical plasticity, strain gradient plasticity, discrete dislocation mechanics, molecular dynamics, and quantum mechanics. Classical plasticity is described in terms of traditional continuum mechanics, which describes the relationships between stress and strain and is applicable for predicting behavior from a size of approximately 100 micrometers and greater. Molecular dynamics (MD) is at the other end of the scale and involves the generation, mobility, and interaction between individual dislocations, twinning, stacking faults, and other defects. It is only applicable at the lower end of the scale since it is based on large scale numerical simulation. Therefore, it is subsequently limited by current computational power (i.e., systems approximately one million atoms in size). In the regime between classical plasticity and discrete dislocation mechanics, a theory called strain gradient plasticity has been developed in the last decade to describe material behavior [4]. It considers the effect of gradients in strain in the description of flow behavior. A large number of theories have been proposed. However, as will be discussed in Section 4, most of these theories exhibit unreasonable predictions as the size of the structure approaches one nanometer. For this reason, its applicability is limited to structures with minimum dimension of a few hundred nanometers. Between this theory and molecular dynamic, a model based on discrete dislocation dynamics has been postulated [5–7]. These models are currently in an early stage of development so they are not discussed here in detail. The mechanical response of thin films depends on many factors. Of particular importance is the existence of film thickness effects that arise because of geometrical constraints on dislocation motion. Size effects on mechanical properties begin to play a dominant role when one or more of the structure’s dimensions begins to approach the scale of the material microstructural features. The onset of plastic

deformation depends strongly on the ability of dislocations to move under an induced stress [8, 9]. The ease of their movement can be hindered by any number of obstacles such as grain boundaries, precipitates, interfaces, etc. Specimen size then begins to govern plastic behavior by creating geometrical constraints, surface effects, and the competition of deformation mechanisms (i.e., dislocation motion versus twinning or phase transitions). Other effects that specimen size can have on plastic deformation involve microstructural changes. This includes grain size, morphology, and crystallographic texture. Preferential grain orientations can result from a minimization of surface energies [10, 11]. The average grain size is also typically on the order of the film thickness, due to an effect called the “specimen thickness effect” which depends upon grain boundaries being pinned by their surface grooves, occurring when the mean equivalent grain diameter is on the order of the film thickness [12, 13]. Several theoretical models, based on single dislocation motion, have been proposed to explain the size effect phenomenon [14–16]. However, each predicts strength increases far below experimentally obtained values. The higher yield point of metallic thin films is likely the result of a combined interaction between strain hardening and deformation mode transition from dislocation motion to twinning. Several pioneering studies have experimentally identified the existence of size effects on the plasticity of metals. These studies were able to obtain experimental nanoindentation data showing a strong size effect as evidenced by material hardness decrease as indentation depth increases [17– 19]. Figure 2 is a reproduction of the data from Ma and

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0

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Figure 2. Plot of hardness vs plastic depth illustrating how hardness increases with smaller plastic depth. Reprinted with permission from [18], Q. Ma and D. R. Clarke, J. Mater. Res. 10, 853 (1995). © 1995, Materials Research Society.

Micro- and Nanomechanics

Clarke [18] of nanoindentation performed on epitiaxially grown silver on sodium chloride and shows that the hardness increases by a factor of two to three as penetration depth decreases. Their results have been verified and expanded upon in subsequent studies [20–27]. Other pioneering work involved bending strips of metal of varying thickness around a rigid rod [28] and applying a torque load to copper rods of varying diameter [29]. The strips varied in thickness from 12, 25, and 50
m and each was bent around a rigid rod whose diameter was scaled to the film thickness to ensure identical states of strain in each strip. Figure 3 shows the results in the form of normalized bending moment versus surface strain. It is clear from this plot that as each strip was strained to the same degree, the thinner strips required a larger bending moment. The copper rod experiment used rods of varying diameter, 12–170
m. A torque was applied to each rod in order to twist them all to the same degree (i.e. to identical states of strain). A plot of torque versus twist per unit length is shown in Figure 4 and indicates an increase in strength by a factor of three for the smallest rod over the largest. Direct tensile tests were also performed on identically sized copper rods (Fig. 4). The authors concluded that for the most part, no size effects existed when subjected to direct tension. The results of these tests show a strength increase for smaller structures over larger ones when subject to bending and torsional loads. In these pioneering studies, the size dependence of the mechanical properties was considered to be a result of nonuniform straining [23, 29, 30]. It was shown that classical continuum plasticity could not predict the size dependence

Figure 3. Plot of normalized bending moment vs surface strain illustrating how the thinner films require more bending moment for the same state of strain. Reprinted with permission from [28], J. S. Stolken and A. G. Evans, Acta Mater. 46, 5109 (1998). © 1998, Elsevier Science.

563

Figure 4. Plot of applied torque vs twist for copper rods of varying diameter and stress–strain of identical rods subject to direct tension. Reprinted with permission from [29], N. A. Fleck et al., Acta Metal. Mater. 42, 475 (1994). © 1994, Elsevier Science.

in this regime. The generally accepted size limit for accurate description of plasticity by the classical theory is systems with dimensions greater than approximately 100
m. As previously mentioned, molecular mechanics can accurately describe material behavior at the atomic level. However, due to the computational cost and limitations on performing atomistic simulations for more than one million atoms, the maximum size regime computationally approachable is systems with dimensions 53

Tensile test

045 ± 023

172 ± 064

Tensile test Torsion test

0.27–0.95 0.6a

11–63

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Comments varies with diameter

Ref. [184] [160] [152]

arc-discharge MWCNT compressive modulus and strength very long MWCNT outermost layer

[188] [154]

[189] [164] [153]

Shear modulus G.

h

0

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s (nm)

Figure 42. Curvature and height of buckles along a bent carbon nanotube. The white scale bar (in (a) represents 300 nm and all figures are to the same scale. A 20-nm-diameter tube was manipulated from its straight shape [(a), inset)] into several bent configurations (a)–(d). The height and curvature of the bent tubes along its centerline [indicated by the arrow in (a)] are shown in (e)–(h). The upper trace in each graph depicts the height relative to the substrate; the lower trace depicts the curvature data. Height values are relative to substrate height. The “ripple”-like buckles migrate as the tube is manipulated into different configurations. The appearance and disappearance of the ripple buckles, as well as the severe buckle at s ≈ 500 nm (e)–(f), suggest elastic reversibility. The large buckle at s ≈ 325 nm (e), (f) retains its raised topographical features even after straightening (g), (h), suggesting that damage has occurred at this point; but the tube does not fracture. The average of the buckle interval histogram [(d), inset)] and the average of the Fourier transforms [(c), inset) for a wide range of bent configurations establish the dominant interval as 68 nm. Reprinted with permission from [156], M. R. Falvo et al., Nature 389, 582 (1997). © 1997, American Association for the Advancement of Science.

in nanotube resistance were small unless the nanotubes fractured or the metal–nanotube contacts were perturbed. However, Tombler et al. [206] succeeded in bending individual SWNTs with an AFM tip and measuring conductance as a function of deflection. The study revealed that the conductance of SWCNT changed dramatically under the applied deformation. Figure 44 represents the schematic of their experiment and measured values. Quantum mechanical modeling was employed to verify and explain the experimental findings. The conclusion reached by the authors was that interaction between the AFM tip and the SWCNT deformed the nanotube to a point where the bonding in the nanotube was converted from sp2 to sp3 . However, in previous studies, the nanotubes were more or less uniformly bent or strained; hence, the chemical bonding evidently remained sp2 .

Figure 43. Rolling behavior of CNTs on the graphene substrate (a)–(f) as it is manipulated from left to right. The tube is imaged before and after each of the five manipulations. The insets between each topographical image show the lateral force during each manipulation. The tube is moving from left to right, not gradually but in sudden slips in a stick–slip type rolling motion. In (g), three overlapped signals from separate rolling trials are shown for the lateral force as the tube is pushed through several revolutions of stick–slip rolling motion. The features of the force traces are reproducible. The 85 nm periodicity in the signal, indicated by the dashed lines, is equal to the circumference of the tube at its ends. Reprinted with permission from [157], M. R. Falvo et al., Nature 397, 236 (1999). © 1999, Macmillan Publishers Ltd.

590

Figure 44. Bending of SWCNT by an AFM tip and the corresponding electrical conductance evolution. (a) Top view of an SWCNT partly suspended over a trench for electromechanical measurements; (b) AFM image of an SWCNT with suspended length l ≈ 605 nm; (c) Side view of the AFM pushing suspended SWCNT. (d)–(f) cantilever deflection and nanotube electrical conductance evolution during repeated cycles of pushing the suspended SWCNT. $ is the tube bent angle. Initial tip– tube distance is 65 (d), 30 (e), and 8 nm (f), and the speed of the tip motion was about 22 (d), 34 (e), and 44 nm/s (f). It is seen that the conductance of an SWCNT is reduced by two orders of magnitude when deformed by an AFM. Reprinted with permission from [206], T. W. Tombler et al., Nature 405, 769 (2000). © 2000, Macmillan Publishers Ltd.

4. THEORETICAL MODELING AND SCALING During the 1980s and 1990s, a host of experiments on the micrometer and submicrometer scale, including microindentation [15], microtorsion [29, 30], and microbending [28], revealed a strong size effect on the yield strength and hardening of metals. Similar size effects were observed also in metal matrix composites with particle diameters in the micrometer and submicrometer scale [255, 256]. The classical plasticity theories cannot predict these size effects because they involve no material characteristic length. To explain them, several strain gradient theories were developed. The first one was a phenomenological theory by Fleck and Hutchinson [30] based on the existence of a potential. This theory was later extended and improved, in several versions [31, 257, 258] while retaining the same basic structure. Another strain gradient theory which received considerable attention was the mechanism-based strain-gradient

Micro- and Nanomechanics

(MSG) theory [33, 35] derived under certain simplifying assumptions from the concept of geometrically necessary dislocations. Based on numerical experience, this theory was recently improved as the Taylor-based nonlocal (TNT) theory [259], and the improvement consisting in the form of strain gradient dependence of the hardening function, made the theory conform to a revision proposed by Bažant [260, 261] on the basis of scaling analysis. Another noteworthy theory was Acharya and Bassani’s strain gradient plasticity theory based on the idea of lattice incompatibility [262, 263], which represented a generalization of the incremental theory of plasticity. The asymptotic characters of these strain gradient theories were analyzed recently and it was found that the small-size asymptotic size effect predicted by some of the theories is excessive and unreasonable [259–261]. It might seem that the small-size asymptotic behavior of gradient plasticity is irrelevant because it is approached only at sizes below the range of validity of theory, for which the spacing of the geometrically necessary dislocations (about 10 to 100 nm) and the crystal size are not negligible, and other physical phenomena, such as surface tension, gradation of crystal size, and texture, intervene. However, knowledge of both the small-size and large-size asymptotics is very useful for developing asymptotic matching approximations for the intermediate range, for which the solutions are much harder to obtain. For the purpose of asymptotic matching, the asymptotic behavior must be physically reasonable even if attained outside the range of validity of the theory (this has been demonstrated in the modeling of cohesive fracture when the small-size plastic asymptote is often approached only for specimen sizes much smaller than the inhomogeneity size, e.g., the aggregate size in concrete [260]). The present chapter reviews and summarizes several recent papers in which it was shown that the main theories proposed in the past, including couple stress theory, stress and rotation gradient theory, MSG, TNT, and the Acharya and Bassani’s theory, suffer from excessive asymptotic size effect and some exhibit an unrealistic shape of the loaddeflection curve. Simple adjustments of all these theories suffice to achieve reasonable asymptotic behavior and thus to make asymptotic matching approximations feasible. The main strain gradient theories will be briefly introduced and their asymptotic analysis presented by Bažant and Guo [264] will be outlined. After that, a simple asymptoticmatching approximation, suitable for predictions of yield limit and plastic hardening on the micrometer scale, will be presented.

4.1. Strain Gradient Theories First we will consider Fleck and Hutchinson’s phenomenological strain gradient theory [29, 30] and its successive versions. In these theories, the effect of strain gradient tensor is incorporated into the potential energy density function, in a manner similar to the classical theories of Toupin [265] and Mindlin [266] in which only linear elasticity was considered. A higher order stress tensor needs to be introduced in these theories to provide a work conjugate to the strain gradient tensor, and the boundary condition of classical solid mechanics also needs to be modified as well. The classical J2 deformation theory of plasticity (i.e., Hencky-type solid

Micro- and Nanomechanics

591

strain theory) is chosen as the basis of strain gradient generalization. Gao and Huang’s MSG theory [33, 35] does not use the potential energy approach (and actually, potential energy even does not exist in that theory). Rather, this theory is based on the Taylor relation between the shear strength and dislocation density. A multiscale framework is used to introduce the higher order stress tensor and to establish the virtual work balance. Numerical simulations showed that while the higher order stress tensor is affected by the material length characterizing the size of the framework cell (called the mesoscale cell), the stress and strain tensors are almost unaffected. This observation triggered a reformulation in the form of the TNT theory [259], in which the strain gradient is numerically simulated as a nonlocal variable and the higher order stress disappears. This reformulation coincided with a revision proposed by Bažant [260, 261] for entirely different reasons—namely, the observation that the presence of couple stresses, dictated by the use of a strain gradient tensor as an independent kinematic variable, causes an excessive small-size asymptotic size effect, indicating that couple stresses should be removed from the formulation. Acharya and Bassani’s strain gradient theory [262, 263] differs significantly from the previous theories. It represents a generalization of incremental plasticity rather than total strain theory. The effect of a strain gradient is considered by changing the tangential modulus in the constitutive relation, while the framework of classical plasticity theory remains.

4.1.1. Fleck and Hutchinson’s Theories The first phenomenological strain-gradient theory developed by Fleck and Hutchinson [29, 30] is called the couple stress theory (denoted by CS). The subsequent modification [31] is called the stretch and rotation gradients theory (denoted by SG). Since the main idea of these two theories is the same, we will consider them jointly. To simplify the problem, only incompressible materials will be considered and the elastic part will be ignored because it is negligible compared to large plastic deformation of metals. In the classical work of Toupin [265] and Mindlin [266], and dealing only with the linear elasticity case, the strain gradient is introduced into the strain energy density W as W = 1/2(!ii !jj +
!ij !ij + a1 8ijj 8ikk + a2 8iik 8kjj + a3 8iik 8jjk + a4 8ijk 8ijk + a5 8ijk 8kij

(27)

where ( and
are the usual Lamé constants, !ij = ui: j + uj: i /2 is the strain, 8ijk = uk: ij is the component of strain gradient tensor
, and an is the additional elastic stiffness constant of the material. The sum of the first two terms on the right-hand side is the classical strain energy density function, while the other five terms are the contributions of the strain gradient tensor. Based on the strain energy density defined as (27), the Cauchy stress ij can be defined as a work conjugate to !ij (i.e. ij = ;W /;!ij ). A higher order stress tensor , work conjugate to the strain gradient tensor
, needs to be defined as 07 (E ∼ 7 MV/cm), deviation from a linear dependence is observed; the origin is not known, but it is probably due to high field breakdown effects. One possible scenario is that at high field, impact ionization generates electron-hole pairs, and the resulting hole current cancels the electron injection. Below 0.1 V, the dependence does not have the voltage dependence characteristic of thermionic emission, and instead one finds a linear dependence of lnI/V  versus 1/T . This dependence is characteristic of hopping conduction, where lnI/V  = f N  − E/kT  At low temperatures (∼40 K), biases higher than 1 V are applied. The length of 1,4 phenylene-diisocyanide is calculated to be 10 Å with the molecule oriented normal to the gold surface. It agrees with the ellipsometry measurement by Henderson et al. [58]. 11

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Figure 19. Schematics of device fabrication: (a) cross section of a silicon wafer with a nanopore etched through a suspended silicon nitride membrane. (b) Au-SAM-Au junction in the pore area. (c) Blowup of (b) showing 1,4-phenylene diisocyanide sandwiched in the junction, with the chemisorbed and evaporated contacts pointed out by the arrows.

where E is the activation energy to hop from one site to another and f N  is a function of the trap concentration [66]. Figure 22 shows this dependence in the regime of bias less than 0.1 V. Whereas the physical interpretation of the thermionic transport barrier is clearly the moleculemetal contact potential, the physical site giving rise to hopping transport is less well defined. Structural defects in the nanopore or edge defects are potential candidates for the low-bias defect-mediated transport.

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Molecular Electronic Devices

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1/T (1/K) Figure 21. Series of plots of lnI/T 2  versus 1/T at biases from 0.1 to 1.0 V with 0.1 V increments, for the Au-SAM-Au junctions. All the straight lines are # 2 fits for respective data sets.

To determine the energetic barriers, we plot the slope of (lnI/T 2  versus 1/T ) versus V 05 in Figure 23. For the isocyanide-Au contact, we obtain for 0.1 V < V < 1 V that the intercept of the line fit gives −q/k, with a thermionic barrier of  = 038 (±001) eV; the slope of the line fit gives a/k, where a = qq/4
0 d05 , with the dielectric constant of the isocyanide film  of 3.5. The effective Richardson constant can be obtained from Figure 21. With a device area of 300 × 300 Å2 , the effective Richardson constant was found to be around 120 A/cm2 at low electrical field and 40 A/cm2 at high fields (E > 7 MV/cm). This could be caused by reduced effective area at high current density/high electrical fields around nonuniform metal-SAM interfacial regions. For 0 V < V < 0.1 V, the slope does not depend on bias voltage. A hopping barrier of E = 03 (±001) eV is obtained from the slope [lnI/V  versus 1/T ] of Figure 22.

Figure 23. Plot of the slope of [lnI/T 2  versus 1/T ] versus V 05 : at 0 < V < 01 V, no bias dependence; at V > 01 V, linear dependence. Thermal barrier height of the Au-SAM-Au junction can be deduced from the intercept of the straight line.

When the junction is biased in the reverse direction such that electrons are injected from the chemisorbed Auisocyanide contact, similar activation behavior is observed from −001 to −1 V (Fig. 24). The current changes more than five orders of magnitude over 200 K at both low and high bias regime. The barrier height is determined in Figure 25, where the slope of [lnI/T 2  versus 1/T ] was plotted against V 05 . The intercept of the line fit gives a thermionic barrier of  = 035 (±001) eV and an effective Richardson constant of 120 A/cm2 . As schematically denoted in Figure 8, the observation of the various mechanisms in a given junction will depend on both the magnitude of the various barriers and the defect density. If the thermionic emission barrier is too large, such as in the case of thiol-like termini onto Au, only the hopping barrier would be observable. As defect-mediated conduction is a complicated function of trap concentration and details, a significantly more extensive study would be necessary to elucidate T (K) 250

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1/T (1/K) Figure 22. lnI/V  versus 1/T at biases less than 0.1 V, for the AuSAM-Au junctions. The straight line is the # 2 fit for the data set.

Figure 24. A series of plots of lnI/T 2  versus 1/T at biases from −001 V to −10 V for the Au-SAM-Au junctions. All the straight lines are # 2 fits for respective data sets.

Molecular Electronic Devices

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the nature and effects of process on the defects. The present study serves to identify the characteristic energy, although the origin and density (and thus the current magnitude) are not well controlled. From our experiment, under negative bias (chemisorbed metal-SAM contact), we only observe thermionic emission, with an unobservable defect component. Under positive bias (evaporated metal-SAM contact), the defect component is larger, and we observe both simultaneously. The above result suggests that defects are likely located at the evaporated metal-SAM interface, possibly introduced during metal evaporation onto the organic film surface.

0.4

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Figure 26. I-V characteristics of a Pd-isocyanide SAM-Pd junction from 50 to 290 K, with 20-K increments. Negative voltage bias corresponds to electron injection from the chemisorbed SAM-Pd contact. The axes are converted into positive values such that I can be expressed in ln scale.

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Because the fabrication technique is generalizable to different termini and metals, it is easy to compare the effects of different contacts. Utilizing the same fabrication technique but instead substituting the metal Au with Pd, Pd1,4-phenylene diisocyanide-Pd junctions were fabricated and measured as before. Figure 26 shows the IV  characteristics from 50 to 290 K at 20-K increments when electrons were injected from the chemisorbed Pd-isocyanide contact. Notice that currents are larger than those of a Au-SAM-Au junction as shown in Figure 20, suggesting a smaller contact barrier. Figure 27 shows plots of: (a) lnI/V  versus 1/T (low bias), illustrating hopping conduction; and (b) lnI/T 2  versus 1/T (high bias), illustrating thermionic emission. The barrier heights are obtained in Figure 28, which illustrates the slope of [lnI/T 2  versus 1/T ] versus V 05 at negative bias, and we have (a) for −01 < V < 0 V, a hopping barrier of E = 019 (±002) eV; (b) for V < −01 V, a thermionic emission barrier of  = 022 (±002) eV, with a fitted Richardson constant of 130 A/cm2 at low field and 30 A/cm2 at high electrical field (E > 5 MV/cm). The larger fitted Richardson constant could be caused by deviation in device area, while the smaller fitted Richardson constant could be due to reduced effective area at high current density/high electrical fields around nonuniform metal-SAM interfacial regions. In this case, the unidentified defect component was

0.2

–V

ln(I/V)

Figure 25. Plot of the slope of [lnI/T 2  versus 1/T ] versus V 05 of a Au-SAM-Au junction shows a linear dependence. Thermal barrier height of the junction can be deduced from the interception of the straight line. The straight line is the # 2 fit for the data set.

0.0

–32 –34

–0.1 V

–36 –38 0.004

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1/T (1/K) Figure 27. Pd-SAM-Pd junction: (a) lnI/V  versus 1/T at biases larger than −01 V; (b) series of plots of lnI/T 2  versus 1/T at biases from −01 to −10 V at −01-V increments. All the straight lines are # 2 its for respective data sets.

Molecular Electronic Devices

649

Slope of ln(I/T2) vs 1/T

–500

Thermionic Emission

–1000

Φ = 0.22 eV

gd(ε)

d

–1500 0

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–2000

s

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0

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ε (eV)

–2500

0.0

0.2

0.4

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V0.5 Figure 28. Plot of the slope of [lnI/T 2  versus 1/T ] versus V 05 : at −01V < V < 0, no bias dependence; at V < −01 V, linear dependence. Thermal barrier height of the Pd-SAM-Pd junction can be deduced from the interception of the straight line.

large enough such that both thermionic emission and hopping are observed. When electrons are injected from the evaporated Pd-CN contact, the defect component is so large that only hopping is observed, with a barrier height of 0.21 (±002) eV. As seen from above results, the contact barrier between Au-isocyanide SAM is larger than that of Pd-isocyanide SAM. The difference is most likely caused by different electronic configurations between the two metals. In the noble metal Au, the d shell is completely occupied and there is a single valence s electron on the outer shell. The Fermi level of Au lies far enough above the d band for the s band to intersect F (Fermi surface) at points where it is still quite similar to the free electron band [92]. Consequently, the Fermi surface of Au is a slightly distorted free electron sphere. In the transition metal Pd, electrons are regarded as occupying overlapping s and d bands [93]. Unlike noble metals, the d band in transition metals extends through the Fermi energy. When levels on the Fermi surface are d-derived levels, the Fermi surface no longer resembles a slightly distorted free electron sphere. According to Mott [94], the valence electrons (of Pd) are shared between a wide, low density of states s band and a narrow, high density of states d band. This high density of states arises because the spatial extension of the d-electron wave functions is much less than that for the s electrons, with consequently less overlap from atom to atom. Hence the d band is narrower, yet it has to accommodate ten electrons compared to the s-band’s two electrons. Shown in Figure 29 are some qualitative features of the d-band and s-band contributions to the density of states of a transition metal [92]. In a word, the d band plays a dominant part in the electronic properties of a transition metal such as Pd. When Pd is brought into contact with isocyanide ligand, its d orbital overlaps with the
∗ orbital of a ligand and forms a d
-p
bond. However, when Au comes into contact with isocyanide, since its d bands lie far below the Fermi surface, it cannot “backbond” to isocyanide effectively. The delocalization between Au and isocyanide is therefore not as efficient as that between Pd

Figure 29. Some qualitative features of the d-band and s-band contributions to the density of states of a transition metal. The d band is narrower and contains more levels than the s band. Consequently, when the Fermi level (separating the shaded and unshaded regions) lies within the d band, the density of states gF  is very much larger than the free-electron-like contribution of the s band alone. Reprinted with permission from J. M. Ziman, “Electrons and Phonons: The Theory of Transport Phenomena in Solids.” Oxford Univ. Press, New York, 1960. © 1960, Oxford University Press. Adapted with permission from G. F. Foster, Phys. Rev. 98, 901 (1955). © 1955, American Physical Society.

and isocyanide. This could be responsible for the larger barrier height measured in Au-isocyanide SAM junctions. Table 2 summarizes the results of the transport barriers of through-bond transport of isocyanide on the metals measured in this study. It is observed that thermal emission is the dominant conduction mechanism in chemisorbed metal-isocyanide junctions, while in the evaporated metalisocyanide contact, both hopping and thermal emission can play an important role depending on the defect level introduced during the fabrication process. The barriers of both the chemisorbed and the evaporated contact are approximately the same, which is expected given the symmetry of the structure. It appears that the hopping component in the chemisorbed metal-molecule junction is less significant than that in the evaporated metal-molecule junction, which suggests that there are less defects in the chemisorbed metal-molecular interface. Overall, the Pd-CN contact barrier is smaller than that of a Au-CN junction. The technique reported here elucidates the relevant electronic transport barriers and conduction mechanisms of through-bond metalmolecule contacts, which have been possible through the implementation of microfabricated electronic devices utilizing SAMs. The technique should be applicable to a large range of inorganic and biomolecular transport measurements, to quantitatively measure the dominant electron transport mechanisms. Table 2. Summary of the contact barriers and conduction mechanisms for various metal-isocyanide SAM interfaces. Metal

AU

Pd

Chemical contact

035 ± 001 eV, thermionic

Evaporated contact

038 ± 001 eV, thermionic (03 ± 001 eV hopping at low bias)

022 ± 002 eV, thermionic (019 ± 002 eV hopping at low bias) 021 ± 002 eV hopping

Molecular Electronic Devices

650

5. DEVICE APPLICATIONS OF MOLECULAR LAYERS

5.1. Conductor-Insulator Transition Caused by Molecular Conformation Molecular conformation13 is one of the most important aspects of chemistry. When molecular systems have sufficient degrees of freedom to adopt a variety of shapes or forms, some of these forms can be associated with stretching or bending of bonds. For example, studies on mechanical distortions of bent nanotubes and crossing nanotubes show that they can exhibit substantial tubular deformations as well as bending and buckling, a factor in turn influencing their electronic transport characteristics [97]. On the other hand, molecular conformation is often associated with rotations of substituents around specific bonds. Zhou [63] observed that there exists a transition temperature below which the benzene rings of a tolane-like molecule assume a perpendicular configuration, but above which they assume a coplanar one. These devices are nanoscale Au/Ti/ethyl-substituted 4,4′ -di(phenylene-ethynylene)benzothiolate/Au junctions, fabricated using an inverted nanopore structure [63]. The experiments show that current first decreases gradually as temperature varies from room temperature to 30 K due to thermal activation; then a sharp decrease of two orders of magnitude in conductance resembling a transitional behavior is observed around 25 K (Fig. 30). Calculations by Seminario et al. show that the relative angle between two benzene rings in each tolane molecule determines its conductivity, being maximum at 0 and minimum at 90 [98]. At 10 K, phenyl rings in the tolane molecules show very little tendency to rotate and perpendicular tolanes are more stable than parallel tolane 13 Structures that differ only by rotation about one or more bonds are defined as conformations of a compound.

10–5

coplanar

perpendicular

Current (A)

Electronic switching and memory effects are known to exist in a wide variety of inorganic and organic materials. In 1979, Potember et al. [95] reported bistable, reproducible, and nanosecond electronic switching and memory phenomena in an organometallic charge-transfer complex salt CuTCNQ formed by TCNQ (7,7,8,8-tetracyano-p-quinodimethane), which acts as an electron acceptor with metallic copper as the electron-rich donor. In these materials the switching and memory phenomena are given rise to by the field-assisted structural changes such as phase transitions, crystallization, and metal filament formation assisted by highly localized Joule heating. However, the electronic behavior of these materials is mostly not stable or reproducible and usually requires high switching voltage [96]. In this section we discuss stable and reproducible switching and memory effects in SAM. We first present results on conformation-induced transition behavior and then demonstrate the realization of stable and reproducible large negative differential resistance (NDR) and charge storage in electronic devices that utilize a single redox-centercontained SAM as the active component. The devices exhibit electronically programmable and erasable memory bits with bit retention times greater than 15 min at room temperature.

–4

10

10–6

1.0 V 0.9 V 0.8 V 0.7 V 0.6 V 0.5 V 0.4 V 0.3 V 0.2 V 0.1 V

Conducting

–7

10

10–8 –9

10

10–10 0

Non-conducting 50

100

150

200

250

300

Temperature (K)

Figure 30. I-T characteristics at different biases (0.1–1 V) of a Au/Ti/ ethyl-substituted 4,4′ -di(phenylene-ethynylene)-benzothiolate/Au junction. A sharp decrease in conductivity is observed around 25 K.

molecules—giving rise to smaller conductivity. At 30 K, the tolane rings are able to freely rotate with respect to each other, allowing the tolane molecules to be planar at some instant in time, consequently reaching higher conductivity.

5.2. Negative Differential Resistance in Molecular Junctions The discovery of NDR in semiconductor diodes has opened a new chapter in semiconductor device physics and device development [98–104]. Through the use of NDR devices, circuits with complicated functions can be implemented with significantly fewer components [105–110]. There are various NDR devices such as Esaki tunnel diodes [98], Gunn effect diodes [99], resonant tunneling diodes [100], etc. caused by various physical mechanisms. For example, a Gunn effect diode, also known as a transferred electron diode, is given rise to by a field-induced transfer of conduction band electrons from a low-energy, high-mobility valley to higherenergy, low-mobility satellite valleys [101]. NDR was first discovered by Esaki [98] in 1958 in a tunnel diode (a highly degenerate p-n junction). The physical basis of the tunnel diode, which is also called the Esaki diode, is interband tunneling between the valence band and the conduction band. Another type of well-known NDR device is the resonant tunneling diode (RTD). Tsu and Esaki and co-worker proposed resonant tunneling shortly after molecular beam epitaxy (MBE) appeared in the field of compound semiconductor crystal growth in 1973 [100]. A RTD typically consists of an undoped quantum well layer (GaAs) sandwiched between undoped barrier layers (AlGaAs) and heavily doped emitter and collector contact regions [108]. Resonant tunneling through the double barrier structure occurs when the energy of the electrons flowing from the emitter coincides with the energy of the quantum well state (resonant state) in the quantum well. The effect of the external bias, V , is to sweep the alignment of the emitter and resonant states (E0 ). Thus a resonant tunneling current starts to flow when the Fermi level EF in the emitter reaches the resonant state. There are also some organic switching devices that exhibit NDR behavior, whereas their NDR behavior has been attributed to the formation of highly conducting filaments [111–113]. These filaments are formed by local joule heating which produces material rearrangement or even melting.

Molecular Electronic Devices NH2 Z O2N NH4OH

1, Z = S–

Figure 31. The structures of active molecular compound 1, and its precursors, the free thiol 1b and the thiol-protected system 1a.

exhibits a robust and large NDR. Some device-to-device variations of peak voltage position (∼ × 2) and peak current (∼ × 4) were observed as shown in Figure 33. Curve clusters 1–3 are from three different devices (numbered 1 through 3, respectively) on two different batches of wafers fabricated. Curves within each cluster are from the same device but from different runs at different time. Device-to-device current fluctuations can be attributed to fluctuations in the pore diameter size. As total voltage applied to the molecular junction can be divided into the voltage drop on the molecules and the voltage drop on the metal-molecule contacts, device-to-device peak voltage fluctuations can be caused by different voltage drops on the metal-molecule contacts. As shown by Di Ventra et al. [61], the detailed metal-molecule contact configuration plays an important part in the conductance of metal-molecular junctions. Different contact geometries caused by differences in fabrication processes, such as in etching and metallization, could result in different contact potentials. The IV  curve is fully reversible upon change in bias sweep direction (from negative bias to positive bias) as shown in Figure 34; for a given device, small fluctuations (∼1% in voltage peak position and ∼6% in peak current) are observed with consecutive positive and negative sweeps but could be attributed to temperature fluctuations of ∼2 K (within the experimental thermal stability). The 1.2

Ipeak = 1.03 nA 1.0 0.8 0.6 0.4 0.2

Ivalley = 1 pA

T = 60 K 0.0 0.0

The starting compound (1a) was prepared by sequential Pd/Cucatalyzed coupling of 2,5-dibromo-4-nitroacetanilide with phenylacetylene and 4-ethynyl (thioacetyl) benzene. 15 Weak room-temperature NDR has been previously reported; See [114]. 14

1a, Z = SCOCH3 1b, Z = SH 1c, Z = H

I (nA)

This type of organic switching device is insensitive to the polarity of the applied field but suffers from some material rearrangement or damage. Besides, the devices also need high switching power consumption, and the type of metal that was used for contacts also plays an important role. For instance, Gundlach and Kadlec have observed NDR in Al(Al oxide)-arachidic acid-Al (or Au) junctions using the L–B technique [111], but short circuits were observed when they used Au for both junction electrodes. The presence of Al oxide is vital for their experiment to block leakage current around domain boundaries or defects in the L–B film (with a sample area of approximately 1 mm2 . The NDR they observed is not repeatable. Here we discuss the realization of large NDR behavior and room temperature operation in an electronic device that utilizes special molecules as the active component. Unlike in Esaki diodes or in RTDs, the monolayer thickness is determined by the SAM thickness, which inherently/ultimately solves the monolayer fluctuation problem at the interfaces. Being different from bulk organic switching devices, our nanoscale NDR devices are both reproducible and reversible [38]. A molecule containing a nitroamine redox center [2′ amino-4,4′ -di(ethynylphenyl)-5′ -nitro-1-benzenethiolate] is used in the active SAM in the nanopore configuration discussed previously (Section 3). Its structure is illustrated in Figure 31. Apart from the ethynylphenyl-based backbone, there is a redox center introduced in the middle benzene ring: the electron-withdrawing nitro (-NO2 ) group and the electron-rich amino (-NH2 ) group. To deposit the SAM layer onto gold electrode, we transfer the prefabricated nanopores into a 0.5-mM 2′ -amino4,4′ -di(ethynylphenyl)-5′ -nitro-1-(thioacetyl)benzene (1a)14 in THF solution. The thioacetyl groups are then selectively hydrolyzed with ammonium hydroxide (concentrated aqueous 14.8M NH4 OH, 5 L per mg of 1a) in THF to yield the free thiol, 2′ -amino-4,4′ -di(ethynylphenyl)-5′ nitro-1-benzenethiol (1b), which then forms the thiolate, 2′ amino-4,4′ -(diethynylphenyl)-5′ -nitro-1-benzenethiolate (1) upon exposure to Au after 48 hr [60] under an inert atmosphere of Ar. The sample was then prepared and characterized as discussed previously. A device containing a SAM of conjugated molecules similar to 1 but not bearing the nitroamine functionalities was fabricated and measured in nearly identical conditions [63] and did not exhibit any NDR behavior. Therefore, the nitroamine redox center is responsible for the NDR behavior. Typical IV  characteristics of a Au-(1)-Au device at 60 K are shown in Figure 32. Positive bias corresponds to hole injection from the chemisorbed thiol-Au contact and electron injection from the evaporated contact. The peak current density for this device was greater than 53 A/cm2 , the NDR is less than −380 * cm2 , and the peak-to-valley (PVR) is 1030:1. Unlike previous devices that also used molecules to form the active region15 [114], this device

651

0.5

1.0

1.5

2.0

2.5

Voltage (V) Figure 32. IV  characteristics of a Au-1-Au device at 60 K. The peak current density is ∼50 A/cm2 , the NDR is ∼−400 * cm2 , and the PVR is 1030:1.

Molecular Electronic Devices

652 T = 60 K

5.0

3.0n

4.0

2

2.0n

3.0

1

2.0

1.0n

Current (nA)

Current (A)

3

1.0 0

0.0

1 2

4

2

6

V

0.0 3

V)

Figure 33. IV  characteristics of Au-1c-Au devices at 60 K. Curve clusters 1–3 are measured from different samples, while curves within one cluster are from the same sample but from different runs.

( ge lta Vo

0

50 4

100 5

rature Tempe

150

(K)

Figure 35. IV  T  characteristics of a Au-1c-Au device.

performance exceeds that observed in typical solid-state quantum well resonant tunneling heterostructures [115– 118]. In addition to the obvious size advantages for scaling, the intrinsic device characteristics (that is, the valley current shutoff) may be superior to that of solid-state devices. The intrinsic PVR of the molecule may be considerably greater than that reported here because the valley currents observed (on the order of picoamperes) are comparable to typical leakage currents in the silicon nitride film.

5.3. Temperature Dependence All of the Au-1c-Au devices examined exhibit peak voltage position and current magnitude shifts with temperature such as shown in Figure 35. We observe a decrease in peak intensity with increasing temperature. This could be caused by scattering in the junction. However, the fact that the peak intensity has a maximum at 60 K is not understood yet. It

could be caused by thermally activated conformation change in the SAM layer. We also observe that the peak position shifts to smaller voltage with increasing temperature (Fig. 36a). The shift can be fit by the following expression: Vpeak =

This expression can be explained by a two energy level model using a Boltzmann distribution, where the 34 (±07) meV corresponds to the activation barrier from the (a)

3

T = 60 K 3.0n

I (A)

2.0n

Vpeak

I (A)

3.0n

2.0n

1+

c1 −34107meV /kT  e

2

1.0n

5 consecutive sweeps 1st +sweep 1st –sweep 2nd +sweep 2nd –sweep 3rd +sweep

1

0.0 2.5

3.0

3.5

4.0

4.5

5.0

V

0

1.0n

50

100

150

200

T (K) (b)

0.0 –2

0

2

4

6

Ea = 34 meV

V Figure 34. Forward (−2 → 6) V and reverse (6 → −2) V sweeps on a Au-1c-Au junction at 60 K. The inset shows the blowup of the sweeps around peak.

Figure 36. (a) Peak voltage versus temperature relationship of the same device. (b) Possible physical picture of the trap state.

Molecular Electronic Devices

653

(a) T = 300 K 400.0p

Current (A)

300.0p

200.0p

100.0p

+64 NO2 Z

+48

Current, uA

bound state as proposed in Figure 36b, and c1 is a proportionality constant. More supporting evidence for the above model comes from the temperature dependence of peak width (Fig. 35). It remains constant at low temperature and widens at higher temperature. Further discussions on temperature dependencies and comparison with other compounds will be carried on next. Similar NDR behavior is also observed in devices with nitro only moiety (2). The PVR is smaller than that of 1, but NDR behavior persisted from low temperature to room temperature. IV  characteristic of a Au-(2)-Au device at 300 K is shown in Figure 37a. The device has 300 K characteristics of a peak current density greater than 16 A/cm2 , NDR smaller than −144 m* cm2 , and a PVR of 1.5:1. At 190 K (Fig. 37b), the NDR peak is much sharper than that of 1, although its PVR is not as big as that of 1. The degradation in PVR (decreasing in peak current) can probably be caused by increased inelastic scattering with increasing temperature. Figure 38 shows the cyclic voltammagram curve for compound 2c where the reduction potentials peaked at −139 V and −209 V, respectively. The potentials are shifted about 0.3 V less than that of the nitro-amino device. The next experiment that naturally follows is the electronic transport and electrochemistry experiments of

2: Z = S– 2c: Z = H

+32

+16

0

–16 0

–0.4

–0.8

–1.2

–1.6

–2.0

–2.4

Potential, V Figure 38. Cyclic voltammagram of compound 2c shows two distinct reduction peaks at −139 V and −209 V.

an amino only molecule [2′ -amino-4,4′ -di(ethynylphenyl)1-benzenethiolate, compound 3]. We observe no NDR behavior in 3 at both low temperature (60 K) and room temperature, as shown in Figure 39. To avoid breakdown of the molecular junction, bias at room temperature was restricted to 1 V to limit current through the junction. Its CV curve did not exhibit any reduction peak in the range of interest. Concluding from above experimental results, we suggest that the nitro group is responsible for the NDR behavior. Further understanding of the underlying mechanism and experimentation with various redox centers should allow us to engineer molecular compounds in the future to improve PVR at room temperature and above. Shown in Figure 40 is the temperature dependence of peak positions of a Au-2-Au device. The peak voltage is observed to drop linearly with increasing temperature: Vpeak = −0025 T . It appears to be very different from

0.0 0.0

0.5

1.0

1.5

2.0

2.5

T = 60 K

Voltage (V)

1.5µ

T = 295 K

(b) T = 190 K

800.0p

I (A)

1.0µ

Current (A)

600.0p

500.0n 400.0p

200.0p

0.0

0

0.0 0.0

0.5

1.0

1.5

2.0

2.5

Voltage (V) Figure 37. IV  characteristics of a Au-2-Au device at (a) 300 K and (b) 190 K.

1

2

3

V Figure 39. IV  characteristic of 2′ -amino-4,4′ -di(ethynylphenyl)-1benzenethiolate (3) at 60 and 295 K. No NDR behavior was observed. Bias across 3 was restricted to 1 V at room temperature to avoid junction breakdown.

Molecular Electronic Devices

654 (a)

∆V = –0.004 ∆T

3

∆Vpeak = –0.025 ∆T

2

2

Vpeak

Vpeak

3

∆V = –0.034 ∆T

1

1

40

80

0

120

50

that of a Au-1c-Au device. To compare possible effects of different redox centers on temperature dependence, we show in Figure 41 a plot of temperature versus voltage values at a constant current of 10 nA of a Au-3-Au device. Interestingly, it can also be fit to a two-level model, 1+

c3 −30meV /kT  e

0.8

V @ I = 10–8 A

0.6

0.4

0.2

0.0

100

200

0.8 ∆V = –0.005 ∆T 0.6

0.4

0.2

where c3 is a proportionality constant and the binding energy for the trap state on 3 is around 30 (±02) meV. On the other hand, the transition region of Vpeak versus T of a nitroamine redox molecule can be fit in piecewise to linear relationship as shown in Figure 42a, with V = −0014 T and V = −0034 T , respectively, and the transition region of V@10 nA versus T of an amine-only moiety can also be fit to a linear relationship as shown in Figure 42b, with V = −0005 T . The fitting results and comparison between compounds 1c, 2, and 3 of positive voltage sweeps (referred to S1+ s) are summarized in Table 3. As shown in Table 4, the temperature dependence of subsequent positive voltage

0

150

(b)

V @ I = 10–8 A

Figure 40. Peak voltage versus temperature of a Au-2-Au device.

V@10 nA =

100

T (K)

T (K)

300

T (K) Figure 41. Voltage values at a constant current of 10 nA versus temperature of a Au-3-Au device.

0.0

0

100

200

300

T (K) Figure 42. Piecewise linear fitting in the transition region of (a) peak voltage versus temperature of a Au-1c-Au device; (b) Voltage values at a constant current of 10 nA versus temperature of a Au-3-Au device.

sweeps (referred to S2+ s) is very similar to that of sweeps S1+ s. The difference has to do with the memory effects that will be discussed next. The above result suggests that the presence of the amine group gives rise to a bound state around 30 meV in the molecule, whereas the nitro group is responsible for NDR behavior. The exact mechanism of linear shift of peak position with temperature is not understood at this stage. Possible explanations can be complex; for example, interactions with vibrational modes can cause instantaneous dipole changes in the molecule (Fig. 43) which in turn interact with electrons passing through the molecule, changing the transmission coefficient. Based on our experiments, the electron-withdrawing nitro group is responsible for NDR behavior, whereas the electron-donating amine group gives rise to a bound state in the molecule of approximately 30 meV. We have learned that conformational change (rotation) and/or charging can change the conjugation of molecular orbitals. Further exploration on design and engineering of molecules with various redox substituents should help to realize nonlinear electronic devices with multiple functionalities.

Molecular Electronic Devices

655

Table 3. Comparison between compounds 1c, 2, and 3 on temperature dependence of S1+ sweeps. V versus T Redox center Nitro-only (2) Nitro-amine (1c) Amine-only (3)

NDR √ √

×

Best fit

Piecewise linear fit

Vpeak = −0025 T c1 Vpeak = 1 + e−34meV/kT  V@10

nA

=

c3

1 + e−30meV/kT

5.4. Molecular Memory Effects The programmable storage of digital information as packets of charge is beginning to reach not only technological but fundamental limits. Electronic memories that operate at the charge limit (e.g., by single electron effects) have been demonstrated16 [120, 121] but have not yet addressed the dimensional limit (i.e., a single molecule). Although memory phenomena have been studied in bulk organic materials (such as organometallic charge-transfer complex salts [95]), we will demonstrate nanoscale electronically programmable and erasable memory devices utilizing molecular SAM and a memory cell applicable to a random access memory (RAM). Figure 44 lists the molecules used in this study. (They were introduced previously; we list them again for convenience.) The four systems studied are: Au-(1)-Au [1: 2′ -amino-4,4′ -di(ethynylphenyl)-5′ -nitro-1-benzenethiolate]; Au-(2)-Au [2: 4,4′ -di(ethynylphenyl)-2′ -nitro-1- benzenethiolate]; Au-(3)-Au [3: 2′ -amino-4,4′ -di(ethynylphenyl)1-benzenethiolate]; as well as Au-(4)-Au [4: 4, 4′ -di(ethynylphenyl)-1-benzenethiolate] that had neither the nitro nor amine functionalities. The memory device operates by the storage of a high or low conductivity state. Figure 45 shows the write, read, and erase sequences for (1). An initially low conductivity state (low ) is changed (written) into a high conductivity state (high ) upon application of a voltage pulse. The direction of current that flows during this “write” pulse is diagrammed. The high  state persists as a stored “bit,” which is unaffected by successive read pulses. Molecules with the nitro moieties (1 and 2) are observed to change conductivity state, whereas the amine only (3) and the unfunctionalized molecule (4) do not exhibit storage. In the following, we first describe the characteristics obtained by linear voltage sweeps (so as to generate I(V ) characteristics). Second, we demonstrate the same effects and a circuit using voltage pulses. Figure 46 shows the I(V ) characteristics of a Au-(1)-Au device at 200 K initially (defined as “0”) and after (defined as “1”) a write pulse, as well as the difference between the two (defined as “1”−“0”). Positive bias corresponds to hole injection from the chemisorbed thiol-Au contact. The device initially probed with a positive voltage sweep from 0 to 2 V exhibits a low conductivity state. Subsequent positive sweeps show a high conductivity state with I(V ) characteristics identical to the previous values (“1”). Device bias swept in the reverse bias direction from 0 to −2 V causes the I(V ) to 16 A single electron memory operating at 4 K was demonstrated in [121].

V = −0014 T

V = −0034 T V = −0005 T

Ebinding 34 meV 30 meV

be identically reset to the initial, “0” I(V ) characteristic. The characteristics are repeatable to high accuracy and device degradation is not observed. This ability to program, read, and refresh the state of the molecular device accomplishes the functionality of a RAM. Figure 47 shows the difference characteristic (“1”−“0”) of (1) as a function of temperature. The peak current difference decreases approximately linearly with increasing temperature. A characteristic bit retention time was obtained by measuring the stored high conductivity state at various time intervals after programming the Au-(1)-Au device. After an initial positive write sweep from 0 to 2 V, a second sweep was measured at different time intervals, and the difference between the first and the second sweeps at peak current position was taken and plotted against time in Figure 48a. It is found that the difference “1”−“0” exhibits an exponential decay with a time constant (,) of approximately 800 seconds at 260 K. Similar measurements were performed from 260 to 190 K.17 The stored state was found to decay exponentially with increasing time constants at lower temperatures. Shown in Figure 48b is a plot of the decay time constant (retention time) at different temperatures, exhibiting an exponential dependence with 1/T. It indicates an activation behavior: , = ,0 expEa /kT , suggesting activation over a single trap state. The activation energy Ea for this molecule over this bias regime was found to be approximately 80 meV. A similar memory effect was also observed under negative bias [122]. Contrary to the positive bias, the molecular junction initially is in a higher conductivity state, whereas it is changed to a lower conductivity. After applying a positive sweep, we observe that the junction is set back to the initial negative trace. Memory effects are also observed in devices with the molecules having only the nitro moiety (2), although in this case the storage was of a low conductivity state18 after an initial positive sweep, opposite to that of molecule (1) [122]. A characteristic bit retention time of approximately 900 seconds at 300 K was observed. Memory effects are not observed in molecule (3) with the amine-only group. Shown in Figure 49 are typical I(V ) characteristics of an Au-(3)-Au device at 60 and 295 K, respectively. The first and second traces at a constant temperature overlap with each other. The current level is higher than that of both Au-(1)-Au and Au-(2)-Au devices, suggesting that Below 190 K, the I(V ) characteristic changes considerably, with the NDR peak shifting much toward higher voltage. No appreciable decay of current was observed. 18 Not including the NDR region, where current level is higher than the initial state. 17

Molecular Electronic Devices

656

Table 4. Comparison between compounds 1c, 2, and 3 on temperature dependence of S2+ sweeps. V versus T Redox center

H

√

Amine-only (3)

×

Best fit

Piecewise linear fit

Vpeak = −0005T Vpeak = −0010T

Vpeak =

V@10

nA

c1

N+

Formal negative charge

read Au

O2N NH2 I

NH2

:O : –

30 meV

write Au

O 2N

Figure 43. Nitromethane and its dipole.

erase Au

O2N

O2N

NH2 I

NH2

Au

(1)

Au

(2)

Ti / Au

(3)

(4)

O2N NO2

NH2

S

S

Au

Au

low σ

high σ

S

S

Au high σ

Au low σ

Figure 45. The operation principle of the storage and memory. The memory device operates by the storage of a high or low conductivity state. An initially low conductivity state (low ) is changed into a high conductivity state (high ) upon application of a voltage. The directions of current that flows during the “write” and “erase” pulses are diagrammed by the arrows. The high  state persists as a stored “bit.”

is a trap state, and the energetic characteristics of that trap state. These trap levels can cause different electronic distributions, leading to various conductivity states of the molecule. From Figure 46, 1 is initially in a low conductivity state (L). As the junction is biased positively, the barrier is tipped over, and the electron falls into state H (Fig. 50b). When the bias is removed, the electron remains undisturbed in the same localized state H it occupied under bias for a period of time equal to (-P )−1 where - is the attempting frequency

150.0p

T = 200 K

"0" "1" "1"–"0"

Current (A)

the presence of nitro group impedes charge transport, causing a high conductivity state in (1) (with nitro-amine group) and a low conductivity state in (2) (with nitro-only group). Consequently, the 80 meV energy level observed in (1) is most likely associated with the nitro group. The above observation leads us to the following preliminary model for the memory effect (Fig. 50). We have identified from above experimental results that the nitro group is responsible for the memory effect, while the presence of the amine group changes the initial conductivity states of the molecule (most likely caused by the different dipole distribution it introduces to the molecule). Here we use molecule 1 as an example. Depending on its history, 1 can be in one of the two states, L (low conductivity state) or H (high conductivity state). We propose that the different conductivity states are caused by different trap levels occupied by electrons as shown in Figure 50a. Different trap levels occupied by electrons in a molecule could mean either different electronic states with different charge distributions (such as different dipole distribution), or different conformation states in a molecule (such as rotational conformations, about various axes), or both. The microscopic origin of the trap states is at this point unknown; we stress that regardless of the microscopic origin, we have determined here that the origin Au

V = −0005T

initial Au

Formal positive charge

32 meV

V = −002T

/kT  1 + e−32meV c3 = 1 + e−30meV /kT 

Ebinding

:

C

Nitro-amine (1c)

:O :

H H

Nitro-only (2)

NDR √

100.0p

50.0p

NH2

0.0 S

S

S

S

Au

Au

Au

Au

0.00

0.25

0.50

0.75

1.00

Voltage (V) Figure 44. The molecular junctions (1–3) used in this study. Junction 4 was studied by Zhou [63], drawn here for comparison purpose. There are approximately 1000 molecules sandwiched between the two Au contacts. Only one molecule is drawn for simplicity.

Figure 46. I(V ) characteristics of a Au-(1)-Au device at 200 K. “0” denotes the initial state, “1” the stored written state, and “1”−“0” the difference of the two states.

Molecular Electronic Devices

657 600.0n

100.0p

Current (A)

50.0p

T = 295 K NH2

3:

SAc

300.0n

I (A)

"1"–"0"

First trace Second trace

Temperature 210 K 220 K 230 K 240 K 250 K 260 K

0.0

0.0 T = 60 K

0.00 0.00

0.25

0.50

0.75

Figure 47. Difference I(V ) characteristics (“1”−“0”) of a Au-(1)-Au device as a function of temperature.

T = 260 K

ln(I–I0)

τ = 789 s

–25

–26

800

Figure 49. I(V ) characteristic of 2’-amino-4,4’-di(ethynylphenyl)-1benzenethiolate (3) at 60 and 295 K. First and second traces overlap with each other.

EFl

EFr V

T (K) 260

240

1.00

1600

t (s) (b)

0.75

to escape and P is the probability of escaping the localized state H. In general P is proportional to the Boltzmann factor exp(−E/kT ), where E denotes the energy barrier of the localized state H. It corresponds to the measured 80 meV as shown in Figure 48. For subsequent positive biases at times t < -P −1 , the electron is trapped in state H (Fig. 50c). Only with negative bias can the electron be “liberated” and go back to state L (Fig. 50d). At times t > -P −1 , the electron leaks through the barrier and finally returns to state L. The electron will be trapped in state L with following negative sweeps, and it can only be refreshed to the H state by positive bias. This explains well that the first negative sweep on the junction shows a high conductivity state (i.e., the initial H state after positive sweeps). The following negative

(a)

0

0.50

V

Voltage (V)

–24

0.25

1.00

220

200 4000 L

8.0 H

3000

(a)

(b)

τ (s)

lnτ

7.5

V

2000

–V

7.0

1000 6.5 0.0040

0.0045

0.0050

1/T (1/K) Figure 48. Bit retention as a function of time and temperature. (a) Bit retention for (1) exhibits an exponential decay with a time constant (,) of 790 seconds at 260 K. (b) Temperature dependence of , gives an activation energy Ea = 76 ± 7 meV.

(c)

(d)

Figure 50. Proposed model for the memory effect. Lowering of EF r corresponds to positive bias. (a) Initial low conductivity state, zero bias; (b) first positive sweep, “write,” changed into a high conductivity state— H; (c) consecutive positive sweeps, “read,” remained in the high conductivity state; (d) first negative sweep, “erase,” back to low conductivity state.

Molecular Electronic Devices

658 traces show low conductivity state, and a positive trace resets the state. In Figure 51, we see a final example of a molecule (biphenyl dinitro) that exhibits this large resettable conductivity at room temperature. Here the high conductivity state on probe is set into the low conductivity state, which is persistent until the application of a negative bias pulse, after which the high conductivity state is recovered. This type of behavior is illustrated with the above model of a bistable state; although the microscopic origin of these states is complex, the same generic behavior is generically seen in this class of oligomer systems.

2.0 1.5 1.0

Figure 52 shows a constructed sense circuit diagram for a molecular memory cell operation. Transistor transistor logic (TTL) level signal (5 V) from a function generator is first converted to the operating point of the memory cell (set at the points diagrammed in Fig. 53, 1.5 V) and applied to the molecular junction (DUT). The current through DUT is measured via a feedback resistor Rsense and amplified 10 times using low noise operational amplifiers. Then the signal is fed into a comparator (LM339) and compared with the “1” set-point (low conductivity state) as measured in Figure 52. To demonstrate the storage of a low conductivity state, the signal is inverted and gated with the input pulse from the function generator. A measured logic diagram utilizing the above sensing circuit and a Au-2-Au device is shown in Figure 54, demonstrating a molecular RAM cell at ambient temperature. 10/3 kΩ

2

1

se

ep

1.5

qu

4 3

en

5

Vol 2.0 2.5 tag e (V 3.0 3.5 )

5.5. Demonstration of a Molecular Memory Storage Cell

ce

6

0.5 0.0 0.0 0.5 1.0

1st sweep subsequent sweeps 2nd sweep after a negative bias subsequent sweeps 3rd sweep after a negative bias

Sw e

Current (nA

)

2.5

NO2 NO2

S

Figure 51. I-V characteristics of a Au-biphenyl-dinitro-Au device. (a) First sweep shows a high-conductivity ON state and two NDR peaks; the prominent peak current is 2.5 nA, the PVR is 7:1. The subsequent sweeps show a low-conductivity OFF state. After a negative sweep, the high conductivity ON state recovered and repeated with the first sweep. The subsequent sweeps show same low conductivity. After a negative sweep, the high-conductivity ON state recovers.

R sense 20 kΩ

10 kΩ

DUT OPA 124 2 kΩ

OPA 111

OPA 111 2.5 kΩ 2 kΩ

20 kΩ Function

10 kΩ

generator

10 kΩ 15 V

10/3 kΩ

2 kΩ OPA 124

10 kΩ Tek 2221

OPA 124

Oscilloscope 74 HC00 2.5 kΩ

Figure 52. Diagram of the sense circuit for a molecular memory cell.

LM 339

15 V

Molecular Electronic Devices

659 The present devices utilize nanoscale structures that limit the number of molecules in the active region to ∼1000, which is determined by lithographic limitations in defining the contacts. We have seen no evidence in the device characteristics indicating that limitations exist for scaling the number of molecules in the active region to one, assuming that an appropriate fabrication scheme can be identified.

800.0p T = 300 K

"0" "1" 600.0p

Current (A)


400.0p

6. CONCLUSIONS

200.0p


0.0 1.00

1.25

1.50

1.75

2.00

Voltage (V) Figure 53. I(V ) characteristics of stored and initial/erased states in Au(2)-Au at 300 K. The set-point indicated is the operating point for the circuit of Figure 52.

The upper trace shown in Figure 54 is an input waveform applied to the device, and the lower is the RAM cell output. The first positive pulse configures the state of the cell by writing a bit, and the second and third positive pulses read the cell. The third pulse (and subsequent read pulses, not shown here for simplicity) demonstrates that the cell is robust and continues to hold the state up to the limit of the bit retention time. This demonstration highlights the dramatically long bit retention time. The negative pulse erases the bit, resetting the cell. The second set of four pulses repeats this pattern, and many hours of continuous operation have been observed with no degradation in performance. Currently the speed of the memory device is limited by the RC time constant of the circuit. There is a 1 pF capacitance between the two Au electrodes in the nanopore configuration. The current level of the devices is less than 10 nA, which can be attributed to the 0.7-eV S-Au barrier [33, 61] in the molecular junction. Engineering of molecules with smaller contact barriers (e.g., use CN terminated molecules and Pd contacts) to obtain a higher current level while minimizing contact area to decrease parasitic capacitance should improve the RC limit. read

Voltage (5V/div)

read

Input

Output 0

20

t (s) write

write erase erase

Figure 54. Measured logic diagram of the molecular random access memory.

Molecular electronics uses molecular structures whose function involves discrete molecules, which are distinguished from organic thin-film transistors that use bulk materials and bulk-effect electron transport. It provides a bottom-up way to produce subnanometer-sized functional devices. We have developed a nanolithography technique to demonstrate directed self-assembly, generating intermixed SAMs—conjugated SAM in an insulating background. In particular, we have demonstrated that programmable patterning of a SAM of dodecanethiol can be performed by applying voltage pulses from a STM tip. After patterning, conjugated oligomers are introduced and they are observed to be subsequently chemisorbed onto the patterned sites. This technique combines a scanning probe microscopebased lithography technique and the design of molecular units with specific structural, chemical, and electronic properties. It can be used to generate SAMs with arbitrary compositions and geometries at ambient temperature, opening up many new possibilities for molecular-scale bottom-up fabrication. Up to now, molecular electronics has been mostly about conductance measurements of molecules. For nanoscale molecules, most conductance measurements are restricted to two terminals because of fabrication issues and screening effects. Molecule-metal contact plays a vital part in these measurements. The quest for a small SAM-metal contact barrier has thus been long going, and has become a bottleneck in through-bond transport in molecular systems. We have investigated the contact barrier between isocyanide SAM and metal systems. Nonohmic behaviors—thermionic and hopping conduction—are observed to be the dominant conduction mechanisms. We have shown that thermal emission is the dominant conduction mechanism in chemisorbed metal-isocyanide junctions, while in the evaporated metalisocyanide contact, both hopping and thermal emission can play an important role depending on the defect level introduced during the fabrication process, suggesting that there are less defects in the chemisorbed metal-molecular interface. Overall, the Pd-CN contact barrier is smaller than that of a Au-CN junction, in agreement with the more efficient
bond formed between Pd-CN. Our results also show that the contact barrier between
-bonded isocyanide SAM-metal is less than that of the more extensively studied -bonded thiol SAM-metal systems. The technique reported here elucidates the relevant electronic transport barriers and conduction mechanisms of through-bond metal-molecule contacts, which have been possible through the implementation of microfabricated electronic devices utilizing SAMs. The technique should be applicable to a large range of inorganic and biomolecular transport measurements, to quantitatively measure the dominant electron transport mechanisms.

Molecular Electronic Devices

660 We demonstrated novel non-FET switching devices and a prototype of memory cell using single SAMs as the active component. We learned that conformational change like rotation of molecular bonds can change the conjugation of molecular orbitals, leading to the observed conductorinsulator type of transition that can be thermally controlled. We have realized two-terminal NDR devices with large PVR at low temperature and NDR devices at room temperature. The NDR behavior is caused by the reduction nature of substituents on ethynylphenyl molecules. Based on our experiments, the electron-withdrawing nitro group is responsible for NDR behavior, whereas the electron-donating amine group gives rise to a bound state in the molecule of approximately 30 meV. Through the design of the molecular switches we learned that incorporation of different redox centers can change charge distribution and/or conformation in a molecule, leading to different conjugation of molecular orbitals. Further exploration on design and engineering of molecules with various redox substituents should help to realize nonlinear electronic devices with multiple functionalities. We also discovered erasable storage effects in redox-center-containing ethynylphenyl molecules. The storage behavior can be discretely added on a molecule by engineering electron-withdrawing or/and electron-donating sidegroups onto its backbone. We have concluded from our experiments that the electron-withdrawing nitro group is responsible for the observed memory effects, while the presence of the electron-donating amine group changes the storage of different conductivity states. Our results show that the storage behavior is controlled by a single thermal activation process, associated with the nitro group. Further experiments with various redox centers should make molecular memories with different retention times possible. Finally, we successfully demonstrated an erasable molecular memory cell that can store a high conductivity state with a bit retention time orders of magnitude longer than that of a DRAM. Further engineering of different molecules shall permit potential applications such as nonvolatile memories on flexible substrates. We have mainly focused on polyphenylene-based molecular wires in this study. What we have sampled and studied consists of only a tiny portion of a copious family of prospective molecules that possess unique characteristics for electronic applications. Even with the subject of our work, there still remains a lot to be explored. For instance, to further investigate through-bond transport of metal-molecule-metal systems, engineering and measurements of molecules with different backbones should help to elucidate its role versus the role of metal-molecule contacts. As to a molecule with specific end groups, one can vary its length (e.g., single ring vs multiple ring), conjugation (e.g., aliphatic ring vs aromatic ring), and charge distribution (electron-withdrawing group vs electron-donating group), and map out the functional table of each component. To minimize metal-molecule contact barriers, different kinds of end groups need to be explored (e.g., what will happen if there is no end group, what if one introduces electron-withdrawing group on one end but electron-donating group on the other end?). To improve the film robustness (e.g., against post-process heating or top metallization), novel organic-inorganic complex

SAMs may be designed and engineered, which could preserve band engineering flexibility through the organic component and in the mean time improve film robustness through the inorganic component. To reduce the number of interconnects between different molecules, one can integrate the demonstrated prototype molecular switches and memories by synthesizing one specific molecule with different functional parts capable of performing the desired tasks. Will the various functional components behave as expected when they are “assembled” into one new unit (molecule)? Molecular electronics is still in its infancy but holds great promise in that it potentially provides a conceptually new path without the inherent tolerance problems of a lithographic approach. We believe that the most exciting discovery in molecular electronics is its ability to explore new architectures and devices unique to molecular-based systems themselves, which are yet to be made.

GLOSSARY Alkanethiol A molecule with a structure of CH3 (CH2 )n−1 SH. Conjugated oligomer A molecular type consisting of an alternation of multiple and single bonds linking a sequence of bonded-atoms, such that there is an extended series of overlapping p orbitals. Highest occupied molecular Orbital (HOMO) The highest orbital among the molecular orbitals that contain electrons. Langmuir–Blodgett monolayer A molecular monolayer formed on a substrate by the physical attachment due to molecular hydrophilic/hydrophobic interaction with the substrate surface. Lowest unoccupied molecular orbital (LUMO) The lowest orbital among the molecular orbitals that do not contain electrons. Molecular electronics A new concept in electronics of utilizing molecules as self-contained electronic device components. Negative differential resistance An electronic property that resistance (conductance) increases (decreases) over a certain voltage range. Self-assembled monolayer A molecular monolayer formed on a substrate surface by the chemical interaction process of functional end groups of molecules with the substrate surface materials. Tunneling An electronic transport process such that charge carriers tunnel through a thin barrier.

ACKNOWLEDGMENT We thank A. M. Rawlett, M. Kozaki, Y. Yao, R. C. Jagessar, S. M. Dirk, D. W. Price, J. M. Tour, D. S. Grubisha, and D. W. Bennett.

REFERENCES 1. M. A. Reed and T. Lee, Eds., “Molecular Nanoelectronics,” American Scientific Publishers, Stevenson Ranch, California, 2003. 2. R. R. Birge, Ed., “Molecular and Biomolecular Electronics.” American Chemical Society, Washington, DC, 1991.

Molecular Electronic Devices 3. A. Aviram and M. A. Ratner, Ed., “Molecular Electronics: Science and Technology,” Annals of the New York Academy of Sciences, Vol. 852. New York Academy of Sciences, 1998. 4. J. McMurry, “Organic Chemistry.” Brooks/Cole, Belmont, MA, 1996. 5. J. S. Schumm, D. L. Pearson, and J. M. Tour, Angew. Chem. Int. Ed. Engl. 33, 1360 (1994). 6. J. M. Tour, R. Wu, and J. S. Schumm, J. Am. Chem. Soc. 113, 7064 (1991). 7. J. C. Ellenbogen and J. C. Love, Proc. IEEE 88, 386 (2000). 8. T. A. Skotheim, Ed., “Handbook of Conducting Polymers.” Dekker, New York, 1986. 9. D. D. C. Bradley, Chem. in Britain 719, August (1991). 10. M. F. Rubner, in “Molecular Electronics” (G. J. Ashwell, Ed.). Wiley, New York, 1992. 11. S. Kivelson, Phys. Rev. B 25, 3798 (1982). 12. D. Emin, in “Handbook of Conducting Polymers” (T. A. Skotheim, Ed.), Vol. 2, p. 915. Dekker, New York, 1986, and references therein. 13. R. R. Chance, J. L. Bredas, and R. Silbey, Phys. Rev. B 29, 4491 (1984). 14. N. F. Mott and E. A. Davis, “Electronic Processes in NonCrystalline Materials.” Clarendon, Oxford, 1979. 15. P. Sheng, B. Abeles, and Y. Arie, Phys. Rev. Lett. 31, 44 (1973). 16. M. A. Ratner, B. Davis, M. Kemp, V. Mujica, A. Roitberg, and S. Yaliraki, Ann. N. Y. Acad. Sci. 852, 22 (1998). 17. M. Magoga and C. Joachim, Phys. Rev. B 56, 4722 (1997). 18. M. A. Ratner, J. Phys. Chem. 94, 4877 (1990). 19. J. W. Evenson and M. Karplus, Science 262, 1247 (1993). 20. M. P. Samanta, W. Tian, S. Datta, J. I. Henderson, and C. P. Kubiak, Phys. Rev. B 53, R7636 (1996). 21. R. Landauer, IBM J. Res. Dev. 1, 223 (1957). 22. S. Datta, “Electronic Transport in Mesoscopic Systems.” Cambridge Univ. Press, 1995. 23. C. Zhou et al., in “Molecular Electronics” (J. Jortner and M. Ratner, Eds.). Blackwell Science, Oxford, UK, 1997. 24. J. I. Pascual et al., Science 267, 1793 (1995). 25. S. J. Tans et al., Nature 386, 474 (1997). 26. G. Neofotistos, R. Lake, and S. Datta, Phys. Rev. B 43, 2442 (1991). 27. G. L. Closs et al., J. Am. Chem. Soc. 110, 2652 (1988). 28. A. Aviram and M. A. Ratner, Chem. Phys. Lett. 29, 277 (1974). 29. R. M. Metzger, B. Chen, U. Holpfner, M. V. Lakshmikantham, D. Vuillaume, T. Kawai, X. Wu, H. Tachibana, T. V. Hughes, H. Sakurai, J. W. Baldwin, C. Hosch, M. P. Cava, L. Brehmer, and G. J. Ashwell, J. Am. Chem. Soc. 119, 10455 (1997). 30. M. A. Reed, U.S. Patent 5, 475, 341, 1995. 31. M. A. Reed, U.S. Patent No. 5, 589, 629, 1996. 32. C. J. Muller, Ph.D. Thesis, Leiden, Netherlands, 1991. 33. M. A. Reed, C. Zhou, C. J. Muller, T. P. Burgin, and J. M. Tour, Science 278, 252 (1997). 34. C. Kergueris, J.-P. Bourgoin, S. Palacin, D. Esteve, C. Urbina, M. Magoga, and C. Joachim, Phys. Rev. B 59, 12505 (1999). 35. C. Zhou, M. R. Deshpande, M. A. Reed, L. Jones II, and J. M. Tour, Appl. Phys. Lett. 71, 611 (1997). 36. K. S. Ralls, R. A. Buhrman, and T. C. Tiberio, Appl. Phys. Lett. 55, 2459 (1989). 37. J. Chen, L. C. Calvet, M. A. Reed, D. W. Carr, D. S. Grubisha, and D. W. Bennett, Chem. Phys. Lett. 313, 741 (1999). 38. J. Chen, M. A. Reed, A. M. Rawlett, and J. M. Tour, Science 286, 1550 (1999). 39. M. A. Reed, J. Chen, et al., “1999 International Electron Device Meeting,” 1999. 40. G. Binnig, H. Rohrer, C. Gerber, and H. Weibel, Phys. Rev. Lett. 49, 57 (1982). 41. D. M. Eigler and E. K. Schweizer, Nature 344, 524 (1990).

661 42. L. A. Bumm, J. J. Arnold, M. T. Cygan, T. D. Dunbar, T. P. Burgin, L. Jones II, D. L. Allara, J. M. Tour, and P. S. Weiss, Science 271, 1705 (1996). 43. M. Dorogi, J. Gomez, R. Osifchin, R. P. Andres, and R. Reifenberger, Phys. Rev. B 52, 9071 (1995). 44. A. Aviram, J. Am. Chem. Soc. 110, 5687 (1988). 45. J. J. Hopfield, J. Nelson, and D. Beratan, Science 241, 817 (1988). 46. C. P. Collier, E. W. Wong, M. Belohradský, F. M. Raymo, J. F. Stoddart, P. J. Kuekes, R. S. Williams, and J. R. Heath, Science 285, 391 (1999). 47. E. Tekman and S. Ciraci, Phys. Rev. B 40, 10286 (1989). 48. S. Ciraci, A. Baratoff, and I. P. Batra, Phys. Rev. B 41, 2763 (1990). 49. H. Park, A. K. L. Lim, J. Park, A. P. Alivisatos, and P. L. McEuen, Appl. Phys. Lett. 75, 301 (1999). 50. J. Park, A. N. Pasupathy, J. I. Goldsmith, C. Chang, Y. Yaish, J. R. Petta, M. Rinkoski, J. P. Sethna, H. D. Abruna, P. L. McEuen, and D. C. Ralph, Nature 417, 722 (2002). 51. W. Liang, M. P. Shores, M. Bockrath, J. R. Long, and H. Park, Nature 417, 725 (2002). 52. J. G. Kushmerick, D. B. Holt, S. K. Pollack, M. A. Ratner, J. C. Yang, T. L. Schull, J. Naciri, M. H. Moore, and R. Shashidhar, J. Am. Chem. Soc. 124, 10654 (2002). 53. D. R. Lombardi, Ph.D. Dissertation, Yale University, 1997. 54. A. Bezryadin, C. Dekker, and G. Schmid, Appl. Phys. Lett. 71, 1273 (1997). 55. D. Porath, A. Bezryadin, S. de Vries, and C. Dekker, Nature 403, 635 (2000). 56. P. E. Laibinis, G. M. Whitesides, D. L. Allara, A. Parikh, Y. T. Tao, and R. G. Nuzzo, J. Am. Chem. Soc. 113, 7152 (1991). 57. C. D. Bain, J. Evall, and G. M. Whitesides, J. Am. Chem. Soc. 111, 7155 (1989). 58. J. I. Henderson, S. Feng, G. M. Ferrence, T. Bein, and C. P. Kubiak, Inorg. Chim. Acta 242, 115 (1996). 59. J. J. Hickman, C. Zou, D. Offer, P. D. Harvey, M. S. Wrighton, P. E. Laibinis, C. D. Bain, and G. M. Whitesides, J. Am. Chem. Soc. 111, 7271 (1989). 60. J. M. Tour, L. Jones II, D. L. Pearson, J. S. Lamba, T. P. Burgin, G. M. Whitesides, D. L. Allara, A. N. Parikh, and S. Atre, J. Am. Chem. Soc. 117, 9529 (1995). 61. M. Di Ventra, S. T. Pantelides, and N. D. Lang, Phys. Rev. Lett. 84, 979 (2000). 62. T. Vondrak, H. Wang, P. Winget. C. J. Cramer, and X.-Y. Zhu, J. Am. Chem. Soc. 122, 4700 (2000). 63. C. Zhou, Ph.D. Dissertation, Yale University, 1999. 64. S. Datta, W. Tian, S. Hong, R. Reifenberger, J. Henderson, and C. P. Kubiak, Phys. Rev. Lett. 79, 2530 (1997). 65. E. Burstein and S. Lundqvist, “Tunneling Phenomena in Solids.” Plenum, New York, 1969. 66. D. R. Lamb, “Electrical Conduction Mechanisms in Thin Insulating Films.” Methuen, London, 1967. 67. S. M. Sze, “Physics of Semiconductor Devices,” 2nd ed. Wiley, New York, 1981. 68. C. P. Collier, G. Mattersteig, E. W. Wong, Y. Luo, K. Beverly, J. Sampaio, F. M. Raymo, J. F. Stoddart, and J. R. Heth, Science 289, 1171 (2000). 69. M. A. Reed, J. Chen, A. M. Rawlett, D. W. Price, and J. M. Tour, Appl. Phys. Lett. 78, 3735 (2001). 70. A. Ulman, “An Introduction to Ultrathin Organic Films from Langmuir-Blodgett to Self-Assembly.” Academic Press, Boston, 1991. 71. L. A. Bumm, J. J. Arnold, T. D. Dunbar, D. L. Allara, and P. S. Weiss, J. Phys. Chem. B 103, 8122 (1999). 72. D. J. Wold, R. Haag, M. A. Rampi, and C. D. Frisbie, J. Phys. Chem. B 106, 2813 (2002). 73. X. D. Cui, X. Zarate, J. Tomfohr, O. F. Sankey, A. Primak, A. L. Moore, T. A. Moore, D. Gust, G. Harris, and S. M. Lindsay, Nanotechnology 13, 5 (2002).

662 74. R. Holmlin, R. Haag, M. L. Chabinyc, R. F. Ismagilov, A. E. Cohen, A. Terfort, M. A. Rampi, and G. M. Whitesides, J. Am. Chem. Soc. 123, 5075 (2001); M. A. Rampi and G. M. Whitesides, Chem. Phys. 281, 373 (2002). 75. W. Wang, T. Lee, and M. A. Reed, Phys. Rev. B 68, 035416 (2003). 76. B. Mann and H. Kuhn, J. Appl. Phys. 42, 4398 (1971). 77. E. E. Polymeropoulos and J. Sagiv, J. Chem. Phys. 69, 1836 (1978). 78. F. F. Fan, J. Yang, L. Cai, D. W. Price, S. M. Dirk, D. V. Kosynkin, Y. Yao, A. M. Rawlett, J. M. Tour, and A. J. Bard, J. Am. Chem. Soc. 124, 5550 (2002). 79. K. Slowinski, H. K. Y. Fong, and M. Majda, J. Am. Chem. Soc. 121, 7257 (1999). 80. J. F. Smalley, S. W. Feldberg, C. E. D. Chidsey, M. R. Linford, M. D. Newton, and Y. Liu, J. Phys. Chem. 99, 13141 (1995). 81. W. Franz, in “Handbuch der Physik” (S. Flugge, Ed.), Vol. 17, p. 155. Springer-Verlag, Berlin, 1956. 82. C. Joachim and M. Magoga, Chem. Phys. 281, 347 (2002). 83. G. Lewicki and C. A. Mead, Phys. Rev. Lett. 16, 939 (1966); R. Stratton, G. Lewicki, and C. A. Mead, J. Phys. Chem. Solids 27, 1599 (1966); G. H. Parker and C. A. Mead, Phys. Rev. Lett. 21, 605 (1968). 84. B. Brar, G. D. Wilk, and A. C. Seabaugh, Appl. Phys. Lett. 69, 2728 (1996). 85. J. G. Simmons, J. Appl. Phys. 34, 1793 (1963). 86. J. G. Simmons, J. Phys. D 4, 613 (1971); J. Maserjian and G. P. Petersson, Appl. Phys. Lett. 25, 50 (1974). 87. X. D. Cui, A. Primak, X. Zarate, J. Tomfohr, O. F. Sankey, A. L. Moore, T. A. Moore, D. Gust, L. A. Nagahara, and S. M. Lindsay, J. Phys. Chem. B 106, 8609 (2002). 88. C. Boulas, J. V. Davidovits, F. Rondelez, and D. Vuillaume, Phys. Rev. Lett. 76, 4797 (1996); M. Fujihira and H. Inokuchi, Chem. Phys. Lett. 17, 554 (1972); S. G. Lias, J. E. Bartmess, J. F. Liebman, J. L. Holmes, R. D. Levin, and W. G. Mallard, J. Phys. Chem. Ref. Data 17, Suppl. 1 (1988). 89. M. J. Robertson and R. J. Angelici, Langmuir 10, 1488 (1994). 90. K. Shih and R. J. Angelici, Langmuir 11, 2539 (1995). 91. J. E. Huheey, “Inorganic Chemistry.” Harper & Row, New York, 1983. 92. N. W. Ashcroft and N. D. Mermin, “Solid State Physics.” p. 290. Harcourt Brace, Orlando, FL, 1976. 93. H. Jones, in “Handbuch der Physik” (S. Flugge, Ed.), Vol. 19, p. 227. Springer-Verlag, Berlin, 1956. 94. N. F. Mott, Proc. Roy. Soc. London Ser. A 153, 699 (1936).

Molecular Electronic Devices 95. R. S. Potember, T. O. Pochler, and D. O. Cowan, Appl. Phys. Lett. 34, 405 (1979). 96. R. S. Potember, T. O. Poehler, D. O. Cowan, and A. N. Bloch, in “The Physics and Chemistry of Low-Dimensional Solids”, (L. Alcbcer, Ed.). Reidel, Dordrecht, 1980. 97. T. Hertel, R. E. Walkup, and Ph. Avouris, Phys. Rev. B 58, 13870 (1993). 98. L. Esaki, Phys. Rev. 109, 603 (1958). 99. L. B. Gunn, Solid State Commun. 1, 88 (1963). 100. L. L. Chang, L. Esaki, and R. Tsu, Appl. Phys. Lett. 24, 593 (1974). 101. H. Kroemer, Proc. IEEE 52, 1736 (1964). 102. L. G. Sollner et al., Appl. Phys. Lett. 43, 588 (1983). 103. M. Tsuchiya, H. Sakaki, and J. Yoshino, Jpn. J. Appl. Phys. 24, L466 (1985). 104. S. M. Sze, Ed., “High-Speed Semiconductor Devices.” Wiley, New York, 1990. 105. F. Capasso and R. A. Kiehl, J. Appl. Phys. 58, 1366 (1985). 106. N. Yokoyama, K. Imamura, S. Muto, S. Hiyamizu, and N. Nishi, Jpn. J. Appl. Phys. Part 2 24, L583 (1985). 107. F. Capasso, in “Picosecond Electronics and Optoelectronics” (G. A. Mourou, D. M. Bloom, and C. H. Lee, Eds.). Springer, Berlin, 1985. 108. L. Esaki, IEEE Trans. Electron Dev. 12, 374 (1965). 109. Seabaugh and R. Lake, Encycl. Appl. Phys. 22, 335 (1998). 110. H. Mizuta and T. Tanoue, “The Physics and Applications of Resonant Tunneling Diodes.” Cambridge Univ. Press, 1995. 111. K. H. Gundlach and J. Kadlec, Phys. Status Solidi A 10, 371 (1972). 112. C. Hamann et al., Phys. Status Solidi A 50, K189 (1978). 113. A. R. Elsharkawi and K. C. Kao, J. Phys. Chem. Solids 38, 95 (1977). 114. M. A. Reed, Proc. IEEE 87, 652 (1999). 115. J. H. Smet, T. P. E. Broekaert, and C. G. Fonstad, J. Appl. Phys. 71, 2475 (1992) 116. J. R. Söderström, D. H. Chow, and T. C. McGill, J. Appl. Phys. 66, 5106 (1989) 117. J. Day et al., J. Appl. Phys. 73, 1542 (1993). 118. H. H. Tsai et al., IEEE Trans Electron. Devices. Lett. 15, 357 (1993). 119. H. J. Gao et al., Phys. Rev. Lett. 84, 1780 (2000). 120. S. Tiwari, F. Rana, H. Hanafi, A. Hartstein, E. F. Crabbe, and K. Chan, Appl. Phys. Lett. 68, 1377 (1996). 121. N. J. Stome and H. Ahmed, IEEE Trans, Electron. Devices Lett. 20, 583 (1999). 122. J. Chen, Ph.D. Dissertation, Yale University, 2000.

Encyclopedia of Nanoscience and Nanotechnology

www.aspbs.com/enn

Molecular Gradient Nanoassemblies Jan Genzer, Rajendra R. Bhat, Tao Wu, Kirill Efimenko North Carolina State University, Raleigh, North Carolina, USA

CONTENTS 1. Introduction 2. Methods of Preparing Gradients 3. Methods of Measuring Gradient Properties 4. Properties of Molecular Gradients 5. Applications of Gradients on Substrates 6. Extension of Two-Dimensional Gradients to Three Dimensions 7. Summary Glossary References

1. INTRODUCTION It is generally agreed that the concept of nanotechnology was conceived by Richard Feynman’s visionary lecture at Caltech in 1959 [1]. However, it was only the last decade that saw key advances made in the manipulation and control of materials on a “small” scale [2]. This sudden outburst has been fueled, in part, by the potential for exploiting unique properties of nanostructures in commercially important applications, including sensors [3], high-efficiency solar cells [4], single-molecule detectors [5], and electroluminescent devices [6]. One of the milestones on the pathway toward materializing the grand vision of nanotechnology is to assemble the “small” building blocks at a desired location on a tangible substrate. To this end, recent advances in the field of self-assembly combined with new deposition technologies, such as soft-lithography techniques [7], have enabled alternative means of fabricating two- and threedimensional surface structures. Most soft-lithography techniques are based on selective and controlled deposition of self-assembled monolayers (SAMs) on material surfaces [8]. Various structural patterns with lateral dimensions ranging from hundreds of nanometers to several micrometers are created on the ISBN: 1-58883-061-6/$35.00 Copyright © 2004 by American Scientific Publishers All rights of reproduction in any form reserved.

material surface using an elastomeric “pattern-transfer element” (or stamp) that has a three-dimensional structure molded onto its surface. Because of the molecular nature of the SAMs, the surface patterns generated via “soft lithography” are rather thin (thicknesses range from several angstroms to several nanometers). Some applications, particularly those involving subsequent microfabrication steps, such as etching, require that thicker layers of the surface coating be formed. Hence, techniques involving the patterning of thicker polymer layers grafted to the substrate have been developed [9–15]. The latter group of technologies is based on selectively decorating the material surfaces with polymerization initiators and then growing the macromolecules directly from the surface (so-called “grafting from”). Using this method, the thickness of the overcoat film can be adjusted by simply varying the polymerization conditions (time, monomer concentration, temperature). The soft-lithography technologies always produce sharp boundaries between the distinct chemical regions on the substrate. This feature makes soft lithography useful for decorating substrates with well-defined chemical patterns of various shapes and dimensions. However, for some applications, it is desirable that the physicochemical characteristics, such as wetting of the substrate, change gradually. This can be accomplished by producing surfaces with a position-dependent and gradually varying chemistry. In these so-called “gradient surfaces,” the gradient in surface energy is responsible for a position-bound variation in physical properties, most notably the wettability [16]. Recent studies have reported on the preparation of molecular gradients on length scales ranging from nanometers to centimeters [17, 18], thus offering the prospect of meeting the demands of a variety of novel applications. For example, such gradient substrates can be useful in high-throughput studies of the interfacial behavior of molecules and macromolecules [19] (the entire behavioral spectrum can be accessed in a single experiment), they can serve as templates for further processing, or they can be used as active elements in controlled surface transport of materials. The aim of this review is to demonstrate the usefulness of the gradient substrates in nanotechnology. Several examples will be referenced documenting the utility of the

Encyclopedia of Nanoscience and Nanotechnology Edited by H. S. Nalwa Volume 5: Pages (663–676)

Molecular Gradient Nanoassemblies

664 wettability gradients in combinatorial studies of adsorption, phase behavior in thin liquid and polymer films, templating, and material transport on surfaces. The dual nature of the molecular gradients (discrete on molecular scales, continuous on meso scales) endows them with unique properties that can be exploited to generate combinatorial libraries, which, in turn, will find use in the discovery of new materials and phenomena. Moreover, utilizing molecular gradients will provide simple means of mimicking molecular and biomolecular transport.

2. METHODS OF PREPARING GRADIENTS Over the past 40 years, several strategies for making molecular gradients have been conceived and developed. Each has its advantages and disadvantages and each is best applied on one length scale (Table 1). These methods are briefly described below and discussed in a recent review [20]. The first report describing the formation of wettability gradients dates back to the mid-1960s. Carter described a technique based on evaporating palladium metal on cellulose acetate–covered glass [21]. A short length of stainlesssteel rod was first placed in contact with the cellulose acetate film and a small amount (≈2 mg) of fine palladium wire, positioned at a distance of approximately 10 cm from the rod, was evaporated under vacuum. This setup produced a relatively heavy deposition of palladium, which clearly outlined the intervening rod. However, owing to the scattering of metal particles, a much finer deposit of palladium extended beyond the visibly shadowed area and tapered in the narrowing angle under the curved surface of the rod. The technique is very simple, but does not offer much control over the gradient properties. In the mid-1980s, Elwing et al. proposed a new method for preparing molecular gradients [22]. In this technique (Fig. 1a), the wettability gradient on the solid silicon oxide–covered substrate was produced by diffusion of dichlorodimethyl silane (DDS) between two organic solvents that have different densities but are mutually soluble. In a

typical experiment, a silica-covered substrate was placed vertically into a container that was filled with xylene (XYL). Trichloroethylene (TCE) was mixed with a small amount of DDS and was delivered under the XYL phase in the container. During incubation, the two solvents interdiffused; the DDS diffused to the XYL region and was simultaneously attached to the silica surface. The technique is relatively simple, but it offers limited control over the gradient properties—except the length, which can be controlled by varying the diffusion time. The main limitation of the liquid diffusion technique—namely, that the shape of the diffusion profile was always Fickian—was removed in the density gradient solution method developed by Gölander and co-workers [23]. In this technique (Fig. 1b), a solution of TCE was mixed continuously and pumped from a mixing chamber into the bottom of a container containing vertically positioned silica-covered substrates. Simultaneously, the TCE solution was replenished in the mixing chamber with a solution from a second flask that contained DDS dissolved in diiodomethane (DIM). The concentration of DDS in the mixing chamber increased with time, and, as a result, a vertical density gradient containing a DDS concentration gradient built up in the container containing the substrates (with increasing concentration from the bottom). The wettability gradient was formed upon chemisorption of DDS to the silica substrate. While it allows for multiple gradient profiles, this technique is rather laborious. Ueda-Yukoshi and Matsuda showed that poly(vinylene carbonate) (PVCa) can be hydrolyzed to produce poly(hydroxyl methylene) (PHM) in an alkaline solution (Fig. 1c). These researchers utilized this chemical conversion method to produce a wettability gradient on a PVCa surface [24]. A glass slide was first covered with a thin layer of PVCa, dried, and gradually immersed into an alkaline solution of NaOH. This process produced a surface, whose position-dependent wettability changed from hydrophobic (PVCa) to hydrophilic (PHM). By controlling the immersion speed, the gradient steepness was allowed to vary from several millimeters to several centimeters.

Table 1. Comparison of various methods used to produce chemical gradients. Spatial range Gradient preparation method Shadowing evaporation [21] Liquid diffusion [22] Density gradient solution [23] Hydrolysis of poly(vinylene carbonate) [24] Radio frequency plasma discharge [25] Corona discharge [26] Gradient UVO treatment of hydrophobic SAMs [27] Vapor evaporation [16] Vapor evaporation on flexible substrates [17] Diffusion of alkanethiols in polysaccharide [28, 29] Electrochemical desorption of alkanethiols [30] Replacement lithography [18] Polyatomic deposition [31] Heterobifunctional photolinkers [32, 33] Microfluidic networks [34–37]

nm


m

mm

cm

‹. . . . . . . . . . . . . . .› ‹. . . . . . . . . . . . . . .› ‹. . . . . . . . . . . . . . .› ‹. . . . . . . . . . . . . . .› ‹. . . . . . . . . . . . › ‹. . . . . . . . . . . . . . . . › ‹. . . . . . . . . . . . › ‹. . . . . . . . . . . . . . .› ‹. . . . . . . . . . . . . . . . › ‹. . . . . . . . . . . . › ‹. . . . . . . . . . . . › ‹. . . . . . . . . . . . . . . . › ‹. . . . . . . . . . . . . . . . . . . . › ‹. . . . . . . . . . . . . . . . › ‹. . . . . . . . . . . . . . . . ›

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665

Figure 1. Schematic illustrating the formation of wettability gradient using (a) liquid diffusion technique, (b) density gradient solution method, (c) hydrolysis of poly(vinylene carbonate), (d) radio frequency plasma discharge, (e) plasma discharge, (f) diffusion of alkanethiols in polysaccharide matrix, (g) molecular gradients via replacement lithography, (h) gradients of proteins by means of heterobifunctional photolinkers, and (i) solution and surface gradient using microfluidics.

A versatile method for decorating polymer surfaces with chemical gradients is based on moving a shutter over the polymer surface during exposure of the surface to a radio frequency plasma discharge [25] (Fig. 1d). This technique is capable of producing various gradient shapes on a variety of polymers under various gas conditions. However, the chemical nature of the plasma-modified surfaces is not well defined—the surface consists of a mixture of various hydrophilic groups and radicals. Moreover, some materials have a tendency to roughen when exposed to a radio frequency plasma discharge. Lee and co-workers produced a wettability gradient on a low-density polyethylene surface by treating the polymer sheets in air with the corona from a knife-type electrode whose power gradually increased along the sample length [26] (Fig. 1e). While this method has the same characteristics as that based on a radio frequency plasma discharge, it is easier to accomplish and the treatment can be done under ambient conditions. Roberson and co-workers developed a simple method for preparing surfaces with gradually varying wetting properties on a millimeter scale [27]. They first deposited SAMs made of n-octyl trichlorosilane (OTS) on flat silica surfaces

and exposed such surfaces to a gradient UV/ozone (UVO) radiation. To produce the gradient of UVO, Roberson and co-workers used a variable-density filter made of fused silica that was modified with inconel (a Ni, Cr, Fe alloy). The optical density varied from 0.04 to 1.0 (measured at  = 330 nm) across the fused silica optical filter in 11 equidistant steps (4 mm each), giving a linear transmission gradient in the intensity of the UV radiation. The filter was placed close to the SAM-covered surface. Atomic oxygen, generated from molecular oxygen in the proximity of the surface by the UV radiation, converted a fraction of the CH2 and CH3 groups in the hydrophobic OTS moieties into hydrophilic functional groups (e.g., COOH). The molar concentration of the atomic oxygen (and thus the density of the hydrophilic groups on the surface) was directly proportional to the incident UV intensity. Measurements using contact angle and time-of-flight secondary ion mass spectrometry confirmed the existence of linear wettability gradients; the surface energy was shown to increase from 26 mJ/m2 , on the untreated side, to 72 mJ/m2 , close to the UVO-modified side of the substrate.

666 Liedberg and Tengvall prepared molecular gradients by cross-diffusion of two different -substituted alkanethiols from opposite ends of a polysaccharide matrix deposited on top of a gold-covered planar substrate [28] (Fig. 1f). As the two alkanethiols interdiffused, they bonded to the underlying gold substrate and formed a self-assembled monolayer, whose composition changed along the diffusion path. Liedberg and co-workers demonstrated that this methodology can be used to prepare one-dimensional molecular gradients with hydrophilic/hydrophobic variation [28] as well as ordered/disordered structures [29]. The ability to control electrochemically the adsorption/desorption of alkanethiol molecular assemblies on/from a noble metal surface and its utilization in preparing structures with spatiotemporal characteristics has been exploited by Bohn and co-workers [30]. They first formed a selfassembled monolayer of n-octanethiol (OT) on a goldcoated substrate. OT gradients were formed by applying a 15-nV/mm in-plane potential gradient, which selectively removed the OT molecules from the regions exposed to a higher potential. After washing with pure solvent, the sample was reimmersed into another solution containing a hydrophilic mercapto propionic acid (MPA), whose molecules filled the bare areas on the gold substrate. A twocomponent linear gradient in composition (and hence wettability) was thus generated. Gorman and co-workers recently developed a novel technique for preparing molecular gradients, whose dimensions can be controlled on the nanometer scale [18] (Fig. 1g). In their methodology, an organized SAM of an -substituted alkanethiol was formed on an atomically flat gold substrate. Such a substrate was then immersed into a dodecane solution containing another -substituted alkanethiol. The substrate-bound SAM was repeatedly imaged with scanning tunneling microscopy without apparent change in its appearance under conditions of set-point bias of +1 V (positive substrate bias) and set-point current between 6 and 8 pA. Upon changing the bias to +30 V or slightly higher (up to + 40 V), replacement of the thiolate on the surface by the different thiol in solution occurred. This replacement was observed by scanning the tip in one area at the higher voltage, reducing the set-point voltage back to 1 V, and scanning the tip across a larger area. By rastering the tip in a defined pattern above the substrate, features with a resolution of approximately 10–15 nm and a variety of pattern shapes were generated. Wijesundara and co-workers showed that surfaces with gradient wettabilities can be obtained by hyperthermal polyatomic ion deposition [31]. A poly(methyl methacrylate) (PMMA)/fluorocarbon gradient was produced by exposure of the PMMA surface to C3 F+ 5 ions. A linear variation in wettability was achieved by linearly increasing the fluence of the C3 F+ 5 ions while allowing the ion source to scan across the PMMA substrate. The researchers also established that a polyatomic deposition method can be used to form wettability gradients on other materials, including polymers (polystyrene, PS), semiconductors (H-terminated silicon), and oxides (Al2 O3 ). In each case, the parameters of the gradients can be tuned by varying the ion type, the fluence, and the scanning speed.

Molecular Gradient Nanoassemblies

Hypolite and co-workers proposed a method for creating microscale gradients using photoreactive cross-linking agents [32] (Fig. 1h). In their methodology, a conjugation reagent containing a photoactive benzophenone (BP), a water-soluble tetraethylene glycol (TEG) spacer, and an amine-reactive N -hydroxysuccinimide (NHS) ester was prepared and used to derivatize a protein, R-phycoerythrin (PE). A surface with a PE concentration gradient was created by scanning a Cd/He laser beam across the surface in a raster pattern but with increasing scanning speed in consecutive lines. Exposure to the laser beam activated the BP, which set up a reaction scheme that resulted in protein immobilization on the substrate. Increasing the exposure time of the surface to the laser beam increased the amount of BP–TEG–PE immobilized on the surface. Higher scanning velocities (shorter exposure times) resulted in lower concentrations of immobilized protein relative to the slower velocities. Caelen and co-workers utilized similar technology to form discrete gradients of immobilized proteins on surfaces [33]. They mixed protein probes with the photolinker polymer OptoDex (a polysaccharide-based polymer substituted with aryldiazirines). The solution was deposited on the surface in a gradient fashion via ink-jet printing. After drying, the surface was irradiated with light of 350 nm wavelength. Photoactivation of the aryldiazirine molecules led to the formation of reactive carbenes. Some carbenes underwent insertion reactions with covalent bonds of probe proteins; others bound to the underlying polystyrene surface. A discrete protein gradient on the surface was formed by removing the non-covalently attached protein by washing. Caelen and co-workers proposed that gradients of immobilized proteins on surfaces can be prepared by utilizing microfluidic networks [34]. In this methodology, a poly(dimethyl siloxane) (PDMS) substrate was placed across the channels of a microfluidic network made on micromachined silicon to pattern lines of proteins onto the PDMS substrate. Capillary forces between a solution containing proteins and the hydrophilized walls of the microfluidic network induced filling of the channels and the protein was gradually depleted by fast adsorption of the proteins to the hydrophobic regions of the PDMS substrate exposed to the filled channels. After separating the PDMS from the microfluidic network, the underivatized areas of PDMS were blocked with bovine serum albumin. In the final step, fluorescently labeled immobilized antigens with antibodies were attached to the protein gradient areas to visualize the gradient. Whitesides and co-workers utilized a network of multi-inlet microfluidic channels to fabricate gradients in composition in solution and gradients in topography on the surface [35–37] (Fig. 1h). A microfluidic gradient generator comprising multiple generation branches in a poly(dimethyl siloxane) network was fabricated by rapid prototyping [37] and soft lithography. Multiple solutions were simultaneously infused into the network through the inlets. As the fluid streams traveled down the network, they were repeatedly split, mixed, and recombined. After several generations of branched systems, each branch contained different proportions of the infused solutions. A gradient was established—perpendicular to the flow—in a single large channel that combined all branches. Various gradient shapes and profiles were generated, including periodic gradients,

Molecular Gradient Nanoassemblies

asymmetric gradients, superposed gradients, and dynamic gradients. By flowing hydrofluoric acid through the microfluidic network, a gradient in the surface topography was also generated on the silica. In this review, we will outline several strategies for producing gradient-based surfaces. All the methodologies are based on generating the wettability gradient using the vapor deposition technique suggested more than 10 years ago by Chaudhury and Whitesides [16]. In this method, shown schematically in Figure 2, an organosilane (either chloro- or alkoxy-based) is mixed with paraffin oil (PO) and the mixture is placed in an open container that is positioned close to an edge of a silicon wafer. As the silane evaporates, it diffuses in the vapor phase and generates a concentration gradient along the hydrophilic substrate. Upon impinging on the substrate, the silane molecules react with the substrate OH functionalities and form an organized SAM. The breadth and position of the silane molecular gradient can be tuned by varying the silane diffusion time and the flux of the silane molecules. The latter can be conveniently adjusted by varying the silane : PO ratio and/or the temperature of the silane : PO mixture. After the gradient SAM deposition, any physisorbed silane molecules are removed by thoroughly washing the substrates with warm deionized water (75 C; resistivity, >16 M · m) for several minutes. In some instances, the molecular gradients serve as precursors for further processing. Specifically, we document later that molecular gradients can be used as templates for the adsorption of nanosized objects and the formation of threedimensional (3D) structures by allowing polymer chains to grow from the molecules within the gradient (the so-called “grafting from” technology).

3. METHODS OF MEASURING GRADIENT PROPERTIES Many different surface analytical techniques can be applied to study the properties of the gradient substrates. Perhaps the easiest and most widely available technique is based on measuring the wettability using either static or dynamic contact angles. In static contact angle experiments, one measures the wetting angle of a small volume of probing liquid on the surface. While in some instances contact angles are reported for cases where the droplet is separated from the needle, most measurements are performed under conditions where the needle and the probing liquid are not separated. The latter set of measurements allows for determining so-called advancing and receding contact angles. Contact angle measurements on wettability gradients are usually performed such that the needle is in contact with the probing liquid. Separating the needle from the liquid

Figure 2. Schematic showing the method of preparing molecular gradient by vapor deposition of organosilanes onto hydrophilic substrates.

667 would allow the liquid to move on the surface (see [16]), particularly in gradients with steep boundaries between the hydrophobic/hydrophilic regions. The dynamic contact angle (DCA) measurements are usually performed using the Wilhelmy plate techniques. Examples of the DCA measurements on gradient substrates can be found elsewhere [38]. While useful in providing macroscopic-level information about the chemistry of the gradient surfaces, contact angle methods are not capable of delivering information about the structural properties of the gradients on a molecular level (such as concentration of a particular chemical group, orientation of molecules, etc.). For information regarding the above, one has to turn to more sophisticated methods. Ruardy and co-workers discuss several examples describing the utilization of X-ray photoelectron spectroscopy (XPS) and infrared spectroscopy (IR) [38]. Recently, near-edge X-ray absorption fine structure (NEXAFS) spectroscopy has been applied to study the physicochemical characteristics of the gradient surfaces. NEXAFS turned out to be very beneficial because it allowed for simultaneous investigation of both the surface chemistry and the molecular orientation.

3.1. NEXAFS Spectroscopy NEXAFS involves the resonant soft X-ray excitation of a K or L shell electron to an unoccupied low-lying antibonding molecular orbital of or symmetry, ∗ and ∗ , respectively [39]. The initial-state K or L shell excitation gives NEXAFS its element specificity, while the final-state unoccupied molecular orbitals provide NEXAFS with its bonding or chemical selectivity. A measurement of the intensity of NEXAFS spectral features enables identification of chemical bonds and determination of their relative population density within the sample. Because of the fixed geometry between the sample and the X-ray beam and the fact that the 1s → ∗ and 1s → * excitations are governed by dipole selection rules, the resonance intensities vary as a function of the direction of the electric vector E of the incident polarized X-ray relative to the axis of the ∗ and ∗ orbitals. This, coupled with the fact that sharp core-level excitations for elements C, N, O, and F occur in the soft X-ray spectral region, makes NEXAFS an ideal technique for probing the molecular orientations of organic molecules. Since its first introduction as a routine analytical technique, NEXAFS has proven advantageous in determining the orientation of both small molecules, as well as large macromolecular systems. Recently, we have demonstrated that NEXAFS can be used to sense the chemistry and determine the molecular orientation of gradient materials surfaces [40, 41]. To measure the spatial distribution of a given molecule, the sample is mounted onto a goniometer, which controls the orientation of the sample with respect to the polarization vector of the X-rays and enables horizontal and vertical sample motion. After tuning the monochromator energy to that corresponding to a given characteristic 1s → ∗ (or 1s → ∗ ) transition, the sample is moved with small increments (usually between 0.5 and 1 mm), and after each step a new NEXAFS data set is recorded. To determine the concentration of a given chemical moiety, the angle between the sample normal and the electric vector E of the polarized X-ray beam, , is set at  ≈ 50–55 . At this angle—the so-called “magic angle”—the

Molecular Gradient Nanoassemblies

668 NEXAFS intensity is independent of the molecular orientation on the substrate. If orientation information is required, the above procedure is repeated for at least three different angles  (usually 20 , 50 , and 90 ), and the molecular orientation is evaluated using standard techniques (for details, see [39, 40]).

4. PROPERTIES OF MOLECULAR GRADIENTS

-cos(θW) (deg)

0.0 -0.2 -0.4

m-F8H2

0.8

46

0.6

48

0.4

50 52

0.2

a)

0.0 1.0

54 35

d-F8H2

0.8

40

0.6 45

0.4 0.2

50

b)

0.0 1.0

t-F8H2

0.8

-0.6 -0.8 -1.0 0

0.4

30

Figure 3. Cosine of contact angles of deionized water measured on “double” molecular gradients prepared by vapor deposition of n-octyl trichlorosilane (OTS) from two opposite ends of a silica-covered silicon wafer for 60 s (squares), 180 s (circles), and 300 s (triangles). The solid lines are the best fits to the data using the Fickian diffusion profile.

substrate

c) 0

50

10 20

0.0 10 20 30 40 Position on the substrate (mm)

55 0

0.6

0.2

60 s 180 s 300 s

(deg)

0.2

44

1.0

Fraction of F8H2 in SAM

One of the most important properties of a molecular gradient is its wettability, which is determined primarily by the terminal group of the SAM and the concentration of molecules attached to the substrate at a given position along the gradient. In Figure 3, we show the contact angles of water measured on “double” molecular gradients made by vapor deposition of OTS (OTS : PO = 1 : 5) from two opposite ends of the silica-covered silicon substrate. The data in Figure 3 show that at short diffusion times the two diffusion profiles stay isolated, forming a “wettability well.” However, upon increasing the diffusion time of the molecules in the vapor, the two profiles start to interfere and the wettability well starts to fill up. The notion of double gradients can be further extended to form gradients of two chemically different species. Such heterogeneous double gradients on planar silica-covered substrates were recently prepared by forming mixed molecular gradients prepared by vapor interdiffuson of aminopropyl triethoxysilane (APTES) and 1H ,1H ,2H ,2H -perfluorodecyltrichlorosilane (t-F8H2) [42]. The gradual variation of the grafting density of the surface-bound molecules is expected to have a profound influence on the organization of the molecules in the gradients. By studying how the gradient-forming molecules are arranged across the gradient interfacial region, one can learn more about the mechanisms and nature of

self-assembly in organosilane SAMs. The gradient geometry offers the advantage of constraining the self-assembly growth in a given direction. This is in contrast to the classical case of “uniform” self-assembly on a substrate, where the incorporation of the molecules in the final SAM takes place at random in all directions. The ability of NEXAFS to determine the molecular orientation of the surfacebound molecules can be utilized to study the orientation of the SAMs across the gradient. In Figure 4, we plot the dependence of the fraction of the F8H2 molecules on the surface (normalized by the maximum SAM coverage) (solid lines) and the variation of the average tilt of the semifluorinated part of the F8H2 molecule with respect to the surface normal, F8 , (dashed lines) as a function of the position on the silica surface for mono-, di-, and trifunctional 1H,1H ,2H,2H -perfluorodecyl organosilanes, m-F8H2, d-F8H2, t-F8H2, respectively (for chemical formulas, see the Appendix). By comparing the information about the concentration and orientation of F8H2 in the molecular gradient, the following picture emerges. Close to the diffusing sources, the density of the F8H2 molecules is high and, as a result, complete SAMs form, similar to homogeneous F8H2 SAMs [40, 43]. At larger distances from the diffusing sources, the concentration of F8H2 molecules decreases. Interestingly, the functional dependence of the concentration profiles varies, depending on the type of bonding on the substrate. This can be due to several factors. First, with the exception of the monofunctional m-F8H2

40 50

10

20

30

40

50

Position on substrate (mm) Figure 4. Fraction (solid lines) and molecular orientation (dashed lines) of F8H2 in the molecular gradients made of (a) m-F8H2, (b) d-F8H2, and (c) t-F8H2 organosilanes as a function of the position on the substrate. The inset to the figure shows a schematic of the molecular orientation of a single F8H2 molecule and denotes the definition of F8 .

Molecular Gradient Nanoassemblies

molecules, both d-F8H2 and t-F8H2 species have a tendency to form larger multimolecular clusters. This behavior has been known for some time and is relatively well documented [44]. These clusters can form either in the vapor phase or after the molecules hit the silica surface. Recall that only minute concentrations of water are needed to hydrolyze the Si–Cl bond, thus converting it into Si–OH [8]. Hydrogen bonds between the hydroxyls from several molecules can be responsible for the formation of a relatively stable cluster. Moreover, the long life of such clusters is further facilitated by rather strong intermolecular van der Waals forces acting helices [8]. Thus, unlike between two or more (CF2 )8 the m-F8H2 SAMs, which are formed primarily by deposition of single molecules, the d-F8H2 and t-F8H2 SAMs may be built by inserting clusters containing multiple molecules. The second factor, which is closely associated with the first one, has to do with the way the F8H2 organosilanes are packed. Genzer and co-workers have recently reported that the orientation of the F8H2 molecules in homogeneous SAMs depends on the bonding environment of the F8H2 molecule. The average tilt angles of the semifluorinated part of t-F8H2, d-H8H2, and m-F8H2 moieties from the surface normal, F8 , were 10 ± 2 , 35 ± 2 , and 45 ± 3 , respectively [45]. The increase in the tilt angle with increasing number of methyl groups attached to the silicon terminus was associated with the steric hindrance of those methyl groups close to the bonding substrate. From Figure 4, F8 increases as one moves away from the diffusing source along each gradient. This behavior suggests that the chains start deviating from the tilt angles in their respective homogeneous SAMs. This molecular reorganization of the F8H2 molecules is in part due to the decreasing grafting density on the surface. Considering that the spot size of the X-ray beam on the sample during the NEXAFS experiments, about 1 mm2 , is much larger than the area occupied by a single t-F8H2 molecule, the tilt angle F8 determined from NEXAFS represents only an average value. Hence, there is no straightforward way to discriminate between the case of all t-F8H2 molecules homogeneously tilting by the same angle and the case of a disordered system with a broad distribution of tilt angles. Therefore, the increase in F8 observed in the region of the gradient in which the concentration decreases cannot be unambiguously interpreted by using the NEXAFS data alone. Complementary measurement of another physical property along the gradient—such as the density and/or the thickness—is required [40]. One of the limitations of the vapor deposition technique is that the current setup produces rather broad wettability gradients with very little tunability. Hence, our goal was to develop technologies leading to greater control over the characteristic size of the gradients. On a flexible substrate, this can be achieved by fine-tuning the grafting density of the molecules by fabricating mechanically assembled monolayers (MAMs), structures that are based on the synergism between self-assembly and mechanical manipulation of the grafted molecules on the surfaces [46]. The technique (Fig. 5) is based on the combination of (i) the wellknown grafting reaction between -(CH2 )n SiCl3 molecules (typically,  = CH3  CF3  NH2  CH CH2  CN) and OH functionalities present on silicon-based surfaces, [Si]≡substrate (Scheme 1), and (ii) mechanical manipulation

669 (a)

(b)

(c) ∆x

PDMS

(d)

(e)

UV + O3

PDMS-UVO

θ Figure 5. Top panels are schematics illustrating the technological steps leading to the production of MAMs. (a) A pristine PDMS network film is prepared by casting a mixture of PDMS and a cross-linker into a thin (≈0.5 mm) film and curing it at 55  C for about 1 h. (b) After soxhlet extraction in chloroform for 24 h, which removes any non-cross-linked PDMS oligomers, the film is cut into small strips (≈1 × 5 cm2 ) and mechanically stretched by a certain length, x. (c) Subsequent exposure to a UVO treatment produces hydrophilic PDMS surfaces (PDMS–UVO) composed mainly of hydroxyl groups as revealed from Fourier transform infrared and NEXAFS experiments. By increasing the length of the UVO treatment, the number of surface hydrophilic groups increases, causing the water contact angle to decrease. The HO–[Si]surface groups are particularly important because they serve as attachment points for the chlorosilane molecules. (d) The FyHx molecules are deposited from vapor onto this stretched substrate and form an organized SAM. (e) Finally, the strain is released from the PDMS–UVO film, which returns to its original size, causing the grafted FyHx molecules to form a densely organized MAM. To remove weakly physisorbed FyHx molecules, we wash the samples thoroughly in warm (≈60  C) distilled water for 1 min and dry them with nitrogen. The bottom panels show photographs of a water droplet spreading on each of the substrates. Reprinted with permission from [46], J. Genzer and K. Efimenko, Science 290, 2130 (2000). © 2000, American Association for the Advancement of Science.

of the grafted -(CH2 n SiCl3 molecules on the substrate. The method consists of five operational steps. First, a pristine poly(dimethyl siloxane) (PDMS) network film is prepared by casting a mixture of PDMS and a cross-linker into a thin film (thickness ≈ 0.5 mm) and curing at 55 C for about 1 h. In the second step, the cross-linked PDMS substrate is cut into small strips (≈1.5 × 5 cm2 ) and uniaxially stretched to various strains, x. The stretched substrate is then exposed to an ultraviolet/ozone (UVO) treatment to produce the OH surface functionalities (PDMS–UVO) [47]. The molecular gradient of -(CH2 )n SiCl3 SAM is then formed following the vapor diffusion technique [16] described earlier. Finally, the strain is released from the PDMS–UVO film, which returns to its original size, causing the grafted -(CH2 )n Si molecules to form a gradient with a steeper concentration profile as compared to a nonstretched PDMS–UVO substrate. Figure 6 shows static contact angles of deionized water along gradient ω-(CH2)n-SiCl3

HO-[Si]substrate -3HCl

-3HCl

ω-(CH2)n--Si ≡ O-[Si]substrate -3H2O

+3H2O

ω-(CH2)n-Si(OH)3 Scheme 1.

HO-[Si]substrate

Molecular Gradient Nanoassemblies

670 0.4

∆x =

0.2

-0.2 -0.4

110 100 90 80 70 60

-0.6

50

-0.8

40 30

-1.0

θwater (deg)

-cos(θwater)

0.0

0% 5% 10% 15% 20% 25% 30% 40% 50%

10 0

5

10 15 20 25 30 35 Position along gradient (mm)

40

Figure 6. Contact angles of deionized water along gradient substrates prepared on PDMS network films that were previously extended by x ranging from 0 to 50% [x equal to 0% ( ), 5% (), 10% (
), 15% (), 20% (), 25% (△), 30% (), 40% (▽), and 50% ()] and treated with UVO for 30 min. The gradients were deposited from vapor (as described in the text) for 5 min. The vapor source consisted of OTS : PO=1 : 10 mixtures. Reprinted with permission from [17], K. Efimenko and J. Genzer, Adv. Mater. 13, 1560 (2001). © 2001, Wiley-VCH.

substrates prepared with x ranging from 0 to 50%. In all cases, the exposure time of the PDMS to the UVO was 30 min, and the vapor diffusion time for a 1 : 10 OTS : PO mixture was 5 min. The data show that, as expected, the gradient steepness changes with changing x. Specifically, the span of gradient decreases from about 40 mm down to 15 mm as x increases from 0 to 50%. In all cases, the profiles exhibit excellent Fickian-type diffusion profiles [17].

5. APPLICATIONS OF GRADIENTS ON SUBSTRATES Continuous or discrete molecular gradients represent a chief tool for combinatorial chemistry and materials science [48, 49]. The combinatorial approach leads to rapid technological development with improved efficiency and lower research cost [50]. In addition, as documented below, the unique properties of the gradient substrates can also be utilized to study transport phenomena on surfaces.

5.1. Combinatorial Studies of Cell/Substrate Interactions Successful application of a biomaterial inside the body necessitates that it mimic the function of the body part where it will be implanted. This requires that the implants respond to protein adsorption, cellular adhesion, and inflammatory reactions in the same way as the body part does. Most of the above-mentioned functions are influenced by wettability of the biomaterial surface. Traditional experiments designed to study the effect of wettability suffered from the different surface chemistries of the various biomaterials used to achieve a wide behavioral spectrum. For example, it was often difficult to segregate the effect of wettability on the studied phenomenon from that of the surface

chemistry of the surface. This incertitude is minimized to a great extent by studying protein and cell adsorption on a molecular gradient surface, where the observed response can be attributed primarily to variation in wettability along the surface. In addition, it has been recognized that immobilization of proteins and peptides on the surface of a material offers a powerful method for probing cell response and migration, biodetection, and activity control. The need for such well-defined surfaces as well as the requirement of reducing the number of specimens necessary for these studies has stimulated the development of methodologies providing gradients of biological macromolecules. Several techniques listed previously have been utilized in these studies. A recent review summarizes the progress in the application of gradient substrates in studies of cellular interaction phenomena up until 1997 [38].

5.2. Thin-Film Behavior on Gradient Substrates There is a considerable need for understanding the structure, stability, and phase behavior of thin liquid and polymer films. Several studies have appeared that reported on utilizing combinatorial approaches to study the coalescence of droplets on chemically heterogeneous gradient substrates [51], order–disorder transition in grafted oligoalkanes on surfaces [29], phase separation in immiscible polymer blends [52], and interfacial behavior of block copolymer melts [53]. For example, Genzer and Kramer studied the phase separation in thin films of poly(ethylene propylene) (PEP) and its deuterated analog (dPEP) deposited on wettability gradient substrates prepared using the diffusion of alkanethiols in polysaccharide matrix [28]. By adjusting the composition of the alkanethiol solutions used to produce the wettability gradient, the surface energy (SAM ) was allowed to vary over a narrow window (from 30 to 21 mJ/m2 ). Elastic recoil detection was used to measure the volume fraction profiles of dPEP and PEP in the samples. In Figure 7, we plot a series of such volume fraction versus depth profiles of dPEP for various positions along the gradient substrate (open circles). It is evident that the air/mixture interface is always wet by the dPEP-rich phase. The situation at the mixture/SAM interface is more complex. For SAM < 25 mJ/m2 , the mixture/substrate interface is wet by a dPEP-rich phase. However, the thickness of this layer depends strongly on SAM and decreases with increasing SAM . At SAM = 256 mJ/m2 , the mixture/SAM interface is wet by the PEP-rich phase. The results in Figure 7 also show that, as the thickness of the dPEP phase at the mixture/substrate interface decreases, the thickness of the dPEP-rich phase at the air/mixture interface increases. This observation indicates that as SAM increases there is a redistribution of dPEP material from the mixture/SAM interface to the air/mixture interface. This pretransitional behavior was shown to originate from the longrange nature of the van der Waals interaction between layers and was predicted by a simple model that considered the dependence of the free energies of the two dPEP-rich layers at the surface and substrate interfaces on their thicknesses.

Molecular Gradient Nanoassemblies

0.6 0.4

c) SAM on Au

0.6 0.4 0.2

e)

f)

0.6 0.4 0.2 0.0 -0.4

SAM on Au

0.0 0.8

SAM on Au

d)

SAM on Au

Volume Fraction of dPEP

0.2 0.0 0.8

SAM on Au

b)

0.0

0.4

0.8

1.2-0.4

0.0

0.4

0.8

1.2

Depth / L

5.4. Molecular Gradients as Two-Dimensional Templates Gradient substrates have also been utilized as molecular templates for controlling the spatial distribution of nonpolymeric objects. Plummer and Bohn reported on electrochemically generating a gradient of amino-terminated thiol-based self-assembled monolayer on a gold-covered substrate [58]. To produce particle gradients, Plummer and Bohn attached carboxylic acid–modified, fluorescently doped polystyrene nanospheres (diameter of 200 nm) to the amino termini of the gradient SAM. Bhat and co-workers prepared assemblies of 17-nm gold nanoparticles with continuous gradients in number density on flat silica-covered substrates [59] (Fig. 8). Their methodology consisted of first forming a one-dimensional molecular gradient of amino groups ( NH2 ) on the substrate by vapor diffusion of amineterminated silane molecules, followed by attachment of gold nanoparticles to the NH2 functional groups by immersing the substrate in a colloidal gold solution. Experiments

(x=4)

(x=15)

5.3. Motion of Liquids on Gradient Substrates Chemical gradients are capable of transporting materials in a directional manner and are responsible for driving many important biological and physical processes [38]. Initial empirical observations have evolved into deliberate efforts to direct liquid motion along chemical gradients [54]. It has long been known that a continuous liquid film can spontaneously break into droplets that move freely over surfaces without application of an obvious external force. For example, the formation of wine drops from a continuous liquid film spreading over the wineglass surface is driven by the change in surface tension caused by the evaporation of alcohol. Variations in surface tension and the resulting changes in wetting behavior of the liquid by composition or temperature gradient were studied and explained over 100 years ago and are associated with the name of the Italian physicist Carlo Marangoni [55]. Motion due to chemical gradients on the substrate was demonstrated by Chaudhury and Whitesides [16] with droplets of water moving on a surface of varying hydrophobicity created by coating a silicon wafer partially with n-decyl trichlorosilane (DTS). A drop of water moved from the hydrophobic end to the hydrophilic end of the wafer, but only very slowly and only over a distance on the order of 1 mm. Very recently, much higher drop speeds

(x=25)

(x=29)

(x=30)

400

APTES deposition time 1.0 3 mins 5 mins 0.8

300

0.6

200

0.4

100

0.2

500

0 0

5

10

15

20

25

30

0.0 35

PEY NEXAFS intensity from N-H (a.u.)

2

Figure 7. Volume fraction profiles of deuterated poly(ethylene propylene) (dPEP) in PEP/dPEP mixtures measured by elastic recoil detection (ERD) (open circles) for samples cast on substrates with SAM equal to (a) 20.5, (b) 21.2, (c) 21.7, (d) 22.3, (e) 23.3, and (f) 25.6 mJ/m2 and annealed at 41  C for 2 weeks. The dashed and solid lines denote the actual dPEP volume fraction profiles and the volume fractions corrected for the finite ERD resolution (ca. 90 nm), respectively. The depth coordinate has been normalized by the total film thickness, L. Reprinted with permission from [52], J. Genzer and E. J. Kramer, Europhys. Lett. 44, 180 (1998). © 1998, EDP Sciences.

have been observed for small water droplets formed by condensation of steam onto a gradient surface [56] and droplets on vibrating gradient surfaces [57].

Particle number density (particles/µm )

a) SAM on Au

0.8

671

Distance from left edge of the substrate, x (mm)

Figure 8. (Upper panel) Scanning force microscopy images of gold nanoparticles (diameter ≈ 7 nm) adsorbed along a substrate prepared by evaporating a (3-aminopropyl) triethoxysilane (APTES)/paraffin oil (PO) mixture (50/50 w/w) for 5 min followed by immersion in colloidal gold solution (pH ≈ 6.5) for 24 h (edge of each image = 1
m). (Lower panel) Particle number density profile (left) for two gradients prepared by evaporating APTES/PO mixtures for 3 ( ) and 5 (
) min. The data points represent an average from three transverse scans along the gradient taken at the center of the sample (y = 0 mm) and y = −3 mm, and y = +3 mm. The line represents the partial electron yield (PEY) nearedge X-ray absorption fine structure (NEXAFS) profile (right) of N–H bonds from an ATEPS gradient prepared by evaporating an APTES/PO mixture for 5 min. The area around the PEY NEXAFS line denotes the measurement uncertainty (based on nine line scans along the gradient taken between −3 mm and +3 mm from the center of the sample). Reprinted with permission from [59], R. R. Bhat et al., Langmuir 18, 5640 (2002). © 2002, American Chemical Society.

Molecular Gradient Nanoassemblies

672

6. EXTENSION OF TWO-DIMENSIONAL GRADIENTS TO THREE DIMENSIONS Recently, it has been recognized that molecular gradients can serve as useful templates for creating three-dimensional structures. For example, Lee and co-workers utilized the corona discharge method to produce a molecular gradient of radicals on the surface of poly(ethylene). This gradient surface was then used as a template for “grafting from” radical polymerization of poly(acrylic acid) [60] and poly(ethylene oxide) [61] with gradual variation of grafting densities. Wu and co-workers recently prepared substrates with a gradient variation of grafting densities on silica substrates [62, 63]. A gradient of 1-trichlorosilyl-2(m/p-chloromethylphenyl) ethane (CMPE), the polymerization initiator, was formed on the surface using the vapor deposition technique, and the unexposed regions on the substrate containing unreacted OH functionalities were treated with OTS in order to minimize any physisorption of the monomer and/or the polymer formed in solution on the parts of the substrate that do not contain the CMPE– SAM. NEXAFS was utilized to measure the concentration of the CMPE along the SAM gradient. The concentration of CMPE in the sample decreased as one moved from the CMPE side of the sample toward the OTS–SAM; the functional form closely resembled that of a diffusion-like profile (Fig. 9). Experiments using variable-angle spectroscopic ellipsometry (VASE) confirmed that only a single monolayer was formed on the substrate. Monodisperse poly(acryl amide) (PAAm) chains with gradual variation in grafting densities were synthesized by the “grafting from” reaction of acryl amide using atom transfer radical polymerization (ATRP), as described earlier [64–66]. VASE was used to measure the thickness of the dry polymer film, h, as a function of the position on the substrate. Because the polymers grafted on the substrate have all roughly the same degree of

-2

PAAm brush grafting density (nm ) 0.1 0.05 0.01 0.005 0.15

H (nm)

25

20

h (nm)

15 CMPE density (a.u.)

using scanning force microscopy revealed that the number density of nanoparticles on the substrate varied continuously as a function of the position on the substrate. NEXAFS studies confirmed that the nanoparticle number density gradient was closely correlated with the concentration gradient of NH2 groups anchored to the substrate. Bhat and co-workers demonstrated that the number density of nanoparticles within the gradient and the length of the gradient can be tuned by controlling the vapor diffusion of the silane molecules. In addition, this simple methodology can be further extended to create double gradients, thus producing “a valley in nanoparticle concentration.” The adhesive molecular template can be modified to attract different kinds of particles for different applications, all of them arranged in a gradient pattern. The ability to vary and control the concentration of captured particles allows one to devise sensors, filters, and so on. Some components of fluids, for example, could pass through the gaps in the lessconcentrated part of the particle gradient, but be blocked by the thicker concentration. Such filters could also be tailored to detect or capture harmful viruses or toxins. The controlled variation in distribution of particles also allows rapid testing of potential catalysts—always in demand by industry.

4 2 0

0

5

10

15

20

Position on the substrate (mm) Figure 9. Dry (h, open symbols) and wet (H , closed symbols) thickness of the PAAm brush and the CMPE concentration (solid line) as a function of the position on the substrate. Reprinted with permission from [63], T. Wu et al., J. Am. Chem. Soc. 124, 9394 (2002). © 2002, American Chemical Society.

polymerization, the variation of the polymer film thickness can be attributed to the difference in the density, , of the CMPE grafting points on the substrate. The data in Figure 9 (for CMPE : PO = 1 : 1) reveal that h decreases gradually as one moves across the substrate starting at the CMPE edge. Note that the concentration profile of the polymer follows that of the initiator (solid line in Fig. 9). The substrates with the grafted PAAm were placed into a solution cell that was filled with deionized (DI) water (pH ≈ 7), a good solvent for PAAm, and incubated for at least 5 h. The wet thickness of PAAm-grafted polymer in DI water, H , was measured using VASE. The values of H for samples prepared on CMPE : PO = 1 : 1 gradients are shown in the top part of Figure 9. The data show that H decreases as one traverses across the substrate starting at the CMPE side. In Figure 10, we plot the wet polymer thickness as a function of the PAAm grafting density on the substrate. The data in Figure 10 reveal that, at low , H is independent of the grafting density. Hence, the chains are in the mushroom regime. At high polymer grafting densities, H increases with increasing , indicating the brush behavior. The crossover between the two regimes occurred at ≈ 0065 nm−2 . By fitting the data in the brush regime to H ∼ N n , we get n equal to 037 ± 004 (CMPE : PO = 1 : 1), 039 ± 005 (CMPE : PO = 1 : 2), and 040 ± 006 (CMPE : PO = 1 : 5). These results are in close agreement with the predicted value of n = 1/3 [67, 68]. We previously demonstrated that wettability measurements provide quick and reliable means of probing the physicochemical properties of gradient substrates. In Figure 11, we plot the negative cosine of DIW as a function of the grafting density of PAAm on substrates comprising CMPE : PO = 1 : 1 (squares) and CMPE : PO = 1 : 5 (triangles) gradients. As anticipated, the data collapse on a single master curve. A close inspection of the results in Figure 11 reveals that the data can be divided into three distinct regions. For > 01 nm−2 , the chains are

Molecular Gradient Nanoassemblies

673 We speculate that the small difference between the widths of the mushroom-to-brush region inferred from both types of experiments is likely associated with the inaccuracy in H, which was obtained indirectly by the model fitting of the VASE data.

3.5 30

CMPE:PO ratio 1:1 1:2 1:5

3.0

2.0 H~σ H~σ

10

H/Rg

H (nm)

2.5

1/3

0

1.5

mushroom regime

brush regime

0.01

1.0

0.1 -2

PAAm brush grafting density (nm ) Figure 10. Wet thickness of the PAAm brush (H ) as a function of the PAAm brush grafting density. Results for three different ratios of CMPE : PO are shown: 1 : 1 (
), 1 : 2 (), and 1 : 5 (⊞). Reprinted with permission from [63], T. Wu et al., J. Am. Chem. Soc. 124, 9394 (2002). © 2002, American Chemical Society.

expected to be in a brush regime—the wettabilities are close to that of pure PAAm [− cosDIW  ≈ −079]. For < 002 nm−2 , the PAAm chains form mushroom conformations on the substrate. In this regime, the wettabilities change slightly because the distance between the chains also changes, although they are already loosely separated on the substrate. At grafting densities 0.02 nm−2 < < 01 nm−2 , the slope of − cosDIW ) changes rather rapidly. The data in Figure 11 show that the position of the mushroom-tobrush crossover determined using the wettability approach is in accord with the ellipsometric measurements (the transition location was established to be at ≈ 0065 nm−2 ). However, in the former case, the transition region extends over almost one order of magnitude in , which is broader than the transition region predicted by the H versus data. 0.0 -0.1

-cos(θDIW)

-0.2

-2

σ=0.065 nm

7. SUMMARY We have reviewed various methodologies leading to the fabrication of molecular and macromolecular gradients on material substrates. Several examples were referenced documenting that wettability gradients can be utilized in combinatorial studies of bioadsorption, phase behavior in thin liquid and polymer films, templating, and material transport on surfaces. The dual nature of molecular gradients (discrete on molecular scales, continuous on meso scales) endows them with unique properties that can and will be further exploited in the synthesis of novel materials, generating combinatorial libraries, which, in turn, will find use in the discovery of new material phenomena. Utilizing molecular gradients will provide simple means of mimicking molecular and biomolecular transport. These structures are thus expected to provide a new paradigm for advancing the fundamental understanding of the structure–property relationship of material behavior.

GLOSSARY Macromolecular gradient Assembly of surface-anchored polymers with a position-dependent gradual variation of length, and/or grafting density, and/or composition on the substrate. Molecular gradient Array of surface-bound self-assembled oligomers with a position-dependent gradual variation of grafting density on the substrate. Near-edge X-ray absorption fine structure spectroscopy (NEXAFS) Provides information about bond population density in and orientation of surface-adsorbed molecules. Organosilane Chloro- or alkoxy-terminated molecule, typically alkane or alkane-based, capable of self-assembly on oxide-covered surfaces. Self-assembled monolayer Organized array of amphiphiles chemically bound to a substrate.

-0.3 -0.4

ACKNOWLEDGMENTS

-0.5

The authors acknowledge the generous financial support from various sources, including the National Science Foundation (Grants DMR98-75256 and CTS-02-09403), the Camille Dreyfus Foundation, the 3M Company, and NACE International. The NEXAFS experiments were carried out at the National Synchrotron Light Source at the Brookhaven National Laboratory, which is supported by the U.S. Department of Energy, Division of Materials Sciences and Division of Chemical Sciences. We also thank our collaborators, Drs. Petr Vlˇcek and Vladimír Šubr (both from the Institute of Macromolecular Chemistry in Prague) and Drs. William Wallace and Daniel Fischer (both from NIST) for their invaluable assistance during various portions of the research.

-0.6 -0.7 -0.8

CMPE:PO ratio 1:1 1:5

1E-3 0.001

0.01

0.1 -2

PAAm grafting density (nm ) Figure 11. Negative of cosine of the contact angle of DI water as a function of the PAAm grafting density on the substrate for samples prepared on substrates containing the initiator gradients made of CMPE : OTS mixtures (w/w) 1 : 1 (squares) and 1 : 5 (triangles). The lines are meant to guide the eyes.

Molecular Gradient Nanoassemblies

674

APPENDIX: CHEMICAL FORMULAS

Abbreviation

Compound

APTES

Aminopropyl triethoxysilane

Chemical formula

O O

NH2

Si O

O BP

Benzophenone

CMPE

1-Trichlorosilyl-2-(m/p-chloromethylphenyl) ethane

Cl Cl

CH2Cl

Si Cl

Cl DDS

Dichlorodimethyl silane

DIM

Diiodomethane

Si Cl

I

I

Cl DTS

n-Decyl trichlorosilane

Cl

Si Cl

F m-F8H2

d-F8H2

1H,1H ,2H,2H-Perfluorodecyl dimethylchlorosilane

Cl

Si

F

F

Cl

1H,1H ,2H,2H-Perfluorodecyl methyldichlorosilane

Si

t-F8H2

1H,1H ,2H,2H-Perfluorodecyl trichlorosilane

Cl Cl

Si Cl

F

F

F F

F

F

F

F

F

F

F

F

F

Cl

F

F

F F

F

F

F

F

F F

F F F F

F F

F F F F

F F

F F F F

F

F

F

F

F

F F

F

F

O MPA

Mercapto propionic acid

OH

HS

O NHS

N -Hydroxysuccinimide ester

O O N O

OT

n-Octanethiol

HS continued

Molecular Gradient Nanoassemblies

675

Abbreviation

Compound

OTS

n-Octyl trichlorosilane

Chemical formula

Cl Cl

Si Cl

PAAm

*

n

*

Poly(acryl amide)

H2N PDMS

Poly(dimethyl siloxane)

Si

PEP

Poly(ethylene propylene)

PHM

Poly(hydroxyl methylene)

n

O

*

*

n

*

*

*

*

n OH OH

PMMA

n

*

Poly(methyl methacrylate)

O

O

n

* PS

*

Polystyrene

* PVCa

*

Poly(vinylene carbonate)

n

*

O O O

TCE

Cl

Trichloroethylene

Cl Cl

TEG

Tetraethylene glycol

XYL

Xylene

REFERENCES 1. R. P. Feynman, Eng. Sci. 23, 22 (1960). A copy of Feynman’s famous talk is also available on the Internet at http://www.zyvex. com/nanotech/feynman.html. 2. “Engineering a Smaller World: From Atomic Manipulation to Microfabrication,” Special issue of Science 254, 1277 (1991); C. N. R. Rao and A. K. Cheetham, J. Mater. Chem. 11, 2887 (2001). 3. H. Wohltjen and A. W. Snow, Anal. Chem. 70, 2856 (1998). 4. B. Oregan and M. Gratzel, Nature 353, 737 (1991). 5. S. Nie and R. S. Emory, Science 275, 1102 (1997). 6. V. L. Colvin, M. C. Schlamp, and A. P. Alivisatos, Nature 370, 354 (1994).

HO

O

4

H

7. Y. Xia and G. M. Whitesides, Angew. Chem., Int. Ed. Engl. 37, 550 (1998); Y. Xia, J. A. Rogers, K. E. Paul, and G. M. Whitesides, Chem. Rev. 99, 1823 (1999). 8. A. Ulman, “An Introduction to Ultrathin Organic Films from Langmuir–Blodgett to Self Assembly.” Academic Press, New York, 1991. 9. M. Husseman, D. Mecerreyes, C. J. Hawker, J. L. Hedrick, R. Shah, and N. L. Abbott, Angew. Chem., Int. Ed. Engl. 38, 647 (1999). 10. R. Shah, D. Mecerreyes, M. Husemann, I. Rees, N. L. Abbott, C. J. Hawker, and J. L. Hedrick, Macromolecules 33, 597 (2000). 11. N. L. Jeon, I. S. Choi, G. M. Whitesides, N. Y. Kim, P. E. Laibinis, Y. Harada, K. R. Finnie, G. S. Girolami, and R. G. Nuzzo,

676

12. 13. 14. 15. 16. 17. 18. 19. 20.

21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32.

33. 34. 35. 36. 37. 38. 39. 40.

Appl. Phys. Lett. 75, 4201 (1999); N. Kim, N. L. Jeon, I. S. Choi, S. Takami, Y. Harada, K. R. Finnie, G. S. Girolami, R. G. Nuzzo, G. M. Whitesides, and P. E. Laibinis, Macromolecules 33, 2793 (2000). B. de Boer, H. K. Simon, M. P. L. Werts, E. W. van der Vegte, and G. Hadziioannou, Macromolecules 33, 349 (2000). P. Ghosh, W. M. Lackowski, and R. M. Crooks, Macromolecules 34, 1230 (2001). D. M. Jones and W. T. S. Huck, Adv. Mater. 13, 1256 (2001). J. Hyun and A. Chilkoti, Macromolecules 34, 5644 (2001). M. K. Chaudhury and G. M. Whitesides, Science 256, 1539 (1992). K. Efimenko and J. Genzer, Adv. Mater. 13, 1560 (2001). R. R. Fuierer, R. L. Carroll, D. L. Feldheim, and C. B. Gorman, Adv. Mater. 14, 154 (2002). J. C. Meredith, A. Karim, and E. J. Amis, MRS Bull. 27, 330 (2002). J. Genzer, in “Encyclopedia of Materials Science” (K. H. J. Buschow, R. W. Cahn, M. C. Flemings, B. Ilschner, E. J. Kramer, and S. Mahajan, Eds.). Elsevier, Oxford, 2002. S. B. Carter, Nature 208, 1183 (1965). H. Elwing, S. Welin, A. Askendal, U. Nilsson, and I. Lundström, J. Colloid Interface Sci. 119, 203 (1987). C. G. Gölander, K. Caldwell, and Y.-S. Lin, Colloids Surf. 42, 165 (1989). T. Ueda-Yukoshi and T. Matsuda, Langmuir 11, 4135 (1995). W. G. Pitt, J. Colloid Interface Sci. 133, 223 (1989). J. H. Lee, H. G. Kim, G. S. Khang, H. B. Lee, and M. S. Jhon, J. Colloid Interface Sci. 151, 563 (1992). S. V. Roberson, A. J. Fahey, A. Sehgal, and A. Karim, Appl. Surf. Sci. 9427, 1 (2002). B. Liedberg and P. Tengvall, Langmuir 11, 3921 (1995). M. Lestelius, I. Enquist, P. Tengvall, M. K. Chaudhury, and B. Liedberg, Colloids Surf., B 15, 57 (1999). R. H. Terrill, K. M. Balss, Y. Zhang, and P. W. Bohn, J. Am. Chem. Soc. 122, 988 (2000). M. B. Wijesundara, E. Fuoco, and L. Hanley, Langmuir 17, 5721 (2001). C. L. Hypolite, T. L. McLernon, D. N. Adams, K. E. Chapman, C. B. Herbert, C. C. Huang, M. D. Distefano, and W.-S. Hu, Bioconjug. Chem. 8, 658 (1997). I. Caelen, H. Gao, and H. Sigrist, Langmuir 18, 2463 (2002). I. Caelen, A. Bernard, D. Juncker, B. Michel, H. Heinzelmann, and E. Delamarche, Langmuir 16, 9125 (2000). N. L. Jeon, S. K. W. Dertinger, D. T. Chiu, I. S. Choi, A. Stroock, and G. M. Whitesides, Langmuir 16, 8311 (2000). S. K. W. Dertinger, D. T. Chiu, N. L. Jeon, and G. M. Whitesides, Anal. Chem. 73, 1240 (2001). D. C. Duffy, J. C. McDonald, O. J. A. Schueller, and G. M. Whitesides, Anal. Chem. 70, 4974 (1998). T. G. Ruardy, J. M. Schakenraad, H. C. van der Mei, and H. J. Busscher, Surf. Sci. Rep. 29, 1 (1997). J. Stöhr, “NEXAFS Spectroscopy.” Springer-Verlag, Berlin, 1992. J. Genzer, D. A. Fischer, and K. Efimenko, Appl. Phys. Lett., 82, 266 (2003).

Molecular Gradient Nanoassemblies 41. The NEXAFS experiments were carried out at the NIST/Dow Soft X-Ray Materials Characterization Facility at the National Synchrotron Light Source at Brookhaven National Laboratory. For detailed information about the NIST/Dow Soft X-ray Materials Characterization Facility at NSLS BNL, see http://nslsweb.nsls. bnl.gov/nsls/pubs/newsletters/96-nov.pdf. 42. K. Efimenko and J. Genzer, unpublished data. 43. J. Genzer, E. Sivaniah, E. J. Kramer, J. Wang, H. Körner, M. Xiang, K. Char, C. K. Ober, B. M. DeKoven, R. A. Bubeck, M. K. Chaudhury, S. Sambasivan, and D. A. Fischer, Macromolecules 33, 1882 (2000). 44. R. Banga, J. Yarwood, A. M. Morgan, B. Evans, and J. Kells, Langmuir 11, 4393 (1995); B. C. Bunker, R. W. Carpick, R. A. Assink, M. L. Thomas, M. G. Hankins, J. A. Voight, D. Sipola, M. P. de Boer, and G. L. Gulley, Langmuir 16, 7742 (2000). 45. J. Genzer, D. A. Fischer, and K. Efimenko, Langmuir, 18, 9307 (2002). 46. J. Genzer and K. Efimenko, Science 290, 2130 (2000). 47. K. Efimenko, W. E. Wallace, and J. Genzer, J. Colloid Interface Sci. 254, 306 (2002). 48. R. B. van Dover, L. F. Scheemeyer, and R. M. Fleming, Nature 392, 162 (1998). 49. B. Jandeleit, D. J. Schaefer, T. S. Powers, H. W. Turner, and W. H. Weinberg, Angew. Chem., Int. Ed. Engl. 38, 2494 (1999). 50. E. J. Amis, X.-D. Xiang, and J.-C. Zhao, MRS Bull. 27, 295 (2002). 51. H. Zhao and D. Beysens, Langmuir 11, 627 (1995). 52. J. Genzer and E. J. Kramer, Europhys. Lett. 44, 180 (1998). 53. A. Karim, personal communication. 54. C. D. Bain, Chemphyschem 2, 580 (2001). 55. L. E. Scriven and C. V. Sternling, Nature 187, 186 (1960). 56. S. Daniel, M. K. Chaudhury, and J. C. Chen, Science 291, 633 (2001). 57. S. Daniel and M. K. Chaudhury, Langmuir 18, 3404 (2002). 58. S. T. Plummer and P. W. Bohn, Langmuir 18, 4142 (2002). 59. R. R. Bhat, D. A. Fischer, and J. Genzer, Langmuir 18, 5640 (2002). 60. H. G. Kim, J. L. Lee, H. B. Lee, and M. S. Jhon, J. Colloid Interface Sci. 157, 82 (1993). 61. B. J. Jeong, J. H. Lee, and H. B. Lee, J. Colloid Interface Sci. 178, 757 (1996). 62. J. Genzer, T. Wu, and K. Efimenko, Mat. Res. Soc. Symp. Proc. 705, Y8.8.1 (2002). 63. T. Wu, K. Efimenko, and J. Genzer, J. Am. Chem. Soc. 124, 9394 (2002). 64. X. Huang, L. J. Doneski, and M. J. Wirth, CHEMTECH 19 (1998); Anal. Chem. 70, 4023 (1998). 65. X. Huang and M. J. Wirth, Macromolecules 32, 1694 (1999). 66. T. Wu, K. Efimenko, and J. Genzer, Macromolecules 34, 684 (2001). 67. M. S. Kent, Macromol. Rapid Commun. 21, 243 (2000) and references therein. 68. J. F. Douglas, M. S. Kent, S. K. Satija, and A. Karim, in “Encyclopedia of Materials: Science and Technology,” pp. 7218–7223. Elsevier, Amsterdam, 2001.

Encyclopedia of Nanoscience and Nanotechnology

www.aspbs.com/enn

Molecular Logic Gates Françisco M. Raymo, Silvia Giordani University of Miami, Coral Gables, Florida, USA

CONTENTS 1. 2. 3. 4. 5. 6. 7. 8.

Miniaturization of Electronic Devices Logic Gates Molecular Switches Molecular NOT Gates Molecular OR Gates Molecular AND Gates Combinational Logic with Molecular Systems Combinational Logic with Supramolecular Systems 9. Combinational and Sequential Logic with Multiple Molecular Components 10. Solid-State Molecular Logic Gates 11. Conclusions Glossary References

1. MINIATURIZATION OF ELECTRONIC DEVICES The advent of integrated circuits has improved dramatically our ability to communicate, process, and store information [1]. These arrays of tiny electronic devices can manipulate large volumes of data at amazing speeds. Their impact on practical applications has been and continues to be revolutionary. Not only do they rule our computers; they also control our cars, watches, telephones, faxes, CD players, washing machines, and the many other electronic gadgets that have become part of our everyday lives. The secret of their success has been the continuous miniaturization of their functional components, which allows manufacturers to cram increasing numbers of them into single chips [2]. For example, the number of transistors in microprocessors has increased exponentially over the past three decades [3]. The Intel 4004 processor, built in 1971, had only 2,300 transistors [4]. The Intel Pentium 4 processor, fabricated in 2000, had 42,000,000 transistors. The dramatic raise in the number of components has translated into a huge enhancement in speed from 105 to 109 Hz. This amazing

ISBN: 1-58883-061-6/$35.00 Copyright © 2004 by American Scientific Publishers All rights of reproduction in any form reserved.

improvement in performance is mainly a result of effective miniaturization. Miniaturization has progressed at a tremendous pace since the early days of integrated circuits [5]. Transistors continue to be scaled down at an exponential rate and their number on a chip doubles approximately every 18 months [3, 5]. Unfortunately, the fabrication of remarkably small features is inherently difficult, and present electronic devices have reached dimensions that are not too far from the nanoscale [3]. Shrinking their sizes below 100 nm is expected to be a major technological challenge. Cost-effective miniaturization might not persist below this limit. Furthermore, the bulk properties of semiconductors, which are the constituent materials of most electronic components, vanish at the nanoscale [6–9]. It follows that the operating principles of present microscale devices cannot survive in potential nanoscale counterparts. Alternative design criteria, materials, and fabrication procedures must be devised.

2. LOGIC GATES Logic gates are the fundamental components of digital circuits [10]. These electronic devices process binary data encoded in electrical signals. More precisely, they transduce electrical inputs into electrical outputs according to predefined logic functions. The three basic logic gates and their truth tables are illustrated in Figure 1. The NOT gate converts one input (I) into one output (O). The output is 1 when the input is 0. The output is 0 when the input is 1. The AND and OR gates convert two inputs (I1 and I2) into a single output (O). In the AND gate, the output is 1 only when both inputs are 1. It is 0 in the other three cases. In the OR gate, the output is 0 only when both inputs are 0. It is 1 in the other three cases. Networks of interconnected logic gates can be assembled by contacting their input and output terminals [10]. The logic functions of the resulting arrays are a combination of the operations executed by the individual gates. It follows that digital circuits able to perform specific functions can be designed by choosing the right number, type, and configuration of their constituent gates. This modular approach offers access to an unlimited number of combinational and sequential logic circuits and provides the opportunity to implement all conceivable logic functions.

Encyclopedia of Nanoscience and Nanotechnology Edited by H. S. Nalwa Volume 5: Pages (677–692)

678

Molecular Logic Gates I1

O

I2

AND

O

I

I1 I2

O

NOT

OR

I1 I2 O

I

O

I1 I2 O

0

0

0

0

1

0

0

0

0

1

0

1

0

0

1

1

1

0

0

1

0

1

1

1

1

1

1

1

Figure 1. The three basic logic gates and their truth tables [10].

The signals that enter the input terminals of logic circuits, propagate across the network of gates, and leave the output terminals are electrical [10]. Binary digits are encoded in them by the application of simple logic conventions. Arbitrary logic thresholds are established first. Then, in a positive logic convention, binary 0 and 1 are assigned to the signals that are below and above, respectively, the fixed threshold. Alternatively, the assignment can be reversed in a negative logic convention. Relying on these simple considerations, complex strings of binary digits can be encoded in the electrical signals elaborated by interconnected logic gates.

4. MOLECULAR NOT GATES A NOT operator (Fig. 1) converts an input signal into an output signal [10]. In particular, the output is high when the input is low and vice versa. Numerous organic molecules satisfy this relatively simple signal transduction protocol and, therefore, can execute NOT operations. For example, a fluorescent molecule that loses its ability to emit light upon protonation is, indeed, a molecular NOT gate. The fluorescence is high when the concentration of H+ is low. The fluorescence is low when the concentration of H+ is high. If a positive logic convention (low = 0, high = 1) is applied to the optical output and the chemical input, this signal transduction translates into the truth table of the NOT operator (Fig. 1). In 1993, de Silva recognized the analogy between NOT gates and pH-sensitive fluorophores [30]. In a seminal article, he demonstrated that the pyrazole derivative 1 (Fig. 2) emits only when the concentration of H+ is low. Photoinduced electron transfer from the central pyrazoline unit to the pendant benzoic acid quenches the fluorescence of the protonated form. Thus, a change in the concentration of H+ from a low to a high value switches the emission intensity from a high to a low value. The inverse relation between the chemical input (concentration of H+ ) and the optical output (fluorescence intensity) corresponds to a NOT operation. A related example of a molecular NOT gate is the anthracene derivative 2 (Fig. 2) [31]. This molecular switch

3. MOLECULAR SWITCHES Organic molecules are emerging as possible building blocks for innovative information storage, processing, and communication devices [11–14]. The tremendous power of modern chemical synthesis offers easy access to billions of potential molecular building blocks with designed properties and nanometer-sized dimensions [15]. Furthermore, organic molecules can be engineered to produce detectable outputs in response to input stimulations [16]. Indeed, simple binary switching operations can be reproduced at the molecular level with these chemical systems, which are commonly referred to as molecular switches [17]. The obvious analogy between logic gates and molecular switches continues to stimulate the design of chemical systems able to execute AND, NOT, and OR operations as well as more complex logic functions [18–22]. One of the major challenges in the implementation of molecular logic gates is the identification of viable procedures to address them and to detect their response. In the case of conventional logic gates, electrical wires carry the information that reaches their input terminals and departs from their output terminals. However, the direct connection of individual molecules or even collections of them to electrical wires is not an easy task [23–29]. Fortunately, molecules can be stimulated effectively in solution phase with chemical, optical, or redox stimulations [16–18]. Their response can be probed with conventional spectroscopic and electrochemical techniques. As result, most of the work on molecular logic gates has focused so far on the analysis of the logic behavior of molecular switches dissolved in organic or aqueous phases [18]. In this chapter we illustrate the operating principles and properties of the numerous molecular logic gates that have been developed in less than a decade.

−

N

NH

N

O2 C

N H

N H

N H

NH2

2

1

O

− O

O

O − O

O

N

N

O O O

N

O

OH

Me

3

O−

4

N

O O−

O N

O

O

O

O

N

N

N

COO−

NC R

N N

5

CN

6

SO2Me

N

7

R

Figure 2. Molecular NOT and OR gates based on chemical inputs and optical outputs [30–34].

679

Molecular Logic Gates

is extremely versatile. Depending upon the choice of pH and metal ions, different logic functions can be implemented. In particular, NOT operations can be executed at a pH of 4.5. Under these conditions, the anthracene fluorophore emits. The oligoamino arm appended to the fluorophore, however, can chelate metal ions, forming stable complexes. The bound metal center affects the emissive response of the anthracene fragment. In fact, the addition of Cu2+ ions produces a drastic decrease in the fluorescence intensity. Once again, the optical output (fluorescence intensity) of the molecular switch is high only when its chemical input (concentration of Cu2+ ) is NOT high. It is important to note that the inverse relation between the input and output of a NOT gate is not limited to pH-induced fluorescence quenching. Similar correlations

can be found between chemical inputs and redox outputs, for example. It follows that a careful search in the chemical literature would almost certainly reveal hundreds of molecules capable of similar signal transductions. Most of them, however, have not been recognized or described as molecular NOT gates.

5. MOLECULAR OR GATES An OR operator (Fig. 1) combines two inputs into a single output [10]. To reproduce this logic function at the molecular level, compounds able to respond to two input signals must be identified. In particular, they have to produce a detectable output when one or both inputs are applied. The compounds 3–7 (Table 1, Fig. 2) satisfy these conditions

Table 1. Molecular and supramolecular logic gates with one or two input terminals and a single output terminal.a Logic NOT OR

AND

Compound

Input 1 (I1)

Input 2 (I2)

Output (O)

1 2

+

Ref.

H Cu2+

— —

Fluorescence Fluorescence

[30] [31]

2 3 4 5 6 7 8 9 10 11 12

Cd2+ K+ Ca2+ Ca2+ Ca2+ Cu2+ H+ H+ H+ H+ H+

Zn2+ Rb+ Mg2+ Mg2+ Mg2+ Ni2+ Na+ K+ or Na+ Na+ Na+ Ca2+

Fluorescence Fluorescence Fluorescence Fluorescence Fluorescence Fluorescence Fluorescence Fluorescence Fluorescence Fluorescence Fluorescence

[31] [30] [32] [32] [32] [33, 34] [30] [35] [35] [36] [37]

b

13

NAND NOR

XOR

XNOR INH

R-NH

+b 3

R1

R2 Fluorescence

[38]

OH OH SCN− SCN− Light Light Light Voltage Light Light Light

Fluorescence Fluorescence Absorbance Fluorescence Absorbance Current Absorbance Absorbance Fluorescence

[39] [39] [40] [41, 42] [43, 44] [45] [46] [47] [48]

14 15 16 18 20 22 23 24 25

Ba2+ or Ca2+ Ba2+ or Ca2+ Cs+ , K+ , Li+ , Na+ , or Rb+ H+ H+ H+ Magnetic field Light Light

26 27 2 28 29 30

H+ dAMPd Cu2+ H+ H+ H+

ATPc dTMPd Ni2+ O2 Zn2+ Hg2+

Fluorescence Fluorescence Fluorescence Luminescence Fluorescence Fluorescence

[49] [50] [31] [51] [52] [52]

Ca2+ Butylamine Light Ca2+ Voltage

H+ H+ Light H+ Voltage

Transmittance Fluorescence Absorbance Absorbance Absorbance

[37] [59] [61] [37] [60]

O2

Luminescence

[53, 54]

31 39 • 40 43 + 45 31 41 • 42 32

H+

a The inputs and outputs are chemical, electrical, magnetic, or optical signals. The chemical inputs are the concentrations of the species listed. The electrical and magnetic inputs/outputs are the magnitudes of the parameters indicated. The optical inputs/outputs are the light intensities, the fluorescence intensities, or the magnitude of the parameters listed. b The behavior of 13 was studied in the presence of d-glucosamine. However, distinct alkylammonium and diol components could be employed to reproduce the same signal transduction. c ATP stands for adenosine triphosphate. d dAMP and dTMP stand for deoxyadenosine monophosphate and deoxythymidine monophosphate, respectively.

680 [30, 32–34]. They generate an optical output (fluorescence) in response to one or two chemical inputs (metal cations). In the absence of metal cations, photoinduced electron transfer from the tertiary amino groups to the anthracene appendages in 3, 4, and 7 and to the pyrazoline fragment in 5 and 6 quenches their fluorescence. After the complexation of a metal cation in the cryptands of 3 and 7 and in the carboxylate clefts of 4–6, the quenching process is suppressed and high fluorescence intensity is detected. It is important to note that each of these compounds responds to either one of two different metal cations. Thus, the fluorescence intensity is high when one OR the other metal cation is added. If a positive logic convention (low = 0, high = 1) is applied to the fluorescence intensity (optical output) and to the concentrations of the two metal cations (chemical inputs), the signal transduction of 3–7 translates into the truth table of the OR operator (Fig. 1). The anthracene derivative 2 (Table 1, Fig. 2) reproduces a NOT operation at a pH of 4.5 and an OR function at a pH of 10 [31]. Under basic conditions, photoinduced electron transfer from the oligoamino arm to the anthracene fluorophore quenches the emission. In the presence of Cd2+ and/or Zn2+ , the quenching efficiency of the amino groups is suppressed as a result of metal coordination. Thus, the behavior of this compound at a pH of 10 is equivalent to that of the molecular OR gates 3–7. In all cases, an optical output (fluorescence intensity) is controlled by two chemical inputs (concentrations of two metal cations) according to an OR function.

Molecular Logic Gates

O

O

O

R

O

O

N

O

O O

O

O

O

8 CN

O

O HO

− − O O

O

10

N

11

(HO)2B O

N

N

N O

N

Ph

R

OH

9

Et2N

O

N N

12

O

O O

NC

13 O

O

NC

N

OH

N

N

OH

N

O

14 1

O

OH +

O

15 2

18

O

H+ AND Light

n

O

O

19

O O

n

6. MOLECULAR AND GATES An AND operator (Fig. 1) combines two inputs into a single output [10]. Thus, molecules able to respond to two input signals must be designed to execute this particular logic function. In addition, the molecule has to produce a detectable output only when the two input stimulations are applied simultaneously. The compounds 8–12 (Table 1, Fig. 3) satisfy these conditions [30, 35–37]. They generate an optical output (fluorescence) only when two chemical inputs (H+ and metal cation) are applied simultaneously. In the absence of H+ , photoinduced electron transfer from their tertiary amino group to the anthracene fluorophore quenches the emission. In the absence of metal cations, photoinduced electron transfer from the benzocrown ether or tetracarboxylate cleft to the anthracene fluorophore quenches the emission. Thus, a high emission intensity (optical output) is observed only when the concentrations of H+ AND a metal cation (chemical inputs) are high. The fluorescence intensity is low in the other three cases. If a positive logic convention (low = 0, high = 1) is applied to the optical output and the two chemical inputs, this signal transduction translates into the truth table of the AND operator (Fig. 1). The compounds 13–15 (Table 1, Fig. 3) share similar operating principles with 8–12. They all convert two chemical inputs into an optical output according to an AND operation. In the case of 13, the two chemical inputs are the concentrations of an ammonium cation and a diol, and the optical output is the anthracene fluorescence [38]. Indeed, a high emission intensity is observed only after

O O O

O

O O

O

+M

O

HO O

N O

16

HO

O

M+ AND Light

O NO2

+N

NO2

O

−O

17

Figure 3. Molecular AND gates based on chemical and optical inputs and optical outputs [30, 35–42].

the complexation of an ammonium cation in the azacrown ether receptor AND the chelation of a diol by the boronic acid fragment. Under these conditions, the photoinduced electron transfer processes from the two tertiary amino groups to the anthracene fluorophores are suppressed. In the case of 14 and 15, the two chemical inputs are the concentrations of a metal cation (Ba2+ or Ca2+ ) and SCN− , and the optical output is the pyridoimidazopyrazine fluorescence [39]. Indeed, a low emission intensity is detected when the concentrations of Ba2+ or Ca2+ AND SCN− are high. Under these conditions, photoinduced electron transfer from the SCN− anion to the heteroaromatic fragment efficiently quenches the emission. If a positive logic convention (low = 0, high = 1) is applied to the chemical inputs and the optical output of 13 while a negative logic convention

681

Molecular Logic Gates i-Pr3Si NC

CN

O

Me2N

O

O

O

O

+

+

N

N

H+ AND Light

i-Pr3Si

20

i-Pr3Si

NC

+

N

CN

N

O

O

O

+

Me2HN

+

(low = 1, high = 0) is applied to the fluorescence outputs of 14 and 15, the signal transductions operated by 13–15 translate into the truth table of the AND operator (Fig. 1). The molecular AND gates 16, 18, and 20 combine chemical and optical inputs into an optical output (Table 1, Figs. 3 and 4). The chemical input of 16 is the concentration of a metal cation (Cs+ , K+ , Li+ , Na+ , or Rb+ ), and its optical input is the intensity of an ultraviolet pulse [40]. No significant changes in the absorption spectrum of 16 can be observed when one of the metal cations is added. Ultraviolet irradiation produces a colored merocyanine, which reisomerizes thermally to 16 in the absence of a metal cation. Instead, the irradiation of 16 in the presence of Cs+ , K+ , Li+ , Na+ , or Rb+ generates the complex 17, which is stabilized by the metal cation bound in the crown ether appendage. Under these conditions the photogenerated species does not reisomerize thermally, and a strong band is observed in the visible region of the absorption spectrum. Thus, the absorbance of this band (optical output) is high only when the concentration of a metal cation (chemical input) AND the intensity of the ultraviolet stimulation (optical input) are high. Similarly, the compound 18 can be operated with ultraviolet light (optical input) and H+ (chemical input) [41, 42]. The irradiation promotes a trans to cis isomerization. The resulting cis isomer reisomerizes thermally to the original form 18 under neutral conditions. However, it switches to the 4′ -hydroxyflavylium cation 19 in acidic media. This particular compound is fluorescent and emits (optical output) in the visible region. Thus, H+ AND ultraviolet light promote the interconversion of 18 into 19, producing an increase in the emission intensity. In a similar fashion, the compound 20 responds to H+ (chemical input) and visible light (optical input) [43, 44]. The irradiation promotes the ring opening of the dihydroazulene fragment at one end of the trans-tetraethynylethene core. The addition of H+ protonates the dimethylaniline fragment at the other end. Thus, the simultaneous application of the two inputs produces the compound 21, which has a strong absorption band at 500 nm (optical output). It follows that the absorbance at this particular wavelength is high only when the optical AND the chemical inputs are applied. In summary, the signal transductions operated by 16, 18, and 20 translate into the truth table of the AND operator (Fig. 1), if a positive logic convention (low = 0, high = 1) is applied to their inputs and outputs. The [2]catenane 22 is a unique example of a molecular AND gate able to transduce chemical and electrical inputs into an electrical output (Table 1, Fig. 4) [45]. Its macrocyclic polyether component encircles one of the two bipyridinium dications, as a result of cooperative electrostatic and charge-transfer terms. This co-conformation imposes distinct redox responses on the encircled and free bipyridinium dications. Indeed, the cyclic voltammogram shows four consecutive monoelectronic reduction processes. The first and second redox waves correspond to the reduction of the free and encircled, respectively, bipyridinium dications to the corresponding radical cations. The third and fourth redox waves are associated with the reduction of the free and encircled, respectively, radical cations to the corresponding neutral forms. These observations indicate that the macrocyclic polyether remains around the same

O

O

22

i-Pr3Si

21

N

N H

N NH

HN

H N

N

O

23

N

O

O

N

O

O

O

O N

N

N O

O

O

O N

N

O

O

24

Figure 4. Molecular AND gates based on chemical, electrical, magnetic, and optical inputs and electrical or optical outputs [43–48].

bipyridinium unit after the first reduction process. In the presence of H+ , however, the secondary amino group is protonated and the cyclic voltammogram shows only three reduction waves. The first and second waves correspond, once again, to the reduction of the free and encircled bipyridinium dications, respectively, to the corresponding radical cations. After these two reduction processes, the macrocyclic polyether shuttles from the encircled radical cation to the secondary alkylammonium cation. In the resulting coconformation, the two radical cations are identical and only one redox wave is observed for their simultaneous reduction to the corresponding neutral forms. Thus, the reduction of the encircled bipyridinium unit (electrical input) and the addition of H+ (chemical input) result in the disappearance of the fourth redox wave (electrical output) in the cyclic voltammogram. The current for this particular redox wave is low when the voltage is lowered below the second reduction potential AND the concentration of H+ is high. If a negative logic convention (low = 1, high = 0) is applied to the electrical input and output and a positive logic convention (low = 0, high = 1) is applied to the chemical input, the signal transduction operated by the [2]catenane 22 translates into the truth table of the AND operator (Fig. 1). The carotenoid-porphyrin-fullerene triad 23 combines magnetic and optical inputs into an optical output (Table 1, Fig. 4) [46]. Excitation of the porphyrin core at 590 nm is followed by electron transfer to the fullerene end. The photogenerated hole in the porphyrin is filled after a second electron transfer from the carotenoid fragment. The final result is a charge-separated state, which absorbs light at 980 nm and undergoes charge recombination on a microsecond time scale at 77 K. Under the influence of a magnetic field, the lifetime of the charge separated state increases by

682 50%. Thus, the absorbance at 980 nm (optical output) measured after an appropriate interval of time from excitation (optical input) is high only when a high magnetic field (magnetic input) is applied. This signal transduction corresponds to the truth table of the AND operator (Fig. 1), if a positive logic convention (low = 0, high = 1) is applied to inputs and outputs. The compound 24 and HNO3 (25) are all-optical AND gates (Table 1, Fig. 4). Both convert two optical inputs into a single optical output. The irradiation of 24 at 420 nm (optical input) excites selectively the piperidinylnaphthalene imide donor, and it is followed by the transfer of an electron to the naphthalene diimide acceptor [47]. After 2 ns, a second laser pulse at 480 nm (optical input) promotes the electron transfer from the reduced form of the naphthalene diimide to the naphthalene imide spacer and finally to the benzene diimide tail. The reduction of the benzene diimide acceptor is accompanied by the appearance of an absorption band at 720 nm (optical output). Thus, only when both optical inputs are applied one after the other is an optical output detected. Similarly, an infrared stimulation (optical input) followed by an ultraviolet stimulation (optical input) induces the dissociation of HNO3 (25) into OH and the fluorescent NO∗2 [48]. Thus, the fluorescence of the photogenerated NO∗2 is only observed when both inputs are applied. The signal transduction behavior of 24 and 25 corresponds to an AND operation, if a positive logic convention (low = 0, high = 1) is applied to their inputs and outputs.

7. COMBINATIONAL LOGIC WITH MOLECULAR SYSTEMS Combinational logic circuits can be assembled by connecting the input and output terminals of the three basic logic gates AND, NOT, and OR [10]. The resulting arrays execute logic functions that are a combination of the three basic logic operations. Figure 5 illustrates simple examples of combinational logic circuits able to convert two binary inputs (I1 and I2) into a single output (O) according to the functions summarized in the corresponding truth tables. To reproduce their logic behavior at the molecular level, molecular switches that respond to two input signals producing a detectable output must be designed. For example, the two compounds 26 and 27 (Table 1, Fig. 6) convert two chemical inputs into an optical output according to a NAND function (Fig. 5). At neutral pH, the anthracene fluorophore of 26 emits [49]. After the addition of either H+ or adenosine triphosphate (ATP), the fluorescence (optical output) remains high. However, the optical output drops in intensity when both chemical inputs (H+ and ATP) are applied. The protonation of the oligoamino arm encourages the supramolecular association of 26 with ATP and, as a result, the quenching of the anthracene fluorescence. Similarly, the fluorescence of the diamidinoindole derivative 27 changes in response to deoxyadenosine monophosphate (dAMP) and deoxythymidine monophosphate (dTMP) [50]. In mixtures of dimethylsulfoxide and water, this compound has an emission band at 475 nm. After the addition of either dTMP or dAMP, the emission intensity probed at 455 nm

Molecular Logic Gates I1

I1 I2

O

I2

O

NAND

NOR

I1 I2 O

I1 I2 O

0

0

1

0

0

1

0

1

1

0

1

0

1

0

1

1

0

0

1

1

0

1

1

0

I1

I1

O

O

I2

I2

XOR

XNOR

I1 I2 O

I1 I2 O

0

0

0

0

0

1

0

1

1

0

1

0

1

0

1

1

0

0

1

1

0

1

1

1

I1

O

I2

INH I1 I2 O 0

0

0

0

1

0

1

0

1

1

1

0

Figure 5. Combinational logic circuits with two inputs and one output [10].

does not change significantly. However, a shift of the emission maximum to shorter wavelengths and a concomitant decrease in emission intensity at 455 nm occur when the two deoxynucleotides are added simultaneously. The formation of a ternary complex between the base pair and the indole derivative is responsible for these changes. Thus, the fluorescence intensity (optical output) is low when the concentrations of dAMP and dTMP are high (chemical inputs). The signal transduction operated by 26 and 27 corresponds to a NAND function (Fig. 5), if a positive logic convention (low = 0, high = 1) is applied to their inputs and outputs. The compounds 28–30 (Table 3, Fig. 6) convert two chemical inputs into an optical output according to a NOR operation (Fig. 5). The chemical inputs of the terbium complex 28 are the concentrations of H+ and O2 , and the optical output is the luminescence intensity of the lanthanide [51]. In the presence of H+ , excitation at 304 nm is followed by the fluorescence of the phenanthridine appendage. In the absence of H+ , the excitation of the phenanthridine fragment is followed by intersystem crossing, electron transfer to the terbium center, and delayed emission from the lanthanide. In the presence of O2 , the tripled state of the phenanthridine appendage is quenched and the terbium emission is not observed. Thus, the optical output (terbium

683

Molecular Logic Gates H2N

+

HN H2N

NH HN

NH2 N H

H2N

26

27

N

O P O N O O P

N

N

H N

N Tb

N

NH2

O N

O P

28

O

29

− O

O

O N

O − − O O

N

N

− O O

N

N N

O

O

31

30 N

O P O O N O O P

P

N Tb

N

O N

O NH

32 N

Figure 6. Molecular NAND, NOR, XOR, XNOR, and INH gates based on chemical and optical inputs and optical outputs [37, 49–54].

emission) is detected only when the two chemical inputs (H+ and O2 ) are not applied. Similarly, the anthracene fluorescence (optical output) of 29 is observed only when its two chemical inputs (H+ and Zn2+ ) are not applied [52]. In the presence of H+ and/or Zn2+ , photoinduced electron transfer from the anthracene to the appended 2,2′ -bipyridine ligand quenches the fluorescence. In the case of 30, the fluorescence of the pyrazoline unit (optical output) is detected only in the absence of H+ and Hg2+ (chemical inputs). Efficient fluorescence quenching occurs in the presence of one or both cationic species. Thus, the optical output of 28– 30 is high only when the chemical inputs are not applied. This signal transduction translates into the truth table of the NOR operator (Fig. 5), if a positive logic convention (low = 0, high = 1) is applied to the inputs and outputs. The anthracene derivative 2 (Table 1, Fig. 2) reproduces a NOT operation at a pH of 4.5, an OR operation at a pH of 10, and a NOR function at a pH of 7 [31]. Under neutral conditions, the anthracene fluorescence (optical output) can be observed only in the absence of Cu2+ and Ni2+ (chemical inputs). Indeed, the binding of one of the two metal

cations to the oligoamino arm is accompanied by the efficient quenching of the anthracene fluorescence. Thus, the behavior of this versatile compound at a pH of 7 is equivalent to that of the molecular NOR gates 28–30. In all cases, an optical output (fluorescence) is controlled by two chemical inputs (metal cations) according to a NOR function. Comparison of the truth tables for the XOR and XNOR gates (Fig. 5) reveals an inverse relation between their output values. The input combinations leading to an output of 0 in the XOR produce an output of 1 in the XNOR and vice versa. Interestingly, both logic functions can be implemented with compound 31 (Table 1, Fig. 6) simply by careful selection of the output parameter [37]. The absorption spectrum of this compound shows a band at 390 nm. The complexation of Ca2+ in the tetracarboxylate cleft shifts this band to shorter wavelengths. Instead, the protonation of the quinoline fragment pushes the same band to longer wavelengths. The opposing effects of the two chemical inputs, however, cancel each other when Ca2+ and H+ are added simultaneously. Under these conditions, the absorption band remains at the same wavelength. It follows that the absorbance probed at 390 nm decreases when only one of the two chemical inputs is applied. In contrast, the transmittance at the very same wavelength increases when only one of the two chemical inputs is applied. Thus, if a positive logic convention (low = 0, high = 1) is applied to inputs and output, this compound reproduces a XNOR function, when the absorbance is taken as the output, and a XOR function, when the transmittance is considered as the output. The INH function (Fig. 5) can be implemented at the molecular level with the terbium complex 32 (Table 1, Fig. 6) [53, 54]. This compound transduces two chemical inputs (H+ and O2 ) into an optical output (terbium luminescence) according to this particular logic function. Under basic conditions, the complex 32 has a weak emission band at 548 nm in either aerated or degassed solutions. After the addition of H+ , the emission intensity increases dramatically only if O2 is absent. The protonation of the quinoline fragment facilitates the energy transfer from the quinoline excited state to the lanthanide excited state, enhancing the emission intensity. In the presence of O2 , however, the partial quenching of the quinoline triplet state suppresses the energy transfer process. Thus, the emission intensity is high only when the concentration of H+ is high and that of O2 is low. If a positive logic convention (low = 0, high = 1) is applied to the two chemical inputs (I1 = H+ , I2 = O2 ) and the optical output, the signal transduction of 32 translates into the truth table of the INH circuit (Fig. 5). The three combinational logic circuits a–c in Figure 7 have three inputs and one output. The circuit d has an additional output terminal and converts three inputs into two outputs. The logic functions of these four circuits have been reproduced at the molecular level with the compounds 18 and 33–38 (Table 4, Figs. 3 and 8). The trans-chalcone 18 switches to the 4′ -hydroxyflavylium cation 19 upon irradiation at 365 nm and the addition of either H+ or sodium dodecyl sulfate (SDS) [55]. The transformation of 18 into 19 is accompanied by an increase in absorbance at 450 nm. Thus, this system responds to an optical (I1) and two chemical (I2 and I3) inputs producing an optical output (O).

684

Molecular Logic Gates

a

b I1

I2

O

− O

O

− − O O

O

I3

I1 I2 I3 O

O O

N

Three-Input INH

EOR

Br O

O

0

0

1

0

0

0

1

0

0

1

0

0

0

1

0

0

1

0

0

0

1

0

0

0

0

1

1

0

0

1

1

0

1

0

1

1

1

0

1

0

1

1

0

1

1

1

0

1

1

1

1

1

1

1

1

0

33

O

O O

O

34

+N

35

37

N O

O

I1 I2 I3 O1 O2 O

0

0

0

0

0

0

0

0

0

0

0

1

0

0

0

1

1

0

0

1

0

0

0

1

0

0

0

1

0

0

1

1

0

0

0

1

0

1

1

1

0

1

1

0

0

1

0

1

1

1

0

1

1

0

1

1

0

0

1

1

0

0

1

1

1

1

1

1

1

1

1

0

Figure 7. Combinational logic circuits with three inputs and one or two outputs [10].

The output is high when the optical input is high and one or both chemical inputs are high. If a positive logic convention (low = 0, high = 1) is applied to the three inputs and the two outputs, this signal transduction translates into the truth table of the EOR gate (a in Fig. 7). The compound 33 (Table 2, Fig. 8) responds to three chemical inputs (I1 = Ca2+ , I2 =
-cyclodextrin, I3 = O2 ) producing an optical output (naphthalene phosphorescence) [52]. The naphthalene phosphorescence is high only when the concentrations of Ca2+ and
-cyclodextrin are high and that of O2 is low. Under these conditions, the metal cation enters the tetracarboxylate cleft, suppressing photoinduced electron transfer from the tertiary amino groups to the naphthalene phosphor. The
-cyclodextrin encircles the naphthalene fragment, preventing bimolecular triplet–triplet annihilation. Finally, the absence of O2 ensures that the naphthalene triplet is not quenched. Thus, the signal transduction operated by this compound translates into the truth table of the three-input INH (b in Fig. 7), if a positive logic convention (low = 0, high = 1) is applied to the three inputs and the single output. The compounds 34 and 35 (Fig. 8) incorporate an anthracene core bridging two recognition sites [56, 57]. In both instances, photoinduced electron transfer from the azacrown ether appendage to the anthracene fluorophore quenches its emission. After the complexation of K+ in the azacrown ether, the quenching mechanism is suppressed and

O

OH

NO2

ht r

rk Da

OH

id

O

O1

I3

I3 I1 I2 I3 O

O

36

I1 I2 O2

O

N O

d

O

O

OPr- i

c

I2

O

OPr- i

O

I1

N O

ig

0

igh to

0

vio let L

0

Ultra

0

−

O

ight le L

0

Ac

0

ib Vis

0

O

N O

I1 I2 I3 O

0

O O

− O

Visible L

I1

I2 I3

O O

O

HO

NO2

Ba s e

+N

OH

NO2

38

Acid

O

Figure 8. Compounds able to reproduce complex combinational logic functions relying on chemical and optical inputs and optical outputs [55–58].

a fluorescence enhancement is observed. In contrast, the complexation of either Na+ in the benzocrown ether receptor of 34 or Cs+ in the calixarene receptor of 35 has no influence on the emission intensity. In the presence of H+ , the amino group of the azacrown of 34 and 35 is protonated and the complexation of K+ prevented. However, protonation activates the photoinduced electron transfer from the catechol fragment to the anthracene fluorophore. The complexation of either Na+ in the benzocrown ether of 34 or Cs+ in the calixarene of 35 suppresses this quenching mechanism, enhancing the fluorescence intensity. In summary, these molecules respond to K+ in the absence of H+ and to either Cs+ or Na+ in the presence of H+ . Three chemical inputs (I1 = K+ , I2 = H+ , and I3 = Cs+ or Na+ ) are transduced into a single optical output (fluorescence). This signal transduction translates into the truth table of the circuit c in Figure 7, if a positive logic convention (low = 0, high = 1) is applied to the three inputs and the single output. The three-state molecular switch 36–38 (Table 2, Fig. 8) responds to two optical and one chemical input producing two optical outputs [58]. The inputs are ultraviolet stimulations (I1), visible light (I2), and H+ (I3). The outputs are the absorbance at 401 nm (O1) of 38 and the absorbance at 563 nm (O2) of 37. Ultraviolet irradiation of 36 induces the formation of 37 and the concomitant appearance of a band at 563 nm in the absorption spectrum. Either in the dark or under the influence of visible light, 37 reisomerizes to 36, and the absorbance at 563 nm fades. The addition of H+ to 36 produces 38 and the concomitant appearance of a band at 401 nm in the absorption spectrum. Under the influence of visible light, 38 reverts to 36 and the absorbance at 401 nm fades. Furthermore, the direct interconversion of 37 and 38 and the associated changes in absorbance at 563 and 401 nm

685

Molecular Logic Gates

can be achieved by controlling the concentration of H+ . In summary, three inputs are converted into two outputs by this three-state molecular switch. If a positive logic convention (low = 0, high = 1) is applied to all inputs and outputs, this signal transduction translates into the truth table of the circuit d in Figure 7.

8. COMBINATIONAL LOGIC WITH SUPRAMOLECULAR SYSTEMS Combinational logic functions can also be implemented with supramolecular systems. In particular, certain host-guest complexes can execute XOR and XNOR functions (Fig. 5) combining chemical, electrical, and optical inputs and outputs. The macrocyclic polyether 39 (Fig. 9) binds the 2,7diazapyrenium dication 40 as a result of electrostatic and charge-transfer terms [59]. The supramolecular association encourages the quenching of the naphthalene fluorescence (optical output). After the addition of H+ (chemical input), the crown ether slips off the guest and a high fluorescence intensity is detected. Similarly, the addition of butylamine (chemical input) produces an amine/diazapyrenium adduct, which promotes the dissociation of 39 from 40. As a result, a high naphthalene fluorescence can be detected once again. When the two chemical inputs are added simultaneously, the protonation of butylamine occurs and the nonfluorescent supramolecular assembly remains unaffected. Thus, the optical output (fluorescence) is high when only one of the two chemical inputs (H+ and butylamine) is applied. The signal transduction operated by the supramolecular system 39 • 40 translates into the truth table of the XOR gate (Fig. 5), if a positive logic convention is applied to the two inputs and the single output. The supramolecular association of the tetracationic cyclophane 41 and the tetrathiafulvalene polyether 42 produces a rotaxane-like complex [60]. The attractive interactions between the complementary electron-deficient and electronrich aromatic units are accompanied by the appearance of O O

O

+N

O

O

O

O O

O N+

O

39

40

O + N

+ N

O

S

S

S

S

O

O O

O

O

OH N +

N +

41

O

42

HO

Figure 9. The molecular components of supramolecular XOR and XNOR gates based on chemical and electrical inputs and optical outputs [59, 60].

a charge-transfer band (optical output) at 830 nm in the absorption spectrum. The oxidation of the neutral tetrathiafulvalene to its radical cation encourages the dissociation of the complex and the disappearance of the charge-transfer band. Similarly, the reduction of the dicationic bipyridinium units to their radical cations results in a dramatic decrease in the magnitude of the supramolecular forces maintaining host and guest together. Under these conditions, the complex dissociates, and, once again, the charge-transfer band disappears. The oxidation of the tetrathiafulvalene unit and the reduction of the bipyridinium dications can be induced electrochemically by the application of appropriate voltages to a working electrode. If the voltage is raised above +05 V (I1), the oxidation of the guest occurs and the optical output fades. If the voltage is lowered below −03 V (I2), the reduction of the bipyridinium dications occurs and the optical output fades. In principle, a solution of the supramolecular assembly 41 • 42 can be stimulated with both inputs with the use of two independent working electrodes. Under these conditions, the charge-transfer absorbance (O) is high only when the voltage input I1 is low and the voltage input I2 is high or vice versa. This behavior corresponds to a XNOR function (Fig. 5), if a positive logic convention (low = 0, high = 1) is applied to I1 and O and a negative logic convention (low = 1, high = 0) is applied to I2.

9. COMBINATIONAL AND SEQUENTIAL LOGIC WITH MULTIPLE MOLECULAR COMPONENTS The relatively complex logic circuits in Figures 5 and 7 can be reproduced at the molecular level with individual compounds rather than networks of communicating molecular gates. There is no need for the output of one molecular logic gate to become the input of another. The overall combinational logic function can be integrated within a single molecular switch. This fascinating approach to digital processing with chemical systems is extremely elegant but has a major limitation. A new molecular switch has to be designed and synthesized every time a different logic function has to be implemented. In contrast, conventional digital circuits are assembled, relying always on the same three basic building blocks. Appropriate combinations of AND, NOT, and OR gates are assembled, interconnecting their input and output terminals. The contact established between them ensures the propagation of binary data across the network of gates and the implementation of specific sequences of the three basic logic operations. To reproduce this modular approach with chemical systems, efficient methods to operate multiple molecular components and, eventually, to communicate signals between them are starting to be developed. The XOR and NOR operations (Fig. 5) and the functions of the combinational and sequential logic circuits illustrated in Figure 10 have all been reproduced with ensembles of cooperating molecular components. The trans-chalcone 43 (Fig. 11) isomerizes to a cis form upon irradiation at 365 nm [61]. At a pH of 4.5, the photogenerated cis isomer switches to the 4′ -methoxyflavilyium cation 44. This compound reverts to the original form 43,

686 a

Molecular Logic Gates OH

b

OMe

I1 I1 O1

O2

O

43

O

I2

I2 OMe +

Half-Adder I1 I2

I 1 I 2 O1 O2

O

O

0

0

0

0

0

0

0 or 1

0

1

1

0

0

1

1

1

0

1

0

1

0

0

1

1

0

1

1

1

0

44

36 N O NO2

c

OH

I1

+

H +N

O

I2 I3

N Me2N

N

46

I1 I2 I3 O 0

0

0

1

0

0

1

0

0

1

0

1

1

0

0

0

0

1

1

1

1

0

1

0

1

1

0

0

1

1

1

0

Ultraviolet Light

Visible Light HO

+N OH

38

NO2

+ N N

Me2N

I1

O2

O1

I2 I3

I2 I3

I1

O

Three-Input NOR I 1 I 2 I 3 O1 O2

N

47

e

d

I1 I2 I3 O

0

0

0

1

1

0

0

0

0

0

1

0

1

0

0

1

0

0

1

0

1

1

0

1

0

0

1

0

0

0

0

1

0

0

0

0

1

1

1

1

0

1

1

0

1

0

1

0

1

1

0

1

0

1

1

0

0

0

1

1

0

0

1

1

1

0

1

1

1

1

0

1

Figure 10. Combinational and sequential logic circuits with two or three inputs and one or two outputs [10].

if the pH is increased. These transformations can be followed by monitoring the change in intensity of the absorption bands of 44. In water, the irradiation of K3 Co(CN)6 (45) at 365 nm results in the release of a CN− anion, which combines with H+ , increasing the pH. When 43 and 45 are codissolved in water, the continuous irradiations at 365 nm produce initially 44 and then CN− . The released anion alters the pH, promoting the transformation of 44 back into 43. A similar result is obtained under pulsed irradiation. A single pulse promotes the formation of 44, and a second pulse induces the CN− release and the reformation of 43. The two

Figure 11. Molecular components of combinational and sequential circuits based on the interplay of optical inputs and outputs [61, 62].

pulses can be considered as two independent optical inputs and the absorbance of 44 as an optical output. It follows that the output is high when only one input is applied. This behavior corresponds to a XOR function (Fig. 5) if a positive logic convention (low = 0, high = 1) is applied to the two inputs and the single output. The logic function of the half-adder (a in Fig. 10) can be implemented by operating in parallel an AND and a XOR gate sharing the same two inputs. The compounds 12 and 31 (Table 1, Figs. 3 and 6) execute AND and XOR functions, respectively, in response to H+ and Ca2+ inputs [37]. Their outputs are the fluorescence (O2) of 12 and the transmittance (O1) of 31. When these two compounds are dissolved in the same solution, they can be operated simultaneously by application of the two chemical inputs. It follows that the signal transduction operated by a solution of 12 and 31 is equivalent to that executed by the circuit a in Figure 10, since the truth table of the half-adder is a combination of the truth tables of an AND and XOR gates. Ultraviolet irradiation of the spiropyran 36 (Fig. 8) produces the merocyanine 37 [58]. The p-nitrophenolate fragment of the photogenerated isomer can abstract a proton from a compatible acid, generating the protonated merocyanine 38. Indeed, ultraviolet irradiation (optical input) of an equimolar solution of 36 and the azopyridinium 46 (Fig. 11) encourages the formation of 38 and the azopyridine 47, as

687

Molecular Logic Gates

irradiation (I1) or addition of H+ (I3) promotes the interconversion of 36 into 37 or 38, respectively. Under these conditions, the fluorescence of 48 is absorbed by either 37 or 38, and a low emission intensity is detected. Upon irradiation with visible light (I2), the merocyanine forms revert to 36 and a high fluorescence intensity is restored. It follows that the optical output can be modulated by addressing the solution of the emitting and absorbing components with two optical and one chemical inputs. If a positive logic convention (low = 0, high = 1) is applied to all signals, this signal transduction translates into the truth table of the combinational logic circuit c in Figure 10. The logic behavior of this multimolecular system is based on the transmission of an optical signal from the emitting to the absorbing component. Since light can travel through space, the two communicating molecular components do not necessarily need to be in the same solution. The design of the optical network in Figure 12 relies on this simple consideration [64]. It incorporates a quartz cell containing an equimolar solution of naphthalene (49), anthracene (50), and tetracene (51) and a second quartz cell with a solution of the spiropyran 36. The excitation source stimulates the emission of the three fluorophores contained in the first cell. These compounds emit light at three different wavelengths. The emitted light passes through the second cell before reaching the detector. Ultraviolet (I1), visible (I2), and H+ (I3) inputs control the interconversion of the three states 36–38. The emission of 49 is absorbed equally by 36–38. The emission of 50 (O1) is not absorbed by 36, but it is “blocked” by 37 and 38. The emission of 51 (O2) is absorbed and blocked only by 37. Thus, three input stimulations modulate in parallel the fluorescence of three different compounds with three

a result of photoinduced proton transfer [62]. Upon visible irradiation (optical input), the protonated merocyanine 38 reverts to the spiropyran 36, releasing H+ , which promotes the transformation of 47 into its conjugate acid 46. The photoinduced transformation of 46 into 47 and vice versa can be followed by monitoring the change in absorbance (optical output) for the characteristic visible absorption band of 46. Thus, ultraviolet (I1) and visible (I2) inputs modulate the intensity of an optical output (O) as a result of the intermolecular communication of a chemical signal (proton transfer) between compatible molecular components. In particular, the intensity of O changes from a high to a low value when I1 is turned on and remains low after I1 is turned off. The intensity of O returns to a high value if I2 is turned on and remains high after I2 is turned off. It follows that this multimolecular system has the ability to memorize the influence of the optical inputs and maintain the value imposed on the output even when the inputs are not applied. This intriguing behavior is equivalent to the sequential logic circuit b in Figure 10, if a positive logic convention (low = 0, high = 1) is applied to the two inputs and the single output. It is important to note that the output for the input combination 00 of this particular circuit can be either 0 or 1. Its value is dictated by the sequence of events leading to that particular combination of inputs. The different absorption properties of 36–38 (Fig. 8) can be exploited to control the emission intensity of pyrene (48) as a result of intermolecular fluorescence modulation [63]. This particular fluorophore emits in a wavelength range where only the two merocyanine forms 37 and 38 absorb significantly. Thus, high fluorescence intensity (O) is detected for an equimolar solution of 36 and 48. However, ultraviolet

rav

Ex

cit a So tion urc e

iol

et L So ight urc Vis e ibl eL i g So ht urc e

State of the Molecular Switch

H

36

37

36

37

36

37

36

37

38

36 100

51 De

tec

tor

50

50 49 0

36

ig

N O NO2

OH

Lig ht or

Visible

Ultra +N

id

37

OH

Ac

50 Fluorophores 51

rk Da

Molecular Switch − O

ight le L

vio le

tL

ht

ib Vis

49

HO

NO2

Ba s e

+N OH

Acid

Figure 12. An optical network for the modulation of multiple optical signals in parallel [64].

NO2

38

Emission Intensity (%)

Ult

688

Molecular Logic Gates

distinct protocols that are dictated by the overlap of the emission and absorption bands of six molecular components. The plots in Figure 12 illustrate the correlation between the emission intensities of 49–51 and the state of the molecular switch. If a positive logic convention (low = 0, high = 1) is applied to the three inputs I1–I3 and the two outputs O1 and O2, the truth table for the circuit d of Figure 10 can be assembled. The outputs O1 and O2 switch between low and high values as the molecular switch is operated. In contrast, the fluorescence of 49 is always low, since its emission is always blocked by the switching element. As a result, this particular output is not included in the truth table and logic circuit. An alternative optical network based exclusively on optical inputs and optical outputs is illustrated in Figure 13 [65]. In this case, a monochromatic beam travels from the visible light source to the detector, passing through three quartz cells containing a solution of the spiropyran 36. Each cell can be addressed independently with ultraviolet inputs. When an ultraviolet source is turned on, the spiropyran 36 in the corresponding cell isomerizes to the merocyanine 37. When the ultraviolet input is turned off, 37 reisomerizes thermally to 36. If the wavelength of the monochromatic signal traveling from the source to the detector is chosen to match the visible absorption band of 37, a high optical output reaches the detector only when all three ultraviolet inputs are not applied. Indeed, if only one of the inputs is turned on, the intensity of the output drops to 3–4%. If two or all three inputs are switched on, the output fades to 0%. Thus, a high output reaches the detector only when all three inputs are off. This particular signal transduction corresponds to the three-input NOR circuit (e in Fig. 10). Interestingly, if one of the three switching elements is removed, the logic operation executed becomes equivalent to the two-input NOR (Fig. 5). If only one switching element is left along the path of the traveling light, the logic function reduces to a simple NOT operation (Fig. 1). In all cases, a high output intensity is detected only when all inputs are NOT on.

Ult

rav

Ult

rav

Ult

rav

iol e So t Lig urc ht e1

iol e So t Lig urc ht e2

iol e So t Lig urc ht e3

De

tec

tor

36 t

Ligh Visible Source

N O NO2 OH

Ultraviolet Light

Visible Light

− O

+N

NO2

OH

37

Molecular Switch

Figure 13. An all-optical three-input NOR gate based on three independent switching elements [65].

10. SOLID-STATE MOLECULAR LOGIC GATES The molecular logic gates listed in Tables 1 and 2 have been investigated in solution. Experimental procedures reproducing their operating principles in solid-state configurations are only starting to be explored. For example, the [2]rotaxanes 52 and 53 (Fig. 14) have been incorporated successfully into two-terminal electronic devices [66, 67]. The [2]rotaxane 52 has a bipyridinium backbone encircled by a macrocyclic polyether. The two bulky tetraarylmethane groups prevent the electron-rich macrocycle from slipping off of the electron-deficient backbone. The [2]rotaxane 53 has an electron-deficient macrocycle threaded on the linear

Table 2. Molecular logic gates with two or three input terminals and one or two output terminals.a b Compound

Input 1 (I1)

Input 2 (I2)

Input 3 (I3)

Output 1 (O1)

Output 2 (O2)

Ref.

12 + 31 18 33 34 35 36 36 × 3 36 + 46 36 + 48 36 + 49–51

Ca2+ Light Ca2+ Cs+ or Na+ Cs+ or Na+ H+ Light Light H+ H+

H+ H+
-Cyclodextrin H+ H+ Light Light Light Light Light

— SDSc O2 K+ K+ Light Light — Light Light

Fluorescence Absorbance Phosphorescence Fluorescence Fluorescence Absorbance Light Absorbance Fluorescence Fluorescence

Transmittance — — — — Absorbance — — — Fluorescence

[37] [55] [52] [56, 57] [56] [58] [65] [62] [63] [64]

a The inputs and outputs are chemical or optical signals. The chemical inputs are the concentrations of the species listed. The optical inputs/outputs are the light, fluorescence, and phosphorescence intensities or the magnitude of the parameter listed. b The circuits and truth tables corresponding to these molecular logic gates are illustrated in Figures 7 and 10. The half-adder (a in Fig. 10) is equivalent to the combination of 12 and 31. The EOR (a in Fig. 7) corresponds to 18. The three-input INH (b in Fig. 7) is equivalent to 33. The circuit c in Figure 7 corresponds to 34 or 35. The circuit d in Figure 7 is equivalent to 36. The three-input NOR (e in Fig. 10) is equivalent to the all-optical network based on three switching elements each containing 36. The circuit b in Figure 10 corresponds to the combination of 36 and 46. The circuit c in Figure 10 is equivalent to the combination of 36 an 48. The circuit d in Figure 10 is equivalent to the optical network based on 36 and 49–51. c SDS stands for sodium dodecyl sulfate.

689

Molecular Logic Gates

O

O

52

O

53

O O

O

O

O

O

O

O

O

54

O N

O

N

O

O

O

N

N S

S

S

S

N O

O

N

S

S

S

Reduction N

N

O

O

O

O

S

O

O

Oxidation

O

N

O

N

N

O

N

O HO

O O

O

O

O

Top Electrode

Bottom Electrode

Bottom Electrode

O O

O

O

O

O

O O

O O

O

O

O

O

O

O

O

O

Figure 14. The molecular components of solid-state logic gates consisting of interconnected electrode/molecular layer/electrode cross-junctions [66, 67].

portion of an electron-rich dumbbell-shaped component. Once again, terminal tetraarylmethane groups mechanically trap the macrocyclic component. Attractive electrostatic and charge-transfer interactions maintain the bipyridinium cyclophane around the tetrathiafulvalene fragment of the dumbbell-shaped component. After the tetrathiafulvalene oxidation, electrostatic repulsion forces the tetracationic cyclophane to move away from the newly formed cationic unit, producing the [2]rotaxane 54. After reduction, the neutral form of the tetrathiafulvalene fragment is restored and the original [2]rotaxane 53 is regenerated. Thus, the reversible interconversion between 53 and 54 can be controlled by oxidizing and reducing the electroactive tetrathiafulvalene unit. The fabrication of solid-state devices incorporating the [2]rotaxanes 52 and 53 relies on the amphiphilic character of these compounds. Indeed, these molecules can be compressed into organized monolayers at the air/water interface of a Langmuir trough. The resulting films can be transferred on the surface of parallel electrodes patterned lithographically on silicon chips. Then the deposition of a top elec-

trode perpendicular to the bottom electrodes can produce pairs of interconnected cross-junctions (Fig. 14). In the case of the [2]rotaxane 52, aluminum fingers covered by an aluminum oxide layer are used for the bottom electrodes. In the case of the [2]rotaxane 53, the bottom electrodes are silicon wires with a silicon dioxide overlayer. In both instances, the top electrode is a titanium wire covered by an aluminum overlayer. For a cross-junction containing a monolayer of the [2]rotaxane 52, high current is measured at the top electrode only when the voltage of the bottom electrode is lowered below −07 V [66]. Under these conditions, the bipyridinium centered LUMOs mediate the tunneling of electrons from the bottom to the top electrode. An AND gate can be constructed by operating two cross-junctions with a common top electrode in parallel. Indeed, voltage inputs can be applied to the two independent bottom electrodes, and a single current output can be measured at the common top electrodes. Only when both voltage inputs are lowered below −07 V is a current output greater than 3 pA measured. When a negative voltage convention is applied to the inputs (low = 1,

690 high = 0) and a positive logic convention (low = 0, high = 1) is applied to the output, the signal transduction translates into an AND operation. If the logarithm of the current is taken as the output and the same logic conventions are applied, an OR function can be implemented. The logarithm of the current is greater than −9, when at least one voltage input is below −07 V. Furthermore, a three-input OR gate can also be realized by the operation of three cross-junctions with a common top electrode, following the same logic conventions. The voltages of the three bottom electrodes can be varied independently while the current at the top electrode is monitored. Once again, the logarithm of the current is greater than −9, when at least one voltage input is below −07 V. In the case of the [2]rotaxane 53, the junction conduction probed at +02 V can be switched between high and low values with the application of voltage pulses of −2 and +2 V to the bottom electrode [67]. A positive voltage pulse promotes the oxidation of the tetrathiafulvalene unit and the shuttling of the tetracationic cyclophane to produce the [2]rotaxane 54. The redox-induced change in the stereoelectronic properties of the molecules sandwiched between the two crossing electrodes significantly affects their ability to mediate the tunneling of electrons through the junction. As a result, the conduction probed at +02 V grows significantly after a +2 V pulse. However, the original value can be restored by applying a −2 V pulse. The negative voltage pulse promotes the reduction of the cationic form of the tetrathiafulvalene fragment back to its neutral state. This process is accompanied by the shuttling of the bipyridinium cyclophane to the original position, regenerating the [2]rotaxane 53. Following this strategy, it is possible to configure two-dimensional logic circuits consisting of interconnected cross-junctions. Indeed, appropriate voltage pulses can be exploited to predefine the conduction of each junction and impose desired current/voltage characteristics on the overall circuit. The potential of this approach for the implementation of logic functions was demonstrated by configuring nine interconnected cross-junctions to execute a XOR function [67]. In addition to rotaxanes, single-wall carbon nanotubes have also been exploited to reproduce logic functions with solid-state devices [68]. Individual nanotubes have been incorporated into ultraminiaturized transistors. One of them is illustrated schematically in Figure 15. The carbon nanotube lies on an insulating aluminum oxide layer deposited on an aluminum electrode. The two ends of the carbon nanotubes are in contact with gold electrodes. The voltage applied to the aluminum gate affects the electronic properties of the carbon nanotube, altering its ability to mediate the flow of electrons from the gold source to the gold drain. More precisely, the drain current at a source to drain bias of ca. −13 V jumps from ca. 0 to ca. 50 nA when the gate voltage is lowered from −10 to −13 V. This behavior is equivalent to that of a conventional enhancement-mode p-type field effect transistor [1]. A moderate change in the gate voltage produces a dramatic change in the drain current. Multiple nanotube transistors can be fabricated on the same silicon chip, and the interconnection of their terminals with appropriate configurations results in the assembly of nanoscale digital circuits. For example, NOT and NOR gates have been implemented with this approach [68]. The NOT

Molecular Logic Gates

a

Output Voltage

Source Gold

Nanotube Aluminum Gate

Input Voltage

b

Source Gold

Nanotube Aluminum Gate

Input Voltage

Source Gold

Nanotube Aluminum Gate

Input Voltage

–1.5 V

Drain Gold

Aluminum Oxide Insulator

Drain Gold

Aluminum Oxide Insulator

Output Voltage

–1.5 V

Drain Gold

Aluminum Oxide Insulator

Figure 15. Solid-state logic gates based on single-wall carbon nanotube transistors [68].

gate (a in Fig. 15) consists of an off-chip bias resistor connected to the drain terminal of a nanotube transistor with the source grounded. The voltage output probed at the drain terminal varies with a voltage input applied to the gate, since the nanotube conductance is determined by the gate voltage. In particular, the nanotube resistance decreases below that of the bias resistor when a voltage input of −15 V is applied. Under these conditions, the voltage output drops to 0 V. The nanotube resistance increases above that of the bias resistor when the voltage input is raised to 0 V. As a result, the voltage output becomes −15 V. In summary, the output switches from a high (0 V) to a low (−15 V) level when the input changes from a low (−15 V) to a high (0 V) value. The inverse relation between input and output corresponds to a NOT operation, if a negative logic convention (low = 1, high = 0) is applied to both signals. The NOR gate (b in Fig. 15) incorporates two nanotube transistors. Their source terminals are grounded. Their drain terminals are connected to an off-chip bias resistor. The two transistors are operated by independent input voltages but share the same output voltage. The common output is 0 V when the resistance of at least one of the two nanotubes is below that of the bias resistor. The output is −15 V when the resistance of both nanotubes is higher than that of the bias resistor. Thus, the output is high (0 V) if a low voltage input (−15 V) is applied to one or both transistors. The output is low (−15 V) when both voltage inputs are high (0 V). If a negative logic convention (low = 1, high = 0) is applied to all signals, the signal transduction behavior translates into the truth table of a NOR gate (Fig. 5).

11. CONCLUSIONS The three basic logic operations AND, NOT, and OR can be implemented with chemical systems relying on fascinating molecular switches. These compounds respond to

Molecular Logic Gates

chemical, electrical, magnetic, and/or optical inputs producing detectable electrical or optical outputs. Relatively complex combinational logic functions able to transduce two or three inputs into one or two outputs can be also reproduced at the molecular level. Indeed, the combined functions of multiple basic operators can be designed into single molecular switches thanks to the high level of sophistication reached by chemical synthesis. In addition, combinational and sequential logic functions can be reproduced with ensembles of cooperating molecular components. In these systems, distinct molecular switches share the same input stimulations and can be operated in parallel. Alternatively, the output of one molecular component can be communicated intermolecularly to a second component, offering the opportunity of operating molecular switches sequentially. The intermolecular communication of signals can rely on the transfer of protons from one molecule to another, or it can exploit the transmission of optical signals from emitting to absorbing species. This exploratory research in the realm of molecular switches and digital processing has demonstrated already that information can be manipulated at the molecular level. However, the chemical systems developed so far are rudimentary examples of digital processors. At this stage, they remain far from potential applications in information technology. In addition, most of these studies rely on the bulk addressing of molecular switches in solution, rather than on the stimulation of single molecules in solid-state configurations. The major challenge in this research area lies in the identification of practical methods to scale these operating principles down to the unimolecular level and to reproduce the functions already demonstrated in solution with molecule-based solid-state devices. Fundamental studies in these directions will reveal if similar chemical processors for the elaboration and storage of binary data can, indeed, evolve into practical devices for information technology.

GLOSSARY Digital circuits Networks of interconnected logic gates. Fluorescence Emission of light from a singlet excited state of a molecule. Logic gates Devices able to convert binary inputs into binary outputs according to defined logic functions. Molecular switches Molecules undergoing reversible transformations under the influence of external stimulations. Supramolecular chemistry Area of the chemical sciences studying the noncovalent association of independent molecular building blocks into multicomponent assemblies.

REFERENCES 1. R. S. Muller and T. I. Kamins, “Device Electronics for Integrated Circuits.” Wiley, New York, 2002. 2. M. J. Madou, “Fundamentals of Microfabrication: The Science of Miniaturization.” CRC Press, Boca Raton, FL, 2002. 3. “International Technology Roadmap for Semiconductors.” International SEMATECH, Austin, TX, 2000. 4. Processor Hall of Fame, Intel Corporation, Santa Clara, CA, 2002. 5. G. E. Moore, Electronics 114 (1965).

691 6. D. Goldhaber-Gordon, M. S. Montemerlo, J. C. Love, G. J. Opiteck, and J. C. Ellenbogen, Proc. IEEE 85, 521 (1997). 7. M. Schultz, Nature 399, 729 (1999). 8. D. A. Muller, T. Sorsch, S. Moccio, F. H. Baumann, K. EvansLutterodt, and G. Timp, Nature 399, 758 (1999). 9. J. D. Meindl, Q. Chen, and J. D. Davies, Science 293, 2044 (2001). 10. R. J. Mitchell, “Microprocessor Systems: An Introduction.” Macmillan, London, 1995. 11. A. J. Bard, “Integrated Chemical Systems: A Chemical Approach to Nanotechnology.” Wiley, New York, 1994. 12. A. P. Alivisatos, P. F. Barbara, A. W. Castleman, J. Chang, D. A. Dixon, M. L. Klein, G. L. McLendon, J. S. Miller, M. A. Ratner, P. J. Rossky, S. I. Stupp, and M. E. Thompson, Adv. Mater. 10, 1297 (1998). 13. Special issue on Photochromism: Memories and Switches, Chem. Rev. 100, 1683 (2000). 14. Special issue on Molecular Machines, Acc. Chem. Res. 34, 409 (2001). 15. K. C. Nicolau and E. C. Sorensen, “Classics in Total Synthesis.” VCH, Weinheim, 1996. 16. V. Balzani, A. Credi, F. M. Raymo, and J. F. Stoddart, Angew. Chem. Int. Ed. 39, 3348 (2000). 17. B. L. Feringa, Ed., “Molecular Switches.” Wiley-VCH, Weinheim, 2001. 18. M. D. Ward, J. Chem. Ed. 78, 321 (2001). 19. A. P. de Silva, N. D. McClenaghan, and C. P. McCoy, “Electron Transfer in Chemistry” (V. Balzani, Ed.), p. 156. Wiley-VCH, Weinheim, 2001. 20. A. P. de Silva, G. D. McClean, N. D. McClenaghan, T. S. Moody, and S. M. Weir, Nachr. Chem. 49, 602 (2001). 21. A. P. de Silva, D. B. Fox, T. S. Moody, and S. Weir, Pure Appl. Chem. 73, 503 (2001). 22. F. M. Raymo, Adv. Mater. 14, 401 (2002). 23. C. Y. Liu and A. J. Bard, Acc. Chem. Res. 32, 235 (1999). 24. R. M. Metzger, Acc. Chem. Res. 32, 950 (1999). 25. J. K. Gimzewski and C. Joachim, Science 283, 1683 (1999). 26. C. Joachim, J. K. Gimzewski, and A. Aviram, Nature 408, 541 (2000). 27. M. A. Reed and J. M. Tour, Sci. Am. 282, 86 (2000). 28. J. R. Heath, Pure Appl. Chem. 72, 11 (2000). 29. A. R. Pease, J. O. Jeppesen, J. F. Stoddart, Y. Luo, C. P. Collier, and J. R. Heath, Acc. Chem. Res. 34, 433 (2001). 30. A. P. de Silva, H. Q. N. Gunaratne, and C. P. McCoy, Nature 364, 42 (1993). 31. S. Alves, F. Pina, M. T. Albeda, E. García-España, C. Soriano, and S. V. Luis, Eur. J. Inorg. Chem. 405 (2001). 32. A. P. de Silva, H. Q. N. Gunaratne, and G. E. M. Maguire, J. Chem. Soc., Chem. Commun. 1213 (1994). 33. P. Ghosh, P. K. Bharadwaj, S. Mandal, and S. Ghosh, J. Am. Chem. Soc. 118, 1553 (1996). 34. P. Ghosh, P. K. Bharadwaj, J. Roy, and S. Ghosh, J. Am. Chem. Soc. 119, 11903 (1997). 35. A. P. de Silva, H. Q. N. Gunaratne, and C. P. McCoy, J. Am. Chem. Soc. 119, 7891 (1997). 36. S. A. de Silva, B. Amorelli, D. C. Isidor, K. C. Loo, K. E. Crooker, and Y. E. Pena, Chem. Commun. 1360 (2002). 37. A. P. de Silva and N. D. McClenaghan, J. Am. Chem. Soc. 122, 3965 (2000). 38. C. R. Cooper and T. D. James, Chem. Commun. 1419 (1997). 39. S. Iwata and K. Tanaka, J. Chem. Soc., Chem. Commun. 1491 (1995). 40. M. Inouye, K. Akamatsu, and H. Nakazumi, J. Am. Chem. Soc. 119, 9160 (1997). 41. F. Pina, A. Roque, M. J. Melo, M. Maestri, L. Belladelli, and V. Balzani, Chem. Eur. J. 4, 1184 (1998). 42. F. Pina, M. Maestri, and V. Balzani, Chem. Commun. 107 (1999).

692 43. L. Gobbi, P. Seiler, and F. Diederich, Angew. Chem. Int. Ed. 38, 674 (1999). 44. L. Gobbi, P. Seiler, F. Diederich, V. Gramlich, C. Boudon, J. P. Gisselbrecht, and M. Gross, Helv. Chim. Acta 84, 743 (2001). 45. P. R. Ashton, V. Baldoni, V. Balzani, A. Credi, H. D. A. Hoffmann, M.-V. Martínez-Díaz, F. M. Raymo, J. F. Stoddart, and M. Venturi, Chem. Eur. J. 7, 3482 (2001). 46. D. Kuciauskas, P. A. Liddell, A. L. Moore, and D. Gust, J. Am. Chem. Soc. 120, 10880 (1998). 47. A. S. Lukas, P. J. Bushard, and M. R. Wasielewski, J. Am. Chem. Soc. 123, 2440 (2001). 48. T. Witte, C. Bucher, F. Remacle, D. Proch, K. L. Kompa, and R. D. Levine, Angew. Chem. Int. Ed. 40, 2512 (2001). 49. M. T. Albelda, M. A. Bernardo, E. Garcia-España, L. GodinoSalido, S. V. Luis, M. J. Melo, F. Pina, and C. Soriano, J. Chem. Soc., Perkin Trans. 2 11, 2545 (1999). 50. H. T. Baytekin and E. U. Akkaya, Org. Lett. 2, 1725 (2000). 51. D. Parker and J. A. G. Williams, Chem. Commun. 245 (1998). 52. A. P. de Silva, I. M. Dixon, H. Q. N. Gunaratne, T. Gunnlaugsson, P. R. S. Maxwell, and T. E. Rice, J. Am. Chem. Soc. 121, 1393 (1999). 53. T. Gunnlaugsson, D. A. Mac Dónail, and D. Parker, Chem. Commun. 93 (2000). 54. T. Gunnlaugsson, D. A. Mac Dónail, and D. Parker, J. Am. Chem. Soc. 123, 12866 (2001). 55. A. Roque, F. Pina, S. Alves, R. Ballardini, M. Maestri, and V. Balzani, J. Mater. Chem. 9, 2265 (1999).

Molecular Logic Gates 56. H.-F. Ji, R. Dabestani, and G. M. Brown, J. Am. Chem. Soc. 122, 9306 (2000). 57. H. Xu, X. Xu, R. Dabestani, G. M. Brown, L. Fan, and S. Patton, J. Chem. Soc., Perkin Trans. 2 636 (2002). 58. F. M. Raymo and S. Giordani, J. Am. Chem. Soc. 123, 4651 (2001). 59. A. Credi, V. Balzani, S. J. Langford, and J. F. Stoddart, J. Am. Chem. Soc. 119, 2679 (1997). 60. M. Asakawa, P. R. Ashton, V. Balzani, A. Credi, G. Mattersteig, O. A. Matthews, M. Montalti, N. Spencer, J. F. Stoddart, and M. Venturi, Chem. Eur. J. 3, 1992 (1997). 61. F. Pina, M. J. Melo, M. Maestri, P. Passaniti, and V. Balzani, J. Am. Chem. Soc. 122, 4496 (2000). 62. F. M. Raymo and S. Giordani, Org. Lett. 3, 3475 (2001). 63. F. M. Raymo and S. Giordani, Org. Lett. 3, 1833 (2001). 64. F. M. Raymo and S. Giordani, J. Am. Chem. Soc. 124, 2004 (2002). 65. F. M. Raymo and S. Giordani, Proc. Natl. Acad. Sci. USA 99, 4941 (2002). 66. C. P. Collier, E. W. Wong, M. Belohradsky, F. M. Raymo, J. F. Stoddart, P. J. Kuekes, R. S. Williams, and J. R. Heath, Science 285, 391 (1999). 67. Y. Luo, C. P. Collier, J. O. Jeppesen, K. A. Nielsen, E. Delonno, G. Ho, J. Perkins, H.-R. Tseng, T. Yamamoto, J. F. Stoddart, and J. R. Heath, Chemphyschem 3, 519 (2002). 68. A. Batchtold, P. Hadley, T. Nakanishi, and C. Dekker, Science 294, 1317 (2001).

Encyclopedia of Nanoscience and Nanotechnology

www.aspbs.com/enn

Molecular Nanotechnology with 2D Protein Crystals Uwe B. Sleytr, Dietmar Pum, Margit Sára, Bernhard Schuster Universität für Bodenkultur Wien, Vienna, Austria

CONTENTS 1. Introduction 2. S-Layer Proteins 3. Secondary Cell Wall Polymers 4. S-Layer Fusion Proteins 5. S-Layer Monolayer Formation on Solid Surfaces 6. S-Layer Templating of Nanoparticle Arrays 7. Spatial Control of the S-Layer Reassembly 8. Lipid Membranes 9. Liposomes 10. Planar Lipid Membranes 11. S-layer Ultrafiltration Membrane (SUM)-Supported Lipid Membranes 12. Solid-Supported Lipid Membranes 13. Conclusions Glossary References

1. INTRODUCTION The cross-fertilization of biology, chemistry, and material sciences is opening up a great variety of new opportunities for innovation in nanosciences and biomimetics. Moreover, one of the most relevant areas of research in the nanosciences will be at the interface between biology and solid state physics. One of the key challenges is the technological utilization of self-assembly systems, wherein molecules spontaneously associate under equilibrium conditions into reproducible supramolecular aggregates (“bottom-up” strategy). The attractiveness of such “bottom up” processes lies in their capability to build uniform, ultra small functional units and the possibility to exploit such structures at meso- and macroscopic scale for

ISBN: 1-58883-061-6/$35.00 Copyright © 2004 by American Scientific Publishers All rights of reproduction in any form reserved.

life and nonlife science applications. The immobilization of biomolecules in an ordered fashion on solid substrates and their controlled confinement in definite areas of nanometer dimensions are key requirements for many applications, including the development of bioanalytical sensors, biochips, molecular electronics, biocompatible surfaces, and signal processing between functional membranes, cells, and integrated circuits. The use of crystalline bacterial cell surface proteins (S-layer proteins) provided innovative approaches for the assembly of supramolecular structures and devices with dimensions of a few to tens of nanometers (for review see [1–5]). S-layers have proven to be particularly suited as building blocks in a biomolecular construction kit involving all major classes of biological molecules (protein, lipids, glycans, nucleic acids, and combinations of them) and nanoparticles. This chapter will provide a survey on the application potential of S-layers in life and nonlife sciences.

2. S-LAYER PROTEINS S-layer proteins form the outermost cell envelope component of a broad spectrum of bacteria and archaea (for review see [1–9]) (Fig. 1). S-layers are composed of a single protein or glycoprotein species with an apparent relative molecular mass of 40,000–230,000 and exhibit either oblique (p1, p2), square (p4), or hexagonal (p3, p6) lattice symmetry with unit cell dimensions in the range of 3–30 nm (Fig. 2). One morphological unit consists of one, two, three, four or six identical subunits, respectively. S-layers are generally 5–10 nm thick and show pores of identical size (diameter, 1.5– 8 nm) and morphology. In general, the topography of the outer face (with respect to the orientation of the S-layer on the bacterial cell) is smooth and the surface exhibits a charge neutral characteristic, while the inner face is often corrugated and net negatively or positively charged. Due to the crystalline character of S-layers functional groups, such as carboxyl or amino groups, are repeated with the periodicity of the protein lattice. This property of S-layer enables

Encyclopedia of Nanoscience and Nanotechnology Edited by H. S. Nalwa Volume 5: Pages (693–702)

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Figure 1. Transmission electron micrograph of a freeze-etching preparation of a bacterial cell showing an S-layer with hexagonal lattice symmetry. Bar, 100 nm.

a geometrically controlled immobilization of molecules and nanoparticles. Up to now, most nanotechnological applications have focused on S-layers present in gram-positive bacteria. In these organisms S-layers are linked to a rigid supporting layer [6].

3. SECONDARY CELL WALL POLYMERS The rigid cell wall of Gram-positive bacteria contains, beside peptidoglycan, large amounts of accessory (secondary) cell wall polymers (SCWPs) composed of either teichoic acids, teichuronic acids, lipoteichoic acids, or lipoglycans [10]. Depending on the type, the polymer chains are either p1

p3

p2

p4

p6

Figure 2. Schematic drawing of different S-layer lattice types. The regular arrays exhibit either oblique (p1, p2), square (p4), or hexagonal (p3, p6) lattice symmetry. One morphological unit (darker shades) consists of one, two, three, four, or six identical subunits, respectively [1]. Reprinted with permission from [1], U. B. Sleytr et al., Angew. Chem. Int. Ed. 38, 1999. © 1999, Wiley-VCH.

tethered to a lipid anchor or covalently linked to the peptidoglycan backbone. Although SCWPs are essential for cell viability, their exact physiological role is not really understood. Thus, very general functions such as binding of bivalent cations, keeping the peptidoglycan sacculus in an expanded state by charge repulsion, binding proteins to create an acidic cell wall during bacterial growth and division, or providing a biophysical barrier to prevent diffusion of nutrients and metabolites have been assigned to these polymers. Recently, evidence was provided that in Grampositive bacteria, SCWPs function as anchoring structures for S-layer proteins [11, 12]. Accordingly, S-layer proteins can be considered as cell-surface-carbohydrate-binding proteins and the binding mechanism could correspond with that occurring between polysaccharides and lectins [12]. By sequence comparison, S-layer-homologous (SLH) motifs [13] have been identified at the N-terminal part of many S-layer proteins [14–19]. Typically, S-layer proteins possess three repeating SLH motifs each consisting of 50–60 amino acids. Secondary cell wall polymers have now been recognized to serve as binding sites for the SLH motifs of S-layer proteins [13]. In addition, SCWPs are highly specific for binding only S-layer proteins from those organisms from which they had been originally isolated [11]. As SCWP can be functionalized (e.g., by the introduction of thiol groups) gold substrates, but also other relevant inorganic surfaces can be covered by the SCWP to provide a specific binding matrix for a certain S-layer protein in a well-defined orientation. In addition, the concept of generating oriented functional protein lattices may also imply that appropriate glycolipids comprising the smallest functional units of SCWPs are synthesized and incorporated into liposomes or Langmuir lipid films [20].

4. S-LAYER FUSION PROTEINS For production of S-layer–based biosensors [21], affinity microparticles [22], and solid-phase immunoassays [23–25], functional groups in the S-layer lattice were exploited as covalent binding sites for biologically active macromolecules, such as enzymes, antibodies, or ligands. As alternatives to the existing technology, namely, immobilization by chemical methods, genetic approaches are particularly attractive for incorporation of functional peptide sequences into S-layer proteins, which have to be done at positions that do not interfere with their self-assembly properties and interaction with SCWP. To guarantee that the integrated or fused functional sequence remains located on the outer surface of the S-layer lattice and available for further binding reactions, the specific interactions with the SCWP is used to achieve an oriented binding of S-layer fusion proteins on artificial supports. By the fusion of streptavidin to the S-layer protein SbsB of Geobacillus stearothermophilus PV72/p2, new templates for nanopatterned molecular arrays and building blocks for nanobiotechnology have been generated [26]. The fusion proteins and streptavidin were produced independently in E. coli, isolated and mixed to refold heterotetramers of 1:3 stoichiometry (Fig. 3). Self-assembled chimeric S-layers could be performed in suspension, on liposomes, silicon wafers, and SCWPs containing cell wall fragments. The

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a

b

c

d

e

Figure 3. Digital image reconstructions from transmission electron micrographs of negatively stained preparations of Geobacillus stearothermophilus PV72/p2 (SbsB) (a) and streptavidin S-layer fusion protein (S1)3S1B1 (b). The region of highest protein mass in the SbsB lattice is the SLH-domain (a, thin arrow). In the lattice of the fusion protein, streptavidin showed up as additional protein mass (b, thick arrow) attached to the SLH-domain. Bars, 10 nm. Cell wall fragments carrying a chimeric S-layer formed by the fusion protein BS1(S1)3 (c) were capable of binding biotinylated ferritin (d), Bars, 100 nm. The lattice of bound ferritin molecules resembles the underlying S-layer lattice. The cartoon in (e) shows the orientation of BS1(S1)3 after SLHenabled self-assembly with the streptavidin carrying outer face of the S-layer exposed. Self-assembly was enabled by the specific interaction between an accessory cell wall polymer that is part of the cell wall of G. stearothermophilus PV72/p2 and the SLH-domain of the fusion protein. Reprinted with permission from [26], D. Moll et al., Proc. Natl. Acad. Sci. USA 99, (2002). © 2002, National Academy of Sciences.

two-dimensional protein crystals displayed streptavidin in defined, repetitive spacing and were capable of binding D-biotin and biotinylated proteins in a regular fashion (Fig. 3). Therefore, the chimeric S-layer can be used as a

self-assembling, nanopatterned molecular affinity matrix to arrange biotinylated compounds on a surface. In a further example, the sbpA gene encoding the S-layer protein SbpA of B. sphaericus CCM2177 was sequenced, cloned, and expressed in E. coli [27]. As a C-terminally truncated form revealed an improved accessibility compared to the recombinant SbpA, the chimeric gene encoding an S-layer fusion protein comprising the sequence of Bet v1, the major birch pollen allergen, was cloned and expressed in E. coli. The SbpA/Bet v1 fusion proteins selfassembled to regularly structured protein lattices. The functional sequences are aligned at a predefined distance in the nanometer range on the outermost surface of the S-layer lattice and therefore remain available for further binding reactions (e.g., with antibodies directed to Bet v1). These specific features of S-layer fusion proteins imply a considerable application potential as patterning elements and as nanostructures as required for biochip developments, proteomics, or genomics.

5. S-LAYER MONOLAYER FORMATION ON SOLID SURFACES One of the most remarkable properties of isolated S-layer proteins is their capability to reassemble into monomolecular arrays in suspension, at the liquid-air interface, solid surfaces, floating lipid monolayers, and on liposomes (for review see [1–5]). An important key to the fabrication of highly ordered functional arrays of nanoparticles and functional molecules lies in the development of suitable templates for spatially controlled particle deposition. S-layer proteins seem to be perfectly suited for this purpose since they have the intrinsic property to reassemble into two-dimensional arrays at various surfaces, including silicon, metals, and polymers. Functional groups are repeated (with the periodicity of the S-layer lattice) at a distance of approximately 10 nm, leading to regular arrays (superlattices) of bound functional molecules and particles [2, 3]. Crystal growth at interfaces, such as the liquid-solid interface, starts at several nucleation sites and proceeds in plane until the front edges of the growing crystalline areas meet [28, 29]. In this way, a closed mosaic of crystalline domains is formed. Nucleation points may be either protomers, oligomers, or small self-assembly products adsorbed from the solution. Size and orientation of the crystalline domains are mainly determined at a very early stage in the process of crystal formation by the lateral density and orientation of the nucleation points. It is assumed that a higher mobility of the proteins will lead to larger crystalline domains since the chance of an S-layer protein to contribute to an already existing domain is higher. Depending on the bacterial strain from which the S-layer was derived and the surface properties of the substrate used, an average patch size of individual crystalline domains of up to 20
m in diameter may be obtained. The reciprocal influence of the surface properties of the solid support and the S-layer proteins determines which S-layer face (inner or outer face) will be attached to the support. This is a consequence of the asymmetry in the physicochemical surface properties of S-layer proteins. For

696 example, the S-layer protein SbsB of Geobacillus stearothermophilus PV72/p2 forms monolayers with individual areas larger than 10
m in diameter on silicon surfaces within 4 hours, whereas on gold the recrystallization takes much longer and the size of the monocrystalline patches is much smaller. Despite the different recrystallization behavior on solid surfaces (SiO2 or Au), in both cases, the S-layer lattice of SbsB was attached with its outer surface to the substrate. In a similar way, S-layer protein SbpA from Bacillus sphaericus CCM2177 forms extended crystalline domains on hydrophilic silicon surfaces (patch size up to 5
m in diameter), while only small patches are found on hydrophobic ones (patch size ca. 500 nm in diameter) (Györvary, unpublished results). Furthermore, accurate control of chemical composition of the subphase (e.g., pH, ion content, and ion concentration), temperature, and recrystallization time are important for obtaining large scale coherent S-layer domains. For example, the S-layer protein SbsB requires a pH of 4.1, while SbpA needs a pH of 9.0 and calcium in the subphase [29, 30]. Recently, different types of genetically engineered S-layer proteins were investigated with respect to their recrystallization behavior on solid surfaces (Györvary et al., unpublished results). These studies are particularly important since genetically modified S-layer proteins incorporating functional domains will play a key role in the specific and regular binding of appropriately functionalized nanoparticles [26]. Based on the results from the recrystallization experiments with wild-type S-layer proteins, it has to be decided where functional domains (e.g., binding regions of streptavidin) have to be inserted in the polypeptide chain. For example, from six streptavidin-SbsB heterotetrameric fusion protein constructs only one retained the capability of forming monocrystalline domains (patch size of ca. 400 nm in diameter) on silicon wafers. An alternative approach for inducing crystallization of S-layer proteins in an appropriate orientation with respect to solid supports or lipid films induces binding or adsorption of SCWP on surfaces and interfaces (see Section 3 on SCWP).

6. S-LAYER TEMPLATING OF NANOPARTICLE ARRAYS Current state-of-the-art methods for self-assembly of nanoparticle arrays that generally involve bifunctional linkers, molecular recognition, or Langmuir–Blodgett techniques, do not offer the control and flexibility of the S-layer systems. The S-layer approach features adjustable lattice constants and control over template surface properties by chemical or genetic modifications [1–5] (Fig. 4). The first approach in using S-layers as lithographic templates in the formation of ordered nanoparticle arrays was developed by Douglas and Clark [31]. In a three-step process, S-layer fragments of Sulfolobus acidocaldarius were deposited on a smooth carbon surface, metal coated by evaporation (1 nm thick Ta/W), and finally thinned by ion milling. Under ion bombardment, 15 nm diameter holes appeared in the protein-metal structure resembling the hexagonal lattice symmetry with a spacing of 22 nm. Subsequently, in a similar approach, a nanostructured titanium

Molecular Nanotechnology with 2D Protein Crystals

Figure 4. Freeze-etched preparations showing ferritin molecules bound by (a, b) covalent or (c) electrostatic interactions to S-layer lattices with different lattice symmetries and spacing. The regularly arranged ferritin molecules (12 nm diameter) resemble the underlying S-layer lattice. Bar in (a) and (b), 100 nm; bar in (c) 200 nm. Reprinted with permission from [2], U. B. Sleytr et al., “Supramolecular Polymerization” (A. Ciferri, Ed.), p. 177. Marcel Dekker, New York, 2000. © 2000, Marcel Dekker.

oxide layer with 10 nm pores was derived after coating S-layer fragments deposited on a smooth graphite surface [32]. Recently, the same group used low-energy “electron enhanced etching” to pattern the surface properties of silicon through the regularly arranged pores of the S-layer [33]. After etching and removal of the S-layer, the resulting structure was oxidized in an oxygen plasma yielding a regular array of etched holes with an 18 nm diameter. In the final step, evaporation of titanium onto the surface led to the formation of an ordered array of metal clusters. In a similar approach using argon-ion etching the S-layer of Deinococcus radiodurans was used for patterning ferromagnetic films [34]. A uniform hexagonal pattern of 10 nm wide dots and lattice constants of 18 nm was fabricated from 2.5 nm-thick sputter-coated Co, FeCo, Fe, FeNi, and NiFe films. More recently, wet chemical processes were developed for the fabrication of metallic and semiconducting nanoparticle arrays using S-layers as templates [35–38]. In a first approach, self-assembly products from the S-layer protein of Geobacillus stearothermophilus NRS2004/3a variant 1 and Bacillus sphaericus CCM2177 were used for biocrystal templating of CdS superlattices [35]. Addition of a Cd(II) solution followed by slow reaction with hydrogen sulfide (H2 S) resulted in site-specific nucleation in the pore regions producing organized arrays of CdS nanoparticles. These experiments were repeated with the S-layer protein from Bacillus sphaericus CCM2177 recrystallized as monolayers on silicon wafers. After introduction of thiol groups on the S-layer surface, the protein structure was used as template for the precipitation of a tetrachloroauric (III) acid solution [36] (Fig. 5). Reduction of the gold (Au(III)) was either

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7. SPATIAL CONTROL OF THE S-LAYER REASSEMBLY

Figure 5. Transmisson electron micrographs of gold nanoparticles (5 nm diameter) formed in the pores of the square lattice of the S-layer of Bacillus sphaericus CCM2177 by wet chemistry. The S-layer has square lattice symmetry and a lattice constant of 13.1 nm. Bar, 50 nm.

performed by exposing the metalized S-layer to an electron beam in a transmission electron microscope or by slow reaction with H2 S. Gold nanoparticles with diameters of 4–5 nm were formed. Transmission electron microscopical studies in combination with digital image processing demonstrated that the metal nanoparticles had been formed in the pore region of the S-layer. As determined by electron diffraction, the gold nanoparticles were crystalline (cubic lattice symmetry) but in the long-range order not crystallographically aligned. The wet chemical approach was also used in our group in the precipitation of palladium, nickel, platinum, lead, and iron nanoparticle arrays (unpublished results). Wet chemistry was also applied for producing platinum nanoparticles on the S-layer of Sporosarcina ureae [37–38]. One morphological unit of the S-layer lattice of Sp. ureae revealed seven Pt cluster sites with diameters of ca. 1.9 nm. An alternative method for generating regularly arranged nanoparticles arrays on S-layers is based on the binding of preformed standardized nanoparticles. Based on the work on binding biomolecules, such as enzymes or antibodies, onto S-layers (Fig. 4) it has already been demonstrated that gold or CdSe nanoparticles can be electrostatically bound in regular arrangements on S-layers [39, 40] (Fig. 6). The formation of superlattices was possible due to the repetitive arrangement of functional groups such as carboxylic acid, hydroxyl, and amino groups. The nanoparticles were either negatively charged due to surface citrate ions or positively charged due to surface capping with poly-l-lysine.

Figure 6. Transmission electron micrograph of preformed gold nanoparticles (5 nm diameter) regularly bound on the square lattice of the S-layer of Bacillus sphaericus CCM2177. Bar, 100 nm.

While S-layer protein templates allow a precise deposition of nanoparticles with spatial resolution on the molecular scale, it is also necessary to spatially control the assembly of S-layers within (sub)micrometer resolution on the substrate. This will allow the deposition of nanoparticle arrays as functional units on target areas with micrometer scale spacing. This may be especially useful when hybrid micronanoelectronic structures are developed. To approach this task, inexpensive conventional optical lithography [41] and soft lithography (micromoulding) has already been utilized. Deep ultraviolet radiation (ArF; wavelength = 193 nm) was used to pattern monolayers of the S-layer protein of Bacillus sphaericus CCM2177 recrystallized on silicon wafers (Fig. 7). The S-layer was ablated from the silicon surface at the exposed regions but retained its crystalline and functional integrity in the unexposed areas. Subsequently, the remaining unexposed S-layer areas could be used to bind functional molecules or nanoparticles. For using patterned S-layers as nanonatural resists, the S-layer was reinforced for subsequent reactive ion-etching by silylation. Micromoulding in capillaries was also used for spatially controlling the recrystallization of S-layer proteins on silicon hν

a

Si

b

Si

c

d

Si

Si

Figure 7. Schematic drawing of patterning S-layer protein monolayers on silicon substrates by optical lithography. A microlithographic mask is brought in direct contact with the S-layer (a). Upon exposure to ArF excimer laser irradiation the S-layer is removed in the exposed regions but remains unaffected in the unexposed areas (b). The remaining S-layer may either be used as an ultra high resolution resist after enhancement by a metallization procedure (c) or for binding molecules and nanoparticles (d). Scanning force microscopical image of a patterned S-layer (e), Bar, 3
m. Reprinted with permission from [1], U. B. Sleytr et al., Angew. Chem. Int. Ed. 38, 1034 (1999). © 1999, Wiley-VCH.

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wafers. For this approach, a poly(dimethylsiloxane) (PDMS) mould was placed on a silicon wafer and the empty channels were filled with S-layer protein solution. Subsequently, the PDMS mould was removed after a defined recrystallization time and a network of S-layer protein monolayers was obtained [42].

8. LIPID MEMBRANES A fascinating intrinsic feature of S-layer proteins is the possibility to self-assemble the isolated constituent protein subunits and oligomeric precursors on liquid/lipid interfaces like Langmuir films, and on planar and spherical bilayer lipid membranes to form closed crystalline S-layer lattices [43]. This section focuses on the formation and application potential of these composite structures mimicking the supramolecular assembly of archaeal cell envelope structures (Fig. 8a) composed of a cytoplasmic membrane and a closely associated S-layer [44, 45]. In this biomimetic architecture (Fig. 8b) either a tetraether lipid monolayer or a phospholipid mono- or bilayer replaces the cytoplasmic membrane and bacterial S-layer proteins are recrystallized on one or both sides of the lipid film [3, 4, 43]. The aim of this biomimetic approach is to reinforce the fragile lipid membranes [46–49], but retaining its fluidity and also isolating structural and dynamic properties [50–56]. Since a great variety of biological processes are membranemediated, there has always been lively interest in the mesoand macroscopic reconstitution of biological membranes.

Particularly functional integral and peripheral membrane proteins have a broad potential for biomimetic, biotechnological, and bioanalytical applications. Langmuir lipid films [57–58], the most simple model lipid membranes, are very suitable to study the recrystallization process of S-layer subunits since the charge and size of the lipid head groups and the phase state of the lipid layer at the air/water interface can be reproducibly controlled (Fig. 9a). Moreover, the mutual influence of the S-layer lattice and the lipid monolayer can be investigated in great detail. Generally, the recrystallization of S-layer proteins forming a closed monolayer on phospholipid films depends on (1) the phase state of the lipid film; (2) the nature of the lipid head group (size, polarity, and charge); and (3) the ionic content and pH of the subphase [59–60]. The binding force between exposed domains on the S-layer protein and certain lipid head groups is primarily electrostatic interaction. Large, closed S-layer monolayers could be obtained on lipid films with positively charged and zwitterionic head groups [60]. In contrast, S-layer proteins crystallized poorly under most lipids with negatively charged

Assembly of lipid molecules into membranes

Injection of S-layer subunits into the subphase

Microscopical images of S-layer/lipid structures

air monolayer

transmembrane protein liquid

S-layer

a archaeal cell envelope lipid membrane

S-layer lattice

a phospholipid membrane

b

liposome

S-layer coated liposome

tetraetherlipid membrane

bilayer

liquid b Figure 8. Schematic illustration of (a) an archaeal cell envelope structure composed of the cytoplasma membrane with integral membrane proteins and an S-layer lattice integrated into the cytoplasma membrane. (b) Copying this supramolecular architecture, biomimetic membranes have been generated. The cytoplasma membrane is replaced by a phospholipid bilayer or a membrane-spanning (tetraether) lipid monolayer and bacterial S-layer proteins are crystallized from the subphase to form a closed lattice on the lipid film. Subsequently, integral membrane proteins can be reconstituted in the composite S-layer-supported lipid membrane. Reprinted with permission from [4], U. B. Sleytr et al., Progr. Surf. Sci. 68, 231 (2001). © 2001, Elsevier Science.

c Figure 9. Schematic illustrations of lipid films generated by different procedures and the crystallization of S-layer protein, which has been injected into the subphase. A coherent S-layer lattice can be generated on (a) phospholipid or tetraetherlipid monolayers floating on the air/subphase interface; (b) spontaneously self-assembled spherical phospholipid bilayer membranes (liposomes); and (c) a phospholipid bilayer spanning a Teflon aperture that separates two compartments filled with subphase. On the right-hand-side, a TEM image of each composite S-layer/lipid membrane is given. The bar in the TEM-images represents 100 nm. Modified with permission from [4], U. B. Sleytr et al., Progr. Surf. Sci. 68, 231 (2001). © 2001, Elsevier Science.

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head groups. The crystallization process could be facilitated by adding a small amount of positively charged lipid analogue [61] and surfactants like hexadecylamine [50, 62] to the zwitterionic lipids. The influence of an attached S-layer lattice on the hydrophobic part of the lipid film was investigated [59]. At a low surface pressure of the lipid monolayer (∼5 mN/m), the protein crystallization affected the order of the alkane chains and drove the fluid lipid into a state of higher order. Injection of S-layer protein underneath a condensed monolayer (∼28 mN/m) resulted only in a slight increase in the segmental alkyl chain order [52–54, 59]. However, the results provided definite evidence that the S-layer protein did not interpenetrate the hydrophobic section of the lipid monolayer. By contrast to the hydrophobic part, a partial insertion of domains on the S-layer protein into the head group region of the lipid monolayer has been observed [52–54]. Presumably, one amino acid side chain per three to four lipids dips into the lipid head group region at least to the phosphate moieties and probably further beyond. To accommodate the interpenetrating amino side chains, the orientation of the lipid head groups was tilted toward the surface normal. It is not known whether the amino acid side chains interpenetrated the lipid monolayer rather homogeneously, or, more likely, peptides might cluster within the polar part of the lipid membrane. In the latter case, some lipid head groups directly associated with amino acid side chain groups were strongly affected while others, for example, located at the membrane region spanning the pore of the S-layer, were not [52].

9. LIPOSOMES Lipid molecules spontaneously self-assemble in an aqueous environment forming closed, spherical structures called liposomes [63–65]. In order to enhance the stability of liposomes and provide a biocompatible outermost surface structure for controlled immobilization, isolated S-layer proteins were crystallized on the outer shell of vesicles (Fig. 9b) [55, 62, 66–68]. These S-layer–coated liposomes are biomimetic structures resembling the supramolecular construction principle of virus envelopes and cell wall envelope structures of archaea. The crystallization of S-layer proteins resulted in a completely covered surface and did not affect the morphology of the liposomes [62, 68]. In order to enhance the stability of liposomes composed of a single lipid bilayer and provide a biocompatible outermost surface structure, S-layer lattices are recrystallized on their surface. Specific physicochemical surface properties and functions of S-layer–coated liposomes are introduced by crosslinking and/or chemical modifications of S-layer lattices, by immobilization of functional molecules or by using genetically engineered S-layer fusion proteins. The potential of S-layer– coated liposomes is currently exploited for new drug delivery and cell targeting vehicles in medicine, adjuvants in vaccination, signal enhancers carriers in medical diagnostics as well as in analytical biochemistry, and solubilizers for various ingredients [2–5].

10. PLANAR LIPID MEMBRANES Lipid bilayers as relevant models for biological membranes have improved the knowledge on structure and function of cell envelopes. It became evident that a stabilization of lipid bilayers is imperatively necessary to utilize the function of cell membrane components for practical applications, as typically free-standing bilayer lipid membranes (BLMs) only survive for minutes to hours and are very sensitive toward vibration and mechanical shocks [48–49, 69]. S-layer proteins can be exploited as supporting structures for BLMs (Fig. 9c), since they stabilize the lipid film and largely retain their physical features (e.g., thickness, fluidity). An uniform hydrostatic pressure has been applied to unsupported and S-layer–supported lipid membranes [70]. Unsupported lipid membranes, independent from which side pressurized and S-layer–supported lipid membranes pressurized from the lipid-faced side revealed a pronounced increase in capacitance. A maximal hydrostatic pressure gradient of 11 N/m2 resulted in an almost doubling of the capacitance of the bilayers. By contrast, the S-layer–supported lipid membrane pressurized from the protein-faced side revealed only a minute increase in capacitance reflecting only minor pressure induced area expansion. In this context, it is interesting to note that mechano-sensitive ion channels like the family of epithelial Na+ -channels (ENaCs) can be activated by a hydrostatic pressure difference [71, 72]. Thus, S-layer–supported lipid membranes may be used to investigate the water flow-induced activation of ENaCs by excluding at the same time a curvature-induced mechanical activation if the composite structure is pressurized from the protein-faced side. Up to now, the membrane-active peptides alamethicin, gramicidin, and valinomycin and the pore-forming protein -hemolysin have been reconstituted in planar S-layer– supported lipid membranes [73–75]. All membrane-active molecules exhibited the same ion-selectivity and channel conductance, respectively, compared with the reconstitution in corresponding freestanding lipid membranes. But most important, functionalized S-layer/lipid structures showed the advantage of an enhanced long-term stability [73–74]. In addition, the gating of single -hemolysin pores reconstituted in composite S-layer/lipid membranes could be performed [75].

11. S-LAYER ULTRAFILTRATION MEMBRANE (SUM)-SUPPORTED LIPID MEMBRANES The following two subsections describe the most promising methods to attach lipid membranes on porous or solid supports (Fig. 10) in order to generate attractive membrane protein-based devices for technical applications. In general, lipid membranes generated on a porous support combine the advantage of possessing an essentially unlimited ionic reservoir on each side of the bilayer lipid membrane and easy manual handling. However, the surface properties of porous supports, like roughness or great differences in pore size, significantly impaired the stability of attached BLMs. In this section, the strategy to use an S-layer ultrafiltration

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a

metal electrode

b

gold substrate

c

gold electrode

d

gold electrode

e

gold or silicon substrate

f

SUM

S-layer protein

phospholipid

thiolipid

membrane spanning lipid

thiol group solvent

thiopeptide

polymer

lipid tethers

Figure 10. Schematic drawings illustrating the concept of solidsupported lipid membranes. In (a), a painted lipid membrane was generated on a metal electrode. The roughness of the metal surface causes a considerable amount of solvent in-between the two phospholipid leaflets. In (b), a soft polymer cushion (actual thickness is much larger than that of the lipid bilayer) is present as separating, biocompatible layer. In (c), the generation of the lipid bilayer makes use of the strong chemisorption of thiolipids to gold. The second leaflet of phospholipids was transferred from a Langmuir trough or by vesicle fusion onto the thiolipid monolayer. (d) The increase of the ionic reservoir between the membrane and the gold electrode can be accomplished by the addition of tether lipid molecules or thiopeptides. (e) As an alternative, an S-layer is located between the solid support and the lipid layer. Optionally, the external leaflet of the lipid bilayer can be stabilized by the attachment of an S-layer cover. In (f), the lipid bilayer has been generated on the S-layer on the surface of an S-layer ultrafiltration membrane. Again, the external leaflet of the lipid bilayer can be stabilized by an attached S-layer cover. Reprinted with permission from [4], U. B. Sleytr et al., Progr. Surf. Sci. 68, 231 (2001). © 2001, Elsevier Science.

membrane (SUM) with the S-layer as a stabilizing and biochemical layer between the BLM and the porous support is described (Fig. 10f). S-layer ultrafiltration membranes are isoporous structures with very sharp molecular exclusion limits and were manufactured by depositing S-layer–carrying cell wall fragments under high pressure on commercial microfiltration membranes (MFMs) with an average pore

size of approximately 0.4
m [76–78]. After deposition, the S-layer lattices are crosslinked leading to a coherent smooth surface ideally suited for depositing lipid membranes. Due to the additional S-layer cover, SUMs revealed a smoother surface than MFMs. Composite SUM-supported bilayers are tight structures with breakdown voltages well above 500 mV during their whole life-time of about 8 hours [79]. For a comparison, lipid membranes on a plain nylon MFM revealed a lifetime of about 3 hr. When voltage ramps were applied, the BLM on the MFM ruptured at a magnitude of about 210 mV. Specific capacitance measurements and reconstitution experiments revealed that the lipid membrane on the SUM consisted of two layers as the pore-forming protein -hemolysin could be reconstituted into lytic channels. For the first time, opening and closing behavior of even single HL pores could be measured with membranes generated on a porous support. In contrast, no pore formation was observed with BLMs generated on the MFM [79]. The present results indicated that the S-layer lattices of the SUM represent a water-containing layer for the closely attached lipid bilayer and provide also a natural environment for protein domains protruding from the membrane. The main phospholipid (MPL) of Thermoplasma acidophilum, a membrane-spanning tetraether lipid, has also been transferred on a SUM by a modified Langmuir– Blodgett technique [80]. This is a very easy and reproducible method to generate supported lipid membranes. Again, SUM-supported MPL membranes allowed reconstitution of functional molecules, as proven by gramicidin, and measurements on single pores could be performed. S-layer ultrafiltration membrane-supported MPL membranes showed a lifetime of 83 ± 29 hr. An additional monomolecular S-layer protein lattice, recrystallized on the lipid-faced side, increased the lifetime significantly to 212 ± 31 hr [80]. In addition, the thermal, chemical, and long-term stability of tetraether lipids [81–83] and mechanical stability of SUMsupported membranes [79] have attracted interest in their potential with respect to biotechnological applications such as membrane protein-based biosensors for DNA-sequencing and high throughput screening and may finally end up in the lab-on-a-chip technology [84–87].

12. SOLID-SUPPORTED LIPID MEMBRANES Solid-supported membranes were developed in order to overcome the fragility of freestanding BLMs, but also to enable biofunctionalization of inorganic solids (e.g., semiconductors, gold-covered surfaces) for the use at sensing devices [88–90]. Various types of solid-supported lipid membranes are reported in the literature (Fig. 10a–d) [43, 91– 96]. However, they often show considerable drawbacks as there is a limited ionic reservoir at the side facing the solid support, membranes often appear to be leaky (noninsulating), and large domains protruding from the membrane may become denatured by the inorganic support. Again, S-layer proteins have been studied to elucidate their potential as stabilizing and separating ultrathin layers, which also maintains the structural and dynamic properties of the lipid membranes (Fig. 10e).

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Silicon substrates have been covered by a closed S-layer lattice and bilayers were deposited by the Langmuir– Blodgett technique [57, 58, 97]. Lateral diffusion of fluorescently labeled lipid molecules in both layers have been investigated by fluorescence recovery after photobleaching studies [51]. In comparison with hybrid lipid bilayers (lipid monolayer on alkylsilanes) and lipid bilayers on dextran, the mobility of lipids was highest in S-layer–supported bilayers. Most important, the S-layer cover could prevent the formation of cracks and other inhomogenities in the bilayer [51]. These results have demonstrated that the biomimetic approach of copying the supramolecular architecture of archaeal cell envelopes opens new possibilities for exploiting functional lipid membranes at meso- and macroscopic scale. Moreover, this technology has the potential to initiate a broad spectrum of developments in many areas like sensor technology, diagnostics, (nano)biotechnology, electronic or optical devices, and high throughput screening for drug discovery.

13. CONCLUSIONS Basic and applied S-layer research has demonstrated that nature provides most elegant examples for nanometer size, molecular self-assembly systems. The remarkable intrinsic features of S-layer proteins and the possibility for combining S-layer lattices with other functional molecules (e.g., proteins, lipids, glycans, and nucleic acids) in a spatial predictable way make them unique structural and patterning elements in molecular nanotechnology and biomimetics. The infrastructure needs for nanobiotechnology and, in particular, for S-layer technology are similar to those for other fields: multiuser facilities providing access to specialized technologies, funding mechanisms, and organization structures encouraging multidisciplinary teams for breaking new grounds.

GLOSSARY Secondary cell wall polymer (SCWP) The rigid cell wall of Gram-positive bacteria contains, beside peptidoglycan, large amounts of accessory (secondary) cell wall polymers (SCWPs) composed of either teichoic acids, teichuronic acids, lipoteichoic acids, or lipoglycans. S-layer Bacterial surface layer. Crystalline bacterial cell surface layers (S-layers) are one of the most common outermost cell envelope components of prokaryotic organisms (archaea and bacteria). S-layer fusion protein Genetically engineered functionalized protein consisting of a (truncated) S-layer protein and a (biochemical) functionality fused to it either at the N- or C-terminal end. S-layer ultrafiltration membrane (SUM) Ultrafilter membranes consisting of a porous microfiltration membrane and a complete S-layer coating attached to it. The effective pore size is defined by the pores in the S-layer. Cut-off in the ultrafiltration range. Solid-supported lipid membrane A lipid membrane often functionalized by incorporated or attached biochemically active molecules attached to a solid support.

ACKNOWLEDGMENTS The contribution of Erika Györvary to the formation of nanoparticle arrays is gratefully acknowledged. This work was supported by the Austrian Science Fund (project P14419-MOB), the Austrian Federal Ministry of Education, Science, and Culture, the Austrian Federal Ministry of Transportation, Innovation, and Technology, the European Commission (5. FP, project BIOAND; IST-1999-11974 and Nanocapsules; HPRN-CT-2000-00159), and the Volkswagen Foundation (I/77710).

REFERENCES 1. U. B. Sleytr, P. Messner, D. Pum, and M. Sára, Angew. Chem. Int. Ed. 38, 1034 (1999). 2. U. B. Sleytr, M. Sára, and D. Pum, in “Supramolecular Polymerization” (A. Ciferri, Ed.), p. 177. Marcel Dekker, New York, 2000. 3. U. B. Sleytr, M. Sára, D. Pum, and B. Schuster, in “Nano-Surface Chemistry” (M. Rosoff, Ed.), p. 333. Marcel Dekker, New York, 2001. 4. U. B. Sleytr, M. Sára, D. Pum, and B. Schuster, Progr. Surf. Sci. 68, 231 (2001). 5. U. B. Sleytr, M. Sára, D. Pum, B. Schuster, P. Messner, and C. Schäffer, in “Biopolymers” (A. Steinbüchel and S. Fahnestock, Eds.), Vol. 7, p. 285, Wiley-VCH, Weinheim, 2002. 6. U. B. Sleytr and T. J. Beveridge, Trends Microbiol. 7, 253 (1999). 7. M. Sára and U. B. Sleytr, J. Bacteriol. 182, 859 (2000). 8. U. B. Sleytr, P. Messner, D. Pum, and M. Sára, in “Crystalline Bacterial Cell Surface Layer Proteins (S-Layers)” (U. B. Sleytr, P. Messner, D. Pum, and M. Sára, Eds.), p. 5. R. G. Landes Company, Austin, 1996. 9. T. J. Beveridge, Curr. Opin. Struct. Biol. 4, 204 (1994). 10. A. R. Archibald, in “Bacillus Subtilis and Other Gram-Positive Bacteria” (A. L. Sonnenshein, Ed.), p. 381. ASM Press, New York, 1993. 11. M. Sára, Trends Microbiol. 9, 47 (2001). 12. M. Sára and U. B. Sleytr, J. Bacteriol. 182, 859 (2000). 13. A. Lupas, H. Engelhardt, J. Peters, U. Santarius, S. Volker, and W. Baumeister, J. Bacteriol. 176, 1224 (1994). 14. R. D. Bowditch, P. Baumann, and A. A. Yousten, J. Bacteriol. 171, 4178 (1989). 15. S. Ebisu, A. Tsuboi, H. Takagi, Y. Naruse, H. Yamagata, N. Tsukagoshi, and S. Udaka, J. Bacteriol. 172, 1312 (1990). 16. H. Engelhardt and J. Peters, J. Struct. Biol. 124, 276 (1998). 17. N. Ilk, P. Kosma, M. Puchberger, E. M. Egelseer, H. F. Mayer, U. B. Sleytr, and M. Sára, J. Bacteriol. 181, 7643 (1999). 18. B. Kuen, A. Koch, E. Asenbauer, M. Sára, and W. Lubitz, J. Bacteriol. 179, 1664 (1997). 19. M. Lemaire, I. Miras, P. Gounon, and P. Beguin, Microbiol. 144, 211 (1998). 20. U. B. Sleytr, M. Sára, C. Mader, B. Schuster, and F. M. Unger, Austrian Patent No. A 409, 423 (2002). 21. D. Pum, M. Sára, and U. B. Sleytr, in “Immobilised Macromolecules: Application Potential” (U. B. Sleytr, P. Messner, D. Pum, and M. Sára, Eds.), p. 141. Springer-Verlag, London, 1993. 22. C. Weiner, M. Sára, and U. B. Sleytr, Biotechnol. Bioeng. 43, 321 (1994). 23. A. Breitwieser, S. Küpcü, S. Howorka, S. Weigert, C. Langer, K. Hoffmann-Sommergruber, O. Scheiner, U. B. Sleytr, and M. Sára, BioTechniques 21, 918 (1996). 24. A. Breitwieser, C. Mader, I. Sochor, K. Hoffmann-Sommergruber, W. Aberer, O. Scheiner, U. B. Sleytr, and M. Sára, Allergy 53, 786 (1998).

702 25. U. B. Sleytr and M. Sára, Trends Biotechnol. 15, 20 (1997). 26. D. Moll, C. Huber, B. Schlegel, D. Pum, U. B. Sleytr, and M. Sára, Proc. Natl. Acad. Sci. USA 99, 14646 (2002). 27. N. Ilk, C. Völlenkle, E. M. Egelseer, A. Breitwieser, U. B. Sleytr, and M. Sára, Appl. Environ. Microbiol. 68, 3251 (2002). 28. D. Pum, M. Weinhandl, C. Hödl, and U. B. Sleytr, J. Bacteriol. 175, 2762 (1993). 29. D. Pum and U. B. Sleytr, Supramol. Sci. 2, 193 (1995). 30. D. Pum and U. B. Sleytr, Colloids and Surfaces A: Physicochem. Eng. Aspects 102, 99 (1995). 31. K. Douglas and N. A. Clark, Appl. Phys. Lett. 48, 676 (1986). 32. K. Douglas, G. Devaud, and N. A. Clark, Science 257, 642 (1992). 33. T. A. Winningham, H. P. Gillis, D. A. Choutov, K. P. Martin, J. T. Moore, and K. Douglas, Surf. Sci. 406, 221 (1998). 34. M. Panhorst, H. Brückl, B. Kiefer, G. Reiss, U. Santarius, and R. Guckenberger, J. Vac. Sci. Technol. B 19, 722 (2001). 35. W. Shenton, D. Pum, U. B. Sleytr, and S. Mann, Nature 389, 585 (1997). 36. S. Dieluweit, D. Pum, and U. B. Sleytr, Supramol. Sci. 5, 15 (1998). 37. M. Mertig, R. Kirsch, W. Pompe, and H. Engelhardt, Europ. Phys. J. 9, 45 (1999). 38. W. Pompe, M. Mertig, R. Kirsch, R. Wahl, L. C. Ciachi, J. Richter, R. Seidel, and H. Vinzelberg, Z. Metallkd. 90, 1085 (1999). 39. S. R. Hall, W. Shenton, H. Engelhardt, and S. Mann, Chem. Phys. Chem. 3, 184 (2001). 40. E. Györvary, A. Schroedter, D. V. Talapin, H. Weller, D. Pum, and U. B. Sleytr, J. Nanosci. Nanotechnol. (submitted) (2003). 41. D. Pum, G. Stangl, C. Sponer, W. Fallmann, and U. B. Sleytr, Colloids and Surfaces B: Biointerfaces 8, 157 (1997). 42. E. S. Györvary, A. O’Riordan, A. Quinn, G. Redmond, D. Pum, and U. B. Sleytr, Nanoletters, in press. 43. B. Schuster and U. B. Sleytr, Rev. Mol. Biotechnol. 74, 233 (2000). 44. O. Kandler, in “Archaebacteria” (O. Kandler, Ed.), p. 149. Gustav Fischer Verlag, Stuttgart, 1982. 45. H. König, Can. J. Microbiol. 34, 395 (1988). 46. H. F. Knapp, W. Wiegräbe, M. Heim, R. Eschrich, and R. Guckenberger, Biophys. J. 69, 708 (1995). 47. X. Lu, A. Ottova-Leitmannova, and T. H. Tien, Bioelectrochem. Bioenerg. 39, 285 (1996). 48. T. H. Tien and A. L. Ottova, J. Membr. Sci. 189, 83 (2001). 49. M. Zviman and H. T. Tien, Biosens. Bioelectron. 6, 37 (1991). 50. B. Schuster, U. B. Sleytr, A. Diederich, G. Bähr, and M. Winterhalter, Eur. Biophys. J. 28, 583 (1999). 51. E. Györvary, B. Wetzer, U. B. Sleytr, A. Sinner, A. Offenhäusser, and W. Knoll, Langmuir 15, 1337 (1999). 52. M. Weygand, B. Wetzer, D. Pum, U. B. Sleytr, K. Kjaer, P. B. Howes, and M. Lösche, Biophys. J. 76, 458 (1999). 53. M. Weygand, M. Schalke, P. B. Howes, K. Kjaer, J. Friedman, B. Wetzer, D. Pum, U. B. Sleytr, and M. Lösche, J. Mater. Chem. 10, 141 (2000). 54. M. Weygand, K. Kjaer, P. B. Howes, B. Wetzer, D. Pum, U. B. Sleytr, and M. Lösche, J. Phys. Chem. B 106, 5793 (2002). 55. C. Mader, S. Küpcü, M. Sára, and U. B. Sleytr, Biochim. Biophys. Acta 1418, 106 (1999). 56. B. Wetzer, D. Pum, and U. B. Sleytr, J. Struct. Biol. 119, 123 (1997). 57. A. Zasadzinski, R. Viswanathan, L. Madson, J. Garnaes, and K. D. Schwartz, Science 263, 1726 (1994). 58. I. Langmuir and V. J. Schaefer, J. Am. Chem. Soc. 59, 1406 (1937). 59. A. Diederich, C. Hödl, D. Pum, U. B. Sleytr, and M. Lösche, Colloids and Surfaces B: Biointerfaces 6, 335 (1996). 60. B. Wetzer, A. Pfandler, E. Györvary, D. Pum, M. Lösche, and U. B. Sleytr, Langmuir 14, 6899 (1998).

Molecular Nanotechnology with 2D Protein Crystals 61. R. Hirn, B. Schuster, U. B. Sleytr, and T. M. Bayerl, Biophys. J. 77, 2066 (1999). 62. S. Küpcü, M. Sára, and U. B. Sleytr, Biochim. Biophys. Acta 1235, 263 (1995). 63. D. Papahadjopoulos, Ann. N. Y. Acad. Sci. 308, 1 (1978). 64. D. D. Lasic, in “Structure and Dynamics of Membranes” (R. Lipowsky and E. Sackmann, Eds.), p. 491. Elsevier, Amsterdam, 1995. 65. D. D. Lasic. Am. Sci. 80, 20 (1992). 66. C. Mader, S. Küpcü, U. B. Sleytr, and M. Sára, Biochim. Biophys. Acta 1463, 142 (2000). 67. T. Hianik, S. Küpcü, U. B. Sleytr, P. Rybár, R. Krivánek, and U. Kaatze, Coll. Surf. A 147, 331 (1999). 68. S. Küpcü, K. Lohner, C. Mader, and U. B. Sleytr, Molec. Membrane Biol. 15, 69 (1998). 69. B. Raguse, V. Braach-Maksvytis, B. A. Cornell, L. G. King, P. D. J. Osman, R. J. Pace, and L. Wieczorek, Langmuir 14, 648 (1998). 70. B. Schuster and U. B. Sleytr, Biochim. Biophys. Acta 1563, 29 (2002). 71. I. I. Ismailov, V. G. Shlyonsky, and D. J. Benos, Proc. Natl. Acad. Sci. USA 94, 7651 (1997). 72. M. S. Awayda, I. I. Ismailov, B. K. Berdiev, and D. J. Benos, APStracts 2, 49 (1995). 73. B. Schuster, D. Pum, and U. B. Sleytr, Biochim. Biophys. Acta 1369, 51 (1998). 74. B. Schuster, D. Pum, O. Braha, H. Bayley, and U. B. Sleytr, Biochim. Biophys. Acta 1370, 280 (1998). 75. B. Schuster and U. B. Sleytr, Bioelectrochem. 55, 5 (2002). 76. M. Sára and U. B. Sleytr. J. Bacteriol. 169, 2804 (1987). 77. S. Weigert and M. Sára, J. Membrane Sci. 106, 147 (1995). 78. S. Weigert and M. Sára, J. Membrane Sci. 121, 185 (1996). 79. B. Schuster, D. Pum, M. Sára, O. Braha, H. Bayley, and U. B. Sleytr, Langmuir 17, 499 (2001). 80. B. Schuster, S. Weigert, D. Pum, M. Sára, and U. B. Sleytr, Langmuir, in press. 81. M. G. L. Elfterink, J. G. de Wit, A. J. M. Driessen, and W. N. Konings, Biochim. Biophys. Acta 1193, 247 (1994). 82. C. Nicolini, Biosens. Bioelectron. 10, 105 (1995). 83. B. A. Cornell, G. Krishna, P. D. Osman, R. D. Pace, and L. Wieczorek, Biochem. Soc. Trans. 29, 613 (2001). 84. J. J. Kasianowicz, E. Brandin, D. Branton, and D. W. Deamer, Proc. Natl. Acad. Sci. USA 93, 13770 (1996). 85. T. Stora, J. H. Lakey, and H. Vogel, Angew. Chem. Int. Ed. 38, 389 (1999). 86. D. W. Deamer and M. Akeson, Trends Biotechnol. 18, 147 (2000). 87. H. Bayley and P. S. Cremer, Nature 413, 226 (2001). 88. E. Sackmann, Science 271, 43 (1996). 89. E. Sackmann and M. Tanaka, Trends Biotechnol. 18, 58 (2000). 90. B. A. Cornell, V. L. Braach-Maksvytis, L. G. King, P. D. Osman, B. Raguse, L. Wieczorek, and R. J. Pace, Nature 387, 580 (1997). 91. H. M. McConnell, T. H. Watts, R. M. Weis, and A. A. Brian, Biochim. Biophys. Acta 864, 95 (1986). 92. E. Kalb, S. Frey, and L. K. Tamm, Biochim. Biophys. Acta 1103, 307 (1992). 93. A. L. Plant, Langmuir 9, 2764 (1993). 94. S. Heyse, T. Stora, E. Schmid, J. H. Lakely, and H. Vogel, Biochim. Biophys. Acta 1376, 319 (1998). 95. D. P. Nikolelis, T. Hianik, and U. J. Krull, Electroanalysis 11, 7 (1999). 96. W. Knoll, C. W. Frank, C. Heibel, R. Naumann, A. Offenhäusser, J. Rühe, E. K. Schmidt, W. W. Shen, and A. Sinner, Rev. Mol. Biotechnol. 74, 137 (2000). 97. K. J. Blodgett, J. Am. Chem. Soc. 57, 1007 (1935).

Encyclopedia of Nanoscience and Nanotechnology

www.aspbs.com/enn

Molecular Planar Technology J. M. Köhler Institute for Physical High Technology, Jena, Germany

W. Fritzsche Technical University Ilmenau, Ilmenau, Germany

CONTENTS 1. Introduction 2. Limits of Nanopatterning by Conventional Planar Technology 3. Patterned Molecular Monofilms 4. Molecules and Nanoparticles as Lithographic Masks 5. Supermolecular Constructions at Surfaces 6. Nanoparticle Arrangements at Planar Surfaces 7. Outlook Glossary References

1. INTRODUCTION 1.1. Development of Planar Technology Planar technology represents a class of fabrication methods used in the development and production of electronic and other miniaturized devices. The whole computer industry, consumer electronics, and communication technology are currently based on chip devices made by planar technology. Planar technology also plays an important role in recent research developments in nanofabrication. The main issue in planar technology is the use of planar surfaces as a working plane or at least as a reference plane for all operations (Fig. 1). The limitation to planar surfaces is the key prerequisite for precise positioning of single micro- or nanofabricated, structural, and/or functional elements in relation to each other and in relation to an outside coordinate system. In addition, the convention of an operation plane supports a series of important fabrication technologies, in which the control of the third dimension is critical for achieving high quality in processes (including lithographic operations like photolithography and electron beam lithography) and in detection procedures using

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microscopic imaging by light, particle beams, or scanning probes. The possibility to control not only the size and shape but also the coordinates of all produced microdevices as well as nanofeatures in relation to outside coordinate systems is the precondition of the construction of physical interfaces between functional elements of different micro- and nanodevices and conventional devices including interfaces between machines and people. Thus, well-defined coordinates enable us to integrate huge numbers of single micropatterned functional elements inside microdevices and to integrate sets of integrated microdevices like integrated circuits (ICs), sensors, and interfaces, for example, in hierarchically organized complex device systems. Planar technology has its roots in traditional mechanical procedures, in which plane surfaces are produced or reproduced, such as mechanical planning. In addition to mechanical techniques, optical methods call for geometrical restriction to a planar reference surface. So the restrictions in the third dimension connected with the depth of optical focus have required the use of plane layers for lightsensitive films since the beginning of photography about 170 years ago. In photolithography, the use of a plane of optical focus in the exposure system has relied up to now on plane surfaces for the exposure of a photosensitive layer (e.g., in resist technologies in IC fabrication). The beginning of lithographic planar technology is connected with the development of art lithographs, of printed lithographs, and of printing technology in general. The use of planar surfaces is strongly connected with film technology. The deposition and the patterning of films, particularly thin-film technology, allow the construction of devices composed of different materials by planar technology. In many cases of thin-film technology application, the vertical dimension of thin-film structures can be neglected in comparison with the lateral extension of a surface. In other cases, the plane surface is reconstructed after patterning of films by planarization techniques. The preparation of plane surfaces for lithographic purposes started with the preparation of lithographic plates

Encyclopedia of Nanoscience and Nanotechnology Edited by H. S. Nalwa Volume 5: Pages (703–722)

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Figure 1. Planar technology as a fundamental principle for technological operations in lithographic micro- and nanofabrication.

by mechanical splitting of natural layered limestone. Alternatively, the mechanical preparation of plane and smooth surfaces was developed by different cutting, sawing, and polishing technologies. The plane surface of clean molten liquids is used in the fabrication of high-quality glass surfaces. Ultimate high-quality surfaces were obtained by splitting or sawing of single crystalline material along crystallographic planes with low Miller indices. This technique is used, for example, in the case of semiconductor single crystalline material like silicon or compound semiconductors. It is also practiced in the preparation of very smooth substrates for scanning probe techniques, in which mica is used because of its very good ability to separate along a crystal plane. With increasing aspect ratios (ratio of height to width of lithographic pattern), an urgent need for technical methods of high-quality planarization evolved. In addition to planarization by spinning processes for resists and other polymeric materials, chemo-mechanical polishing (CMP) was developed as a procedure for the planarization of topographic microfeatures consisting of inorganic materials or covered by inorganic top layers. Thin-film techniques are very essential for the buildup of micro- and nanodevices. Planar technology offers a powerful toolbox for the deposition of very different materials of homogeneous thickness on plane substrates. By techniques like chemical surface modification, spin-on deposition, evaporation, sputtering, reactive sputtering, chemical vapor deposition, galvanic film deposition, and molecular beam epitaxy, a material spectrum ranging from metals and alloys, semiconductors, and semiconductor compounds over different inorganic dielectric materials, piezoelectric materials to organic compounds, very different types of particular polymers are available. The typical thickness of thin films is in the range of about a few hundred nanometers up to a few micrometers. The homogeneity of thickness is better than 3% in most cases. The same techniques can also be used for the deposition of films with thicknesses in the range below 100 nm. Films of 10 to about 50 nm are particularly important for recent nanofabrication. Several techniques allow the preparation of homogenous films with a thickness of a few nanometers and in some cases down to one or a few atomic monolayers.

Molecular Planar Technology

For the patterning of thin films, additive, subtractive, and lift-off-techniques are used. The basic methods of micropatterning were mainly developed in the context of microelectronic fabrication between about 1965 and 1980. Subtractive patterning by etching represents the most important group of patterning methods. Some wet etching techniques have been used for the characterization of semiconductor materials since the middle of the twentieth century. Dry etching methods like plasma etching (PE), sputter etching, reactive ion etching (RIE), ion beam etching (IBE), and reactive ion beam etching (RIBE) are preferentially used for the preparation of submicrometer and nanometer features (Fig. 2). Its application in the submicrometer and in the nanometer range dates mainly from the end of the 1970s. Under wellcontrolled conditions and in case of low aspect ratios, wet chemical etching techniques are also applied for the preparation of submicrofeatures and nanofeatures in thin films.

1.2. Molecular Methods in Traditional Micropatterning and Nanofabrication Molecular materials and chemical processes involving inorganic as well as organic molecules already play an important role in conventional lithographic technologies. In film formation, chemical vapor deposition (CVD) techniques and plasma polymerization are typical examples of molecular methods. In CVD processes, molecular species are transported in the gaseous phase onto the substrate surface and chemically decomposed by physical activation processes releasing solid material at the surface. The by-products are gaseous and are removed through the gas phase. In addition to simple decomposition processes, interaction of different gas molecules takes place in many CVD processes, for example, for the formation of dielectrical layers containing silicon, like silicon oxide or silicon nitride made by reaction for halogen silanes or low-molecular-weight siloxanes with oxygen or ammonia. Organic films are made by surface polymerization processes. For this purpose, organic monomers are deposited through the gas phase onto a substrate surface and polymerize under plasma activation. Thin films of polymers are formed as a result.

Figure 2. Scheme of important lithographic and etching methods for nanofabrication in planar technology.

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Lithographic resist technologies represent the most important class of molecular-based techniques in IC fabrication. The formation of adhesive micromasks on top of functional layers to be patterned is a fundamental step in the major part of lithographic procedures. Therefore organic materials are needed that are stable against the attack in etching processes and can be processed by spinning, exposition, development, and rinsing. Different types of polymers and specific additives are used, depending on the lithographic procedures. Photosensitive additives based on naphthochinonbisazides are mainly used in positive photoresist processes to get high differences in the solubility of novolak polymer films in weak alkaline solutions used as developers. Acrylate-based polymers or similar materials are applied as resists in lithographical procedures using higher energy radiation, such as deep ultraviolet (DUV) lithography, in electron beam lithography (EBL), in ion beam lithography (IBL) and in X-ray lithography (XRL). Molecular processes are also used in conventional planar technology for the improvement of adhesion of films. The local adhesive forces of surfaces regarding further material deposition can be enhanced by the reaction of small molecules with reactive sites at the surface of substrates and deposited films. A hydrophobization of surfaces is of particular importance because of the strong chemisorption of water molecules in the presence of surface OH groups, which can bind water by dipole-dipole interaction and hydrogen bridge bonds and enhance the probability of adhesion of ions by ion-dipole interactions. Such surface layers containing water and ions considerably reduce the interface interactions between the substrate and a deposited film, could disturb film growth, and often leads to the destruction of films during micro- or nanopatterning. In addition, such films can cause local dielectric or semiconducting islands, which influence the electrical properties of the interface. These effects can be reduced, if the hydrogen of surface OH groups is replaced by small hydrophobic groups like trimethylsilyl. A typical example is hexamethyldisalazane (HMDS), which is often used for surface hydrophobization. It reacts by the formation of trimethylsiloxane groups at the surface and release of ammonia, which is easily be solved in aqueous solutions or quickly desorbed in the case of a gas-phase treatment. The capture of surface oxygen atoms suppresses the adsorption of water and ions at the substrate surface. Many etching procedures are also connected with molecular processes. Molecular interactions take place in a variety of wet etching processes as well as in reactive dry etching procedures. Molecular components in etching baths are used for the formation of soluble material from the film elements, which have to be removed. In addition to oxidizing agents, ligands for the formation of soluble complex compounds of ions formed by the chemical or electrochemical oxidation of film or substrate material are of particular importance in wet etching processes. For this purpose, small chemical species like halogenids or other ions and small molecules like ammonia are used, as are organic compounds. Multifunctional organic molecules like dicarbonic acids, dialcohols, hydroxycarbonic acids, diamines, amino acids, or related compounds are frequently introduced as chelated ligands in baths for wet etching.

Gaseous species or chemical species with high vapor pressure must be formed in dry etching procedures. Therefore, the atmospheres in reactive dry etching procedures contain gases supplying components for the formation of fastdesorbing molecules formed from the film materials, which have to be removed. Typically halogen gases and halogensubstituted low-weight alkanes as well as halogen sulfur compounds are constituents of various dry etch gases that provide halogen atoms for the formation of halogen compounds of metals and semiconductors with much lower evaporation temperatures than the metals, semiconductors, or their oxides. Organic polymers can easily be etched in oxygen plasmas because of the formation of CO, CO2 , and water, which are all gaseous at the reduced pressure in the vacuum etching devices and are always quickly desorbed from the surface.

1.3. Methodical and Geometrical Gaps Molecules themselves are nanoobjects. With the reduction of lithographic patterns down to the deep submicrometer range and into the nanometer range, the number of molecules included in single features of micro- or nanodevices or involved in their preparation has been reduced more and more. Conventional planar technology is changing from the use of a lot of anonymous molecules to the use of small ensembles of molecules or even single molecules. Both living nature and synthetic chemistry offer today a huge number of very different molecules. Only a small number of them are really applied in planar technology. The molecular materials used play an assisting role. The use of special molecular properties is restricted to their advantages in technological procedures. But up to now, specific functions of single molecules have not yet been used for the realization of new functions in devices. There is a broad discussion and extended research on the use of properties of single molecules in new electronic or sensing devices as well as in nanoactuators. However, most developments are far from real applications today. In the first view, the dimension of single molecules seems to be the important threshold in the merging of single molecular operations and planar technology. Small molecules are no larger than about half a nanometer on one side, and the standard nanofabrication by EBL and IBE produces in general patterns down to about 50 nm, which means there is a gap in the linear dimension of about two orders of magnitude. But there are much larger molecules. Folded macromolecules have diameters in the range of about 2 and 10 nm (Fig. 3). Stretched linear macromolecules are often much longer than the critical dimension of microfabrication in the mass production of ICs. The DNA of the lambda phage has a length of 16
m. This length is about two orders of magnitude higher then the smallest features made in IC mass production. In addition to linear structures, rings are also available from the biomolecular toolbox: plasmid DNA forms molecular rings with a diameter of several hundred nanometers. Therefore, the geometry cannot be the only and deciding gap between molecular and planar technology. More than geometry, the differences in technical methods are hindering the fast functional merging of molecular construction and lithographic operations.

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Figure 3. Comparison of the sizes of a small atom (hydrogen), a small molecule (methane), and biomacromolecules (proteins) and DNA (schematically).

The development of planar technology was mainly driven by physical thinking and mechanical, electrical, and electronic engineering. Plasma and particle physics, optics and sophisticated mechanical arrangements have mainly governed the development of the methods. Inorganic materials, metals, semiconductors as well as inorganic dielectrics play a much more important role than organic materials in the construction of micro and nanodevices up to now. Planar technology is traditionally connected with solid-state technology. Well-defined solids, single crystals, and stiff features determine the character of devices and the related preparation processes. The largest methodical gap lies in the differences concerning the relation of chemical or planar technological elements in space. Chemists are working with gases and fluids, which means ensembles of molecules consisting of huge numbers of single particles, which are oriented and positioned in a random manner. The number of molecules in a given system can be determined more or less precisely by measuring the concentration, but in normal cases the exact number of molecules in a given system is not known and often is not of importance. Chemistry and biochemistry offer many very small and well-differentiated new functional elements, but they do not supply them in the right spatial order, and so the production of suitable interfaces between molecules and solid-state planar devices is a strong challenge.

Molecular Planar Technology

geometry of a molecule on the basis of chemical structures in general, the overwhelming number of larger synthetical molecules possess only a defined binding topology, but this topology of chemical bonds allows the formation of a variety of different geometries due to rotable bonds. The number of possible geometries increases very quickly with the number of rotable bonds (Fig. 4). It can be restricted by stiff structural motifs in molecules (Fig. 5). In larger biomolecules like nucleic acids and particularly in proteins, a well-defined three-dimensional geometry is achieved by the self-organized formation of a secondary and a tertiary structure. The self-organizing folding procedure leads to highly organized structures in space, which can work like single nanomachines. Biology has learned during evolution to integrate these molecular nanomachines in supermolecular arrangements, which form the basic working units on the subcellular level. Therefore, molecular bilayers of membranes or rodlike supramolecular aggregates of proteins are used as skeleton structures. The combination of self-organizing molecules and the reduction of spatial dimension is one of the fundamental principles in the spatial organization in living beings at the molecular and subcellular level. It includes primarily the formation of linear molecules by condensation processes of standardized building units and the subsequent folding of these linear arrangements into three-dimensional nano-objects, as well as the subdivision of the three dimensions of a cell with membranes as two-dimensional objects. So living nature connects the inside coordinate systems of different molecular elements. The principle of merging of coordinate systems is successfully achieved by nature from the level of small molecules through macromolecules, organelles, and cells up to tissues, organs, and organisms. In synthetic chemistry, the internal coordinates of atoms are influenced not only by the motion of molecule parts due to movable bonds. In addition, the mobility of molecules in gases and liquids decouples the internal coordinate systems of all molecules (Fig. 6). Whereas the internal geometries at least in stiff molecules can be very precise, there is no defined relation between arbitrarily considered molecules inside a molecular ensemble. Supramolecular chemistry was

1.4. Geometries, Topologies, and the Problem of Related Coordinate Systems Chemistry and biochemistry deal with molecules, that means with very tiny objects of well-defined structure in the nanometer and in the subnanometer range. The atoms inside molecules have a very strong order because of their interconnection by chemical bonds. The bond network is described by the chemical structure. But this chemical structure is in general not a description of a certain geometry. It describes only a network of binding, a topology in the arrangement of atoms. Whereas in the case of small molecules the bond architecture allows one to describe the

Figure 4. The role of formation of chains and rings for the molecular geometry for a given binding topology. Example: organic molecules with six carbon atoms.

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Molecular Planar Technology

Therefore, there is an urgent need for the positioning and orientation of molecules and for their spatially welldefined integration in solid-state devices. The challenge of molecular planar technology is the development of methods and interfaces for the connection of molecules and synthetic procedures with planar micro- and nanodevices made by lithographic procedures. The integration of planar technology and chemical as well as biomolecular technologies gives us the hope of developing techniques in both fields within a common method pool that enable us to construct future single-molecule-based integrated devices.

2. LIMITS OF NANOPATTERNING BY CONVENTIONAL PLANAR TECHNOLOGY Figure 5. Stiffness in molecular construction modules: strategies for the reduction of rotational freedom.

started during the last two decades to overcome this problem. The synthesis of stiff molecules is one important step in the improvement of spatial organization of artificial molecules. The physical thinking in micro- and nanodevice development is determined by the construction of single elementary devices like a transistor, for example, and combining them into complex functional systems. If physicists and electronic engineers are planning and preparing new devices, they are working with well-defined numbers and well-defined positions and orientations of each elementary device in an integrated system. Each small feature has its own position and orientation. Planar technology provides organized micro- and nanoobjects with a certain precision in space. It is particularly suited for the arrangement of numerous elements in the frame of a unique internal coordinate system. It can also connect this internal coordinate system with external technical coordinates.

Figure 6. Problem of five coordinates in the oriented immobilization of molecules at chip surfaces for molecular nanoconstruction: positions x and y, orientation (3 axis).

2.1. Resolution Limits Caused by Lithographic Proximity Effects Standard lithographic methods are based on the interaction of resist materials with radiation. For the realization of a highly resolved pattern, radiation is focused. There are two factors that influence the localization of the action of radiation. At first, the miniaturization of the diameters of foci is principally restricted by the wavelength of the radiation used. Second, radiation penetrating and absorbed by the resist acts not only directly but also by secondary processes, which are connected with a certain length (which is characteristic for the specific processes), wavelengths, particle energies, temperatures, and materials. The spatial effects of the influence of focused radiation in the proximity of areas that have to be exposed are called proximity effects. In optical lithography, the diffraction of light is the main factor in proximity effects. In general, the probability of deposition of light energy decays with the characteristic length of the half-wavelength. This means that in case of the use of visible light, optical proximity effects influence thin-film elements in the area around lithographic edges with an extension between of about 0.2 and 0.4
m. This value can be reduced in the case of application of deep UV light (200 nm wavelength) to about 0.1
m. To reduce it below 100 nm, it is necessary to apply vacuum UV light. The increasing absorbance with decreasing wavelength of the most technical materials is a serious problem for the extension of UV lithography far into the vacuum UV region. The proximity effect of optical lithography can be enhanced by diffusion processes. In positive resist processes, the photoproduct—the chemical species formed by exposition—has a low molecular weight and is comparatively mobile in the polymer matrix. In the case of increasing temperature, and influenced by the pH value of the matrix, the photoproduct can diffuse out of the exposed region and enhance the solubility of resist in regions near the edges outside the exposed areas. In consequence, enlarged microfeatures are observed after the resist development. A strong reduction of exposure wavelength can reduce the diffraction-caused proximity effect significantly. Decreased diffraction effects are observed in the case of the use of weak X-rays (wavelengths typically in the range between 0.2 and 2 nm) or extreme UV light (EUV lithography, wavelengths typically in the range between 10 and 20 nm) for

708 the exposition. If a negative resist is used, the mobility of radiation products by diffusion is low, and, therefore, product diffusion does not enhance the small proximity effects. Unfortunately, XRL and EUV lithography suffer from difficulties in the construction of optical devices and the fabrication of lithographic masks. In addition, high-intensity and high-quality X-rays are only available from synchrotron rings and therefore are not available for local manufacturing. The generation of patterns by low-wavelength radiation is more easily realized with the use of particle beams, particularly accelerated electrons in EBL. Electron beams can be focused down to about 1 nm and are therefore particularly suited for nanolithographic purposes. However, the impact of high-energy electrons with target materials is accompanied by a cascade of electron molecule interactions, leading to the generation of an excitation volume around the axis of the incident beam inside the resist. This area has a diameter of up to some hundreds of nanometers, depending on beam energy and on the average atomic weight of the resist material. So this EBL proximity effect is also serious for the limitation of lithographic resolution. Fortunately, this effect can be reduced by several measures, for example, by the application of special local intensities near the edges of lithographic features, the application of multilayer resist technologies, and contrast-enhancing etching procedures.

2.2. Energy and Radiation Damages Radiation with particles or photons of higher energy is necessary to get lithographic probes that can be highly focused and thus supply high resolution. The problem is that molecular processes and the cleavage of chemical bonds inside solids are always activated by the interaction of one bond with one photon, electron, or ion. At lower energy of single particles, chemical processes are not activated or their activation can be controlled specifically by the choice of resonance energies. This effect is mainly used in photolithography in the visible range or the near-UV range. Incident photons activate only electrons of the dye molecules that should be brought to reaction, but the polymer matrix of resist and—still more important—the underlying material remain unaffected by the radiation. Preferably, electronic transitions between nonbinding orbitals and antibinding orbitals are used, to address specific photoprocesses by the absorption of photons of a certain wavelength. Photochemistry becomes more nonspecific if the energy in photolithography is shifted to the DUV photon range. Below a wavelength of 300 nm and particularly in the border range to the vacuum UV range, transitions between binding and antibinding orbitals can be caused. In addition to -* transitions, which only reduce double-bond interactions, -* transitions are addressed in the low-wavelength range, causing immediate photoinduced bond cleavage. Typically radicals are formed in this process. They can undergo further less or more nonspecific chemical reactions. The problem of nonspecific photochemical activation becomes more serious if EUV or X-ray photons are used for lithography. The absorption of this radiation does not primarily promote valence electrons, but leads to ionization from lower electronic shells. Cascades of relaxation processes are the consequence. In most materials, different processes of cleavage and new formation of chemical bonds are

Molecular Planar Technology

induced. The specifity of the process is low. Single photons cause many chemical reactions, because the photon energy is a multiple of single activation energies. So, a single photon of a weak X-ray with a wavelength of about 1 nM contains enough energy for the activation of 200 molecules. The ratio of energy transported by single particles to the activation energy of chemical processes is still higher in the case of electron and ion beam lithography. In EBL, acceleration voltages of about 20,000 to 40,000 V are usual. An electron energy of 20 kV exceeds the energy of a single chemical bond by 4 orders of magnitude. In the case of the application of high-energy ions, neutrons, or other heavy particles, this factor increases by up to 6 orders of magnitude when radiation in the MeV range is used. High-energy radiation penetrating resist layers can deposit their energy to a significant extent into underlying functional layers. So radiation damage is observed in single crystalline as well as in glassy materials. Molecular films are particularly sensitive to radiation damage. The danger of radiation damage is especially high in the case of EBL because electrons possess much higher penetration potency than ion beams. In addition, X-radiation which is secondarily formed by the impact of high-energy particles in the target, can contribute to the radiation damage. So the advantage of low diffraction of low-wavelength radiation is only one side of the coin. The effect of this radiation on certain target volumes instead of single molecules or bonds is the other side. Therefore, the application of high-energy lithographic probes is a compromise for nanotechnology. EBL and IBL are of high importance for the generation of nanofeatures in the range below 100 nm and down to a few nanometers. EUV lithography and XRL are candidates for the mass production of ICs and other devices with critical dimensions in the range down to a few tens of nanometers. All of these techniques can be handled and advantageously used if thin film-technology of solid material is scaled down into the micrometer and submicrometer range. But the application of this technology could become critical if the lower nanometer range is addressed. The applicability of processes with single molecules and for the activation of single bonds is very problematic because of the high-energy input, which has to be dissipated. In addition to these difficulties, it is expected that EBL, XRL, and related techniques will play a deciding role in nanofabrication. At the least, these techniques are needed for the preparation of medium nanometer-sized structural environments and interfaces for ultimate nanostructures. But they have to be accomplished by other techniques, which are able to address specifically molecules, supramolecular objects, and other nano-objects.

3. PATTERNED MOLECULAR MONOFILMS 3.1. Preparation of Patterned Molecular Surface Films The strategy of miniaturization in planar technology as well as in nanotechnology is frequently connected with the reduction of dimension. The ultimate extension of the principle

Molecular Planar Technology

of thin-film technology is the reduction of film thickness to one molecular or one atomic layer. Monolayer technologies are, therefore, very important for nanotechnology. The well-defined construction of monocrystalline inorganic thin films is usually achieved by so-called epitactic deposition processes. They are frequently applied for the production of highly pure compound semiconductor films [1]. These films consist of stacks of several dozen to several thousand atomic layers. A more sophisticated procedure is applied in the case of magnetic multilayer stacks for giant magnetoresistance devices. An alternating stack of ferroelectric and nonferroelectric films, each consisting of only a very few atoms, is built up by vacuum deposition processes and results in the specific magnetic coupling behavior of ferroelectric films [2]. In these films the atoms are more or less randomly distributed, so that the films are not defined by an exact number of atomic layers. Strongly alternating films of only atomic monolayers can be produced by the so-called ALE processes. ALE process is an atomic layer epitaxy realized by alternating CVD processes (chemical vapor deposition [3]) producing single atomic layers with a specific reactive surface for the chemical coupling of the molecules generating the following layer [4]. These inorganic monofilms can be patterned lithographically by standard resist procedures like photolithography, EBL, or IBL. In addition to ultrathin inorganic layers, molecular monofilms are of particular interest in nanotechnology. They provide the possibility of introducing organic materials in a well-defined way [5]. Molecular monofilms are the basic procedure for molecular construction at plane surfaces (Fig. 7). Ordered molecular monofilms can be produced by the technique of self-assembled monolayers (SAM) [6] or by the Langmuir–Blodgett Technique (LB technique) [7]. In SAMs, the ability of self-arrangement of molecules is used, which are adsorbed at a solid surface but possesses a high surface mobility. This effect is well characterized for thiol-containing molecules at metal and semiconductor surfaces (particularly in the case of alkyl thiols at gold); another example is silane layers on silicon surfaces. A broader spectrum of film-forming organic materials can be processed by LB

Figure 7. Variants of the use of self-organized molecular films in planar technology. Left: In-situ formation by amphiphilic species (SAM technique). Right: Film formation at an assistant interface (liquid surface) and transfer of the completely formed monofilm or molecular multilayer film to the solid surface.

709 techniques. Thereby, a liquid is used as an assisting phase to achieve a high mobility of amphiphilic molecules, which occupy a liquid surface. A molecular monofilm is produced by mechanical compression of amphiphilic molecules in the film at the liquid surface. This film can be transferred in a second step to a plane solid surface. The disadvantage of the LB technique is the comparatively high tendency of formation of holes in the films. These defects are transferred to the solid surface together with the films. Micro- and nanopatterning of molecular films can be easily realized by nanoimprinting or soft printing procedures [8]. Free-standing LB films work as nanoporous membranes and are suited for separation processes [9]. SAMs of functionalized alkanethiols on gold surfaces are a well-studied system. They rely on a simple principle: an alkane chain, typically with 10–20 methylene units, is given a head group with a strong preferential adsorption for the substrate used. Thiol (S-H) head groups and Au (111) substrates yield excellent results. A preferred adsorption of the thiol molecules from solution to the gold can be observed, creating a dense monolayer with the tail group pointing away from the surface. By variation of the tail groups, the resulting chemical surface functionality can be widely varied. Furthermore, it is also possible to chemically functionalize the tail groups by performing reactions after assembly of the SAM. The (111) direction is the preferred crystal face for alkanethiolate SAM preparation on gold substrates. It can be obtained either by using single crystal substrates or by evaporation of thin Au films on flat supports, typically glass or silicon. Several different solvents are usable at the low thiol concentrations in the lower millimolar range that are used in preparation of SAMs. Ethanol is the most commonly used solvent. Although the monolayer formation takes place very rapidly on the substrate, it is necessary to use incubation times of 12 h or more to obtain well-ordered, defect-free SAMs. Multilayers do not form, and adsorption times of several days are optimal for the formation of the highest quality monolayers. Molecular monofilms for planar nanotechnology can also be produced by the attachment of molecules at plane surfaces. The interaction of single molecules with surfaces can be based on nonspecific adsorption, more or less specific chemisorption, and highly specific chemical bonding. In general, the strength of a certain chemical bond alone does not decide the character of binding between molecules and surfaces. The kind of interaction, the mobility of the attached molecule, and the number and the local arrangement of bonds determine the character of immobilization. Therefore, the strategies of binding of molecules at surfaces are rather diverse. They range from simple van der Waals interactions through dipole-dipole interactions, interactions between antagonistic charged surfaces and molecules, charged molecules and permanent or induced dipole groups to more specific covalent and coordinative bonds as well as polyvalent interactions, for example, by groups of ionic and dipole-dipole interactions and including groups of directed H-bridge bonds. Molecular monofilms are sensitive against lithographic radiation. So some types of LB films and SAMs were patterned by EBL because of their intrinsic sensitivity for

710 electron beams [10–13]. Minimal lateral feature sizes of 50 nm and less can be achieved. Molecular monofilms can also be patterned with scanning force microscopes or scanning tunneling microscopes. Here feature sizes down to about 10 nm were realized [14]. Nanopatterned molecular monofilms support the construction of more complex molecular compositions at surfaces, if they contain additional functional groups for secondary coupling processes. So such film elements can be used in different film synthesis strategies like the introduction of special film geometries, the control of surface density of functional groups, the control of chemical surface compatibility, the embedding of special guest molecules like dyes or enzymes in patterned ultrathin films, or combinatorial surface-directed chemical synthesis. A special case of nanofunctional molecular monofilms is represented by biomembranes or biomimetic membranes including functional nanomachineries like membrane proteins. Such films can be transferred from solutions to chip surfaces to put them in a planar technological surrounding [15]. Biomembranes or bioanalogous membranes can be modified by the incorporation of different organic molecules, but also by the inclusion of metal and semiconductor nanoparticles [16].

3.2. Pattern Transfer from Molecular Films into Inorganic Layers In some cases, lateral nanopatterned molecular monofilms are interesting for the realization of nanotechnical functions. More frequently, they are applied as masks for the patterning of underlying inorganic functional films. Monomolecular films are suited as masks for wet chemical etching processes as well as for dry etching processes if the resistance of the monofilm against the etching medium is high enough. SAMs of octylthiole were tested as masks for the nanofabrication of GaAs films. Radiation by 50-keV EBL results in a positive resist behavior of the octadecylthiol film. The remaining film elements are resistive against an ammonia/hydrogen peroxide mixture, which was applied as an etchant for GaAs [17]. The exposure of a SAM film of an aromatic thiole by low-energy electron beams led to a negative contrast. In addition to monofilms, ultrathin organic films are used for pattern transfer. Arrays of SiO2 and metal pillars with diameters down to about 10 nm were fabricated by imprinting of ultrathin PMMA films and pattern transfer by a liftoff process [18].

Molecular Planar Technology

the last decade, such films found particular interest for the construction and modification of molecule libraries in the form of biochips, which have been used meanwhile in medical diagnostics and drug development. The typical length of amphiphilic molecules applied in SAMs and LB films is in the range of about 2 to 3 nm. This length is very well defined by the structure of the molecules. It determines the thickness of the molecular films. Therefore, it can be used for the construction of dielectric films with a determined thickness in the range of the typical tunneling distances for electrons. This property is of great interest for the development of tunneling devices, for example, single-electron tunneling (SET) devices, or for electron pair tunneling devices (Josephson electronics). Arrangements of nano- or micropatterned film stacks consisting of molecular monofilm and thin metal films are of particular interest for molecular electronics in connection with single-electron handling. Molecular films can be used for tunneling barriers as well as for molecular diodes or more complex functions in the connection of localization and transport control of single elementary charges [20]. The length of molecules in monofilms between electrodes determines the thickness of the tunneling barrier and hence the tunneling probability (Fig. 8). Theoretical investigations point to the possibility of integration of Josephson devices with single-photon devices with the use of tunneling barriers [21].

4. MOLECULES AND NANOPARTICLES AS LITHOGRAPHIC MASKS 4.1. Particle Templating Nanoparticles are not only important as a special kind of material. They are very promising in different fields of nanotechnology because of the specific properties of individual particles. This concerns electronic, optical, and chemical functions as well as possibilities for immobilization, designing arrangements of nanoparticles, and nanopatterning of plane surfaces with the use of single nanoparticles and nanoparticle arrays [22].

3.3. Application of Micro- and Nanopatterned Monofilms Lateral micro- or nanopatterned monofilms can be used for the introduction of molecular components in chemical and biochemical sensors and in electronic and optoelectronic micro- and nanodevices. So molecular monofilms are under investigation in the development of immobilization layers for biomolecules and synthetic recognition molecules for chemical and biochemical sensing. Protein-containing membranes are studied extensively because of their high potential for specific interaction or specific catalytic activity [19]. During

Figure 8. Control of barrier height for electron tunneling in metal/molecular film/metal contacts by variation of the length of alkyl chains in dielectric monofilms.

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Molecular Planar Technology

Nanoparticles tend to arrange in regular patterns at surfaces [23]. So it is possible to use them to transfer regular structures with space frequencies of the nanoparticle superlattice from the particle arrangement into substrate layers (Fig. 9) [24]. Colloidal gold particles were used as etch masks for the fabrication of silicon nanopillars. Nanopillars with minimal tip radii below 5 nm were obtained with the use of Au particles with diameters between 10 and 15 nm and silicon etching by RIE in a CCl4 atmosphere [25]. Self-forming clusters of Au, Ag, and Fe also acted as etch masks in the production of silicon nanopatterns with high aspect ratios. The positioning of clusters was achieved by EBL, metal deposition, and a subsequent cluster-forming process at the lithographically patterned surface [26].

4.3. Molecular Networks for Lithographic Masking

Molecular geometries, in addition to electron density distribution, quantum states, and charge, determine the strength and specifity of chemical bonds. The key/lock model for interactions between enzymes and substrates gives an important example of this fact. A particular artificial solution of molecular recognition consists of the imprinting of molecular shape in technical surfaces. Therefore, larger or smaller molecules are embedded in a polymer film or a monomolecular film at a surface. After stabilization of the film, these molecules are removed by a dissolution process without destruction of the shape of the rigid matrix [27]. Holes the shape of molecules remain in the matrix because of the dissolution process, which matches exactly with the shape of the formerly embedded molecules. Molecules of this shape interact preferably with these holes. Therefore, films or surfaces prepared according to this scheme can be used for chemical sensing.

Techniques have to be developed to transfer the molecular dimensions of, for example, biomolecules into applicable technical structures. This development is needed for technical access to the potential of molecular structures. A first step in this process is the use of the dimensions of molecular structures by transfer into traditional materials and processes of thin-film technology. The principle schemes are described in Figure 10. One approach is based on the application of molecular structures as masks in an etching process (left). Therefore, a thin film with the material of interest is deposited on a substrate, and molecules are immobilized on top of this layer. A subsequent etching step removes the film, except in the regions protected by the molecule. This technique provides an elegant way to utilize the potential of complex structures accessible by (bio)chemical synthesis also for technical purposes by transforming these geometries into, for example, a conductive pattern. Proof-of-principle experiments were conducted with microtubules. Microtubules are tube-like protein assemblies that serve in cells primarily as a cytoskeleton. They can be assembled in vitro and result in rigid structures in the micrometer range, thereby providing ideal parameters for experiments. A demonstration used a gold layer as functional layer [28]. Microtubules were adsorbed on this layer and served as a mask in a subsequent dry etching step for the creation of a thin wire beneath the immobilized microtubules. To characterize the yielded nanowires, substrates with prestructured microelectrodes were used, which were connected to the nanowires by electron beam-induced deposition. So electrical measurements were possible, which clearly indicated the fabrication of a continuous metal nanowire by this technique (Fig. 11). Although the demonstration was successful, it did not open the way for a standard technology, for at least two

Figure 9. Formation of regular nanopatterns in planar arrangements by the application of self-organized arrays of nanospheres: deposition through the regular holes between spheres (left), formation of holes in the planar surface of chip by anisotropic etching through the regular holes between spheres (center), and molding of the material at the planar surface by the spheres (right).

Figure 10. Pattern transfer using molecules for patterning of conducting film material: subtractive patterning. Left: 1. Deposition of a chain-like molecule immobilized with both ends at adjacent thin-film electrodes. 2. Etching of the underlying thin film of conductive material by use of the molecule as mask (lift-off). Right: 1. Immobilization of molecule. 2. Deposition of film. 3. Lifting of film elements by removal of the molecule due to a selective etching or dissolution process.

4.2. Molecular Templating

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Figure 11. Nanowire preparation by molecular masking. Microtubules (protein assemblies) protect an underlying gold layer in a dry etching step. Scanning force micrograph (a) and scanning electron micrographs (b, c) were made of microtubules (arrowheads) positioned between microelectrodes and wired by electron-beam-induced line structures (arrows in c). Reprinted with permission from [28], W. Fritzsche et al., Appl. Phys. Lett. 75, 2654 (1999). © 1999, American Institute of Physics.

reasons. First, the resulting structure size depends on several factors during the processes and does not yet show a subnanometer precision. A second and more fundamental point regards the control over the position of the structure. The microtubules were randomly distributed over the surface, and only some electrodes positioned nearby were selected for experiments. Moreover, the final wiring to the prestructured electrodes was realized by nanocontacts based on an electron-beam-induced deposition [29]. The potential of the method is hampered by the missing positional control and the resulting requirement for an additional sophisticated wiring step. Another example of the application of molecular masks used regular 2D arrangements of proteins. Typical examples are the S-layers, a sheet-like compound of bacteria that can be extracted and recrystallized on a variety of technical surfaces [30]. It consists predominantly of proteins with highly specific intermolecular interactions and results in a defined regular pattern with exact dimensions (depending on the species) in the lower nanometer range. The topographic aspect of this pattern can be used for metal coating prior to ion milling, which results in a regularly structured metal film due to differential metal removal and rearrangement due to the protein-metal heterostructure [31]. Another approach utilizes the regular pattern of the charge distribution in the protein, by applying metal deposition techniques catalyzed by charged surface regions [32]. So it is possible to achieve metal clusters in a highly ordered array with defined distances in the lower nanometer range, which is a unique possibility for the study of phenomena related to electron tunneling.

5. SUPERMOLECULAR CONSTRUCTIONS AT SURFACES 5.1. Macromolecules and Supermolecules at Surfaces Planar nanotechnology with supermolecules is based on the physical and chemical handling of supermolecules at surfaces [33]. In general, molecules tend to adsorb at solid

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surfaces. van der Waals forces cause a positive interaction between molecules and solids. The number of atoms contributing to an attachment by van der Waals forces increases with increasing size of a molecule. That is why macromolecules like synthetic polymers, polysaccharides, or proteins like to adsorb at nearly every surface. In addition, charges, dipoles, and interactions between charges, dipoles, and induced dipoles may enforce attractive interactions between molecules and surfaces. So there is not the requirement of attaching them at a planar surface, but it is necessary to look for possibilities of specific and localized application of large molecules at plane technical surfaces. This can only be achieved by the choice of suitable solvents, thermal activation, and rinsing procedures, in which the solvent competes with the surface in the interaction with the molecules. Differentiation of adsorption is mainly controlled by the choice of rinsing protocols. More specific interactions can be caused by coordinative binding. The formation of complex compounds requires the existence of coordinating groups in the molecules and at the surface and the presence of metal ions in the solution. The strength of attachment by coordinative bonds can be controlled over large ranges by adjusting the pH value and the concentration of suitable ions. Specific binding can also be achieved by means of ensembles of weak bonds. The strength of such polyvalent bonds can become comparable to that of strong chemical bonds, if a sufficiently high number of single bonds contribute to the cooperative effect. In particular, groups of H-bridges offer a good possibility of specific interactions because of their directionality. The highest specificity of attachment and high binding strength are achieved by covalent coupling of molecules. Covalent coupling can be performed either by the binding of presynthesized molecules at the chip surface or by stepwise synthesis of molecules at the surface itself. Both techniques are under development now. The stepwise synthesis of linear macromolecules corresponds to the well-known strategy of solid-phase synthesis with the chemistry of protective groups. Variants of this strategy are used, for example, for the in-situ synthesis of oligo-DNA for biochip production by light-directed cleavage of protective groups. The construction or immobilization of supermolecules at a surface demands more sophisticated strategies. Supermolecules are marked by a well-defined three-dimensional geometry. In contrast to most polymers, the real geometry of bonds in space is fixed in addition to the topology of chemical bonds. In standard polymers, the major part of bonds is free for rotation, which means one chemical structure (topology of bonds) can result in a huge number of possible conformations. In supermolecules, the rotability of bonds is restricted by the application of stiff parts, in which the atoms are connected by nonrotatable -bonds, conjugated -bonds, or aromatic systems. Supermolecules contain mostly ring structures, which contribute significantly to the stiffness of a molecule. Synthetic supermolecules are built up, in most cases, by the use of a hierarchy of chemical binding strength. First, molecular modules are synthesized by covalent coupling of atoms and small groups of them. Then these modules are connected by the application of weaker interactions. Therefore, in general, polyvalent bonds are used, like groups of H-bridges and coordinative

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bonds, often supported by electrostatic and van der Waals interactions.

5.2. Molecular Architectures at Plane Surfaces by Immobilization of Supermolecules The tools of conventional chemical synthesis can be largely used if molecules are presynthesized completely in solution and attached to the surface after the molecular construction is finished. This concept is already applied for the immobilization of peptides, proteins, and synthetic recognition structures for biosensors. Meanwhile, sophisticated strategies are developed for highly specific recognition of molecules at the surface and for transduction of molecular interactions into electronic signals [34, 35]. The immobilization of presynthesized molecules was extended to nucleic acids in connection with the production of DNA chips. The fixation of larger molecules with certain functions is the main issue in all of these cases. The molecules must be stable against rinsing processes. The place of supermolecules or recognition structures has to be accessible for the diffusion of molecules of interest. And the chemical or biomolecular function of the immobilized molecules should be not affected by the immobilization. But the precise localization and orientation of the molecule are not of interest or are only of secondary importance. In molecular nanotechnology there is a need for precise localization and orientation of very small ensembles of molecules or even single molecules. Therefore, strategies are needed that combine the localization of attachment at the plane surface and the precise choice of the reacting site for immobilization at the molecule itself. A rather sophisticated way of managing large molecular complexes consists of the connection between the spontaneous self-assembly of biogenic supermolecules and the introduction of functional groups realizing a position-specific attachment at chip surfaces (Fig. 12) [36].

5.3. In-situ Synthesis of Supramolecular Constructions at Plane Surfaces Instead of immobilization of complex molecules, it is often necessary to form the supermolecules by modular construction at a certain reaction site at the planar surface. Supermolecular chemistry offers different methods of construction of larger molecules, which are distinguished from classical polymer molecules by an exact atomic composition, a high rigidity, and, consequently, a much more precisely defined geometry. Comparatively simple examples are given by crown ethers and other host/guest compounds. More complex structures were realized in artificial helical structures like the so-called helicates [37], in catenanes, and in rotaxanes [38]. A simple strategy of constructing larger molecules and particularly spherical molecules is the buildup of dendrimers by initiating dendrimer growth with an immobilized starter molecule. A convincing way to create functional supermolecular architectures at plane surfaces consists of the reassembly or de novo assembly of biomacromolecules or of artificially

Figure 12. Use of recombinant building units of protein complexes to achieve oriented immobilization of large molecules by addressing specifically introduced linking elements.

modified biomacromolecules at chips. The reassembly of bacterial surface proteins forming regular patterns can extend to chip areas of several square centimeters. So twodimensional crystals of regular nanoporous protein layers— so-called S-layers—can be obtained [39]. The formation of a rotating nanomachine made by genetically engineered ATP synthetase coupled with a fluorescence-labeled actin filament succeeded by such an assembly procedure [40–43]. Translational nanomachines can be taken from living nature and transferred into technical surroundings in addition to rotating nanomachines. The tubulin/kinesin system is particularly suited for such experiments [44]. Immobilized kinesin molecules at chip surfaces cause a linear transport of large tubulin supermolecule in the presence of ATP in a suitable buffer [45, 46].

5.4. Application of Chip-Integrated Supermolecules and Molecular Nanodevices New types of electronic devices can be realized by the substitution of inorganic dielectric films with molecular films. Particular interest is attracted by molecular monofilms with a thickness in the range of typical electronic tunneling, meaning thicknesses up to about 3 nm. In addition to the tunneling effect, specific molecular electronic properties of molecular films can contribute to the function of devices with sandwich arrangements of metal or semiconductor nanoelectrodes with intermediate molecular films, namely films with asymmetries in the donor and acceptor properties of chemical end groups of the film-forming species. Such molecules show, in general, diode effects for charge transport [47]. Triode arrangements are realized in transistors with the use of molecular films. Single-electron transistors are realized, if the Coulomb blockade effect of an electronic nanoconfinement can be controlled by a gate electrode [48]. The inclusion of very small molecule ensembles can be detected in planar arrangements electronically if nanogaps in ultrathin metallic films are so small that the electrical conductivity inside the gaps is considerably influenced by adsorption of molecules in the gap region. In principle, the

714 electrical conductivity can reflect the number of molecules attached in the critical area [49]. Chip-integrated molecular architectures and supermolecules have been discussed as a basic idea in molecular electronics for a long time. Electron transport control in larger extended -electron systems will probably become a key element in molecular logic architectures [50].

6. NANOPARTICLE ARRANGEMENTS AT PLANAR SURFACES 6.1. Preparation and Modification of Nanoparticles for Surface Technology Nanoparticles are of particular interest for the bottom-up concept in nanotechnology because of their stiffness and their interesting optical and electronic properties. In contrast to many molecules, the atoms of a nanoparticle are interconnected by a high density of strong bonds, resulting in a nano-object with a fixed and rather stable geometry. This object is, compared with most macromolecules, chemically and mechanically stable. In addition to their stability, nanoparticles provide an interesting feature to molecular constructs: they can act as active components by optical or electronic effects. Nanoparticles are commercially available today in a large spectrum of materials, like metals, dielectric inorganic materials, organic polymers, and elementary and compound semiconductors. Of particular importance for the properties and the processing of nanoparticles is the composition of their surface, in addition to their material composition. Nanoparticles are mostly generated under the formation of charged surfaces to get a stabilization of nanoheterogenous systems. Surface charges cause repulsion between two particles. The aggregation of small particles is avoided by this repulsion. A chemical modification of nanoparticle surface is achieved by exchange reaction of ligands in the molecular shell of particles. In this way DNA-carrying Au nanoparticles are prepared by the substitution of small organic molecules in the molecular shell of the nanoparticles with thiolated oligonucleotides, which attach to the Au surface by their thiol groups. The restoration of surface charge is important for the stabilization of the colloidal state. In the case of exchange of citrate by DNA, the negatively charged small molecule is replaced with a nucleid acid molecule of the same charge.

6.2. Interaction and Immobilization of Functionalized Nanoparticles Functionalized particles can react with each other. They can also react with complementary functionalized surfaces. Spontaneous aggregation of particles can often be observed if the surface charge is removed. Otherwise, antagonistic charged particles will aggregate. A more specific interaction of nanoparticles can be achieved by complementary binding groups. So the principle of hybridization between two single strands of nucleic acids can be transferred to a hybridization of beads. It was shown

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that beads possessing surfaces covered with complementary oligonucleotides aggregate spontaneously [51, 52]. The idea of specific interaction between beads can also be applied to the localized immobilization of nanoparticles in planar technology. Thus the hybridization of oligonucleotidecovered gold beads is possible at microspots of complementary DNA [53, 54]. Lithographically defined binding sites at a chip surface can be used for the localized immobilization of small ensembles of nanoparticles or for the positioning of single beads. The oriented immobilization of GaP, InP, and Si nanowires succeeded by production and subsequent lifting of the semiconductor nanoparticles and reimmobilization under the influence of shear forces by liquid flow. Thus networks of nanowires could be constructed [55]. The position of immobilization of nanoparticles can be controlled by means of manipulating probes or by chemical micropatterning of the chip surface. Therefore, either resist technologies or light-directed chemical processes on chip surfaces can be used. Thus the localized immobilization of gold nanoparticles was done by the UV-initiated cleavage of light-sensitive protecting groups at a reactive monomolecular surface film [56]. The site-selective immobilization of single-stranded DNAcovered Au nanoparticles can be performed by hybridization with complementary DNA at micropatterned molecular spots at chip surfaces [57]. The combination of lithographically patterned surfaces with particular growth processes can be applied to different materials. Regular nanopatterns with high aspect ratios were realized by the production of immobilized single-wall carbon nanotubes at micropatterned catalyst areas at chip surfaces [58].

6.3. Nanoparticles in Labeling Technologies Labeling techniques are an essential tool in microscopic methods for increasing sensitivity and improving the signalto-background ratio. Today’s standard label is based on fluorescence dyes with applications to microscopy and even to DNA array techniques. Metal nanoparticles have been used in labeling techniques for microscopy for decades. In recent years, they have become more and more important for fast optical readout of biochips and in sensor device arrangements. Thus metal nanocluster labels can be used for an efficient readout of binding events of biomolecules at chip surfaces by optical enhancement effects [59]. A simpler readout is based on optical reflection from areas covered with nanoparticles. This effect can be used for DNA chip detection, as demonstrated with the use of microstructured DNA arrays on glass substrates [54]. To increase the dynamic range, a metal enhancement procedure known from electron and optical microscopy can be applied to nanoparticle-labeled surfaces. This development process results in the specific deposition of metal on the nanoparticles, leading to larger particles and therefore stronger signals. This increased signal enables the use of a simple flatbed scanner for the detection of DNA hybridization events [60] or the extremely fast (millisecond time scale) data collection of microstructured arrays [53]. In addition to

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reflective or transmissive measurement, optical readout of nanobead-labeled surfaces can also be done by fluorescence [61] or SPR detection [62]. A combination of protein-modified polymer microspheres with gold nanoparticle labeling was successfully tested for an immunoassay at chip surfaces by means of an electrical readout. The selectively immobilized metallic nanoparticles were thereby used as catalysts for the production of conductive thin films by metal-catalyzed open-circuit metal deposition [63]. This approach was adapted to nanoparticle-labeled DNA on chip substrates containing microelectrode structures [64, 65]. Capture DNA was immobilized at the chip surface in the electrode gap. In the presence of complementary DNA that is nanoparticle labeled, a specific binding occurs and the labeled DNA is situated in the gap. With the metal enhancement, a metal layer is created by the enlargement of the particles on the surface. This metal layer is sensed by a significantly increased conductance over the gap.

6.4. Realization of Nanodevices by Nanoparticle Arrangements at Planar Surfaces The specific immobilization of nanoparticles at well-defined places on chip surfaces attracts much attention in the contemporary research. Therefore, these techniques enable us to construct a new class of chip devices. These devices are in an intermediate situation between integrated circuits for solid-state electronics and (the more or less realized ideas of) molecular electronics. This new class of devices could be called “nanoparticle chip devices” because of the crucial role of nanoparticles, which are functionally integrated. Metal nanowires can be manipulated on chip surfaces like charged molecules by the application of an electrical field. Thus they can brought into bridging functions between lithographically defined electrical thin-film elements for nanocontacts [66]. Carbon nanotubes are a very promising class discussed for molecular electronic devices. Planar arrangements of nanotube contact arrays were proposed for the realization of nonvolatile RAMs for molecular computing [67]. Nanoparticles exhibit interesting electronic properties due to size-related quantum effects. One example of the potential is the proposed SET transistor based on DNA positioning of a colloidal nanoparticle [68]. SET devices are a promising development toward lower energy consumption, which would minimize problems connected with the higher integration densities in today’s microelectronic circuits. However, SET devices need an electron confinement in the lower nanometer size range. Today’s structures are still larger, so they require low temperatures (below 1 K or even 0.1 K) for successful operation. The application of colloidal metal particles, as in electron confinement, was demonstrated, but the seamless integration of these particles into a technological environment is still missing. DNAbased positioning could be the solution, as described in the scheme in Figure 13a–d. A long DNA molecule is positioned between prestructured electrodes as already demonstrated [69]. In a subsequent step, the immobilized molecule is used to position a colloidal particle based on sequence-specific interactions between DNA on the particle and the long

Figure 13. Nanoparticle arrangement using biomolecules. Microelectrode structures (a) are modified (b) to bind an individual DNA molecule (c). (d) This molecule serves as a positioning tool for the specific binding of a DNA-modified nanoparticle. (e) Demonstration of successful passivation of the substrate (bottom part) compared to the electrode (top) against binding of DNA, tested with nanoparticlelabeled DNA. (f) Scanning force micrograph of an individual DNA molecule positioned between microelectrodes. Reprinted with permission from [68], W. Fritzsche et al., in “DNA-Based Molecular Construction” (W. Fritzsche, Ed.), AIP Conference Proceedings, 2002, Vol. 640, p. 83. © 2002, American Institute of Physics.

DNA. Key steps of this procedure could be demonstrated in experiments. The specific binding of nanoparticles modified with DNA to surfaces with immobilized complementary DNA is shown in the upper part of Figure 13e. The lower part shows a background region, which was passivated by chemical modification to suppress nonspecific binding. The low number of particles (especially compared with the strong binding in the upper part) confirms the successful passivation. Figure 13f shows a combination of these principles of specific binding to defined surface regions on an otherwise passivated surface and its application to long (lambda)

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DNA. Electrode structures (visible as bright regions at the top and bottom) were positively charged to induce binding of the negatively charged ends of the DNA. After passivation of the remaining areas and incubation with lambda DNA in a liquid flow, the imaged structure with an individual DNA molecule connecting the two electrodes was achieved. Further steps, such as the positioning of the colloidal particle along the immobilized DNA and the preparation of nanoparticles with a defined tunneling barrier based on self-assembly monolayers, were already demonstrated in the literature and have to be integrated in this setup.

6.5. Arrangement of Single Atoms and Small Atom Ensembles at Plane Surfaces The ultimate nanofabrication technology uses single atoms instead of molecules for the construction of nanopatterns at plane surfaces. Such arrangements can be performed, if atoms are adsorbed at a surface but can be moved by a slight activation. The activation energy can be applied with probes like STM or AFM sensors. The conditions of manipulation are depending on the interaction energy between atoms and solid surface. The manipulation of noble gas atoms can only be performed at very low temperatures, but metal atoms at semiconductor or salt crystal surfaces can also be handled at room temperature. Arrangements of small numbers of atoms can be produced by manipulation of single atoms at plane surfaces by means of scanning probe devices. Dimers and trimers of gold atoms were prepared with an AFM moving single adsorbed atoms on a NaCl single crystal surface [70]. A particular illustrative example of artificially arranged atoms at a plane surface was given by M. F. Crommie et al. They built up a ring of 48 Fe atoms at a Cu single crystal surface. Concentric wavelike signal structures inside this atomic construct were interpreted as the quantum structure of a single electron inside the planar nanoconfinement [71].

Figure 14. Steps of immobilized chain molecules for supporting nanocontacts between micro- or nanolithographically prepared planar electrodes. (1) Immobilization of one end of the molecule at the line electrode and of the other one in the dielectric space between lines resulting in no electrical contact. (2) One-sided immobilization results in no electrical contact. (3) Two-sided immobilization at different thin film electrodes (contact).

the merging between planar technology and single-molecule techniques is successful. The basic functions necessary for molecular transduction are solved in the framework of microchemical and microbiochemical sensing, as demonstrated in a variety of examples [73, 74]. Physical nanofabrication is mainly based on beam lithographic technologies like EBL or IBL and related techniques. Gas-phase processes like thin-film deposition and dry etching are essential for the nanopatterning of thin inorganic films. Both groups of techniques are developed in the frame work of planar technology concepts. But they are not well adapted to single-molecule handling procedures.

7. OUTLOOK

7.2. Single-Molecule Techniques

7.1. Merging of Single-Molecule Techniques and Physical Nanofabrication

Single-molecule manipulation nearby or on planar surfaces requires techniques that address the molecular scale. For manipulations in the liquid phase, methods based on optical

Obviously, the whole potential of nanopatterning can only be used if the self-assembly potential of molecules is technically controlled. On the other hand, molecule-based devices should be integrated into the planar technological concept. The need for technological bridging between supramolecular chemistry and planar nanotechnology for nanofabrication is particularly required for concepts of electronic devices using monomolecular functional elements [72]. The use of molecules for nanoelectronics must always address a highly specific coupling chemistry to get a localized immobilization and orientation of molecules (Fig. 14). Subsequent reinforcement of molecular wires by metal deposition leads to a technology for the preparation of molecular supported nanowires with low electrical resistances of nanowire networks (Fig. 15). In addition to nanowires, electronic switches, or logic elements, the development of transducers for the construction of higher parallelized interfaces between the molecular and the electronic world can come to nanodimensions only if

Figure 15. Steps for the preparation of molecule-supported nanocontacts in planar arrangement.

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interactions are widely distributed [75]. Typical examples are optical tweezers, which can be used for the manipulation of particles in the medium nanometer range [76]. However, molecular manipulations (e.g., the study of DNA restriction on single molecules [77]) usually rely on optical “handles,” particles (e.g., polymeric beads) large enough to be visible in the optical contrast. Therefore, the molecular scale cannot be addressed directly. Another example of optical methods aimed at the lower limits of optical resolution is the focused laser beam (microbeam), which is used, for example, for manipulations of chromosomes inside cells. It was shown that this method achieves cut widths below 200 nm [78]. This experiment was realized using chromosomes spread on a planar surface, thereby demonstrating the general applicability of optical methods to the manipulation of molecules on surfaces. However, the example also points to the limits of the approach: the method requires molecular structures visible in the optical contrast. This problem can be minimized with fluorescence markers, but the resolution is still limited. Thus the advantage of optical manipulation techniques, the combination of imaging and manipulation tools, is also a restriction. To reach molecular dimensions by keeping a combination of imaging and manipulation capabilities, one could aim toward higher resolution imaging techniques. Electron microscopy is the method of choice for imaging molecular structures, such as DNA or proteins. There is also the possibility of manipulating surfaces with the electron beam in scanning electron microscopes by electron beam-induced deposition, as mentioned before. However, this approach is not widely used because of severe restrictions regarding molecular manipulations. The requirements of vacuum conditions and surface metallization are hardly compatible with (bio)molecular modifications, and the needed equipment is expensive and is not standard. A fully new field of imaging methods was opened over 20 years ago with the introduction of the scanning tunneling microscope (STM) [79]. This was the start for the development of scanning probe microscopes (SPMs, also SXM because of the large variety of contrast mechanisms developed in the following years). In principle, SPM methods are based on the interaction of a probe scanned very close (lower nanometer range) over the sample surface (Fig. 16). The initial contrast was based on a tunneling current between a probe tip and a sample surface; both had to be electrically conductive. Tip and sample are engaged, until a predefined tunneling current is reached as the setpoint for a feedback mechanism. The sample height in this point is determined based on the movement of usually piezoceramic actuators, and an adjacent position is addressed. A raster-like scanning over the surface finally results in a 2D array of height values, which represent the final image of the measured surface area. Because of the strong distance dependency of the tunneling current, the very end of the tip interacts with the surface. Because STM, like all SPM methods, is limited regarding the resolution by the probe dimension (comparable to profilometry), the confinement of this interaction to an atomic tip results in atomic resolution. By utilization of the contrast used for imaging also for manipulations, individual atoms can be moved in special cases in an ultrahigh vacuum [80]. Although this resolution

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Figure 16. Scheme of scanning probe microscopy. A probe is rasterscanned over a surface controlled by a feedback mechanism based on highly localized probe-surface interactions.

for both imaging and manipulation is ultimate, STM is not the method of choice for the characterization of molecular structures on surfaces. It requires usually a conductive surface, thereby limiting the range of applicable substrates and molecules. Although there are now methods available for the imaging of isolator surfaces, they are not yet applicable as standard tools [81]. The need for a microscopic method with comparable resolution for isolating substrates led to the development of the scanning force microscope (SFM; also atomic force microscope, AFM) [82]. This SPM method probes the surface topography by raster-scanning a sharp tip (mounted at the end of a flexible cantilever) over the sample. As in the case of a STM, a piezoelectric scanner moves the sample relative to the tip and allows movements with Angstrom precision in the x, y, and z directions. The deflection of the cantilever due to changing surface topography is usually monitored with a light pointer: a laser beam is reflected from the back side of the cantilever top toward a divided photodiode. The signal of the photodiode can be used through a feedback mechanism for keeping the deflection of the cantilever constant by adjusting the z height of the scanner. This mode is called “constant force” (also “isoforce” or “constant deflection”); thereby the height movement of the cantilever represents the sample topography and is used for visualization. Turning the feedback off and monitoring the changing deflection by the diode signal results in an image in the “constant height” mode, which can improve the detection of edge features. The SFM can operate in gases or liquids, thereby opening a huge potential for imaging biological processes in their native environment with nanometer resolution. Two modes differing in the duration of tip-sample contact are in general use. The first is based on steady contact (therefore denoted as “contact mode”) that results in significant shear forces applied to the specimen. Soft molecules or samples with low substrate adsorption (as in the case of molecules adsorbed in buffer) are often unstable in this mode of operation. The “tapping mode” minimizes the shear forces by decreasing the tip-sample interaction, which is achieved by oscillation of the tip normal to the surface. In this case the amplitude of the oscillation is monitored and

718 the feedback mechanism is based on the damping due to surface contact (as detected by the photodiode). A variety of complementary SPM methods were developed based on these basic principles. They exhibit a contrast mechanism based on the determination of tip-sample interactions and result in a mapping of the chosen interaction. Thus sample properties like viscosity, hardness, electrical conductivity, electrostatic interactions, optical absorbance or reflection, temperature or thermal conductivity, magnetic characteristics, etc., can be determined with a resolution in the lower nanometer range. These methods are aimed at minimal tip-sample interactions to avoid sample damages. On the other side, the unique positioning capabilities of the SPM methods lead to another development aimed at surface manipulation. Almost all of the mentioned contrast mechanisms for imaging can also be used to modify the sample surface in a very localized manner (Fig. 17). Thus the SPM family also provides nanofabrication tools that approach the resolution of electron beam fabrication but show fewer restrictions regarding sample preparation, fabrication environment, or applied interaction mechanism. One subset of SPM-based manipulations utilizes a voltage applied between a conductive tip (in STM or SFM mode) and the surface. In the case of thin metal films, an oxidation occurs, which can be used to create nonconductive regions that define (surround) a nanowire. This approach was applied to create a SET transistor, a device that requires nanometer-sized electron confinements contacted by defined tunneling barriers [83]. In addition to this process aimed at reducing the conductivity of surface areas, another voltagebased approach leads to the creation of metal wires by transferring metal (gold) from the tip to the surface with voltage pulses [84]. Thus metal structures smaller than 30 nm could be realized, demonstrating the potential for nanowiring. Other methods for surface manipulation are based on the voltage-induced oxidation of silicon surfaces [85], the electrochemical deposition of silver on graphite surfaces [86], the manipulation of nanoparticles with a SFM tip [87, 88], or nanolithography based on tip-based mechanical manipulation on the substrate surface [89, 90]. The described SPM-based methods have the potential to modify surface regions in the lower nanometer scale. They can be utilized to define binding sites for small ensembles or even individual molecules as a prerequisite for defined molecular structures in a planar technology. Their advantage

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compared with other nanofabrication tools is their compatibility with molecular manipulations. The SPM is a standard characterization method in laboratories involved in molecular surface modifications, and this wide availability leads to fast development and further enhancement of manipulation techniques in this field.

7.3. Development of a Technical Culture of Localized Chemistry Nanotechnology is not only strongly related to the size of single molecules. It is a class of technologies addressing the overlap between physical engineering and chemistry. Engineers are following a top-down strategy to realize smaller and smaller dimensions. They have to learn that the individual molecules and even single atoms can no longer be neglected in the materials used, if the dimensions are reduced. But the problem of reduced numbers of particles is still more serious for chemistry than for physical engineering. Chemists think in molecular structures, which means thinking about the shape and size of single molecules. But classical chemistry deals with huge numbers of equal molecules in technology and in scientific experiments. The exact position and orientation of an individual molecule are of no interest in classical processes. In nanotechnology, chemists have to learn to transport, activate, and characterize single molecules. This is currently possible only under particular circumstances. New diagnostic tools are needed for the manipulation of molecules, the initiation of spontaneous arrangement, coupling and decoupling of molecules, and the destructionless characterization of products. And all of these processes have to be performed with respect to an outside coordination system. In a nanotechnology-orientated chemistry, a technical culture of localized chemical processing with single particles is strongly demanded. This challenge includes the development of a complete set of procedures for single molecular handling and control of spontaneous processes. Chemistry must no longer be a stochastic method regarding the acting molecules, but each chemical step has to become a strongly determined operation with exactly predictable results related to individual particles. Process parameter windows, the frame of operational conditions, must be strongly defined for such a control. The effort spent on the exact definition of individual molecular processes is of particular importance, if many nanotechnical functional elements based on molecular nanotechnology are to be integrated into complex devices.

7.4. Biomolecular Nanoengineering Using Lithographic Tools

Figure 17. SPM-based fabrication applies various interactions to achieve highly localized modifications of the surface.

DNA provides a huge potential for molecular construction. It is mainly based on the highly specific but variable binding of complementary sequences and on the sophisticated toolbox extracted from nature and used in the laboratory (e.g., enzymatic manipulations), but also on the highly developed technology of manipulating and characterizing DNA (e.g., PCR and gel electrophoreses). Well-known examples of the possibilities of DNA superstructures were demonstrated by the group of Seeman [91]. Moreover, because of

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the large demand, an industry has been developed that provides DNA molecules in a chosen sequence, quantity, and quality. On the other hand, the characterization tools for molecular structures on surfaces reached a level that allowed the high-resolution imaging of molecular structures on surfaces even under physiological conditions [92] and in their dynamic [93]. Moreover, techniques developed for the characterization of individual molecules now provide access to the properties of single molecules by integration of molecules into macroscopic measurement setups [94]. This integration is a key point for the technological use of the promising molecular materials and devices, but so far there have been only isolated solutions to this problem. The embedding of molecular structures in a solid substrate is the favored method, based on the above-mentioned microscopic and technological developments. This process uses but is not limited to an adsorption of molecules such as DNA on surfaces, realized, for example, by surface modifications with silanes [95, 96]. It requires a defined orientation and a control over the position of the molecule. The application of prestructured electrodes and alternating voltages to guide DNA molecules in a defined position was demonstrated [97, 98]. Thus different molecules can be positioned by switching the voltage between different electrodes and exchanging the molecules in solution. However, this rather serial approach is limited to a low number of different constructs. A much higher variety could be realized based on self-assembly using a variety of specific binding pairs, as provided by the variability of DNA sequences. Moreover, this process is applicable in a parallel manner, as an important prerequisite for technological applications. The scheme in Figure 16 illustrates this approach. An extended molecule (1) binds with one end to a modified area on a substrate through specific interactions, (2), and in another step the free end of the molecule binds to another specified area, resulting in a molecule positioned in a defined orientation in a planar environment (3). This general approach was realized using about 16-
m-long double-stranded DNA molecules (originating from the lambda phage, therefore called lambda DNA), which exhibit single-stranded overhangs on both ends. Short DNA molecules with a sequence complementary to the ends were immobilized on planar electrode structures, so that the lambda DNA could be immobilized in a stretched state between the electrodes [69]. Such a structure with a DNA molecule of known sequence in a defined position could be used as a positioning tool for higher-order structures. One example is the proposed SET transistor based on immobilized DNA as a positioning tool for a metal nanoparticle [68]. In addition to this rather device-oriented application, DNA-based positioning also provides an interesting access to single-molecule studies in biology and biophysics. It should be possible to position, for example, individual enzymes along the stretched DNA in a defined way with nanometer precision based on specific DNA–DNA interactions. Thus one could arrange different interacting enzymes in a defined geometry and in the focus of additional characterization methods based on electrical or optical principles, or a predefined number of enzymes could be arranged in one reaction chamber.

All mentioned examples rely on the positioning by long DNA and therefore on the defined immobilization of this DNA molecule on a surface. This immobilization requires a prestructured surface, realized either by lithographic tools in a conventional way (photo- or e-beam lithography) or based on novel developments like soft lithography [99], scanning probe-base surface modification [100], or nanoimprint lithography [101]. The combination of prestructured surfaces with (bio)chemical surface modifications, which results in binding sites for small numbers or even individual molecules, is the technological basis for an integration of molecular constructions in today’s technology.

7.5. Construction of Cell Organelle-like Functional Supermolecules Living nature teaches us how complex organized microsystems have evolved. The theory of endocytosymbiosis shows that compartmented cells with specialized subsystems started with the integration of multifunctional individual cells into one supercell, which was followed by a reduction of functional complexity and specialization inside the integrated compartments. The formation and conservation of membranes separating the compartments is the most important morphological precondition for the specialization process. Nanopores and membrane-integrated transfer molecules are responsible for interaction and cooperation between compartments. Separation in space and coupling by transmitters and other signal paths are complementary aspects of working in complex biological micro- and nanosystems. The biomimeting construction of molecular-based nanosystems must copy the biogenic philosophy of the definition of subsystems and morphological separation. Therefore, the compartmentation and the integration of nanopores and functional molecules or nanoparticles in artificial membranes are important strategies for the construction of biomimetic technical nanosystems by bottom-up processes. Cell-organell mimetic systems could be photochemically active like chloroplasts, redox-active like mitochondria, or responsible for storage and transport like liposomes. Many other functions could be addressed. In addition to poor chemical coupling, interactions by exchange of charges or excitation states will probably be the most important communication paths between subsystems. In contrast to biological systems, solid-state nanodevices and functional inorganic nanoparticles can be integrated in such complex technical nanodevices. This vision will come true if molecular selforganization can be connected with positioning and patterning at plane surfaces of technical substrates.

7.6. Vacuum Processes for Supramolecular Construction The spontaneous organization of natural complexity with biomolecular building units is exclusively based on movable particles in a condensed state. The liquid phase dominates biomolecular processes. In addition to some processes in liquids at or near the surface of solids, phases with movable states like gels or liquid crystalline phases are typical for biomolecular self-organizing systems.

720 In semiconductor fabrication as well as in microsystem development, the solid phase is the most important state. The movable phases are used only for the modifications of the surfaces or near-surface films of solids. The role of the movable phase in physical micro- and nanoengineering shows an interesting contrast to biological systems. In planar technology, the route from microfabrication to nanotechnology was guided from more liquid phase operations to gas-phase operations at solid surfaces. Thus earlier deposition and etching procedures frequently used process liquids. The downscaling of technical nanopatterns was accompanied by a shift from wet procedures to dry procedures, from liquids to gases. The substitution of wet etching processes in solid-state electronics with dry etching is a typical example. The question arises, how complex molecular-based nanosystems can be produced by gas-phase processes. Recent analytical operations have shown us that it is possible to transport heavy synthetic molecules as well as proteins through the gas phase, if they can be activated without destruction. This effect is used by laser-stimulated evaporation for time-of-flight mass spectroscopy (MALDI-TOF), for example. In the future nanotechnologists should learn how film deposition techniques can be qualified for the transport and strongly localized deposition of oriented single macromolecules and individual nanoparticles.

7.7. Problems of Molecular Self-Organization in Integrated Planar Devices Molecular self-organization is essential for the construction of complex functional systems in living beings. It is assumed that molecular self-organization can also be used for the construction of technical nanosystems. However, there are some important differences between technical and living systems: living beings are realizing a complete spectrum of functions in all phases of their individual development. The functional set of a technical system is necessary only after completion of, not during, the construction. This fact represents a fundamental advantage of technical systems in comparison with biological ones. In contrast to biological systems, technical construction and preparation strategies can be decoupled from the finally addressed functions. Technology must be efficient and reliable. Yields have to be high, and the set of preparation steps must be reproducible. In living systems, we find two principal strategies of ecological survival. The so-called r-strategy is oriented on high output in the number of offspring with low investment in the single offspring. The r-strategy includes normally high variability, but low yield and low reproducibility. It is the typical case for lower-developed organisms and quickly changing surrounding conditions. The k-strategy is marked by competence. The number of offspring is low, but the investment is high. This strategy corresponds to high reliability and high yield. Technical development is frequently marked by variability and trials and errors. Technical production knows nearly no variation, no modification, and no mutation. Thus it seems that research and development is more comparable to the r-strategy, but the production to the k-strategy. Living systems are a model for technical solutions only to some extent. But there is a necessity to make much more

Molecular Planar Technology

reproducible and reliable systems during production and to generate more variability and degrees of freedom during development. Thus we cannot assume that occasionally self-organization of molecules will solve all future technical problems. However, we can use the spontaneous effects of molecular self-organization for the search for new degrees of freedom in nanotechnical development and in new technology procedures. In a further developed phase, efficient and reproducible self-organization procedures can be included in the production of new devices and technical systems. Miniaturization in the nanometer range with the inclusion of many different materials and more or less sensitive molecular species is accompanied by the problem of a large number of single functional units (nanodevices or molecular complexes) in a highly integrated system. Redundancy concepts are needed, in addition to a maximum of reliability of the single components. The typical lifetime of biological nanosystems and even of synthetic nanomolecular systems is, in general, not sufficient for most technical applications. The stability problem, particularly in connection with excited molecular states (which are frequently necessary for interfaces like nanotransducers), demands biomolecular functions that are technology-adapted and robust for inclusion in technical systems. It is assumed that no molecular systems adapted to the aqueous environment of biological cells will solve this problem. It seems more probable that the combination of small solids with molecular units will enable us to construct nanomachines with new molecular-based functions. Clusters and nanoparticles possess many interesting properties and introduce robustness into the system. The included molecules are responsible for variability, mobility, molecular recognition, and specificity in the interaction of components as well as conversion by chemical processes. The self-organization of nano-objects has to be controlled by the choice of components and the control of interaction conditions. This control includes both chemical and geometrical parameters. Therefore, an integration of planar technology with single-molecule handling and single-particle and single-cluster techniques is required.

GLOSSARY Electron beam lithography (EBL) Preparation of micro or nano patterns by exposition and development of a plane thin film of a beam sensitive polymer by a focussed ray of highly accelerated electrons. Langmuir–Blodgett (LB) film Molecular monolayer transferred from a liquid-air interface onto a solid substrate. Optical lithography Preparation of micro patterns by use of a photochemical active resist layer and exposure through a partially transparent mask by an optical device. Self-assembled monolayers (SAM) Molecular assemblies spontaneousely formed by the immersion of an appropriate substrate into a solution of an active surfactant in an organic solvent. Supermolecules Large molecules with well defined composition, binding topology and geometry, preferably formed by reversible interactions between smaller molecular subunits.

Molecular Planar Technology

REFERENCES 1. H. F. Hadamovsky (Ed.), “Halbleiterwerkstoffe.” Deutscher Verlag für Grundstoffindustrie, Leipzig, 1972. 2. R. L. Edelstein, P. E. Tamanaha, P. E. Sheehan, M. M. Miller, D. R. Baselt, L. J. Whitman, and R. J. Colton, Biosens. Bioelectron. 14, 805 (2000). 3. A. Sherman, “Chemical Vapour Deposition for Microelectronics.” Noyes, Park Ridge, NJ, 1987. 4. T. Suntola, Mater. Sci. Rep. 4, 261 (1989). 5. T. Salditt and U. S. Schubert, Rev. Mol. Biotechnol. 90, 55 (2002). 6. Y. Xia and G. M. Whitesides, Angew. Chem. 110, 568 (1998). 7. A. Ulman, “Ultrathin Organic Films.” Academic Press, London, 1991. 8. A. Kumar and G. M. Whitesides, Appl. Phys. Lett. 63, 2002 (1993). 9. G. Lieser, S. Mittler-Neher, J. Spinke, and W. Knoll, Biochim. Biophys. Acta 192, 14 (1994). 10. W. Geyer, V. Stadler, W. Eck, M. Zharnikov, A. Gölzhäuser, and M. Grunze, Appl. Phys. Lett. 75, 2401 (1999). 11. J. Hartwich, M. Sundermann, U. Kleineberg, and U. Heinzmann, Appl. Surf. Sci. 144–145, 538 (1999). 12. R. C. Tiberio, H. B. Craighead, M. Lercel, T. Lau, C. W. Sheen, and D. L. Allara, Appl. Phys. Lett. 62, 476 (1993). 13. P. M. St. John and H. G. Craighead, J. Vac. Sci. Technol., B 14, 69 (1996). 14. M. A. McCord and R. F. W. Pease, J. Vac. Sci. Technol., B 4, 86 (1986). 15. E. Sackmann and M. Tanaka, Trends Biotechnol. 18, 58 (2000). 16. J. H. Fendler, Chem. Rev. 87, 877 (1987). 17. R. C. Tibero, H. G. Craighead, M. Lercel, T. Lau, W. Sheen, and D. L. Allara, Appl. Phys. Lett. 62, 476 (1993). 18. S. Y. Chou, P. R. Krauss, W. Zhang, L. Guo, and L. Zhuang, J. Vac. Sci. Technol., B 15, 2897 (1997). 19. P. Bianco, Rev. Mol. Biotechnol. 82, 393 (2002). 20. C. Zhou, M. R. Despande, M. A. Reed, L. Jones II, and J. M. Tour, Appl. Phys. Lett. 71, 611 (1997). 21. M. L. Roukes, Physica B 263–264, 1 (1999). 22. A. N. Shipway, E. Katz, and I. Willner, Chem. Phys. Chem. 1, 18 (2000). 23. P. Pileni, Pure Appl. Chem. 72, 53 (2000). 24. M. Pileni, Cryst. Res. Technol. 33, 1155 (1998). 25. P. A. Lewis, H. Ahmed, and P. Sato, J. Vac. Sci. Technol. 16, 2938 (1998). 26. T. Tada and T. Kanayama, J. Vac. Sci. Technol., B 16, 3934 (1998). 27. V. M. Mirsky, T. Hirsch, S. A. Piletsky, and O. S. Wolfbeis, Angew. Chem. 111, 1179 (1999). 28. W. Fritzsche, K. J. Böhm, E. Unger, and J. M. Köhler, Appl. Phys. Lett. 75, 2654 (1999). 29. W. Fritzsche, K. J. Böhm, E. Unger, and J. M. Köhler, Nanotechnology 9, 177 (1998). 30. U. B. Sleytr, M. Sara, D. Pum, and B. Schuster, Prog. Surf. Sci. 68, 231 (2001). 31. K. Douglas, N. Clark, and K. J. Rothschild, Appl. Phys. Lett. 48, 676 (1986). 32. M. Mertig, R. Kirsch, W. Pompe, and H. Engelhardt, Eur. Phys. J. D 9, 45 (1999). 33. R. C. Merkle, Nanotechnology 11, 89 (2000). 34. I. Willner, B. Willner, and E. Katz, Rev. Mol. Biotechnol. 82, 325 (2002). 35. F. W. Scheller, U. Wollenberger, C. Lei, W. Jin, B. Ge, C. Lehmann, F. Lidsat, and V. Fridman, Rev. Mol. Biotechnol. 82, 425 (2002). 36. K. Busch and R. Tampé, Rev. Mol. Biotechnol. 82, 3 (2001). 37. J. M. Lehn, A. Rigault, J. Siegel, J. Harrowfield, B. Chevrier, and D. Moras, Proc. Natl. Acad. Sci. USA 84, 2565 (1987). 38. J. Y. Ortholand, A. M. Z. Slavin, N. Spencer, J. F. Stoddart, and D. J. Williams, Angew. Chem. 101, 1402 (1989). 39. D. Pum, M. Weinhandl, C. Hödl, and U. B. Sleytr, J. Bacteriol. 175, 2762 (1993).

721 40. H. Noji, R. Yasuda, M. Yoshida, and K. J. Kinosita, Nature 386, 299 (1997). 41. O. Pänke, K. Gumbiowski, W. Junge, and S. Engelbrecht, FEBS Lett. 472, 34 (2000). 42. T. M. Duncan, V. V. Bulygin, Y. Zhou, M. L. Hutcheon, and R. L. Cross, Proc. Natl. Acad. Sci. USA 92, 10964 (1995). 43. D. Sabbert, S. Engelbrecht, and W. Junge, Proc. Natl. Acad. Sci. USA 94, 4401 (1997). 44. J. Howard, A. J. Hunt, and S. Baek, Methods Cell Biol. 39, 137 (1993). 45. L. Limberis and R. J. Stewart, Nanotechnology 11, 47 (2000). 46. R. Stracke, K. Böhm, J. Burgold, H.-J. Schacht, and E. Unger, Nanotechnology 11, 52 (2000). 47. A. Vilan, A. Shanzer, and D. Cahen, Nature 404, 166 (2000). 48. W. A. Schooveld, J. Wildeman, D. Fichou, P. A. Bobbert, B. J. v. Wees, and T. M. Klapvijk, Nature 404, 977 (2000). 49. C. Z. Li, H. X. He, A. Bogozi, J. S. Bunch, and N. J. Tao, Appl. Phys. Lett. 76, 1333 (2000). 50. J. C. Ellenbogen and J. C. Love, IEEE Proc. 88, 386 (2000). 51. A. P. Alivisatos, K. P. Johnsson, X. Peng, T. E. Wilson, C. J. Loweth, M. P. Bruchez Jr., and P. G. Schultz, Nature 382, 609 (1996). 52. C. A. Mirkin, R. L. Letsinger, R. C. Mucic, and J. J. Storhoff, Nature 382, 607 (1996). 53. J. M. Köhler, A. Csáki, J. Reichert, R. Möller, W. Straube, and W. Fritzsche, Sens. Actuators, B 76, 166 (2001). 54. J. Reichert, A. Csáki, J. M. Köhler, and W. Fritzsche, Anal. Chem. 72, 6025 (2000). 55. Y. Huang, X. Duan, Q. Wei, and C. M. Lieber, Science 291, 630 (2001). 56. T. Vossmeyer, E. DeIonno, and J. R. Heath, Angew. Chem. 109, 1123 (1997). 57. C. M. Niemeyer, B. Ceyhan, S. Gao, L. Chi, S. Peschel, and U. Simon, Colloid Polym. Sci. 279, 68 (2001). 58. A. M. Cassell, C. L. Asplund, and J. M. Tour, Angew. Chem. 111, 2565 (1999). 59. G. Bauer, F. Pittner, and T. Schalkhammer, Mikrochim. Acta 131, 107 (1999). 60. T. A. Taton, C. A. Mirkin, and R. L. Letsinger, Science 289, 1757 (2000). 61. J. R. Taylor, M. M. Fang, and S. Nie, Anal. Chem. 72, 1979 (2000). 62. L. He, M. D. Musick, S. R. Nicewarner, F. G. Salinas, S. J. Benkovic, M. J. Natan, and C. D. Keating, J. Am. Chem. Soc. 122, 9071 (2000). 63. O. D. Velev and E. W. Kaler, Langmuir 15, 3693 (1999). 64. R. Möller, A. Csáki, J. M. Köhler, and W. Fritzsche, Langmuir 17, 5426 (2001). 65. S. J. Park, T. A. Taton, and C. A. Mirkin, Science 295, 1503 (2002). 66. P. A. Smith, C. D. Nordquist, T. N. Jackson, T. S. Mayer, B. R. Martin, J. Mbindyo, and T. E. Mallouk, Appl. Phys. Lett. 77, 1399 (2000). 67. T. Rueckes, K. Kim, E. Joselevich, G. Y. Tseng, C.-L. Cheung, and C. M. Lieber, Science 289, 94 (2000). 68. W. Fritzsche, G. Maubach, D. Born, J. M. Köhler, and A. Csaki, in “DNA-Based Molecular Construction” (W. Fritzsche, Ed.), AIP Conference Proceedings, 2002, Vol. 640, p. 83. 69. E. Braun, Y. Eichen, U. Sivan, and G. Ben-Yoseph, Nature 391, 775 (1998). 70. X. Bouju, C. Joachim, and C. Girard, Phys. Rev. B 50, 11 (1994). 71. M. F. Crommie, C. P. Lutz, and D. M. Eigler, Science 262, 218 (1993). 72. C. Joachim, J. K. Gimzewski, and A. Aviram, Nature 408, 541 (2001). 73. A. B. Kharitonov, M. Zayatis, A. Lichtenstein, E. Katz, and I. Willner, Sens. Actuators, B 70, 222 (2000). 74. F. Scheller and F. Schubert, “Biosensoren.” Akademieverlag, Berlin, 1989.

722 75. K. O. Greulich, “Micromanipulation by Light in Biology and Biomedicine: Laser Microbeam and Optical Tweezers.” Birkhäuser, Basel, 1998. 76. N. Endlich, C. Hoyer, A. Harim, S. Monajembashi, and K. O. Greulich, Exp. Tech. Phys. 41, 303 (1995). 77. B. Schäfer, H. Gemeinhardt, V. Uhl, and K. O. Greulich, Single Molecule 1, 33 (2000). 78. K. König, I. Riemann, and W. Fritzsche, Opt. Lett. 26, 819 (2001). 79. G. Binnig, H. Rohrer, C. Gerber, and E. Weibel, Phys. Rev. Lett. 50, 120 (1983). 80. D. M. Eigler and E. K. Schweizer, Nature 344, 524 (1990). 81. M. Heim, R. Eschrich, A. Hillebrand, H. F. Knapp, R. Guckenberger, and G. Cevc, J. Vac. Sci. Technol., B 14, 1498 (1996). 82. G. Binnig, C. F. Quate, and C. Gerber, Phys. Rev. Lett. 56, 930 (1986). 83. K. Matsumoto, M. Ishii, and K. Segawa, J. Vac. Sci. Technol., B 14, 1331 (1996). 84. S. Hosaka, H. Koyanagi, A. Kikukawa, M. Miyamoto, R. Imura, and J. Ushiyama, J. Vac. Sci. Technol., B 13, 1307 (1995). 85. P. Avoris, T. Hertel, and R. Martel, Appl. Phys. Lett. 71, 285 (1997). 86. W. Li, J. A. Virtanen, and R. M. Penner, Appl. Phys. Lett. 60, 1181 (1992). 87. R. Resch, A. Bugacov, C. Baur, A. Madhukar, A. A. G. Requicha, and P. Will, Appl. Phys. A 67, 265 (1998). 88. T. Junno, K. Deppert, L. Montelius, and L. Samuelson, Appl. Phys. Lett. 66, 3627 (1995).

Molecular Planar Technology 89. B. Klehn and U. Kunze, J. Appl. Phys. 85, 3897 (1999). 90. S. Miyake, Appl. Phys. Lett. 67, 2925 (1995). 91. N. C. Seemann, H. Wang, X. Yang, F. Liu, C. Mao, W. Sun, L. Wenzler, Z. Shen, R. Sha, H. Yan, M. H. Wong, P. Sa-Ardyen, B. Liu, H. Qiu, X. Li, J. Qi, S. M. Du, Y. Zhang, J. E. Mueller, T.-J. Fu, Y. Wang, and J. Chen, Nanotechnology 9, 257 (1997). 92. D. J. Müller, D. Fotiadis, and A. Engel, FEBS Lett. 430, 105 (1998). 93. S. Kasas, N. H. Thomson, B. L. Smith, H. G. Hansma, X. Zhu, M. Guthold, C. Bustamante, E. T. Kool, M. Kashlev, and P. K. Hansma, Biochemistry 36, 461 (1997). 94. D. Porath, A. Bezryadin, S. de Vries, and C. Dekker, Nature 403, 635 (2000). 95. A. Bensimon, A. Simon, A. Chiffaudel, V. Croquette, F. Heslot, and D. Bensimon, Science 265, 2096 (1994). 96. D. C. Schwartz and A. Samad, Curr. Opin. Biotechnol. 8, 70 (1997). 97. F. F. Bier, N. Gajovic-Eicherlmann, and R. Hölzel, in “DNA-Based Molecular Construction” (W. Fritzsche, Ed.), AIP Conference Proceedings, 2002, Vol. 640, p. 61. 98. M. Washizu, in “DNA-Based Molecular Construction” (W. Fritzsche, Ed.), AIP Conference Proceedings, 2002, Vol. 640, p. 51. 99. Y. Xia and G. M. Whitesides, Angew. Chem. Int. Ed. Engl. 37, 550 (1998). 100. R. Wiesendanger, Proc. Natl. Acad. Sci. USA 94, 12749 (1997). 101. S. Y. Chou, P. R. Krauss, and P. J. Renstrom, Science 272, 85 (1996).

Encyclopedia of Nanoscience and Nanotechnology

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Molecular Sieve Silica Membranes João C. Diniz da Costa, Victor Rudolph, G. Q. Lu The University of Queensland, Brisbane, Australia

CONTENTS 1. Introduction 2. Synthesis and Fabrication of MSS Membranes 3. Spectroscopy and Characterization 4. MSS Membranes and Applications 5. Conclusion Glossary References

1. INTRODUCTION This chapter presents an overview on the development of molecular sieve silica (MSS) membranes. It starts with a brief review of a membrane’s background and general features. The review is then focused on MSS membrane synthesis and characterization processes with an introduction to the theory and principles applicable to sol–gel processing, templates, and film coating. The importance of micropore formation is discussed, in particular related to fractal branched systems, which are responsible for micropore size tailoring. As high-quality MSS membranes generally result in 3 Å average pore sizes, an activated diffusion model is developed to elucidate the transport mechanism. Finally, MSS membranes are reviewed in terms of their performance, transport characteristics, and application.

1.1. Background The development of membranes for gas separation remained a dormant field for almost one century as greater research efforts were directed towards liquid filtration. As early as 1831, rates of escape of gases from natural rubber balloons were known [1]. The first serious efforts to develop inorganic membranes as a technology for gas separation started in the 1940s for the separation of uranium isotopes by the process of gaseous diffusion applied to UF6 [2–4]. In the 1960s, the first attempts to commercially develop membrane gas separation systems were carried out. Initial membranes consisted of a thick dense polymer layer. A major ISBN: 1-58883-061-6/$35.00 Copyright © 2004 by American Scientific Publishers All rights of reproduction in any form reserved.

problem experienced in this pioneering work was the serious limitation encountered with productivity (high flux) [5] because the permeation rate is inversely proportional to the thickness of a membrane’s selective layer [6]. Conversely, by reducing the thickness of membranes, productivity increased at the expense of selectivity. A breakthrough in membrane application was achieved in the 1960s by the development of asymmetric organic membranes by Loeb and Sourirajan [7]. These membranes consisted of a very thin top layer (thickness < 5 m) supported by a porous sublayer (thickness 50–200 m) [6]. By having a very thin dense top layer or a dense selective layer, productivity could be enhanced while adequate mechanical support was provided by a porous support which offers very low resistance to mass flux. In the late 1970s, commercial polymeric membranes including polyether sulfone, polycarbonate, polydimethylsiloxane (PDMS), and polytrimethylsilylpropyne became available for gas applications [5], while dense metal membranes have also been used to purify hydrogen since 1965 [8]. In the second half of the 1980s, industrial laboratories and a large number of universities started focusing on developments of inorganic membranes, most significantly those made of ceramics [2]. The thrust behind inorganic membranes development originated from the inherent limitations of organic membranes for industrial and environmental applications. Incompatible conditions for organic membrane systems included high pressures, temperature, and chemical instability [9, 10]. Inorganic materials such as high-temperature thermally stable alumina composite membranes developed by Lin and Burggraaf [11] overcame these limitations as they have relatively high thermal and chemical stability and good capabilities to operate under high pressure [12]. This allowed applications to be extended into processes involving chemicals, temperature, or pressure conditions far beyond the limitations of the organic polymeric membranes. Koresh and Sofer [13] pioneered the work on the development of carbon molecular sieve (CMS) membranes, initiating extensive research activity in micropore tailoring. CMS membranes were synthesized from different polymeric materials, including cellulose acetate, polyaramides, and polyimides [14] with pore sizes typically in the region

Encyclopedia of Nanoscience and Nanotechnology Edited by H. S. Nalwa Volume 5: Pages (723–741)

Molecular Sieve Silica Membranes

724 of 3–6 Å [15]. However, Jones and Koros [9] found that organic compounds (C6 and higher hydrocarbons) with concentration as low as 0.1 ppm caused severe deterioration in the performance of CMS membranes. The evolution towards MSS membranes started with zeolite and pillared clays in the early 1990s. Zeolite based materials offer the potential to organize matter and manipulate molecules with high spatial precision at the nanometer scale [16]. Various researchers have worked on ceramic zeolite composite membranes for gas separation using templated method [17] or embedding zeolites in the polymer matrix [18–20]. However, most zeolite membranes were prepared using hydrothermal methods which are relatively simple, but have difficulties in controlling the thickness of the membrane layers and the orientation of particles [21]. Pillared clay membranes were tailored using lamellas of nanometer thickness in layered clay as natural blocks suitable to build a framework of nanometer dimension [22]. Dispersed into an aqueous solution, Na-montmorillonite clay lamellas exfoliate and even delaminate due to hydration of the interlayer cations, resulting in crystalline, quasi-two-dimensional sheets that are 0.96 nm thick and a few micrometers in diameter [23, 24]. Vercauteren et al. [25] synthesized pillared clay membranes and reported low permeation. They found that clay platelets are oriented mainly parallel to the surface of the support, thus resulting in a high degree of tortuosity and resistance to permeation. Shelekhin and Dixon [26] provided the initial attempts towards MSS membranes by producing microporous glass hollow fibers resistant to organic solvents with extremely high selectivities but low flows. For some glass membranes, the silica microstructure is not chemically stable due to the existence of active silanols. This has been overcome partially by using chemical agents to make the surfaces of glass membranes hydrophobic [4, 27]. By the mid-1990s, major research efforts were directed towards what is now known as molecular sieving silica (MSS) membranes, which are novel amorphous microporous membranes [28]. Microporous apertures of molecular dimension are formed from polycondensation of silicon co-polymers. MSS membranes are generally synthesized from deposition on a substrate of a liquid film containing a hydrolyzed tetraethylorthosilicate in ethanol solution. MSS membranes can be tailored to have excellent thermal and chemical stability and high mechanical strength. Apart from gas separation, other potential applications of microporous inorganic membranes include catalytic reactors, gasification of coal, molten-carbonate and solid-electrolyte fuel cells, and water decomposition by thermochemical reactions [28].

1.2. General Features A membrane can be described as a semipermeable barrier separating two phases [6]. As depicted in Figure 1, a membrane unit is constituted of a feed stream which generally faces the membrane’s selective layer. For a component of a feed mixture to diffuse through the membrane, there must be a driving force. Depending on the application, the driving forces can be temperature, pressure, concentration, or electrical fields. The flux of gases through the membrane is

Feed

Membrane

Permeate

Driving Force ∆C, ∆P, ∆T, ∆E

Retentate

Figure 1. Schematic representation of a membrane system.

in most cases driven by a pressure gradient [29]. The filtrate and concentrated streams are generally referred to as permeate and retentate, respectively. Two of the most important parameters that describe the performance of a membrane are productivity (i.e., permeability) and quality (i.e., selectivity). Permeability is typically used to provide an indication of the capacity of a membrane for processing the permeate: a high permeability means a high throughput [4]. Permeability denotes the flux of mass through a membrane per unit of area and time, and per unit pressure gradient. Gas permeability is often expressed: • in Barrer units (10−10 · cm3 STP · cm · cm−2 · s−1 · cm Hg−1 ) • or in gas permeation units (10−6 · cm3 STP · cm−2 · s−1 · cm Hg−1 ) as pressure normalized flux • or as a mole flux (mol · s−1 · m−2 · Pa−1 ). Selectivity generally expresses the membrane’s capacity to separate a desired component from the feed mixture. Selectivity is often calculated as permselectivity (ratio of permeation of single gases) or as a separation ratio  for a binary mixture. For good-quality inorganic membranes, a gas with large kinetic diameter is likely to be blocked while a gas with small kinetic diameter will diffuse through the membrane’s selective microporous layer. For poor-quality membranes, selectivities are closer to unity. This gives an indication that the selective layer has large pores or a wide pore size distribution or pinhole defects rendering the membrane ineffective for separation purposes.

2. SYNTHESIS AND FABRICATION OF MSS MEMBRANES 2.1. Sol–Gel Process The sol–gel process is a very useful route for producing molecular sieve films which are essentially of microporous dimensions (psize < 20 Å). Polymeric silicate gels are often synthesized by hydrolyzing monomeric tetrafunctional alkoxide precursors employing a mineral acid (e.g., HCl) or a base (e.g., NH3 ) as a catalyst. The sol–gel process is controlled

Molecular Sieve Silica Membranes

725

by the hydrolysis and condensation reactions as described by Eqs. (1) to (3). In the hydrolysis reaction (Eq. (1)), the alkoxide groups (OR) are replaced with hydroxyl groups (OH) where R is an alkyl group Cx H2x+1 . The silanol groups are subsequently involved in the condensation reaction producing siloxane bonds (Si-O-Si) plus by-products alcohol (ROH) (Eq. (2)) and water (Eq. (3)) [30]: ≡ Si-OR + H2 O ↔ ≡ Si-OH + ROH (hydrolysis)

(1)

≡ Si-OR + HO-Si ≡ ↔ ≡ Si-O-Si ≡ +ROH (alcohol condensation)

(2)

≡ Si-OH + HO-Si ≡ ↔ ≡ Si-O-Si ≡ +H2 O (water condensation)

(3)

Various research groups [10, 31–33] have reported the production of high-quality molecular sieving films using a variety of sol–gel formulations as presented in Table 1. The molar ratio r (H2 O:Si) of these gels was generally limited to values of 5.1 to 6.4 though in the literature r values range from nonhydrolyzed to 50 [30]. Reasonably low r values in acid catalyzed hydrolysis leads to the formation of weakly branched polymeric sols consistent with the formation of microporous materials. A two-step catalyzed hydrolysis with an initial step (r = 1) followed after 90 minutes by an additional step (r ∼ 3) also produced weakly branched structures [34]. For lower r values, the condensation rate is inhibited, forming rather weakly branched systems, which is addressed in Section 2.4. The hydrolysis and condensation reactions lead to the growth and aggregation of clusters resulting in gel formation. Upon gelation, the gel commences to shrink and densify. This process is defined as syneresis and is caused by the spontaneous expulsion of solvents from its pores [30]. Gelation also serves the purpose to freeze in a particular sol configuration [35]. The gelation phenomenon plays a fundamental role in gel microstructure formation. Therefore, the film microstructure of membranes depends upon the preceding formulation and preparation procedures of sols to the gel point as well as the proceeding aging, drying, and heat treatment processes of gels. The aging process of gels observed by nuclear magnetic resonance (NMR) has been investigated by Vega and Scherer [36], and Raman spectroscopy by Orcel et al. [37]. Table 1. Sol formulations of MSS membranes. Chemical composition 1.0TEOS:3.8EtOH:6.4H2 O:0.085HNO3 1.0TEOS:5.0EtOH:6.8H2 O:0.125HNO3 xMTES:(1−x)TEOS:3.8EtOH:5.1H2 O:0.056HCl 1TEOS:3.8EtOH:5.1H2 O:0.05HCl plus surfactant templates 1.0TEOS:3.8EtOH:6.0H2 O:0.10HNO3

Process

Ref.

single-step single-step template two-step template two-step two-step

[31] [32] [10]

TEOS—tetraethylorthosilicate; MTES—methyltriethoxysilane.

[48] [33]

It was found that condensation of silica gels is an ongoing process after gelation due to the substantial amount of hydroxyl groups. Aging causes increased connectivity (crosslink) of the network produced by condensation reactions [30]. In other words, the gel structure stiffens due to the condensation reaction. According to Iler [38], surface tension forces created in a gel during solvent removal will cause the network to collapse. However, the stiffening of the gel network will resist the compressive forces of surface tension and the shrinkage rate is greatly reduced, resulting in greater pore volumes. Conversely, if the condensation reaction rate is inhibited, the gel network collapses, resulting in lower pore volumes. The structural changes of xerogels (dried gels) have been investigated by infrared and Raman spectroscopy and NMR. Bertolluzza et al. [39] showed that both infrared and Raman spectroscopy complemented each other for gels prepared with TEOS. For instance, it was reported that the characteristics of xerogel spectra showed characteristic bands of fused quartz for IR (∼1220 ∼1080 ∼800 ∼460 cm−1 ) and Raman (∼1180 ∼1070 ∼800 ∼430 cm−1 ). These bands are associated with siloxane bonds (Si-O-Si). Duran et al. [40] investigated the structural evolution of xerogels calcined at various temperatures. It was found that the band associated with silanol groups (Si-OH) at ∼3740 and ∼960 cm−1 reduced in intensity while the siloxane bands at ∼800 and ∼1070 cm−1 enhanced their intensity with increasing temperature. These results suggest continuing condensation reactions during heat treatment leading to the strengthening of the network due to cross-linking. For NMR studies, the Qn nomenclature is conventionally used to describe the silicon centers in silicates, where Qn represents the n0 1 2 3 4 number of Si-O-Si linkages attached to silicon [41]. Q4 are fully condensed species having a silicon nucleus with four bridging oxygen atoms while the other species are ascribed to silanol environments (i.e., Q2 has a Si nucleus with two bridging oxygen atoms). Abidi et al. [41] investigated the chemical shifts for xerogels heat treated at various temperatures with NMR chemical shifts for the uncondensed species Q3 and Q2 at −101 and −92 ppm for xerogels treated from 60 to 350  C. It was found that heat treatment enhanced the contribution of condensed species at the expense of uncondensed species. Similar results have been reported by Klemperer et al. [42] for loss of hydroxyl groups and the reduction in intensity of peaks associated with uncondensed species. This phenomenon can be explained by the condensation reactions (Eqs. (2) and (3)) and are in agreement with IR and Raman spectroscopy results. Buckley and Greenblatt [43] investigated the pore characteristics of xerogels prepared with TEOS, ethanol, and water and calcined at 300  C. It was reported that at low r values (e.g., H2 O/Si = 4), the xerogel was characterized by N2 adsorption isotherms of type I, characteristic of microporous materials. By increasing r to a value of 20, the surface area increased and the adsorption isotherm changed to type IV. The latter indicated that the xerogel had less microporosity and a broader pore size distribution. It was also found that no significant effect in the xerogel structure was observed by increasing the ethanol content. Hence, excess

726 water has a detrimental impact in the formation of micropore xerogels. These results can be explained as phase separation of solvents in the micropore during gel formation as ethanol preferentially evaporates, leaving excess water in the pore fluid. Condensation reactions and diminishing solvent quality (e.g., too much water) during drying probably helps to stiffen the xerogel structure and broadens the pore size distribution [35].

2.2. Molecular Imprinting An important technique to tailor the pore size of xerogels is to add organic template agents during the sol–gel process [35]. During gel formation, organic templates are trapped in the gel structure. By heat treating the xerogel above 400  C, organic templates are burnt off leaving within the xerogel matrix a cavity with similar dimensions to those of the template molecules [44]. This process seemingly produces microporous materials based on the imprint of molecular dimension of the template. In other words, the template provides a freeze in xerogel structure of micropore dimension (rpore < 20 Å). There are two methods of sol–gel composites derived from template agents. The first one is a covalently bonded organic template, such as methyl groups (CH3 ) in methyltriethoxysilane (MTES), which has a co-monomer nonhydrolyzable functionality. The second method employs an organic oligomer or surfactant, which interacts with the sol by weak van der Waals forces, hydrogen or ionic bonds, or hydrophilic-hydrophobic interactions. Raman et al. [35] extensively reviewed the template based approach to the preparation of amorphous nanoporous silica. It was stated that the potential advantages of the template approach are that the organic ligand volume fraction may be used to control the volume fraction of the gel network while the pore size is independently controlled by the template size and shape. For gas separation applications, these features will fundamentally determine the overall performance of membrane films as the volume fraction controls permeance (defined as the thickness normalized flux of diffusing molecules transported across the film per pressure difference across the film) while selectivity (separation factor) is determined by pore size and pore size distribution. Raman and Brinker [10] successfully prepared highquality molecular sieve membranes derived from templated xerogel films using TEOS and MTES, a precursor which contains methyl as a covalently bonded organic template. It was reported that templated xerogels treated at 150 and 400  C had N2 sorption isotherms of type I (microporous). Increasing the calcination temperature of the templated xerogel to 550  C yielded type-II isotherms, characteristic of nonporous materials. However, the partial CO2 isotherm showed that the 550  C sample was also microporous. These templated xerogels showed a good pore size control capability because CO2 (dk = 3 3 Å) has a lower molecular kinetic diameter than N2 (dk = 3 64 Å). Kusakabe et al. [45] employed three different templates (octyl-, dodecyl- and octadecyltriethoxy-silanes) in order to test the role that template plays in tailoring pore sizes. They found that the alkyl chain of the template controls the pore size distribution. Hence, the shorter alkyl length produced the narrower pore size distribution. Kim et al. [46]

Molecular Sieve Silica Membranes

prepared microporous silica membranes by reacting TEOS and MOTMS (methacryloxypropyltrimethoxysilane), where the latter one controlled the pore structure formation in the region of pore size of 6 Å. Lu et al. [47] embedded methacryloxypropyl groups into the silica film matrix. They reported that as long as the template ligand volume has been below a critical percolation threshold, the secondary microporosity was inaccessible to N2 . The amount of primary pores only accessible to CO2 decreased with the amount of added organic ligands (covalently bonded templates). The employment of non-covalently bonded organic templates has also been investigated for silica derived membranes, including C6- and C16-surfactants [48] and alkyltriethoxysilanes [49]. Tsai et al. [48] claimed that by applying surfactants the flow resistance through the layers can be minimized and the inherent support defects can be overcome as well as that a narrow PSD can be attained. They used a C6-surfactant (triethyl-hexylammonium bromide) resulting in microporous (dp = 10–12 Å) membranes with a high surface area (575 m2 · g−1 . Yuan et al. [49] used dodecyldimethylbenzylammonium chloride surfactants to achieve surface areas larger than 1000 m2 · g−1 and uniform pore sizes around 10 Å. Ayral et al. [50] prepared silica membranes using TEOS and amphiphilic surfactants (Triton with varying polyoxyethylenic chains). Increasing the chain length of the surfactants resulted in a wider PSD in the same manner as observed by Kusakabe’s co-workers [45] for covalently bonded ligand templates. The broadening of pore size is of particular concern as it leads to poor performance as separation capabilities of membranes are rendered ineffective. On the other hand, surface area and porous volume increased, which facilitates the transport of diffusing molecules through the membrane. Various research groups [51–53] investigated the effect of methyl ligand template by NMR spectroscopy. The chemical shift of species containing methyl ligands was observed in the region of 50∼70 ppm. To differentiate from the silicon nomenclature, the peaks associated with methyl ligands are referred to as Tn · T3 species are bound by three Si-O-Si links and one carbon (CH3  while T2 is formed by two Si-OSi links, one Si-OH, and one carbon. Fahrenholtz et al. [51] reported that the peaks allocated to Tn species increased in intensity with increase in the organic template molar ratio at the expense of Qn -species. Fahrenholtz et al. [51] also investigated the pore structure of templated xerogels calcined at 100  C by varying the MTES/TEOS molecular ratio in a base catalyzed process. In mixtures ranging from 0/100 to 50/50, it was reported that the highest surface area (900 m2 · g−1  and lowest pore volume (0.4 cm3 · g−1  was obtained at 20/80 mixtures. However, these results cannot be compared against the work of Raman and Brinker [10] because the sample calcination was limited to 100  C only. Farenholtz et al. [51] also reported that for mixtures in excess of 50/50 molar ratio, both surface area and total pore volume drastically reduced to zero at ∼70/30 mixtures. Raman and Brinker [10] limited their mixtures to a maximum molar ratio of 50/50. As the molar ratio of MTES increased, the contribution of uncondensed species (Q2 , Q3 , and Tn  also increased, leading to very highly packed structures of no pore volume. Diniz da Costa et al. [54] reported that a higher template MTES:TEOS molar ratio induced the

Molecular Sieve Silica Membranes

727

collapse of the xerogel matrix due to capillary stress, promoting dense xerogels with a broader pore size distribution.

2.3. Fractal Branched Systems Brinker et al. [55] investigated the bulk gel formation in weakly branched systems prepared by a two-step catalyzed hydrolysis of TEOS with r = 5. It was reported that there was a strong relation between weakly branched systems with 29 Si NMR uncondensed species (Q2 and Q3  consistent with fractal dimension df < 2. In 29 Si NMR spectroscopy, siloxane bridges are called Q4 sites, single silanols Q3 sites, and geminal silanols Q2 sites [56]. The mass fractal theory which dictates steric constraints in silicate systems was developed by Mandelbrot [34] and is expressed as d

M1 2 ∝ Rf f 1

+df 2 −d

(4)

where Rf is a radius, M1 2 is the number of intersections, df 1 and df 2 are the fractal dimensions of two structures, and d is the dimension of space d = 3. Mandelbrot [34] showed that for two structures of radius Rf placed independently in the same region of space, the probability of intersections will decrease indefinitely as Rf increases if df < 1 5. Hence, the structures are mutually transparent and they freely interpenetrate one another as they are forced into close proximity by the increasing concentration [57]. For weakly branched systems, there is a higher tendency for structures to interpenetrate, forming large structures of micropore size, resulting in densification. According to de Lange et al. [58], the density of the final individual fractal structure is also dependent on the fractal dimension and Rf , according to d

density ∝

Rf f mass d +d −d = 3 = Rf f 1 f 2 volume Rf

interaction between a silica film and the metal oxide supports. This is a feature of key technological importance for the production of membranes. Recently, Diniz da Costa et al. [33] investigated the fractal formation of single-step and two-step sol–gel processes. The deconvoluted 29 Si NMR spectra showed that the two-step process had a high concentration of silanol groups (Q3 and Q2  while the single-step process had a high contribution of siloxane bonds (Q4 . By using molecular probing, Diniz da Costa and co-workers reported that membranes prepared by the two-step process had a higher activation energy for helium than the single-step membranes. As the activation energy increases as the pore size decreases [59], these results strongly suggest that in fact pore size control and reduction can be achieved by enhancing the concentration of silanol groups as initially proposed by Mandelbrot [34].

(5)

where the density decreases as Rf increases. Dense films are undesirable in view of high resistance to permeation of diffusing molecules. Membrane film structures should have high porosity with small pore size. Hence, a balance must be attained between the two competing parameters to optimize film microstructure. Provided that sol fractals do not completely interpenetrate during film formation, the porosity may be controlled by the size of the fractal species prior to film formation. The bulk gels prepared by Brinker et al. [55] showed extremely low BET surface areas (∼1 cm2 .g−1  consistent with the exterior surface of nonporous materials. It was explained that weak branching combined with limited condensation during film formation promotes dense packing and low pore volume. However, de Lange et al. [58] found that dense films also formed for binary sols containing TEOS and metal oxides with df > 1 5. It was argued that the prediction of the porosity based on fractal dimension and interpenetration alone was difficult. In their view, the condensation rate, penetration rate, and drying rate are also important as far as the film final morphology is concerned. The work of de Lange and co-workers [58] is of considerable importance as it attempts to investigate the potential

2.4. MSS Film Technology 2.4.1. Membrane Film Coating Preparation of MSS membranes is generally conducted by a sol–gel film formation process, namely dip-coating of ceramic oxide supports with colloidal sols containing silica precursors. According to Brinker and Scherer [30], sol–gel film formation requires considerably less equipment and is potentially less expensive than conventional thin-film forming processes such as chemical vapor deposition (CVD), evaporation, or sputtering. It was also indicated that a major advantage of sol–gel process over conventional coating methods is the ability to control precisely the microstructure of the deposited film (i.e., pore volume, pore size, and surface area). Coupled with mechanical, chemical, and thermal stability, MSS composite membranes derived from the sol–gel process potentially offer greater tailorability with respect to the pore size distribution.

2.4.2. Support Effect Most silica thin films are cast on ceramic supports made from oxide powders such as ZrO2 , Al2 O3 , TiO2 , and CeO2 . Alumina supports are most suitable for gas separation [60]. Particle stacking is a major principle behind the preparation of ceramic membranes in order to obtain very narrow pore size distributions [61]. The stacking of particles with different grain sizes allows a reduction in pore volume and pore size as small particles are layered on top of large particles. These materials have been widely used as substrates for the preparation of molecular sieving membranes. According to Bonekamp [62], only a multilayered system can provide a substrate which is sufficiently smooth and flawless to serve as a support on which an almost defect-free microporous membrane can be made. The literature indicates that substrates used for the preparation of MSS membranes are mainly -AlO3 and -AlO3 [10, 29, 31, 58, 63]. The principle of asymmetric membrane is also extensively used for tailoring MSS membranes. By stacking smaller colloids (-alumina) on top of larger colloids (-alumina), a membrane support can be produced in layers in a way that its pore size is reduced from the bottom to the top layer. The membrane’s selective layer is therefore cast on the top layer. The primary function of the support

Molecular Sieve Silica Membranes

728 is to reduce flux resistance of diffusing molecules due to its large pores while providing mechanical stability and integrity to the microporous thin films. Various research groups have prepared high-quality -alumina support with 40–60% porosities [11, 58, 61]. Using boehmite (-AlOOH), Lenaars et al. [61] produced nonsupport -alumina films with pore diameter ranging from 3.7 to 8.9 nm calcined at 200–900  C. However, at 1000  C calcination temperature, -alumina turns into -alumina resulting in pore diameter enlargement by one order of magnitude to 78 nm. Lin and Burggraaf [11] reported large pore radius in the region of 31 nm for support membranes treated at 450  C, while the pore size increased up to 132 nm as the calcination temperature increased to 1200  C. De Lange et al. [58] reported pore diameter in the region of 38 nm, while the inclusion of PVA (polyvinyl alcohol) in the sol–gel process caused the pore diameter to increase slightly to 42 nm. Support characteristics play a vital role in the morphology of the sol–gel films. Bonekamp [62] reviewed the morphological requirements of supports for dip-coat film processing. In his view, layer homogeneity is fundamental in preparing thin films without defects and the support should have (i) small pore size, (ii) low surface roughness, and (iii) low void defect concentration. When large pores and voids are emptied by evaporation, the wall between adjoining pores is subjected to uneven stress that can cause cracking. Similarly, rough surfaces (e.g., edgelike shapes) induce film stress, resulting in microcracks. Support roughness can be reduced by polishing the supports [11, 32]. Although pore size of supports can be reduced by lowering the calcination temperature, this process is clearly dependent upon the calcination temperature of silica thin films. As crystal growth occurs with increasing calcination temperature and pore diameter likewise, there must be a trade-off between the heat treatment that provides the best microporous film while having the least detrimental impact to the support’s integrity. In the literature, supports are generally precalcined prior to film deposition at temperatures ranging from 400 to 600  C and heating rates of 0.5–1.0  C · min−1 [10, 31–33]. Precalcination emulates the conditions of film heat treatment in order to minimize the effect of interparticle heat stress on silica films.

2.4.3. Film Formation Scriven [64] extensively reviewed the dip-coating process and proposed five stages: immersion, start-up, deposition, drainage, and evaporation. In the immersion stage, a substrate or membrane support is immersed in a liquid sol (coating bath) followed by the start-up stage which results in liquid adhering to the substrate surface. As the substrate is withdrawn from the coating bath, deposition (film formation) occurs. The moving substrate entrains the liquid in a fluid mechanical layer that splits in two above the liquid bath surface, returning the outer layer to the bath [64]. Drainage and evaporation of the coating sol occurs during and after withdrawal of the substrate from the coating bath. Brinker et al. [65] also reviewed the sol–gel thin-film formation and suggested a more complete model based on the steady-state dip-coating process. In their model, there

is a sequential order of structural development that results from draining accompanied by solvent evaporation, continued condensation reactions, and capillary collapse. During withdrawal of the substrate from the coating bath, the concentration of the polymeric materials increases close to the surface of the substrate due to gravitational drainage in tandem with severe evaporation and further condensation reactions. Gelation occurs concomitantly and is related to the moment when the condensing network is sufficiently stiff to withstand flow due to gravity, yet is filled with solvent [30]. For sol–gel film formation, aggregation, gelation, and drying occur in seconds [65]. Scriven [64] reported that film thickness is determined by the competition among viscous forces, capillary (surface tension) force, and gravity. According to Brinker and Scherer [30], when the substrate withdrawing speed (U ) and viscosity are low (often the case for sol–gel film deposition), the balance of forces is modulated by the ratio of viscous drag to liquid-vapor surface tension (LV . Hence, the thickness of a film (h) is proportional to U 2/3 in accordance with the Landau and Levich equation. In other words, increasing the speed of withdrawal in the dip-coating process will yield thicker films. Many of the MSS membrane preparation methods cited in the literature do not state withdrawal speed. Researchers at the University of Twente in the Netherlands generally have a slight variation using the dip-coating pendulum system with very high tangential withdrawal speed. On the other hand, withdrawal speeds of 20 cm · min−1 have been reported by Raman and Brinker [10]. The major advantage of the pendulum method is that just one side of the substrate is film-coated because the substrate is immersed tangentially to the coating bath. The normal right-angle dip-coating method requires that one coated side of the membrane is removed by sanding or scraping. Deviations in predicted behavior in film formation were discussed by Brinker et al. [55] and Brinker and Scherer [30]. It was indicated that deviations may be caused by several other factors such as pH, viscosity regimes, and evaporation which increases concentration and viscosity resulting in nonNewtonian behavior. According to Brinker et al. [55], the concentration of the deposited film increases 18- to 36-fold due to evaporation. In turn, this causes the precursors to come into close proximity with each other resulting in closer aggregation, then gelation and drying with significant reorganization of the film matrix. During this process, chemical reaction rates increase quite considerably until gelation occurs and the film matrix continues to evolve during drying, aging, and thermal treatment.

2.4.4. Film Structure The best technique to characterize deposited membrane films is molecular probing, which uses gas molecules of different kinetic diameters to determine the average pore size. However, the characterization of film structures always poses significant technical problems if further information such as surface area and pore volume is required. A qualitative and easy approach is to characterize the bulk xerogels. The disadvantage is that, although the underlying physics and chemistry that govern polymer growth and gelation are

Molecular Sieve Silica Membranes

essentially the same for films as bulk gels, other factors influence structural evolution in films [30]. For instance, the properties of a deposited thin film may be quite different due to nonequivalent gelation and drying conditions [55, 63]. Nonsupported thin films have been prepared by de Lange et al. [58] and de Vos and Verweij [31] for sorption characterization. These films were characterized by N2 sorption isotherms of type I (microporous materials). The preparation procedure of nonsupported films included the evaporation of a sol in a Petri dish leading to gelation. Subsequently, the thin film was dried and then calcined at the desired temperature. De Vos and Verweij [31] reported that the pore sizes of nonsupported and supported membranes were very similar. However, de Lange et al. [58] used -alumina and reported that the pore sizes of supported membranes were slightly higher than those of nonsupported membranes. One point of consideration here relates to the fact that nonsupported films are cast on nonporous glass rather than porous metal oxide supports. As the membrane films are very thin, the morphology of the support or substrate may influence the final structure of the film morphology. A further important parameter to control the microstructure of films relates to the aging of sols. Brinker et al. [65] investigated the effect of aging on silica films. It was reported that the porosity, surface area, and pore size increased monotonically with aging time employed to grow the fractal species prior to film deposition. Their films were microporous for sols aged within 3 days. However, the films became mesoporous with sols aged in excess of 3 days. This trend is also observed in membrane preparation. Various research groups [31–33, 58, 63] used nonaged sols to prepare microporous films. A variation from this approach is used by Raman and Brinker [10] who aged their templated sols for several days. However, their sols contained a methyl ligand template which induces capillary stress resulting in films with low pore volume. Hence, by aging the templated sols a form of pore control is achieved due to cross-linking.

2.4.5. Defects A major problem arising from ceramic membranes relates to defect formation. According to de Vos and Verweij [31], the size and surface density of the defects depend on drying rate, amount and size of particles in the preparation atmosphere, and the thermal processing schedule. The stress in the film formation is large and nearly equal to the tension in the liquid ( = P ) [30]. According to Brinker et al. [65], it is commonly observed for films that adhere well to the support that cracking does not occur if the film thickness is below a critical thickness hc ∼ 0.5–1 m. It was argued that cracking did not occur for films thinner than hc because the energy required to extend the crack was greater than the energy gained from relief of stresses near the crack. However, Leenaars et al. [61] observed that gel films dried at room temperature and relative humidities of 40 to 80% had no cracks if film thickness was less than 20 m. Although reducing film thickness is one of the strategies to avoid stress fractures, some process conditions as reported by Leenaars may allow crack-free thicker films. Many defects in silica films may reflect the morphology of the support or substrate which hampers the functional

729 performance of membranes. Burggraaf [66] indicated that voids cause bubbles in the coating, resulting in pinholes. He also mentioned that cracks can be caused by pinholes and stress buildup due to the difference in expansion coefficient between the top film and substrate. Further defects can be caused by the membrane preparation process. Dust deposition during the film coating and calcining process can cause defects resulting in membranes of poor quality. De Vos and Verweij [31] and Tsai et al. [48] prepared silica films with thickness in the region of 30–90 nm (well below hc ∼ 0.5–1 m) in clean rooms (class 1000) to avoid dust. Saracco et al. [67] reported that permselectivities are greatly enhanced due to the reduction of the statistical interference of particle dust in sol–gel deposition films in clean rooms versus normal laboratories. A method to repair a small concentration of defects in very thin silica films is to repeat the dipping and calcining process of the first silica layer.

3. SPECTROSCOPY AND CHARACTERIZATION The characterization of film structures always poses significant technical problems in view of several factors affecting very thin film formation (i.e., micron scale). A qualitative and easy approach is to characterize xerogels based on the findings of Brinker and Scherer [30] that the underlying physics and chemistry that govern polymer growth and gelation are essentially the same for films as bulk gels. By studying xerogels, the microstructural evolution of the silica matrix can be fully analyzed at different steps of heat treatment process. Hence, fundamental information can be evaluated to tailor pore size of MSS membranes. Several surface characterization techniques such as FTIR (Fourier transform infrared), 29 Si NMR (nuclear magnetic resonance) spectroscopy, and TGA (thermogravimetic analysis) are employed to obtain information on the reaction mechanisms involved in the sol–gel processing. In-situ film characterization techniques such as XPS (X-ray photoelectron spectroscopy) and SEM (scanning electron microscopy) spectroscopy are also used to determine main features of membrane films. Nitrogen adsorption is also used to determine important microstructural characteristics of xerogels such as micropore surface area, pore volume, pore size, and pore size distribution. Adsorption isotherms for gases of interest are obtained using gravimetric methods to determine the isosteric heat of adsorption, an important thermodynamic parameter used in the transport characteristic of MSS membranes.

3.1. Characterization of Xerogels 3.1.1. Thermogravimetry TGA is used to determine weight loss of xerogels during calcination and the temperature at which the compounds are oxidized and burnt off from the xerogel matrix. A typical weight loss curve of the templated and nontemplated xerogels as a function of temperature is depicted in Figure 2. Initial weight losses from room temperature to ∼150  C are mainly attributed to water molecules trapped in the xerogel matrix. From ∼150 to ∼450  C, the rate of weight loss is

Molecular Sieve Silica Membranes

730 100 98 Absorbance (Arbitrary Units)

96 94

Weight (%)

92 90

templated xerogel

88 86 84

600oC

o

500 C

450oC

82 80

50oC

xerogel

78 76 0

1400

100 200 300 400 500 600

basically constant for both xerogel and templated xerogel, suggesting that water and alcohol are continuously expelled from the xerogel matrix due to condensation reactions. The sharp weight loss at about ∼450  C for templated xerogels is attributed primarily to the oxidative pyrolysis of organic templates [10].

3.1.2. Infrared Spectroscopy Infrared transmission spectroscopy is a volume rather than a surface specific technique because the interactions of sample volume with radiation do not define a surface at the atomic scale [68]. Therefore, FTIR spectroscopy is intentionally carried out to determine the molecular functional groups embedded in the bulk xerogel matrix only. As xerogels are optically too dense to measure the transmission spectra directly [69], bulk xerogels are crushed into very small particles and are pressed into KBr pellets. Representative IR spectra of xerogels are depicted in Figure 3. The IR bands corresponding to silanol and silicon alkoxide groups generally appear in the range from ∼1400 to ∼600 cm−1 . The bands assigned to siloxane bonds at ∼800, 1080, and 1220 cm−1 are listed in Table 2. The silanol band at ∼940 cm−1 which appears very strongly at 50  C decreases in intensity with increase in the calcination temperature [39, 40, 68]. This supports the view that polycondensation is the underlying process responsible for the transformation of silanols to silicons, as is also evidenced by the fact that the siloxane bands at ∼1092 cm−1 increase in intensity at high calcination temperatures. It is also observed that siloxane bands at ∼1058 cm−1 at 50  C shift towards ∼1087 cm−1 at 400  C and ∼1092 cm−1 at 550  C. According to Duran et al. [40], this shift involves the strengthening of

1000

800

Wave number (cm )

Temperature ( C)

Figure 2. TGA weight loss curves. Reprinted with permission from [95], J. C. Diniz da Costa, Synthesis and Characterisation of Molecular Sieve Silica (MSS) Membranes, Ph.D. Thesis, University of Queensland, Brisbane, Australia, 2000.

1200

-1

o

Figure 3. FTIR spectra of typical xerogel. Reprinted with permission from [95], J. C. Diniz da Costa, Synthesis and Characterisation of Molecular Sieve Silica (MSS) Membranes, Ph.D. Thesis, University of Queensland, Brisbane, Australia, 2000.

the xerogel network and can be interpreted as a shrinkage produced by polymeric bonding.

3.1.3. Nuclear Magnetic Resonance Solid-state NMR spectroscopy complements IR spectroscopy because IR classifies the surface hydroxyls according to their bond strength (free and bridged silanols) while 29 Si NMR distinguishes single (either isolated or vicinal) from double (geminal) silanols [56]. Xerogel samples are crushed in small particles and spun at a frequency of 2.5 KHz with cross polarization contact time of 8 ms, which is sufficient to allow cross polarization of the silicon functional groups. A typical 29 Si NMR spectrum of a templated xerogel sample is depicted in Figure 4. The spectrum can be deconvoluted using Gauss–Lorentz curve fitting software in order to determine the proportion of the functional groups embedded in the xerogel matrix. In Figure 4, three peaks are observed with chemical shifts ( in the region of −90 to −120 ppm, denoting the presence of Q2 , Q3 , and Q4 species, and the peaks with chemical shifts relative to kaolin at −60 to −70 ppm are associated with Me(OH)2 Si-O-Si bonds [41, 42, 51–53, 56]. To differentiate from the silicon nomenclature, these peaks are referred to as Tn · T3 species are bound by three Si-O-Si links and one Table 2. Assignment of IR absorption spectra for templated xerogels. Ref. 800 cm 960 cm−1 1080 cm−1 1220 cm−1 −1

Stretching mode Si-O-Si symmetric Stretching mode Si-OH TO mode Si-O-Si asymmetric LO mode Si-O-Si asymmetric

[39, 40] [39, 40, 68] [40] [39, 40]

Molecular Sieve Silica Membranes

731 160 o

Q3

Q4

T3

T2

-6 0

Q2

-8 0

-1 0 0

-1 2 0

chemical shift (ppm)

Figure 4. Deconvoluted NMR spectrum of sample 10/90 (400  C). Reprinted with permission from [95], J. C. Diniz da Costa, Synthesis and Characterisation of Molecular Sieve Silica (MSS) Membranes, Ph.D. Thesis, University of Queensland, Brisbane, Australia, 2000.

Volume Adsorbed @ STP (cm3.g-1)

400 C 140 450 oC 120

o

100

500 C

80 o

550 C 60

40

20

carbon while T2 is formed by two Si-O-Si links, one Si-OH, and one carbon. In practical terms, NMR spectroscopy is a powerful tool to assist researchers in developing xerogels with the microstructure required for MSS membranes, in particular directed to inference to fractal theory.

0.0

0.2

0.4

0.6

0.8

1.0

P/Po

Figure 5. N2 sorption isotherms of sample 50/50. Reprinted with permission from [95], J. C. Diniz da Costa, Synthesis and Characterisation of Molecular Sieve Silica (MSS) Membranes, Ph.D. Thesis, University of Queensland, Brisbane, Australia, 2000.

3.2. Adsorption 3.2.1. Volumetric Adsorption Gas adsorption/desorption is one of the most important and extensively used methods in the characterization (porous volume, specific surface area, and pore size distribution) of porous inorganic materials [3, 70]. Physical characterization of bulk xerogels is carried out by nitrogen adsorption at 77 K to determine the micropore volume, surface area, and pore size. In this technique, the samples must be degassed for a period of 3 hours or even longer at 250  C prior to sorption experiments. Typical N2 sorption isotherms for a xerogel sample as a function of calcination temperature are shown in Figure 5. These isotherms are of type I, characteristic of microporous materials. Table 3 shows the results of micropore surface, volume, and average pore size for several xerogel samples. These results are obtained based on the t-plot method. The trend is quite clear that an increase in the calcination temperature reduces micropore surface and volume. There is a strong indication that the xerogel matrix continues to condense as calcination temperature increases. Despite this, no significant changes are observed in Table 3 with respect to pore size, suggesting that pore size remains quite constant in the calcination temperature range of 400–550  C. These trends are generally observed for various sol–gel formulations and are attributed to the densification of the basecatalyzed xerogel matrix [51] and the HCl catalyzed xerogels [10]. Pore size distributions as plots of dV /drh as function of the corresponding rh are shown in Figure 6. V is the micropore volume (cm3 · g−1  and rh is the hydraulic radius (Å). The pore size distribution was calculated according to the improved MP method developed by Zhu et al. [71] and based on nonporous silica adsorption data from Gregg and Sing [70]. For microporous materials, other methods

(HK and SF) for the determination of the pore size distribution can also be used. The pore size distribution ranges in the microporous region, suggesting that these xerogels can be used ideally for molecular sieving applications. It is observed that prominent peaks appear in the pore size range of ∼7.4 ∼8.9 ∼8.4 Å corresponding to pore filling at lower partial pressures as observed from the N2 sorption experiments. As the calcination temperature increases, it promotes densification of the xerogel matrix and reduction in peak height (pore volume), but not much in pore size reduction.

3.2.2. Gravimetric Adsorption Gravimetric adsorption measurements are performed to determine thermodynamic conditions of xerogel materials. This is generally carried out by measuring the displacement of a quartz spring due to the sorption of gas molecules (sorbate) on the xerogel samples (sorbant). The sorption isotherms can be determined for various sorbates in order to calculate the isosteric heat of adsorption. Xerogel samples are degassed overnight at P < 10−3 Torr at 300  C prior to gas adsorption experiments. In this experiment, the bulk xerogel samples are subjected to a step change in sorbate pressure from an initial zero to a final atmospheric pressure. Table 3. Pore structure data of various xerogel samples. Calcination temperature ( C) 400 500 600

Micropore volume (cm3 · g−1 )

Micropore surface (m2 · g−1 )

Average pore radius (Å)

Total pore volume (cm3 · g−1 )

0 193 0 153 0 078

451 7 350 2 176 6

8 6 8 8 8 9

0 199 0 161 0 084

Molecular Sieve Silica Membranes

732

(mol · g−1  versus pressure (kPa). The isotherms at 273– 295 K are nonlinear and of Langmuir type. The Langmuir theory is based on the kinetic principle of equilibria; that is, the rate of adsorption is equal to the rate of desorption from the surface [72]. The Langmuir theory assumes that surfaces are homogeneous (all sites are energetically equivalent) and each site can hold one adsorbate molecule only with no interaction between molecules adsorbed on neighboring sites. The Langmuir adsorption isotherm which gives the relation of the amount of gas adsorbed as a function of the pressure at a given temperature is expressed as follows:

0.10

0.05 o

dV/dr h (cm3.A-1.g-1)

400 C 0.00 0.10 0.05 o

500 C

=

0.00 0.10 0.05 o

600 C 0.00 0

5

10

15

20

25

30

Pore Radius, rh (A)

Figure 6. Pore size distribution of xerogel calcined at 400, 500, and 600  C. Reprinted with permission from [95], J. C. Diniz da Costa, Synthesis and Characterisation of Molecular Sieve Silica (MSS) Membranes, Ph.D. Thesis, University of Queensland, Brisbane, Australia, 2000.

The weight adsorbed is measured as a function of partial pressure. In Figure 7, representative CO2 sorption isotherms are shown at temperatures 273–373 K for xerogels. The isotherms are given by plotting the amount adsorbed 1.1 1.0 273K

0.9

Adsorption (mol.g-1)

0.8 0.7

295K

0.6 0.5 323K

0.4 0.3

c bp q = = cs  qs 1 + bp

(6)

where c is the concentration (mol · m−3 , cs is the concentration at saturation (mol · m−3 , q is the amount adsorbed (mol · gram−1 , b is the adsorption equilibrium constant (Pa−1 , p is the pressure (Pa), and  is the surface coverage. For adsorption on a uniform surface at sufficiently low concentrations, the equilibrium relationship between the gas phase and adsorbed phase concentration will be linear and generally referred to Henry’s law [73]. Hence, Eq. (6) can be simplified to q = qs bp = Kp

(7)

where K is the Henry constant (mol · Pa−1 · gram−1 . At temperatures in excess of 323 K for CO2 adsorption, the isotherms are practically linear implying that they comply with Henry’s law [74] as it is observed in Figure 7. One of the basic quantities in adsorption studies is the isosteric heat, which is the ratio of the infinitesimal change in the adsorbate enthalpy to the infinitesimal change in the amount adsorbed [72]. If Qst is taken to be independent of temperature, the temperature dependence of the Henry constant obeys the Van’t Hoff equation [73]:
 Qst K = K0 exp (8) RT where K0 is a temperature-independent proportionality constant, Qst is the isosteric heat of adsorption (J · mol−1 , R is the gas constant (J · mol−1 · K−1 , and T is the absolute temperature (K). In accordance with Eq. (8), the slope of the natural logarithm of the K versus 1/T yields Qst . The Arrhenius plots of the Henry constant (ln(K) versus T −1  for single-step and double-step xerogels for several gases are depicted in Figure 8. The isosteric heats of adsorption (Qst  reported in the literature for silica xerogel and silicalite zeolites are presented in Table 4 for comparison.

373K

0.2

3.3. Characterization of Membrane Films

0.1

3.3.1. X-ray Photoelectron Spectroscopy

0.0 0

20

40

60

80

100

Pressure (kPa)

Figure 7. CO2 adsorption isotherms for two-step xerogels. Reprinted with permission from [95], J. C. Diniz da Costa, Synthesis and Characterisation of Molecular Sieve Silica (MSS) Membranes, Ph.D. Thesis, University of Queensland, Brisbane, Australia, 2000.

X-ray photoelectron spectroscopy is widely used as a surface analysis technique capable of providing an element analysis of surface within a 10% accuracy [75]. XPS sputter profiles and scanning Auger microscopy are also used in order to complement the silica film thickness SEM characterization, in particular to determine the interface between the silica film and aluminum substrate. In this experimental

Molecular Sieve Silica Membranes

733 40000

-15

O1S

35000 30000

-14

OAUGERS Intensity

Ln K

25000

CH4

-13

20000 Al2S

15000

O2

C1S

10000

Al2P

Si2P O 2S

Si2S

-12 5000

CO2 0 1000

-11 1

2

3

4

800

600

5

1000/T (K )

Table 4. Typical isosteric heat of adsorption Qn kJ · mol−1 . H2

xerogel silica silicalite silicalite silicalite silicalite

15 9 22 3 24 6 24 20 24

11 7 10 3 20 18 6 28 20

7 9 6 1

N2 11

6

17 3 15

6

17 6

Oxygen

50

40

30 Aluminium 20 Silica 10 Carbon 0 0

50

100

150

200

250

300

350

Sputter Depth (nm)

(b) Figure 9. (a) XPS of a templated xerogel film dried at 50  C and (b) XPS sputter profile. Reprinted with permission from [95], J. C. Diniz da Costa, Synthesis and Characterisation of Molecular Sieve Silica (MSS) Membranes, Ph.D. Thesis, University of Queensland, Brisbane, Australia, 2000.

% per nanometer. The carbon concentration profiles are mainly attributed to templates trapped in the silica matrix, indicating that concentrations of carbon groups are between 1 and 2% up to sputter depth of 180 nm with residual levels of less than 1% from there on.

3.3.2. Scanning Electron Microscopy

O2

Ref.

11

[95] [77] [96] [97] [98] [99]

16 3

60 Atomic Concentration (%)

technique, sputter rates by Ar+ ion bombardment are used and are calculated from the calibrated sputter rate for dense Ta2 O5 . [58, 76]. The order of sputter rates for Si2 is in the region of 60 nm · h−1 using Ar+ at 4 keV and 4.5 A. The sputtered area formed a rhombus of 9 × 9 mm. The analyzed surface is centered in the rhombus with a diameter of 4 mm. A typical XPS spectrum for intermediate silica templated film layer cast on -Al2 O3 substrate and dried at 50  C is shown in Figure 9a with an indication of the peaks for oxygen, carbon groups, aluminum, and silica. XPS is an in-situ technique useful to characterize the surface morphology of membrane films. Figure 9b depicts the stratum profiles of a representative MSS membrane which contains four intermediate layers of templated xerogel and four layers of silica xerogel. It shows the XPS sputter profiles for the relative concentration of aluminum, carbon, oxygen, and silica as a function of the sputter depth. The resulting profiles show a decrease of silica concentration with an associated increase of aluminum concentration from a sputter depth of 60 nm. The interface between the silica film and the -Al2 O3 substrate occurs approximately at a crossover sputter depth of 240 nm. From there on, the concentration of silica reduces at a rate of 2 5 × 10−2 atoms

CH4

0

70

Figure 8. Arrhenius plot of the Henry constant. Reprinted with permission from [95], J. C. Diniz da Costa, Synthesis and Characterisation of Molecular Sieve Silica (MSS) Membranes, Ph.D. Thesis, University of Queensland, Brisbane, Australia, 2000.

CO2

200

(a)

-1

Material

400

Binding Energy (eV)

Several researchers [58, 62] have reported that scanning electron microscopy is a relevant in-situ technique to verify the individual layers (microporous) and substrates (mesoporous/macroporous) of membranes. SEM is carried out on a typical membrane to show its profile (cross section) and to determine the silica film thickness. Membrane cross sections are generally platinum or gold coated in highpurity Ar. Transmission electron microscopy (TEM) has also

Molecular Sieve Silica Membranes

734 been employed by researchers [31, 48] to analyze the profile layers of MSS membranes. Typical cross sections of a MSS membrane are shown in Figure 10. The -Al2 O3 substrate is very coarse while its coarseness decreases considerably very close to the silica top film. The silica film thickness varies throughout the membrane mainly due to the roughness of the substrate. The SEM does not show a good resolution at 100 nm dimensions.

4. MSS MEMBRANES AND APPLICATIONS 4.1. Modeling Gas Transport 4.1.1. Transport Mechanisms The mechanisms that govern gas transport in mesoporous membranes (2 nm < dp < 50 nm) are (i) Knudsen diffusion, (ii) Poiseuille flow, and (iii) surface diffusion. Uhlhorn and Burggraaf [8] have shown that transport rate of gas molecules through mesoporous membranes decreases with increasing temperature according to the following: (i) Knudsen diffusion FKn

2$p Kn vr = 3RTℓ

with v¯ =



8RT 'M

(9)

where FKn is the Knudsen permeation (mol · m−2 · s−1 · Pa−1 , $p is the porosity, Kn is a shape factor (equal to 1/(), ( is the tortuosity, R is the gas constant (J · mol−1 · K−1 , T is the absolute temperature (K), v¯ is the average molecular velocity (m.s−1 , r¯ is the modal pore radius (m), ℓ is the layer thickness (m), and M is the gas molecular mass (kg · mol−1 . (ii) Poiseuille permeation FP =

$ p P r 2 P 8RT)ℓ m

(10)

where FP is the Poiseuille permeation (mol · m−2 · s−1 · Pa−1 , P is the reciprocal tortuosity, ) is the gas viscosity (N · s · m−2 , and Pm is the mean pressure across the membrane (Pa). (iii) Surface diffusion JS = app DS S

dq dℓ

(11)

where Js is the surface diffusion flux (mol · m−2 · s−1 , app is the apparent density (kg · m−3 , Ds is the surface diffusion coefficient (m2 · s−1 , s is the reciprocal tortuosity, and dq/dℓ is the surface concentration gradient (mol · kg−1 · m−1 . On the other hand, de Lange et al. [77] have shown that the transport of diffusing molecules through microporous membranes is activated in which the flux J (mol · m−2 · s−1  increases as a function of temperature according to
 −Eact (12) J ∝ J0 exp RT where J is the flux (mol · m−2 · s−1  through the membrane, Eact (kJ · mol−1  is an apparent activation energy, R is the gas constant, and T is the absolute temperature (K).

4.1.2. Single-Gas Transport Mechanism Through Microporous Materials Barrer [78] proposed a model of transport through microporous (single crystal zeolite) membranes as shown in Figure 11. The model can be best described in three sequential steps, namely (j) transport from the gas phase to the micropore, (jj) migration through the micropore, and (jjj) transport from the micropore to the gas phase. Gas-phase transport to the micropore (j) can take place by two parallel fluxes: (j1 ) directly from the gas phase to the pore entrance and (j2 ) via the external surface involving surface diffusion.

j1 j2 ↓ top layer

jj

A l2O3 substrate

jjj2 jjj1

Figure 10. SEM of a middle cross section of a MSS membrane. Reprinted with permission from [95], J. C. Diniz da Costa, Synthesis and Characterisation of Molecular Sieve Silica (MSS) Membranes, Ph.D. Thesis, University of Queensland, Brisbane, Australia, 2000.

Figure 11. Model of gas transport through microporous membranes. Reprinted with permission from [95], J. C. Diniz da Costa, Synthesis and Characterisation of Molecular Sieve Silica (MSS) Membranes, Ph.D. Thesis, University of Queensland, Brisbane, Australia, 2000.

Molecular Sieve Silica Membranes

735

At the pore entrance at the retentate side to the pore exit at the permeate side, micropore diffusion (jj) takes place. Transport from the micropore to the gas phase (jjj) at the permeate side can also take place by two parallel fluxes: (jjj1 ) desorption from the pore exit directly to the gas phase and (jjj2 ) desorption via an external surface to the gas phase. The potential energy profiles for both parallel fluxes (j1 and j2  are shown in Figure 12. E1 is the apparent activation energy for micropore diffusion, 0E is the energy difference between the gas phase and the molecules present in the micropore which is a heat of adsorption and is equal to −Qst Es is the activation energy for pore entrance from the external surface, and 0Es is the energy difference between the molecules adsorbed on the external surface and the gas phase [77]. For a molecule to permeate from the retentate side to the permeate side of a membrane, energy barriers (Es + 0E − 0Es − E1  in 12a or (0E − E1 ) in Figure 12b must be overcome in the case where both internal and external adsorption obey Henry’s law. Using Barrer’s model, de Lange et al. [77] conducted an extensive assessment of the role of the surface diffusion of CO2 and H2 in microporous silica membranes. They found that the surface diffusion contributes only 2% to the total H2 flux while CO2 surface diffusion is not rate determining in the situations studied (291 K < T < 573 K and 0 < p < 4 bar). In the case where interface process does not play a significant role, the surface barriers (Es and 0Es ) are extremely low and the gas-phase diffusion limitations can be neglected. Hence, microporous diffusion is the rate-limiting step as thermodynamic equilibrium is assumed at the interface [31]. As microporous diffusion is an activated transport, external surface diffusion can not be rate determining. According to de Lange et al. [77], the transport from the gas phase to the membrane is not likely to be rate determining either. Using the kinetic gas theory, they determined that even in a pessimistic scenario with a porosity of 1% and sticking probability of 1%, the collisional flux would exceed permeation by more than one order of magnitude. If microporous flux (jj) is rate determining, the energy barriers are 0E and E1 where E1 can be described as the mobility energy (Em ). According to the atomic jump theory, Em represents the energy barrier between two adsorption sites [79]. Hence, Em can be determined from apparent activation energy for permeation (Ea ): (13)

Em = Ea − 0E

Cg0

Cg0 ∆Es ∆E

Es

∆E

θ0

E1

E1 X=0

θ1

θ2

X=0

θ1

θ2

Figure 12. Potential energy profiles of gas transport in membranes. Reprinted with permission from [95], J. C. T. Diniz da Costa, Synthesis and Characterisation of Molecular Sieve Silica (MSS) membranes, Ph. D. Thesis, University of Queensland, Brisbane, Australia, 2000.

where 0E can be determined from the isosteric heat of adsorption (Qst ) by assuming that the contribution of the external surface can be neglected: 0E = −Qst

(14)

The discussion so far is clearly limited to gases operating in the Henry regime. This type of approach may not be applicable to large and branched molecules (i.e., hydrocarbons) because direct entrance is unlikely and an adsorption step at the external surface is necessary [80]. However, hydrocarbons are large molecules and are likely to be discriminated from permeation in micropore membranes by size exclusion.

4.1.3. Activated Transport in Single Gas Permeation Microporous diffusion is assumed to be the rate-limiting step. Hence, the diffusion of molecules in microporous materials is modelled as an activated process according to an Arrhenius relation: 
−Em (15) D = D0 exp RT where D0 is a temperature-independent proportionality constant, Em is the mobility energy (J · mol−1 , R is the gas constant (J · mol−1 · K−1 ), and T is the absolute temperature (K). De Lange et al. [77] and da Costa et al. [74] showed that the sorption of several gases (H2 , CO2 , O2 , Ar, N2 , and CH4  complied with Henry’s law except CO2 which showed a slight nonlinearity for temperatures below 50  C. Hence, gas adsorption is in the low coverage of Henry’s regime: c = Kp

(16)

where p is pressure (Pa) and K is Henry’s constant as a function of temperature according to a van’t Hoff relation (Eq. (8)). Substituting Eqs. (15), (16), and (8) into Fick’s law gives a temperature dependency flux Eq. (17) in the Henry regime: Jx = −D0 K0 exp




 Qst − Em dp RT dx

(17)

The permeance (P /ℓ ) may be defined as an activated transport normalized pressure flux (mol · m−2 · s−1 · Pa−1  as follows:
 Em − Qst DK P = 0 0 exp (18) ℓ ℓ RT Having determined permeance values at different temperatures, the slope of the natural logarithm of permeance versus 1/T will yield Ea , the activation energy of diffusing molecules in amorphous silica membranes given by Eq. (19) (see Eqs. (13) and (14)): Ea = Em − Qst

(19)

Molecular Sieve Silica Membranes

736 Permselectivity (F  is a parameter that describes the separation efficiency of membranes based on single-gas permeation results for gases “A” (JA ) and “B” (JB ): F =

JA JB

(20)

Permselectivity of molecular sieve membranes must be superior as measured against a benchmark separation factor known as the Knudsen ideal separation parameter (∗ ) as given by Eq. (21). In other words, membranes with permselectivity close to Knudsen’s ideal separation parameters are likely to have pore sizes larger than those of molecular sieve materials. Membranes which comply with Knudsen diffusion result in low permselectivity while molecular sieve membranes show high permselectivity:  MA ∗ (21)  = MB

4.2. MSS Membranes MSS membranes reported in the literature generally do not have the same architectural structures, as their configuration and synthesis processes from substrate to top layer may differ. The establishment of appropriate criteria for performance comparison presents some difficulty. Having said that, high-quality membranes are generally characterized by high fluxes, selectivities, and activation energies. A summary of typical permeation results is shown in Table 5 for the production of defect-free MSS membranes using the sol–gel processes such as: • a single-step catalyzed hydrolysis using HNO3 as a catalyst [31, 32, 58] • a templated single-step [45] • or templated two-step catalyzed hydrolysis using HCl followed by pore tuning using nonhydrolyzed tetraethoxysilane diluted in ethanol [10] • a templated two-step catalyzed hydrolysis [48] • a two-step catalyzed hydrolysis [33] Nair et al. [32] reported improved permeation results for MSS membranes and high He/N2 permselectivities of 514 using a single-step sol–gel process. Raman and Brinker [10] prepared membranes using an organic ligand template (MTES) and an unhydrolyzed sol for micropore tuning. Although no separation between He and CO2 was observed, Table 5. Permeation of membranes (10−9 mol · m−2 · s−1 · Pa−1 ). Type

PHe

S S S Tmp -T T Tmp -T Tmp

36

53 51 44

P H2

PCO2

740 591 44 12

80 228 8 0 20 68 9

PN2

PCH4

Ref.

0 7 0 03 0 06 0 95 2 5

[32] [58] [31] [48] [33] [10, 45] [45]

0 07

100

10 0 14 0 08 1 2

Tmp (template), T (two-step), S (single-step).

the templated MSS membranes resulted in CO2 /CH4 permselectivity of 71, indicating a high pore tailorability between the molecular kinetic diameters of CO2 (dk = 3 3 Å) and CH4 (dk = 3 8 Å). Kusakabe et al. [45] also prepared templated membranes using TEOS and alkyltriethoxysilanes (e.g., octyl and dodecylgrietoxysilanes) as template agents. They reported high permeation results for H2 , but permselectivities were relatively low in the order of 10 (H2 /CO2  and less than 1 for N2 /CH4 . The latter permselectivity result indicates that a large diffusing molecule (CH4  was diffusing preferentially in favor of smaller molecule (N2 . De Vos and Verweij [31] reported high permeances and selectivities of H2 and CO2 . The H2 /CO2 permselectivity ranged between 2.5 and 7.5, while for the membranes calcined at 600  C permselectivity increased to values between 18 and 130 with a half reduction in H2 permeance. De Vos and co-workers were able to produce 30-nm-thick silica films by using clean rooms of class 1000 [67]. MSS films prepared in typical non-clean room laboratory facilities have thickness ranging between 500 and 2000 nm, which are 17 to 67 times thicker than the films prepared in clean-room facilities. As the flux of gases is inversely proportional to film thickness, membranes synthesized in clean rooms are likely to achieve H2 permeances in excess of 1 0 × 10−6 mol · m−2 · s−1 · Pa−1 and H2 /CO2 selectivities of as high as 150 due to extremely low dust concentration. Brinker et al. [55] have reported that the two-step catalyzed hydrolysis process of bulk gels resulted in pore size reduction as compared to the single-step process. However, the two-step sol–gel process has only been employed recently by Tsai et al. [48] and Diniz da Costa et al. [33] in the preparation of MSS membrane films. Tsai et al. [48] used a two-step process and added C6 or C16 surfactants (triethylhexylammonium or cetyltrimethylammonium). They reported very high selectivities for H2 /N2 (316) and CO2 /CH4 (150–190), indicating that a high degree of pore size control was achieved for the separation of molecules with kinetic diameters higher than CO2 . Diniz da Costa et al. [33] reported that two-step MSS membranes had average pore sizes of 3.0 Å according to the separation of He (dk = 2 6 Å, H2 (dk = 2 89 Å), and CO2 (dk = 3 3 Å). High selectivities were observed for He/CO2 (255) and H2 /CO2 (60) while permeation of He and H2 was relatively high as listed in Table 5. The literature also presents results for MSS membranes derived from other synthesis processes. Using microporous glass fibers, Shelekhin et al. [26] reported permselectivities as high as 11674 for He and CH4 . Although their He permeation results were very low, in the order of 3 5 × 10−11 mol · m−2 · s−1 , they clearly indicated high control of pore size as permeation decreased by several orders of magnitude with increase in the kinetic diameter of gases. Lin et al. [81] and Wu et al. [82] reported the production of silica membranes with similar qualities made by the CVD method. The He and H2 permeance of their high-quality membranes were in the region of 1 0 × 10−10 to 1 0 × 10−11 mol · m−2 · s−1 with He/H2 and H2 /N2 permselectivities ranging between 1.0 and 7.0 and 2.4 and 513, respectively. Ha et al. [83] and Tsapatsis et al. [84] also made silica membranes by CVD deposition using Vycor glass tubes as substrate. The H2 permeances are similar to those reported by Lin, Wu, and co-workers, but with

Molecular Sieve Silica Membranes

good H2 /N2 selectivities of 880–2040 [83] and 125–1200 [84]. MSS membranes derived by CVD have permeances four to five orders of magnitude below the dip-coating results presented earlier. Discussion of permeance and permselectivity should also include the apparent energy of activation as an extra assessment parameter of membrane quality. The apparent energy of activation for H2 permeation gives a good correlation with the separation factor and may be used as a measure of quality [80]. According to de Lange and co-workers [85], high-quality membranes should have an apparent energy of activation for H2 permeance of at least 10 kJ · mol−1 . Typical results of the apparent activation energy of two-step sol–gel membranes for H2 permeance values range between 10.5 and 17.6 kJ · mol−1 with the majority of the values in excess of 14.0 kJ · mol−1 [33]. These results are higher than the apparent energy of activation for H2 permeance of singlestep MSS membranes of 10 kJ · mol−1 or lower [31, 58]. There are two major contentious points in the literature regarding the thermodynamic properties of diffusing molecules. De Vos and Verweij [31] reported that the activation energy for the permeation of CO2 is negative (−2 to − 4 kJ · mol−1  for membranes prepared by the singlestep silica process. In some cases, the CO2 permeation increased up to 50–100  C, then decreased. However, Diniz da Costa and co-workers [33] found the opposite behavior for two-step membranes. They reported that the CO2 permeation decreased up to 50–100  C, then increased thereafter. Hence, the activation energy for CO2 permeation was positive (4 to 7 kJ · mol−1 . The permeation model discussed above assumes linearity and CO2 permeation shows nonlinearity at low temperatures [74]. It is not clear how this anomalous transport occurs in molecular sieving materials. Hence, the CO2 transport in these materials merits further research. The second contentious point is related to the sorption characteristics of silica films. The major dilemma in this situation is to determine the Qst representative of the microstructure of supported silica films (i.e., excluding membrane support and intermediate layers). The comparison of the isosteric heat of adsorption results with values given in the literature is very important because in principle there is an endeavor to determine Qst values that reflect the molecular sieving characteristics of amorphous silica microporous film. This comparison is made against silicalite which is a pure silica zeolite with elliptical straight channels (5 7 Å × 5 1 Å) and sinusoidal channels of 4 5 − 5 5 Å pore diameter [31, 86]. The pore radius of the produced bulk xerogel is in the order of 8–9 Å [54] which is clearly greater than the silicalite pore radius. In principle, the calculated Qst values for bulk xerogels may not reflect the true Qst of the final membrane molecular sieving silica films in view of different morphology (i.e., pore size). The Qst results of de Lange et al. [58] for unsupported silica films are in the same range of silicalite for CO2 (20–28 kJ · mol−1  and H2 (6 kJ · mol−1  and approximately half for CH4 (19–28 kJ · mol−1 . However, the structural morphology of unsupported silica films and supported membrane films may also differ. The former is prepared on Petri dishes (i.e., nonporous surface) while the latter is cast on porous metal oxides. The substrate morphology affects the

737 overall film microstructure. In view of the considerable technical difficulties to simulate unsupported silica films with the same characteristics as supported silica films, de Vos and Verweij [31] argued that the Qst of silicalite can be regarded as a model system for the microporous membrane silica. In this context, it is important to observe that CH4 has a very strong adsorption capacity in silicalite but a low capacity in unsupported silica films or xerogels.

4.3. Applications In view of molecular separation and pore size tailorability, MSS membranes are ideal for applications requiring gas separation and/or gas stream enrichment. The main advantages of membranes are their high recoveries and versatility in handling different feed compositions under varying feed conditions. Also membranes can be built as compact operational modules which require low capital investment. Some examples of application include: • Petrochemical—separation and/or enrichment of hydrogen gas streams • Petrochemical—hydrogenation and dehydrogenation reactions • Fuel Cells—portable energy generators and vehicles • Energy Generation—integrated gasification combinedcycle systems (IGCC) • Flue Gas—CO2 separation

4.3.1. Transportation and Industrial Applications MSS membrane employment is directly concerned with polymeric electrolyte membrane (PEM) fuel cells, which is a technology being developed for motor vehicles (50–100 kW), residential (2–10 kW), and commercial (250–500 kW) power generation, as well as small/portable generators and battery replacement. PEM fuel cells require a pure hydrogen source for operation. Hydrogen is typically obtained by reforming a hydrocarbon fuel (methanol or gasoline). In this reaction, the product is H2 , CO, CO2 , and water. CO levels of 50 parts per million (ppm) or greater are detrimental for the fuel cell operation due to catalyst poisoning and severe fuel cell degradation [87, 88]. As a modular system, MSS membranes can be easily installed in a fuel cell system to clean partially or totally CO. The use of MSS membrane reactors for the water gas shift reaction in fuel cells is now under investigation as an attractive commercial application. Membrane technology in applications such is fuel cells is part of a system that will reduce airborne emissions compared with traditional internal combustion engines. Fuel cells emit less carbon dioxide and nitrogen oxides per kilowatt of power generated [89]. This technology is likely to be extremely beneficial for cities around the world where health problems are closely related to urban car emissions. As processes become more efficient by employing membranes, they greatly reduce energy consumption, leading to lower usage of fossil fuels and lower emission of greenhouse gases. California and New York in the United States are leading a regulatory clampdown on CO2 emissions, not only from industry, but also from motor vehicles. Legislation requires

Molecular Sieve Silica Membranes

738 that by 2005, 10% of the vehicles sold by vehicle manufacturers in the states be either zero emission vehicles, or a compliance program be offered for assessment which includes a progression to this target through partial zero emission vehicles, starting in 2004. Emphasis on zero emission in future transportation and/or energy generation is paramount and hydrogen fuel cell technology is foreseen as the preferred technology in view of zero tail-pipe emissions. These sorts of regulations are “encouraging” industry to invest in the alternative technologies of the future, with definite timelines being imposed for results. In terms of energy efficiency, membrane reactors can improve conversions up to sixfold depending on the reaction. According to the U.S. Department of Energy, an energy saving of 10 trillion BTU per year (equivalent to 10 billion joules per year) could result from the use of catalytic membrane reactors as replacements for conventional reactors for dehydrogenation reactions [90]. Low-temperature fuel cells with membranes for hydrogen and carbon monoxide have electrical efficiency of 42% [91], which is much higher than the conventional combustion engines’ efficiency of up to 33%. Regarding electrical power generation for buildings, fuel cells are likely to achieve higher energy efficiencies as losses in traditional power distribution lines are as high as 15% and thermoelectric power generation systems have efficiencies on the order of 38–40%. The development in recent years of silica based membranes having consistent quality has paved the way for the application of membranes in high-temperature reactors. MSS membranes can operate up to temperatures of 500–600  C, which is in the range of the majority of the reactions set up in Table 6. In many of these dehydrogenation processes, hydrogen is the reaction product which limits the overall conversion to a maximum dictated by the reaction equilibrium. By removing the hydrogen from the reactor, for example through a membrane process, the reaction is “pushed” to completion rather than equilibrium limited, providing an enhancement of conversion (5–8 times in some reactions) into product materials. According to Julbe et al. [92], membrane reactors are being explored in various configurations, but can be classified as follows: • Extractor—removal of product(s) to enhance conversion by shifting the reaction equilibrium • Distributor—to limit side reaction by controlled addition of reactant(s) • Active Contactor—an engineered catalytic reaction zone by controlled diffusion of reactant(s) Table 6. Application of porous inorganic membrane reactors [100]. Reaction Dehydrogenation of ethane Dehydrogenation of propane Dehydrogenation of n-butane Dehydrogenation of cyclohexane Dehydrogenation of ethylbenzene Dehydrogenation of methanol Reduction of nitrogen oxide with ammonia Steam reforming of methane

Operating conditions 450–600 480–625 400–500 187–297 550–640 300–500 300–350 445–590

C C  C  C  C  C  C  C 



There are also several new applications and innovative membrane reactor configurations. Generally, these systems are still in the research or development stages, addressing identified industrial and commercial concerns, for which current technological solutions are inadequate. These include [67]: • Membrane reactors with separate feed-stock, where the reactants are mixed at different sides of the membrane • Membrane reactors with condensing products • Three-phase membrane reactors for sustained interface between liquids and gases • Gas-phase filter reactors for simultaneous reduction of fly-ash and noxious gases • Diesel exhaust soot converters to destroy incomplete combustion by-product aggregates (soot), which are carcinogenic agents • Fluid bed membrane reactors for filtering slurry Gas separation and enrichment are well-established industrial practices [5]. These include H2 separation and recovery in petrochemical purge stream from hydro-processor, and CH4 /CO2 separation in landfill gas for energy recovery applications. Air separation cannot be achieved with MSS membranes. The kinetic molecular diameters of O2 and N2 are very similar and pore size exclusion cannot be attained. However, CO2 flue gas separation technologies are now attracting major research and industrial attention. Coal power generation plants are responsible for 36% CO2 [93] emissions worldwide. As CO2 sequestration techniques are now becoming socially and technically acceptable, the practicalities of energy supply are leading not to the abandonment of fossil fuels, but to the development of technologies directed towards flue gas separation and CO2 sequestration.

4.3.2. Competitive Advantages In application, membrane systems have to produce clear economic benefits in the form of reduced capital and operating costs, to be used in place of competing traditional separation technology methods for achieving the same outcome such as cryogenics, distillation, and pressure swing adsorption (PSA). The tendency appears for the noncryogenic technologies (membranes and PSA) to dominate the technology at medium to higher capacities, while cryogenics continues to dominate the highest capacities and ultrahigh purities [5]. It is expected that the situation for hydrogen separation will be very similar. Metal (palladium and its alloys—Pd), zeolite, and polymeric membranes are major competitors for MSS membrane technology. Commercial polymeric membranes now have very high selectivity for hydrogen separation though temperature is limited to a maximum of 120  C. Zeolite membranes are very stable up to 500  C, but the pore size of zeolite is generally around 0.5 nm, resulting in very poor separation for hydrogen and other gases. On the other hand, Pd membranes show almost perfect hydrogen separation (close to 100% purity) while hydrogen permeation is similar to MSS membranes. Indeed, Pd membranes are the significant competitor to MSS membranes. However, Pd membranes are very unstable in environments containing steam. Furthermore, carbon monoxide blocks hydrogen, leading to lower permeation. Pd membranes are also very expensive,

Molecular Sieve Silica Membranes

on the order of US$1250 to US$2000 per square meter of membrane area [94]. The current barriers to broader introduction of inorganic MSS membrane technologies relate to the demonstration of long-term reliability and durability, robustness in processing with attention to processing potentially dirty streams, or developing in-situ regeneration and self-cleaning technologies. Further economic issues play a fundamental role regarding lowering the maintenance costs, scaled up methods to manufacture very large surface areas at commercially competitive prices, and the risk factor compared with established processes.

5. CONCLUSION The key issues associated with the fabrication of membranes generally include support, sol–gel, and film technologies. Support substrates must have a narrow pore size distribution, low surface roughness, and extreme low defect density. Nonhomogeneous surfaces propagate stresses resulting in microporous films with a high defect density of large undesirable pores, pinholes, and microcracks. Membrane supports fundamentally provide the mechanical stability and integrity to the microporous thin films at the expense of increased flux resistance of diffusing molecules. The preparation of microporous films depends upon the preceding formulation and preparation procedures of sols as well as the proceeding aging, drying, and heat treatment processes of gels. Based on the fractal theory, weakly branching polymer system promotes dense packing and low pore volume, resulting in microporous films. A primary condition to achieve weakly branching systems is to inhibit the condensation reactions during film formation. This is achievable by preparing sols with low H2 O/Si molar ratio in a single-step or two-step catalyzed hydrolysis process. In film technology, sol–gel film dip-coating is extensively used as compared with chemical vapor deposition. In the dip-coating process, the thickness of the film increases as a function of the withdrawal speed of the substrate from a sol. MSS films are generally calcined between 400 and 600  C at ramping rates of 0.5–1.0  C·min−1 . Film defect concentration can be largely reduced by depositing films in dust-free environments (i.e., clean rooms). The transport of diffusing molecules through microporous silica films is activated diffusion as a function of the isosteric heat of adsorption Qst and the mobility energy Em . There are two major contentious issues within the literature review related to the characterization of the microstructure of the final deposited film. Based on the principle that the underlying physics and chemistry that govern polymer growth and gelation are the same for films and bulk gels, the characterization of bulk gels poses no technical problems as experienced by thin films. However, the gelation and drying conditions of thin films are quite different from bulk gels, which may lead to nonequivalent microstructure. The contentious issue of film morphology is also extended to the adsorption characteristics of films. Although it is relatively easy to conduct adsorption experiments in bulk gels or unsupported films, their structures may not be equivalent to

739 the film microstructure. CO2 permeation also shows anomalous results and further research is required to understand CO2 diffusion in micropores. The outlook for MSS membrane application is excellent, particularly with the forthcoming commercialization of fuel cell vehicles. It is particularly important to clean up the reformate gas as CO poisons fuel cell catalysts, with a potential second spin-off application for the water gas shift reaction. Although membrane reactor industrial applications have yet to materialize to a large extent, MSS membranes have the capability to operate at temperatures up to 500–600  C, ideal for hydrogenation and dehydrogenation reactions in the petrochemical industry. MSS membranes still have to compete against traditional separation technologies. The market outlook for MSS membranes is likely to be small in medium module systems delivering medium- to high-purity separation and recovery.

GLOSSARY Activated transport A transport process in which the permeation (flux) increases with temperature. Activation energy The total energy barrier for the micropore diffusion of a molecule. Adsorption A process in which molecules attach themselves to the surface of a solid material. Asymmetric membranes Membranes having layers with different structural characteristics such as pore size, surface area and pore volume. Fractal structures In silica derived materials, fractal structures refer to a random formation of polyfunctional monomers. Gel It is a substance that contains a continuous solid skeleton enclosing a continuous liquid phase [30]. Membrane A physical barrier device capable of separating gas and liquid molecules. Microporous Pores diameter lower than 20 Å. Mobility energy The energy barrier between two adsorption sites in micropore diffusion. Molecular imprint A cavity left in a material matrix by burning off an organic template. MSS membranes Membranes derived from a sol–gel process results in pore sizes of molecular dimension. Permeance A parameter indicating the flow of molar mass per area of membrane per unit time per pressure difference across the membrane. Permselectivity A ratio of permeance of two different gases in a single gas permeation test. Selectivity A ratio of permeance of two different gases in a gas mixture permeation test. Silanol A silica (Si) atom bonded to a hydroxyl (OH) group. Siloxane An oxygen atom bonded to silica (SI O SI). Sol It is a colloidal suspension of solid particles in a liquid [30].

740 Template A central structure allows network formation. Subsequently, the template can be removed creates a morphological cavity directly related to the features of the template. Xerogel Dry gel.

REFERENCES 1. P. Meares, in “Membranes in Gas Separation and Enrichment,” (P. Meares, Ed.), p. 1. The Royal Society of Chemistry, London, 1986. 2. J. Gillot, in “Inorganic Membranes Synthesis, Characteristics and Application,” (R. R. Bhave, Ed.), p. 1. Chapman and Hall, New York, 1991. 3. K. Keizer and H. Verweij, Am. Chem. Soc. 26, 37 (1996). 4. H. P. Hsieh, “Inorganic Membranes for Separation and Reaction.” Elsevier, Amsterdam, 1996. 5. W. J. Koros and G. K. Flemming, J. Membr. Sci. 83, 1 (1993). 6. M. Mulder, “Basic Principles of Membrane Technology.” Kluwer, Dordrecht, 1991. 7. S. Loeb and S. Sourirajan, Adv. Chem. Ser. 38, 117 (1962). 8. R. J. R. Uhlhorn and A. J. Burggraaf, in “Inorganic Membranes Synthesis, Characteristics and Application,” (R. R. Bhave, Ed.), p. 155. Chapman and Hall, New York, 1991. 9. C. W. Jones and W. J. Koros, Carbon 32, 1427 (1994). 10. N. K. Raman and C. J. Brinker, J. Membr. Sci. 105, 273 (1995). 11. Y. S. Lin and A. J. Burggraaf, J. Am. Ceram. Soc. 74, 219 (1991). 12. A. J. Burggraaf and L. Cot, in “Fundamentals of Inorganic Membrane Science and Technology,” (A. J. Burggraaf and L. Cot, Eds.), p. 1. Elsevier, Amsterdam, 1996. 13. J. Koresh and A. Sofer, Sep. Purif. Tech. 18, 723 (1983). 14. C. W. Jones and W. J. Koros, Carbon 32, 1419 (1994). 15. V. C. Geiszler and W. J. Koros, Ind. Eng. Chem. Res. 35, 2999 (1996). 16. T. Bein, Chem. Mater. 8, 1636 (1996). 17. M. D. Jia, K. V. Peinemann, and R. D. Behling, J. Membr. Sci. 82, 15 (1993). 18. J. M. Duval, B. Folkers, M. Mulder, G. Desgrandchamps, and C. A. Smolders, J. Membr. Sci. 80, 189 (1993). 19. I. F. J. Vankelecom, C. Dotremont, M. Morobe, J. B. Uytterhoeven, and C. I. Vadescasteele, J. Phys. Chem. B 101, 2160 (1997). 20. C. Dotremont, I. F. J. Vankelecom, M. Morobe, J. B. Uytterhoeven, and C. I. Vadescasteele, J. Phys. Chem. B 101, 2160 (1997). 21. Z. A. E. P. Vroon, Synthesis and Transport Studies of Thin Ceramic Supported Zeolite (MFI) membranes, Ph.D. Thesis, University of Twente, Enschede, the Netherlands, 1995. 22. E. R. Kleinfeld and G. S. Ferguson, Science 265, 370 (1994). 23. R. M. Barrer, “Zeolites and Clay Minerals as Sorbents and Molecular Sieves.” Academic Press, London, 1975. 24. A. C. D. Newman, “Chemistry of Clays and Clay Minerals.” Longmans, London, 1987. 25. S. Vercauteren, J. Luyten, R. Leysen, and E. F. Vansant, J. Membr. Sci. 119, 161 (1996). 26. A. B. Shelekhin and A. G. M. Dixon, J. Membr. Sci. 75, 233 (1992). 27. R. Schnabel and W. Vaulant, Desalination 24, 249 (1978). 28. S. Morooka and K. Kusakabe, MRS Bull. 25 (1999). 29. A. J. Burggraaf and K. Keizer, in “Inorganic Membranes Synthesis, Characteristics and Application” (R. R. Bhave, Ed.), p. 10. Chapman and Hall, New York, 1991. 30. C. J. Brinker and G. W. Scherer, “Sol Gel Science: The Physics and Chemistry of the Sol Gel Processing.” Academic Press, San Diego, 1990. 31. R. M. de Vos and H. Verweij, J. Membr. Sci. 143, 37 (1998). 32. B. N. Nair, T. Yamaguchi, T. Okubo, H. Suematsu, K. Kaizer, and S. I. Nakao, J. Membr. Sci. 135, 237 (1997).

Molecular Sieve Silica Membranes 33. J. C. Diniz da Costa, G. Q. Lu, V. Rudolph, and Y. S. Lin, J. Membr. Sci. 198, 9 (2002). 34. B. B. Mandelbrot, “Fractals, Form and Chance.” Freeman, San Francisco, 1977. 35. N. K. Raman, M. T. Anderson, and C. J. Brinker, Chem. Mater. 8, 1682 (1996). 36. A. J. Vega and G. W. Scherer, J. Non-Cryst. Sol. 111, 153 (1989). 37. G. Orcel, L. L. Hench, I. Artaki, J. J. Jonas, and T. W. Zerda, J. Non-Cryst. Sol. 105, 223 (1988). 38. R. K. Iler, “The Chemistry of Silica.” Wiley, New York, 1979. 39. A. Bertolluzza, C. Gagnano, M. A. Morelli, V. Gottardi, and M. Guglielmi, J. Non-Cryst. Sol. 48, 117 (1982). 40. A. Duran, C. Serna, V. Fornes, and J. M. Fernadez Navarro, J. Non-Cryst. Sol. 82, 69 (1986). 41. N. Abidi, B. Deroide, J. V. Zanchetta, L. C. de Menorval, and J. B. d’Espinose, J. Non-Cryst. Sol. 231, 49 (1998). 42. W. G. Klemperer, V. V. Mainz, and D. M. Millar, in “Better Ceramics Through Chemistry II” (C. J. Brinker, D. E. Clark, and D. R. Ulrich, Eds.), p. 15. Materials Research Society, Pittsburgh, PA, 1986. 43. A. M. Buckley and M. Greenblatt, J. Non-Cryst. Sol. 143, 1 (1992). 44. J. S. Beck, J. C. Vartuli, G. J. Kennedy, C. T. Kresge, W. J. Roth, and S. E. Schramm, Chem. Mater. 6, 1816 (1994). 45. K. Kusakabe, S. Sakamoto, T. Saie, and S. Morooka, Sep. Purif. Tech. 16, 139 (1999). 46. Y. S. Kim, K. Kusakabe, S. Morooka, and S. M. Yang, Korean J. Chem. Eng. 18, 106 (2001). 47. Y. Lu, G. Cao, R. P. Kale, S. Prabakar, G. P. Lopez, and C. J. Brinker, Chem. Mater. 11, 1223 (1999). 48. C. Tsai, S. Tam, Y. Lu, and C. J. Brinker, J. Membr. Sci. 169, 255 (2000). 49. Z. Y. Yuan, W. Z. Zhou, and L. M. Peng, Chem. Lett. 10, 1150 (2000). 50. A. Ayral, C. Balzer, T. Dabadie, C. Guizard, and A. Julbe, Catal. Today 25, 219 (1995). 51. W. G. Fahrenholtz, D. M. Smith, and D. W. Hua, J. Non-Cryst. Sol. 144, 45 (1992). 52. J. J. Yang, I. M. El-Nahhal, I. S. Chuang, and G. E. Maciel, J. NonCryst. Sol. 209, 19 (1997). 53. F. Brunet, J. Non-Cryst. Sol. 231, 58 (1998). 54. J. C. Diniz da Costa, G. Q. Lu, and V. Rudolph, Coll. Surf. A 179, 261 (2001). 55. C. J. Brinker, A. J. Hurd, and K. J. Ward, in “Ultrastructure Processing of Advanced Ceramics” (J. D. Mackenzie and D. R. Ulrich, Eds.), p. 223. Wiley, New York, 1988. 56. E. F. Vansant, P. Van Der Voort, and K. C. Vrancken, “Characterisation and Chemical Modification of the Silica Surface.” Elsevier, Amsterdam, 1995. 57. T. A. Witten and M. E. Gates, Science 232, 1607 (1986). 58. R. S. A. de Lange, J. H. A. Hekkink, K. Keizer, and A. J. Burggraaf, J. Membr. Sci. 99, 57 (1995). 59. M. F. M. Post, in “Introduction to Zeolite Science and Practice” (H. van Bekkun, E. M. Flanigen, and J. C. Jansen, Eds.), p. 1123. Elsevier, Amsterdam, 1991. 60. A. F. M. Lenaars and A. J. Burggraaf, J. Coll. Int. Sci. 105, 27 (1985). 61. A. F. M. Lenaars, K. Keizer, and A. J. Burggraaf, J. Mater. Sci. 19, 1077 (1984). 62. B. C. Bonekamp, in “Fundamentals of Inorganic Membrane Science and Technology” (A. J. Burggraaf and L. Cot, Eds.), p. 141. Elsevier, Amsterdam, 1996. 63. D. L. Meixner and P. N. Dyer, J. Membr. Sci. 140, 81 (1998). 64. L. E. Scriven, in “Better Ceramics Through Chemistry III” (C. J. Brinker, D. E. Clark, and D. R. Ulrich, Eds.). Materials Research Society, Pittsburgh, PA, 1988. 65. C. J. Brinker, A. J. Hurd, P. R. Schunk, G. C. Frye, and C. S. Ashley, J. Non-Cryst. Sol. 147, 424 (1992).

Molecular Sieve Silica Membranes 66. A. J. Burggraaf, in “Fundamentals of Inorganic Membrane Science and Technology” (A. J. Burggraaf and L. Cot, Eds.), p. 259. Elsevier, Amsterdam, 1996. 67. G. Saracco, H. W. J. P. Neomagus, G. F. Versteeg, and V. S. W. P. M., Chem. Eng. Sci. 54, 1997 (1999). 68. A. Burneau and J. P. Gallas, in “The Surface Properties of Silicas” (A. P. Legrand, Ed.), p. 147. John Wiley & Sons, Chichester, UK, 1998. 69. C. J. Brinker and D. M. Haaland, J. Am. Ceram. Soc. 66, 758 (1983). 70. S. J. Gregg and K. S. W. Sing, “Adsorption, Surface Area and Porosity.” Academic Press, New York, 1982. 71. H. Y. Zhu, G. Q. Lu, N. Maes, and E. F. Vansant, J. Chem. Soc. Faraday Trans. 93, 1417 (1997). 72. D. D. Do, “Adsorption Analysis: Equilibria and Kinetics.” Imperial College Press, London, 1998. 73. D. M. Ruthven, “Principles of Adsorption and Adsorption Processes.” John Wiley & Sons, New York, 1984. 74. J. C. D. da Costa, G. Q. Lu, and V. Rudolph, in “Adsorption Science and Technology” (D. D. Do, Ed.), p. 381. World Scientific, Singapore, 2000. 75. R. J. Ward and B. J. Wood, Surf. Interf. Anal. 16, 679 (1992). 76. C. G. Morris and B. J. Wood, Mater. Forum 15, 44 (1991). 77. R. S. A. de Lange, K. Keizer, and A. J. Burggraaf, J. Membr. Sci. 104, 81 (1995). 78. R. M. Barrer, J. Chem. Soc. Faraday Trans. 86, 1123 (1990). 79. P. G. Shewmon, “Diffusion in Solids.” McGraw-Hill, New York, 1963. 80. A. J. Burggraaf, in “Fundamentals of Inorganic Membrane Science and Technology” (A. J. Burggraaf and L. Cot, Eds.), p. 331. Elsevier, Amsterdam, 1996. 81. C. L. Lin, D. L. Flowers, and P. K. T. Liu, J. Membr. Sci. 92, 45 (1994). 82. J. C. S. Wu, H. Sabol, G. W. Smith, D. L. Flowers, and P. K. T. Liu, J. Membr. Sci. 96, 275 (1994).

741 83. H. Y. Ha, S. Woo-Nam, S. A. Hong, and W. K. Lee, J. Membr. Sci. 85, 279 (1993). 84. M. Tsapatsis and G. Gavalas, J. Membr. Sci. 87, 281 (1994). 85. R. S. A. de Lange, J. H. A. Hekkink, K. Keizer, and A. J. Burggraaf, Microporous Mater. 4, 169 (1995). 86. W. J. Bakker, L. J. P. van den Broeke, F. Kapteijn, and J. A. Moulijn A I Ch E J. 43, 2203 (1997). 87. O. Korotkikh and R. Ferrauto, Catal. Today 62, 249 (2000). 88. K. I. Sotawa, Y. Hasegawa, K. Kusakabe, and S. Morooka, Int. J. Hydrogen Energy 27, 339 (2002). 89. ECW, “Fuel Cells for Distributed Generation: A Technology and Marketing Summary.” Energy Centre of Wisconsin, Madison, WI, 2000. 90. H. S. Fogler, in, “Elements of Chemical Engineering Reaction.” Prentice-Hall, Englewood Cliffs, NJ, 1999. 91. D. Rastler, D. Herman, R. Goldstein, and J. O’Sullivan, “State of the Art Fuel Cell Technologies for Distributed Power.” Electric Power Research Institute, Palo Alto, CA, 1996. 92. A. Julbe, D. Farrusseng, and C. Guizard, J. Membr. Sci. 181, 3 (2001). 93. IEA, “CO2 Emissions from Fuel Combustion.” International Energy Agency, Paris, France, 1997. 94. U. Illgen, R. Schäfer, M. Noack, P. Kölsch, A. Kühnle, and J. Caro, Catal. Com. 2, 395 (2001). 95. J. C. Diniz da Costa, Synthesis and Characterisation of Molecular Sieve Silica (MSS) Membranes Ph.D. Thesis, The University of Queensland, Brisbane, Australia, 2000. 96. L. V. C. Rees, P. Bruckner, and J. Hampson, Gas Sep. Purif. 5, 67 (1991). 97. T. C. Golden and S. Sircar, J. Coll. Int. Sci. 162, 183 (1994). 98. V. R. Choudary and S. Mayadevi, Zeolites 17, 501 (1996). 99. J. Dunne, R. Mariwala, M. Rao, S. Sircar, R. J. Gorte, and A. L. Myers, in “Fundamentals of Adsorption” (M. D. LeVan, Ed.), p. 277. Kluwer Academic Boston, 1996. 100. J. Zaman and A. Chakma, J. Membr. Sci. 92, 1 (1994).

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Molecular Tectonics in Sol–Gel Chemistry Marc Henry Université Louis Pasteur, Strasbourg, France

CONTENTS 1. Introduction 2. Sol–Gel Chemistry and Molecular Tectonics of Inorganic Compounds 3. Titanium(IV) Metallo-Organic Complexes 4. Hybrid Organic–Inorganic TiO2 -Based Materials 5. Conclusion and Perspectives Glossary References

1. INTRODUCTION Molecular tectonics [1] is the art of iterating programmed recognition patterns at the molecular level in order to obtain hybrid organic–inorganic infinite networks displaying a wide range of physical or chemical properties (Fig. 1). It is an interdisciplinary area where geometrical and topological concepts are more important than the nature of the chemical bonds formed between atoms. On one hand, some people prefer to play with the whole palette of noncovalent interactions (van der Waals, dipolar, or hydrogen bonding) in order to build fascinating new supramolecular compounds. On the other hand, solid-state chemists use much stronger chemical bonds (covalent, ionic, coordination) leading to amazing microporous architectures. At the present level of knowledge, it is not yet possible to predict the final structure, knowing the nature of the individual tectons (building blocks carrying chemical information imprinted in their molecular structure). This comes in part from our inability to set out a quantitative energy scale for the molecular interactions in which an individual tecton may be engaged, even if all these interactions derive from the single and unique fundamental electromagnetic interaction. At the very beginning, sol–gel chemistry was designed to ISBN: 1-58883-061-6/$35.00 Copyright © 2004 by American Scientific Publishers All rights of reproduction in any form reserved.

obtain glasses [2] or ceramic materials [3] after hydrolysis, condensation, and gelation of metal alkoxides M(OR)n or of metal complexes in aqueous solutions [4, 5] (Fig. 2). Soon after, it was realized that a much broader range of molecular precursors could be used, leading to new hybrid organic–inorganic materials [6]. It then became obvious that sol–gel chemistry and molecular tectonics were indeed two very complementary approaches to the synthesis of materials. In this chapter, we have chosen to focus on materials based on titanium dioxide elaborated through hydrolysis and condensation of hybrid organic–inorganic titanium(IV)based molecular complexes. This choice was motivated by the technological and strategic importance of titanium dioxide and by the lack of a comprehensive review dealing with all the crystalline aspects of Ti O chemical bonds. In fact, most past studies and reviews in sol–gel chemistry focused on materials based on SiO4 , AlO4 , and PO4 tetrahedral building units. Interest in transition metal–based chemistry came from the need to bring electrical, optical, or magnetic properties to an otherwise amorphous gel [7, 8]. With the growing development of the synthesis of tailored porous materials [9–11], it became obvious that hybrid organic– inorganic crystalline assemblies were no longer limited to tetrahedral building block units. Unveiling the assembly route of materials based on octahedral units is thus a real scientific challenge. For that purpose, molecular complexes or solid-state compounds based on titanium(IV) species are probably the best candidates for setting out basic rules that may be further used for a rational design and synthesis of new hybrid materials. Accordingly, with their d0 electronic configuration, TiIV cations may be found under four-, five-, six-, seven- and eightfold coordination, in stark contrast with other p-element (SiIV , AlIII ) or late transition metals. Moreover, in contrast with silicon- or aluminum-based compounds, the TiIII oxidation state may appear upon irradiation or application of an adequate potential, establishing the most simple link toward other transition metals characterized by a partial filling of atomic d orbitals. This unique

Encyclopedia of Nanoscience and Nanotechnology Edited by H. S. Nalwa Volume 5: Pages (743–819)

744

Figure 1. Pictorial survey of molecular tectonics aims and goals. On the floor, one may recognize nanoscale synthesis (electron sink cluster Ni38 Pt6 ). The unmounted painting on the table represents interfacial recognition around colloidal units (Al2 O3 nuclei). On the corner glass shelf is represented microstructural fabrication (Al Mn quasicrystal). Crystal engineering (acircular Al2 O3 nanocrystals) is pictured on the left wall. Finally, on the right wall, supramolecular preorganization (micellar vesicles and liposomes at the right) and cellular processing in biomineralization (radiolar skeleton at the left) may be identified.

position in the periodic table, at the frontier between elements using s, p, and d orbitals (Al, Ga, Si, Sn) and elements using d, s, and p orbitals (transition metals), makes titanium a very attractive element. However, to keep this

Molecular Tectonics in Sol–Gel Chemistry

review to a reasonable length, we have chosen to focus on chemical compounds displaying only Ti O or Ti N bonds, which are the most stable ones for applications in materials chemistry. As most hybrid organic–inorganic compounds based on the Ti O bond display an inorganic titanium–oxygen core surrounded by an otherwise organic shell, this review has been organized as follows. Section 2 is devoted to recent theoretical advances in the understanding of the electronic structure and chemical reactivity of chemical compounds displaying large molecular weights (solids and molecular species displaying hundreds or thousands of constituent atoms). It focuses on aqueous sol–gel chemistry as well as on the structure and properties of solid crystalline phases displaying the TiO2 stoichiometry. To the best of our knowledge, such a comprehensive review is still lacking, and it is of the utmost importance to have an accurate knowledge of the final limiting term common to all these Ti O-based hybrid compounds. In the same spirit, Section 3 is devoted to the other limiting term: coordination chemistry of molecular metallo-organic titanium(IV) complexes. Finally, Section 4 will deal with hybrid organic–inorganic TiO2 -based materials, either as molecular species or as reticulated networks. In conclusion, we will outline some interesting perspectives concerning this important class of compounds.

2. SOL–GEL CHEMISTRY AND MOLECULAR TECTONICS OF INORGANIC COMPOUNDS This section is devoted to a comprehensive review of the structural chemistry and practical applications of purely inorganic phases based on Ti O bonds. It covers the aqueous chemistry of TiIV species, the structural chemistry of crystalline phases displaying the TiO2 stoichiometry, and the various applications of titanium dioxide in materials chemistry. Accordingly, it was our feeling that a good understanding of the structural aspects of hybrid organic– inorganic systems could not be reached without a deep knowledge of purely inorganic phases. In this field, two important theoretical tools developed in our group are also introduced, providing the first systematic rational approach for the understanding of the experimental behavior of such complex systems. It was thus hoped that the philosophy and methodology exemplified here in the case of systems based on Ti O bonds could serve as a general template for compounds based on other metallic centers.

2.1. Aqueous Chemistry of TiIV Species

Figure 2. Pictorial survey of sol–gel chemistry aims and goals. The first steps involve synthesis of functional building units ([Ti18 O28 HOBut 17 ] oxo-alkoxide on the floor) from metal alkoxides (corner glass shelf). The unmounted micrograph on the table illustrates the hydrothermal synthesis of monodisperse anatase nanocrystals after base hydrolysis of titanium alkoxides. On the right wall is represented fabrication of opal-like materials after base hydrolysis at room temperature (right) and design of titanium oxo-acetate fibers via acetic acid modification (left). Finally, the left wall shows elaboration of titania thin films via acetylacetone modification.

The partial charge model (PCM) was introduced more than 13 years ago in its most rudimentary form in an attempt to understand the chemical reactivity of silicon and transition metal alkoxides using Allred–Rochow electronegativity data [7, 12]. Soon after, it was extensively used for the modeling of aqueous sol–gel chemistry [4, 5].

2.1.1. Hydrolysis/Condensation Behavior With the help of this model, it is rather easy to justify the experimental trends observed for metal ion hydrolysis as a function of oxidation state z and pH (Fig. 3). Moreover,

Molecular Tectonics in Sol–Gel Chemistry

745

Figure 4. Sixfold coordination and fourfold coordination numbers for TiIV as found in the crystal structures of titanyl sulfate monohydrate (a) and dibarium titanate (b). Figure 3. Theoretical charge–pH diagram according to the partial charge model. This diagram helps to explain why tetravalent species such as TiIV display a very limited aqueous solution chemistry. It also emphasizes the spontaneous hydrolysis of trivalent species and the four basic processes commonly used in aqueous sol–gel syntheses: acid addition (V2 O5 gels) or reduction (MnO2 gels) for high-valence species (oxy-anions) and base addition and/or oxidation (Fe3 O4 and Fe2 O3 gels) for low-valence species (aquo-cations).

it was also possible to predict from the sole knowledge of the oxidation state z, electronegativity , and preferred coordination number N the hydrolytic behavior of metal cations in aqueous solutions. From the basic PCM equations, it is possible to predict the equilibrium hydrolysis ratio h for the following hydrolysis reaction: [M(OH2 )N ]z+ → [MON H2N −h ]z−h+ + h[H+ ]aq . It mainly depends on the relative electronegativities of the free proton H = EN(H+ ), the water molecule W = EN(H2 O), the solvated proton Rp = z+ z EN[H(H2 O)+ p ], the aquo-cation MN = EN[M(H2 O)N ], and the solution pH according to [4, 5]: h=

N × S − MNz  ⇔ S = Rp + W − Rp  × pH/7 H × S − H =

N × MNz − h H × H N − h H

(1)

Here N = MH2 ON  = M + N W = M + N  O + 2 H 

3424 + 0433 × pH/1339 + 0035 × pH. Figure 5 shows how the hydrolysis ratio h = minhNa  hNb  is predicted to change as the pH is increased from 0 to 14. Within this model, the existence domain (vertical lines in Fig. 5) of a given hydrolyzed complex, [MON -H2N −h ]z−h+ , is defined by the following inequality: pH(h − 05 < pH < pHh + 05. On the acid side, the prediction is in full agreement with experimental data showing that the titanyl cation [TiO(H2 O)5 ]2+ (h = 2) should be the most acidic species in aqueous solutions [15, 16]. On the basic side, however, the most basic species ([TiO(OH)3 ]− anion) remains hypothetical as it has never been experimentally detected. A first possibility is that it does not exist at all. This would, however, be a rather puzzling situation with respect to the existence of anionic aqueous complexes for the closely related ZrIV species [17]. Another possibility is that the equilibrium between the solid phase and the solution is too slow to establish. This last explanation is probably the right one as up to 45 days were needed to reach equilibrium in the case of ZrIV [17]. Another clue is provided by the fact that, as shown in Figure 6a, Zr OH Zr bridges are well known in the molecular state (see, e.g., the crystal structure of the basic salt ZrOCl2 · 8H2 O [18]). This is in stark contrast with TiIV (Fig. 6b) where only oxo bridges (Ti O Ti) have been characterized (see, e.g., the crystal structure of the basic salt Ti8 O12 (H2 O)24 Cl8 · HCl · 7H2 O [19]). The same conclusion is also reached after consideration of the general electronegativity charge plot for solid-phase

(2)

is the global softness of the hydrated cation computed by adding individual atomic softnesses i according to the complex stoichiometry. For the Allred–Rochow electronegativity scale, atomic electronegativities  and softnesses are linked according to = 136 1/2 −1 [4, 5]. With O = 350, H = 210, we get H = 05074, H = H + 1/ H = 4071, W = 1408, W = 2491, and R = 2732 (assuming p = 2, i.e., a proton bridging two water molecules). Now, for TiIV species (z = 4,  = 132, i.e., N = 0640 + N × 1408), the characteristic coordination number is pH dependent with Na = 6 under acid conditions as evidenced in the crystal structure of TiO(SO4 ) · H2 O [13] (Fig. 4a). Under basic conditions, the coordination number is reduced to Nb = 4, as evidenced in the crystal structure of -Ba2 TiO4 [14] (Fig. 4b). Consequently, with 6 = 9087, M64 = 2849, one may write hNa  = 2095 + 0627 × pH/1339 + 0035 × pH, while with 4 = 6271, M44 = 3009 it becomes hNb  =

Figure 5. Theoretical TiIV hydrolysis diagram according to the partial charge model. The solid curves were computed using z = +4 (oxidation state),  0 = 132 (Allred–Rochow electronegativity), Na = 6, and Nb = 4 (see text for details). The vertical lines correspond to the existence domains of each [MON H2N−h z−h+ complex.

746

Molecular Tectonics in Sol–Gel Chemistry

the breaking of a coordinate bond (M OH M + OH− → M OH + M OH− ). In contrast, oxide phase dissolution requires the breaking of a much stronger covalent bond (M O M + OH− → M O− + M OH). Consequently, owing to the very slow kinetics observed for the formation of [Zr(OH)5 ]− anions from solid ZrOx (OH)4−2x phases, one may anticipate an extremely slow kinetics for the formation of soluble [TiO(OH)3 ]− anions from TiO2 solid phases.

2.1.2. Complexation by Anionic Species

Figure 6. Molecular complexes isolated from hydrochloric solutions containing ZrIV and TiIV cations. (a) Hydroxy-based cyclic polymer Zr4 OH8 H2 O16 8+ . (b) Oxo-based cage polymer Ti8 O12 H2 O24 8+ . In both cases, chloride ions behave as simple counterions hydrogenbonded with coordinated water molecules. (c) Square pyramidal TiOCl4 2− ion with its very short terminal Ti O bond.

nucleation (Fig. 7) [4, 5]. Owing to their charge (z = +4) and electronegativity ( 0 = 132), TiIV cations falls inside the “insoluble oxides” domain. This illustrates the instability of any Ti OH Ti bridges (2Ti OH → Ti O Ti + H2 O favored over Ti OH + Ti OH2 → Ti OH Ti + H2 O). On the other hand, ZrIV cations are found borderline and, consequently, both behaviors may be observed, depending on experimental conditions. Now, for hydroxybridged species, the limiting step for dissolution should be

Figure 7. General charge–electronegativity plot for hydrolysis/ condensation reactions. Solid lines are derived after application of the partial charge model using the following critical conditions: + ENMON−1 H2N−z−1  = ENH2 O ( = −1 curve for M OH → M+ + − OH ionization), ENMON H2N−z  = ENH2 O ( = 0 curve for ola−  = ENH2 O ( = tion versus oxolation behavior), ENMON H2N−z−1 − + +1 curve for M OH → M O + H ionization), and ENMOz/2  = EN OH  (qOH = 0 curve for infinite versus limited oxolation).

In its most simple form, the PCM is also able to explain the complexation behavior of anionic species toward aqueous TiIV precursors. Here, the PCM equations [4, 5] furnish a fundamental link between the electronegativity of the q-protonated form of an n-valent anion Xn− (Q = ENHq Xn−q− ]) and the other electronegativities H , MNz , S, W governing the hydrolysis behavior of the cation [M(H2 O)N ]z+ :
 H − MNz H − MNz  −  W H − W  = M M H −S H −Q + q H +  W

(3)

In this equation,  corresponds to the number of water molecules removed from the coordination sphere of the hydrated cation after its association with the anion (coordination mode). For TiIV species (z = 4, N = 6,  = 132), (3) leads to 11108 − 2225 ×  11108 = 4071 − S 4071 − Q + 0507 × q + 1408 × 

(4)

Consequently, for a given n-valent anion Xn− characterized by its coordination mode , the critical pH for complexation with aqueous TiIV -based species may be derived for each protonated form Hq Xn−q− of the ligand, using the S value computed from (4): pH∗ = 7 × S − R/ W − R. Complexation by Chloride Ions Let us consider, for example, the case of the chloride ion characterized by ENCl(H2 O)− 6  = 2395 (q = 0 form) and EN(HCl) = 2438 (q = 1 form). Assuming a monodentate coordination mode ( = 1), the domain of stability of TiIV complexes is found to be pH = 71 ± 21. Above pH ∼ 9, complexes should be dissociated into hydroxo complexes and chloride ions, while, below pH ∼ 5, they should be hydrolyzed, leading to aquo complexes and again chloride counterions. These results could help to explain why no chloride ions are found within the coordination sphere of TiIV centers in the molecular cube [Ti8 O12 (H2 O)24 ]8+ (right complex in Fig. 6). Accordingly, such a complex derives formally from the oxolation of eight [TiO(OH)(H2 O)4 ]+ ions (h = 3 term) that are formed according to the PCM when pH = 38 ± 14 (Fig. 5). Owing to the very small overlap between both domains, only outer-sphere complexes are possible, in good agreement with experiments. Let us recall that these conclusions only apply when water molecules are in large excess relative to all present solute species (dilute solutions). Owing to the mass action law, increasing the chloride ion concentration (typically above 1 M) will always favor complexation.

Molecular Tectonics in Sol–Gel Chemistry

747

Accordingly, tetragonal pyramidal [TiOCl4 ]2− ions displaying a very short terminal Ti O bond (Fig. 6c) have been evidenced in the crystal structure of [NEt4 ]2 [TiOCl4 ] [20]. Complexation by Fluoride Ions Interestingly enough, a quite different behavior may be anticipated for complexation by fluoride anions that are characterized by ENF(H2 O)− 4= 2586 (q = 0 form) and EN(HF) = 2934 (q = 1 form). Assuming again a monodentate coordination mode ( = 1), the domain of stability of TiIV complexes is now found to be pH = −05 ± 53 (Fig. 8). The stability of Ti F bonds in aqueous solution is demonstrated by the isolation in the crystalline state of four different phases. Thus, linear chains of corner-sharing octahedra have been evidenced in the crystal structure of (NH4 )2 TiOF4 (2 -oxo bridges) [21] and (H3 O)TiF5 (2 -fluoro bridges) [22]. In contrast, monomeric [TiF6 ]2− ions have been characterized in the crystal structures of (H3 O)(H5 O2 )TiF6 and (H5 O2 )2 TiF6 · 2H2 O [23]. Complexation by Acetate Ions Acetate ions characterized by ENCH3 COO−  = 2246 (q = 0 form) and EN(CH3 COOH) = 2493 (q = 1 form) are expected to behave in a very similar way to chloride ions in aqueous solutions. Accordingly, considering a monodentate coordination mode ( = 1), as evidenced in the crystal structure of acetato-titanatrane [Ti2 {N(CH2 CH2 O)3 }2 -(CH3 COO)2 ] [24], leads to pH = 82 ± 43 (Fig. 9). As such a pH range overlaps with the pH range for TiO2 precipitation, it is not surprising to find no evidence in the literature of crystalline phases involving the coexistence of aquo, hydroxo, oxo, or acetato ligands within the TiIV coordination sphere. To stabilize such acetato complexes, one thus has to turn toward titanium alkoxides in nonaqueous solvents (vide infra). Complexation by Perchlorate and Nitrate Ions Other common inorganic monovalent anions such as perchlorate (ENClO− 4  = 2857, ENHClO4  = 3101) and nitrate [NO3 ]− (ENNO− 3  = 2762, ENHNO3  = 3077) provide examples of a bidentate behavior ( = 2) toward TiIV as evidenced by the crystal structures of Ti(ClO4 )4 [25] and Ti(NO3 )4 [26]. As shown in Figure 10, perchlorate complexes should be largely dissociated in aqueous solutions (pH = −36 ± 36), explaining why anhydrous conditions are necessary for their isolation and characterization. Figure 11 shows that nitrate ions are expected to behave in a rather similar way, even if one cannot completely rule out some complexation at very low pH (pH = −24 ± 43). Complexation by Oxalate and Sulfate Ions As expected, complexes involving multivalent anions are much more stable than those involving monovalent anions. For example, Figure 12 shows the expected complexation range for oxalate species that are char− acterized by ENC2 O2− 4  = 2329, ENHC2 O4  = 2623, ENH2 C2 O4  = 2832, and  = 2. With critical pH = −38 for Ti O2 C CO2 H + H3 O+ → Ti OH+ 2 + H2 C2 O4 , pH = 18 for Ti O2 C CO2 H + H2 O → Ti OH2 + [HC2 O4 ]− , and pH = 97 for Ti O2 C CO2 + 2OH− → Ti(OH)2 + [C2 O4 ]2− , oxalate complexes can thus be destroyed only under strongly basic conditions. Consequently, under acidic or neutral conditions, crystalline complexes may be easily isolated from the aqueous solutions. The most common species encountered in the presence of such oxalate is thus the

Figure 8. Complexation of aqueous TiIV species by fluoride anions. (a) Theoretical complexation range according to the PCM. (b) Molecular chain found in the crystal structure of NH4 2 TiOF4 . (c) Molecular chain found in the crystal structure of H3 O+ TiF5 − . (d) H-bond pattern around the TiF6 2− anion found in the crystal structure of H3 O+ H5 O+2 TiF6 2− . (e) H-bond pattern around the TiF6 2− anion found in the crystal structure of H5 O+2 2 TiF6 2− .

tetrameric hybrid oxo-anion [Ti4 O4 (C2 O4 )8 ]8− , which may be crystallized in the presence of ammonium [27], potassium [28, 29], or cesium ions [30]. A still wider range of complexation is predicted for sulfate ions characterized by  = 1

748

Figure 9. Theoretical complexation range predicted by the PCM for TiIV aqueous species in the presence of acetate ions. A monodentate coordination mode has been assumed in view of the crystal structure of acetato-titanatrane Ti2 NCH2 CH2 O3 2 CH3 COO2 . Owing to the overlap with the TiO2 precipitation range, such complexes can be isolated only in nonaqueous solvents.

Molecular Tectonics in Sol–Gel Chemistry

Figure 12. Theoretical complexation range predicted by the PCM for TiIV aqueous species in the presence of oxalate anions. A bidentate coordination mode has been assumed in view of the crystal structures of M2 TiOC2 O4 2 M = Li Na K Rb Cs NH4 . − ∗ (Fig. 13), ENSO2− 4  = 2277 (pH = 118), ENHSO4  = 2634 (pH∗ = 10), and ENH2 SO4  = 2872 (pH∗ = −61). This large domain of stability could explain why at least three different crystalline phases have been isolated and characterized in the TiO2 SO3 H2 O phase diagram. All phases are basic salts (h = 2) that may be formulated as TiOSO4 · H2 O [13, 31, 32] and that can be further dehydrated to form -TiOSO4 [33] or -TiOSO4 [13, 32]. The crystal structures of TiOSO4 · H2 O and -TiOSO4 are closely related, as they both contain zigzag [TiO]n chains (cis disposition of the two 2 -oxo groups within the TiIV coordination sphere). In TiOSO4 · H2 O (Fig. 13b), two 3 -sulfato groups are found in the trans position relative to the two 2 -oxo groups, while a third 3 -sulfato group in the axial position is used to bridge two zigzag chains together. The last octahedral axial position is occupied by an aquo ligand forming two

Figure 10. Theoretical complexation range predicted by the PCM for TiIV aqueous species in the presence of perchlorate ions. A bidentate coordination mode has been assumed in view of the crystal structure of TiClO4 4 . Owing to the negative pH range, complexes can be isolated only under anhydrous conditions.

Figure 11. Theoretical complexation range predicted by the PCM for TiIV aqueous species in the presence of nitrate ions. A bidentate coordination mode has been assumed in view of the crystal structure of TiNO3 4 . As most of the complexation domain lies below pH 0, stable complexes are expected only at very low pH.

Figure 13. (a) Theoretical complexation range of TiIV aqueous species by monodentate sulfate ions according to the PCM. (b) Crystal strucchains linked together ture of TiOSO4 · H2 O displaying zigzag TiO2n+ n through 3 -sulfato bridges. (c) Crystal structure of -TiOSO4 displaying the same chains as in TiOSO4 · H2 O but now linked together through 4 -sulfato bridges. (d) Crystal structure of -TiOSO4 with [(cis,trans)Ti2 O2 4n+ zigzag chains linked together through 4 -sulfato n bridges.

Molecular Tectonics in Sol–Gel Chemistry

H bonds with the free vertices of two neighboring 3 -sulfato groups. Similar zigzag chains have also been evidenced in the crystal structure of -TiOSO4 , but here we have a full bridging 4 -sulfato coordination mode between the chains (Fig. 13c). Another kind of zigzag chain has been found in the crystal structure of -TiOSO4 , a phase obtained after digestion of ilmenite FeTiO3 in sulfuric acid above 180  C (Fig. 13d) [33]. Such chains display two kinds of TiO6 octahedra, one sharing cis vertices and the other one sharing trans vertices with two adjacent octahedra. The remaining four vertices of both octahedra are shared with SO4 tetrahedra, which then behave again as 4 -sulfato bridging ligands. Complexation by Phosphate Ions Phosphate ions are also known to bind to TiIV in a bridging monodentate way ( = 1), as evidenced in the crystal structures of Na5 Ti(PO4 )3 [34] (2 -phosphato bridges; Fig. 14c) or MTi2 (PO4 )3 , with M = Na [35, 36], K [37], Rb [38, 39] (4 -phosphato bridges; Fig. 14b). However, owing to the ∗ additional anionic charge, ENPO3− 4  = 1707 (pH = 235), − ∗ ENHPO2−  = 2170 (pH = 101), ENH PO  = 2481 2 4 4 (pH∗ = 14), and ENH3 PO4  = 2705 (pH∗ = −47), a twofold increase in the complexation domain is observed (Fig. 14a). One may notice the very high pH predicted for the occurrence of the ionic cleavage Ti OPO3 + 3OH− → Ti(OH)3 + [PO4 ]3− . Taking into account the fact that a [PO4 ]3− ion cannot exist in aqueous solutions without extensive H bonding with the solvent and assuming one H bond per negative charge would lead to EN(PO3− 4 · 3H2 O) = 2232 (i.e., pH∗ = 128), a much more reasonable value. It remains, nevertheless, that the stability range of TiIV PO4 complexes covers almost all the accessible pH range, which could help to explain why numerous crystalline phases have been isolated from such solutions. For example, we were able to get 173 hits by searching for phases containing Ti, P, and O atoms in the October 2001 release of the ICSD Database in Karlsruhe. By comparison, the same search for Ti, S, and O atoms yielded only 29 hits. This high coordinating power of phosphate ions is immediately evidenced by the existence of three normal hydrogenophosphate salts (h = 0).

Figure 14. Molecular tectonics of titanium phosphates. (a) Theoretical complexation range predicted by the PCM for TiIV aqueous species in the presence of monodentate phosphate ions. (b) Crystal structure of MTi2 PO4 3 M = Na K Rb showing the 4 -bridging monodentate coordination mode of phosphate ions. (c) Crystal structure of Na5 TiPO4 3 showing that phosphate ions may also adopt a 2 -bridging monodentate coordination mode.

749 The most common one, -Ti(HPO4 ) · H2 O, is based on a hexagonal layer of TiO6 octahedra linked together through 3 -O3 POH bridges and holding a water layer with each water molecule engaged in two H bonds with P OH moieties (Fig. 15a) [40–43]. It is readily formed after heating a mixture of amorphous titanium dioxide [41–43] or titanium [40] and phosphoric acid. If one starts from titanium fluoro complexes, another hydrated-phase -Ti(PO4 )(H2 PO4 ) · 2H2 O may be formed [40]. This new layered structure (Fig. 15b) involves an equal amount of 4 -PO4 and 2 O2 P(OH)2 bridges, with free moieties of dihydrogenophosphate bridges engaged into H bonds with water molecules. The same layer-like arrangement of TiO6 and PO4 tetrahedra is found in the dehydrated form -Ti(PO4 )(H2 PO4 ), but H bonds are now made directly between [PO2 (OH)2 ]− tetrahedra [44]. A hydrated normal orthophosphate salt (h = 0) [Ti3 (PO4 )4 (H2 O)2 ] · NH3 has also been obtained after prolonged heating at 190  C of a mixture of TiCl3 , HCl, H3 PO4 , and urea CO(NH2 )2 [45]. Interestingly enough, the preparation from TiCl4 was not successful. Two kinds of Ti atoms in a 1 ! 2 ratio are found within this three-dimensional (3D)

Figure 15. (a) Hybrid hydrated layer based on TiO6 octahedra and 3 -hydrogenophosphato tetrahedra found in the crystal structure of -TiHPO4 2 · H2 O. (b) Hybrid layer based on TiO6 octahedra and mixed (4 -phosphato, 2 -dihydrogenophosphato) tetrahedra found in the crystal structure of -TiPO4 H2 PO4  and -TiPO4 H2 PO4  · 2H2 O. (c) 3D network based on Ti2 O6+ dimers and 4 -phosphato bridges in the crystal structure of Ti2 OPO4 2 H2 O2 . (d) Microporous 3D network based on 4 -phosphato bridges in the crystal structure of Ti3 PO4 4 H2 O2  · NH3 . (e) 3D network based on Ti3 O2 8+ dimers and mixed (4 -phosphato, 3 -hydrogenophosphato) bridges in the crystal structure of M2 Ti3 O2 HPO4 2 PO4 2 M = Rb NH4 . (f) Microporous 3D network based on mixed (4 -phosphato, 3 -phosphato) bridges in the crystal structure of H3 O3 Ti6 O3 PO4 7 H2 O3  · H2 O.

750 structure (Fig. 15d). The first one displays two aquo ligands in the trans position and four 4 -phosphato bridges in the equatorial plane, while the second one is surrounded by six 4 -phosphato bridges, leading to the overall stoichiometry Ti(H2 O)2 (PO4 )4/4 Ti2 (PO4 )12/4 ≡ Ti3 (PO4 )4 (H2 O)2 for the 3D network. This linking of Ti octahedra by phosphate oxygen via Ti O P bonds defines channels running along the c axis of the crystal, with ammonia molecules located at the center of eight-membered rings involving an equal amount of TiO6 octahedra and PO4 tetrahedra. Besides these crystal structures involving nonhydrolyzed TiIV species (h = 0) and protonated [Hq PO4 ]3−q− species (q = 0 1 2), basic salts involving hydrolyzed precursors (0 < h ≤ 2) have also been found. The crystal structure of [Ti2 O(PO4 )2 (H2 O)2 ] provides the first evidence of a 3D network based on a corner-sharing octahedral dimer (h = 1) and PO4 tetrahedra (Fig. 15c) [45, 46]. This compound may be obtained under hydrothermal conditions (T = 190  C during 1 week) from a concentrated mixture of TiCl4 and H3 PO4 . Here, 2 -oxo [Ti2 O]6+ octahedral dimers appear to be complexed on one side by two cis-disposed aquo ligands and three 4 -phosphato bridges, and on the other side by five 4 -phosphato bridges, leading to a 3D network displaying a TiO1/2 (H2 O)2 (PO4 )3/4 TiO1/2 (PO4 )5/4 ≡ Ti2 O(PO4 )2 (H2 O)2 stoichiometry. Another example based on the h = 1 TiIV precursor is provided by the crystal structure of MIL-18 (Fig. 15f) prepared under hydrothermal conditions (T = 210  C) from an aqueous mixture of hydrous titanium oxide, H3 PO4 , HF, and 1,3-diaminopropane [47]. In this structure, 2 -oxo [Ti2 O]6+ octahedral dimers are found complexed on one side by one water molecule and four 4 -phosphato bridges, and on the other side by four 4 - and one 3 -phosphato bridges, leading to a charged 3D network displaying a [TiO1/2 (H2 O) 3− (PO4 )4/4 TiO1/2 (PO4 )4/4 (PO4 )− 1/3 ]3 ≡ [Ti6 O3 (PO4 )7 (H2 O)3 ] stoichiometry. Charge compensation appears to be ensured by three [H3 O]+ countercations in strong interaction with one water molecule [47]. A linear corner-sharing [Ti3 O2 ]8+ trimer (h = 4/3) could be identified in the crystal structures of (NH4 )2 [(Ti3 O2 )(HPO4 )2 (PO4 )2 ] obtained under heating at 190  C of a mixture containing TiCl4 , H3 PO4 , and urea (Fig. 15e) [45]. An isostructural rubidium salt of this phase has also been isolated [48]. In both phases, the terminal Ti atoms of [Ti3 O2 ]8+ trimers appear to be complexed by two 3 -HPO4 and three 4 -PO4 bridges, while the central Ti atom appears to be bonded to two 3 -HPO4 and two 4 -PO4 bridges. The overall stoichiometry may then be written as [TiO1/2 (3 -HPO4 )2/3 (4 -PO4 )3/4 ]2 [TiO2/2 (3 HPO4 )2/3 (4 -PO4 )2/4 ]2− ≡ [Ti3 O2 (3 -HPO4 )2 (4 -PO4 )2 ]2− , with charge compensation ensured by two ammonium or rubidium countercations. This corner-sharing condensation process via 2 -oxo groups can be continued until the formation of infinite linear chains that are characteristic building units of crystalline structures involving TiO2+ (h = 2) precursors. The most simple and symmetric chain is found in the crystal structure of Na4 TiO(PO4 )2 (Fig. 16a) [49]. In this chain, each Ti octahedron displays two trans 2 -oxo groups with four symmetrically disposed 2 -phosphato bridges, explaining the overall [TiO2/2 (PO4 )4/2 ]4− stoichiometry and the occurrence of four sodium countercations between the chains. More

Molecular Tectonics in Sol–Gel Chemistry

Figure 16. Observed chain conformations in the crystal structures of titanyl phosphates. (a) Complexation of linear trans-TiO2+ chains by 2 phosphato bridges in the crystal structure of Na4 TiOPO4 . (b) Linear trans-TiO2+ chain in the crystal structure of -LiTiOPO4 . (c) Alternated trans-TiO2+ chain in the crystal structure of -LiTiOPO4 and -NaTiOPO4 . (d) Skewed cis-TiO2+ chain in the crystal structure of -NaTiOPO4 . (e) Mixed (cis-TiO2+ , trans-TiO2+ ) chain in the crystal structure of KTiPO4 and RbTiOPO4 .

complex chains occur in the crystal structures of phases displaying the MOPO4 (M = Li, Na, K) stoichiometry (Fig. 16). The chain occurring in the crystal structure of -LiTiOPO4 (Fig. 16b) is very similar to that found in the crystal structure of Na4 TiO(PO4 )2 (Fig. 16a), except that it now involves 4 -phosphato bridges leading to the new [TiO2/2 (PO4 )4/4 ]− stoichiometry [50, 51]. An alternate version of this transTiO2+ chain occurs in the crystal structures of -LiTiOPO4 [52] and -NaTiOPO4 [53, 54] (Fig. 16c), while the full cisTiO2+ chain (Fig. 16d) has been characterized in the crystal structure of -NaTiOPO4 [55]. Finally, a mixed alternate (cis-TiO2+ , trans-TiO2+ ) chain forms the building unit of the crystal structure of KTiOPO4 [56–61] and RbTiOPO4 [62– 64] (Fig. 16e). Owing to the high polarizability of the Ti O bonds and their mutual disposition inside strongly distorted octahedra (172.3 pm < dTi O < 2150 pm), such crystals are characterized by large nonlinear optical properties. Compared to similar organic materials, they also display a high radiation damage threshold arising from their rigid framework of PO4 tetrahedra. Complexation by Silicate Ions Our last concern will be the case of silicate ions, which, like phosphate ions, bind to TiIV through monodentate ( = 1) 4 -silicato bridges, as evidenced in the crystal structures of natisite Na2 TiO(SiO4 ) [65, 66] and Li2 TiO(SiO4 ) [67] (Fig. 17b). The interesting feature of these 3D networks is the fivefold square pyramidal coordination observed for titanium atoms. The same coordination polyhedron occurs in the two low-temperature (Fig. 17c) and high-temperature (Fig. 17d) polymorphic

Molecular Tectonics in Sol–Gel Chemistry

Figure 17. Molecular tectonics of silicotitanates. (a) Theoretical complexation range predicted by the PCM for TiIV aqueous species in the presence of nonsolvated monodentate silicate ions. (b) Crystal structure of natisite Na2 TiOSiO4  and Li2 TiOSiO4  showing the 4 -bridging monodentate coordination mode of silicate ions and the square pyramidal fivefold coordination of Ti atoms. (c) Low-temperature modification of a polymorph of Na2 TiOSiO4  network. (d) High-temperature modification of the polymorph shown in (c). (e) trans-TiO2+ octahedral chain occurring in the crystal structure of titanite or sphene CaTiOSiO4 . (f) Cubane-like arrangement of Ti and O atoms in the crystal structures of M4 Ti4 O4 SiO4 3 · 4H2 O phases M = H Na K Cs that are structural analogs of the mineral pharmacosiderite. (g) Chains of cubane-like Ti4 O4 cages linked through linear oxo-bridges in the crystal structures of M2 Ti2 O3 SiO4 · nH2 O (M = H, Na).

751 modifications of Na2 TiO(SiO4 ) [68], whereas an alternate trans-TiO2+ octahedral chain, similar to that observed in LiTiOPO4 or -NaTiOPO4 , occurs in the crystal structure of titanite or sphene CaTiO(SiO4 ) (Fig. 17e) [69–75]. The PCM complexation diagram for this tetravalent ion, charac3− ∗ terized by ENSiO4− 4  = 1161 (pH = 334), ENHSiO4  = ∗  = 2100 (pH = 77), 1721 (pH∗ = 177), ENH2 SiO2− 4 ∗  = 2374 (pH = 06), and ENH SiO  = 2581 ENH3 SiO− 4 4 4 (pH∗ = −46), is shown in Figure 17a. As with the case of phosphate ions, we notice the very large values obtained for ionic dissociation of [HSiO4 ]3− and [SiO4 ]4− . Allowing for some H bonding with the surrounding water molecules ∗ would lead to EN(SiO4− 4 · 4H2 O) = 2126 (pH = 151), 2− ∗ · 3H O) = 2195 (pH = 96), and EN(H EN(HSiO3− 2 2 SiO4 · 3 ∗ 2H2 O) = 2285 (pH = 47). Even with these reasonable corrections, we see that titanosilicate complexes are stable throughout the whole range of pH. This may help to explain the occurrence of more than 500 known crystalline phases (exactly 561 phases containing Si, Ti, and O atoms in the October 2001 release of the ICSD Database in Karlsruhe). There is also another reason to explain the complexity of titanosilicate chemistry. As shown in Figure 7, all previously studied CIV -, NV -, PV -, SVI -, and ClVII -based oxyanions cannot undergo spontaneous oxolation in aqueous solutions owing to their location at the upper right of the diagram in the domain of soluble acids. With SiIV , we have moved to the polyacid domain, meaning that spontaneous oxolation 2Si OH → Si O Si + H2 O may now readily occur in aqueous solutions, leading to polysilicate species. With two systems both able to undergo oxolation after pH changes, we may thus span the whole palette from silicotitanates (titanium oxo-compounds complexed by orthosilicate anions) to titanosilicates (polysilicates complexed by titanyl TiO2+ cations). To keep this review within reasonable limits and in view of our interest in titanium oxo chemistry, we have limited ourselves to the study of silicotitanates gathered in Figure 17. The striking feature is, then, that besides the previously discussed phases (titanite and natisite) only two phases remain to be considered, as most crystalline phases are found to involve Si O Si bonds. The overwhelming abundance of titanosilicates over silicotitanates may be the consequence of the very high affinity of Si O bonds for TiIV , allowing for some depolymerization of the Ti O Ti bonds. Consequently, only the most symmetrical molecular arrangements of the Ti O Ti bonds should be able to resist silicate species. In fact, this is just what has been found experimentally in the crystal structures of M4 Ti4 O4 (SiO4 )3 · 4H2 O phases with M = H, K, Cs [76, 77], or Na [78], which are structural analogs of the mineral pharmacosiderite KFe4 (OH)4 (AsO4 )3 · 6H2 O. These phases can be prepared under hydrothermal conditions (T = 160–200  C, t = 48– 100 h) from amorphous TiO2 –SiO2 gels having Si ! Ti = 2. In this 3D network, cubane-like Ti4 O4 oxo-cages are complexed by six 4 -silicato bridges (Fig. 17f) with each SiO4 tetrahedra bridging two Ti4 O4 cubes. It is interesting to compare this very compact cube to the much larger Ti8 O12 (see Fig. 6) isolated from solutions containing noncoordinating Cl− counteranions [19]. Other related phases Na2 Ti2 O3 SiO4 · 2H2 O [79] and Ti2 (OH)2 OSiO4 · 15H2 O [80] could be obtained upon prolonged heating (t = 10 days at T = 200  C) of

752 solutions obtained by mixing TiCl4 , H2 O2 , silicic acid, and NaOH. As shown in Figure 17g, these 3D networks involve exactly the same Ti4 O4 building units associated again to 4 -silicato bridges, but the cubes are now linked to linear chains through four 2 -oxo bridges. Each cube is complexed by four SiO4 tetrahedra common to two cubes leading to a negatively charged ([Ti4 O4 O4/2 (SiO4 )4/2 ]4− ≡ [Ti2 O3 SiO4 ]2− ) hybrid network needing two countercations (H+ or Na+ ) to ensure charge neutrality.

2.2. Crystalline Titanium(IV) Oxides After this review of the aqueous chemistry of TiIV species, it should be obvious that our PCM approach provides considerable help in rationalizing and understanding the experimental facts. In its most simple form, it suffers, however, from its blindness to the detailed molecular or crystalline structure. For example, if the model readily explains why, under acidic conditions (pH ∼ 0), a titanyl cation (h = 2) should be formed (the fully aquo TiIV complex is just much more electronegative than the most acidic species [H5 O2 ]+ compatible with a water medium), it makes absolutely no distinction between [Ti(OH)2 (OH2 )4 ]2+ or [TiO(OH2 )5 ]2+ species. Referring to the above experimental results showing the occurrence of monomeric [TiO]2+ cation (natisite), dimeric [Ti2 O]6+ (phosphate counteranion), trimeric linear [Ti3 O2 ]8+ (phosphate counteranion), tetrameric square planar [Ti4 O4 ]8+ (oxalate counteranion), cubane-like [Ti4 O4 ]8+ (silicate counteranion), cubic-like [Ti8 O12 ]8+ (chloride counteranions), and chainlike (cis, trans, or mixed) [TiO]2n+ n (fluoride, sulfate, phosphate, and silicate counteranions), it should be clear the real h = 2 aqueous species should be written as [TiO(OH2 )5 ]2+ and not [Ti(OH)2 (OH2 )4 ]2+ . Similarly, if the PCM rightly predicts that the final term of condensation should be a hydrated oxide TiO2 · nH2 O and not a hydroxide Ti(OH)4 , absolutely no distinction is possible among the three common polymorphs of titanium dioxide (rutile, anatase, and brookite). Consequently, during the decade following the achievement of the above formalism [4], considerable work was performed along the following lines: 1. Elaboration of a structure-dependent version based on the Sanderson electronegativity scale in order to compute NMR chemical shifts [81] and treat nonmolecular 3D networks [82]. 2. Use of the Mulliken scale for individual electronegativities and of covalent radii for approximating chemical hardnesses [83, 84]. 3. Improved evaluation of chemical shifts and electric field gradient tensors from crystalline [85] or molecular structures [86]. 4. Use of the Allen spectroscopic electronegativity scale and ab initio atomic radii, allowing probing molecular interactions [87–90] and performing crystal structure optimization [90–92].

2.2.1. PACHA Formalism In the following, we examine this new powerful approach known as PACHA (partial atomic charge and hardness analysis). This model is then applied to the study of TiO2 crystalline phases and some TiIV -based hybrid organic–inorganic

Molecular Tectonics in Sol–Gel Chemistry

molecular networks. Briefly stated, the PACHA model states that for any chemical compound four global mean values, symbolized hereafter as EN, GH, EB, and GI, may be defined. At a local scale (atomic sites), it is further characterized by 2 × n local indexes in the form of n partial charges (qi ) and n frontier indexes (fi ). The parameter EN corresponds to the mean electronegativity (in volts) of the system that may be identified with the energy situated halfway between the HOMO and the LUMO (Fig. 18). It can then be used to determine if a given compound will act as an electron donor (low or negative value) or as an electron acceptor (high EN value). The parameter GH measures the global hardness that should scale like a HOMO–LUMO gap (molecule) or band gap (solids). It can be used to compute the paramagnetic contribution to the chemical shielding of an NMR active atomic nucleus. The EB parameter reflects the energetic balance between all atomic pairs, either attractive (&+ · · · &− ) or repulsive (&+ · · · &+ or &− · · · &− ). A negative value is an indication of a stable compound, whereas a positive value points to a species that must heavily rely on covalent interactions to become stabilized. This parameter can also be used to probe energetic interactions between molecular fragments [87–92]. Briefly stated, within the density functional theory (DFT) framework [93, 94], the total molecular energy E can always be partitioned between the purely electrostatic contribution EB and a purely electronic functional F (, which takes care of all the exchange and electronic correlation: Etot = EB + F (. Now, for the same molecular fragment placed into two different chemical environments (in a vacuum, on one hand, and inside a crystalline lattice, on the other hand, for example), our basic assumption is that F1 ( ∼ F2 (. If this approximation holds, then the interaction energy can be readily evaluated as Eint ∼ EB1 − EB2. This EB value can also be used, through a simplex minimization technique,

Figure 18. Relationships between the PACHA model (mean electronegativity, EN; global hardness, GH; partial charge, q; global ionicity, GI; electrostatic balance, EB), LCAO–MO theory (wave function, ) ; HOMO, LUMO, LCAO–MO coefficients cA and cB ), and density functional theory DFT (electronic density,  (; exchangecorrelation functional, F (; electrostatic functional, vne ( d,). From DFT requirements, EN should correspond to an electronic chemical potential governing electronic density flows between atoms, that is, to a Fermi level, while GH should correspond to the HOMO–LUMO or band gap.  A key feature of the model is the spherical charge approximation ( vne ( d, ∼ EB), providing a very efficient algorithm for the quantification of molecular and crystalline interactions.

Molecular Tectonics in Sol–Gel Chemistry

753

to find the most favorable position for an atom or an atomic group within a molecule or a crystalline network [90–92]. For metal alkoxides, this is particularly useful as it allows us to get a reliable estimate of the atomic coordinates of H atoms. Accordingly, these coordinates are often not included in the refinement process of X-ray data but are nevertheless absolutely needed to get realistic partial charge distributions. Such a minimization technique can also be used to get reliable charge distributions from strongly disordered crystals. Finally, the GI parameter is a global ionicity index, ranging from 0 to 100%, that helps to decide whether a given compound should be considered as ionic or covalent. A purely covalent structure (qi ∼ 0) will then be characterized by GI ∼ 0%, while a purely ionic one (qi values close to the oxidation states) will have GI ∼ 100%. Electronic Signatures The PACHA equations provide a fundamental mathematical link between atomic properties (electronegativities ei0 , atomic sizes ri ) and molecular or crystalline structure via partial charge (qi ) and frontier index (fi ) distributions. Chemical objects are introduced via the knowledge of stoichiometric coefficients ni , oxidation numbers zi , Madelung matrix Mij (in Å−1 ), total charge Q, and number of formula units Z per unit cell:  ni eEN = ni ei0 + ni 1i qi + 144 Mij qj j

with



(5)

n i qi = Q

i

ni e2 GH = ni 1i fi + 144



ni fi = Z (6)

GI/% = 100EBq/EBz1/2

(8)



Mij fj with

i

j

EBq/eV =

 i

Mij qi qj

(7)

j

In its ab initio final form, the PACHA model uses the configuration energy of the elements [95, 96] and atomic orbital radii ri [97] to approximate electronegativity values 10 and chemical hardnesses 1i eV = 1440/ri (pm), respectively. This particular choice confers an absolute character on the reported charge distributions, as these values are fixed by quantum-mechanical laws and not by empirical data commonly used to define other electronegativity or radius scales. This allows us to treat on the same quantitative basis organic or inorganic objects, a very important point if we want to cope with complex mixed organic–inorganic compounds. Another nice aspect linked with this absolute character is the possibility to establish a quantitative correlation between partial charges borne by oxygen atoms qO and protonation constants (−pKa = 173 + 395 × qO ) [87–90]. With this relationship in hand, stating that the higher the charge on the oxygen atom, the higher its acidity, we have a very convenient way to infer acidobasic properties directly from the molecular or crystalline structure. Finally, electrostatic interactions cannot be the whole story for understanding the chemical reactivity of mixed organic–inorganic complexes. Consequently, the model gives us, besides the partial charge qi , a set of frontier indexes fi that can be used as a local probe for hard–soft interactions. To sum up, with four global parameters (EN, GH, EB, and GI) and 2n local

ones (qi and fi ), we may define what we call an “electronic signature” (ES) within the PACHA formalism. Case Study: Carbon Monoxide A good illustration of our strategy is provided by the very simple example of carbon monoxide (CO). First, quantum mechanics or atomic spectroscopy tells us that an isolated carbon atom has an electronegativity C0 = 1505 V [95] and that the radii of the valence orbitals of this element are r2s = 62 pm and r2p = 596 pm [97]. Similarly, for the oxygen atom, we have O0 = 2136 V [95], r2s = 45 pm, and r2p = 414 pm [97]. In the following, we will always assume that the atomic chemical hardness is governed by the most diffuse atomic orbital (here 2s orbitals for both carbon and oxygen atoms). Now we have to introduce the crystalline structure of carbon monoxide (space group P 21 3) [98]. Using an Ewald summation procedure [99], we find that the 2 × 2 Madelung matrix characterizing this structure is MCC = −047897 Å−1 , MCO = MOC = 341636 Å−1 , and MOO = −044559 Å−1 (optimum convergence parameter G = 032 Å−1 ). Inserting these data into the PACHA equations given above leads to the following electronic signature: EN = 1718 V, GH = 184 eV, EB = −298 eV, GI = 116%, qC = −qO = +0231, fC = 0663, and fO = 0334. From this absolute signature, it is possible to deduce that CO should be a very stable and strongly covalent (low ionicity index GI) molecule with a low-lying HOMO (high electronegativity EN) and a wide HOMO–LUMO gap (large global hardness GH). Even if the oxygen atom is found to be negatively charged, it should have no affinity for protons (pKa ∼ −85). For covalentbased interactions (coordination chemistry), the largest f index is found on the C atom and not the O atom, explaining the preferred coordination mode M C O and not M O C. Fortunately, all these predictions are confirmed by experiments. The interesting point is that these properties were derived without any reference to any MO scheme. In particular, the occurrence of a triple carbon–oxygen bond in this molecule has been completely ignored. This example shows the power of our approach, as chemical stability and properties can be predicted without solving the Schrödinger equation. Nevertheless, it also pinpoints its weakness concerning the ignorance of the nature of frontier orbitals and our total inability to predict any spectroscopic properties. A further step is achieved by considering that all these physicochemical properties are not driven by the crystalline structure, but are already engraved in the molecular structure of a single molecule. To check this point, let us forget the whole crystalline network and keep just the single essential information: CO is a molecule displaying a very short C O bond (106.3 pm). Physically speaking, this means that the CO network has been vaporized and that we now face a free isolated CO molecule. For this much simpler situation, the Madelung matrix is just MAA = MBB = 0 (no C · · · C or O · · · O interactions) and MAB = 1/1063 = 0941 Å −1 (no intermolecular C · · · O interactions). Inserting this new matrix into the same equations leads to EN = 1722 V, GH = 199 eV, qC = −qO = 2 × GI = +0224, and f C = 1 − f O = 0656. A simple comparison with previous values derived after a full Madelung summation process will immediately convince the reader that CO forms

754 a truly molecular crystal. This comes from the fact that its electronic signature changes by a very tiny 0.1% on going from the crystalline lattice to the free molecule. This clearly demonstrates that, at least in the case of the CO molecule, the pertinent chemical information is completely included in the knowledge of the molecular geometry and not in the way the molecules are packed inside a crystalline structure. Moreover, we also are now in a position to get a quantitative evaluation of the lattice packing energy for this highly covalent network. Accordingly, for the crystalline network, we know that EBnet  = −298/4 eV = −719 kJ mol−1 , as we have four CO molecules per unit cell (Z = 4). For a positively charged carbon atom (q = +0224) situated at 1.063 Å of a negatively charged oxygen atom (q = −0224) in a free molecule, we should have EBmol  = −69468 × 202242 /1063 = −656 kJ mol−1 . As expected, EBnet  is lower than EBmol  owing to the intermolecular interactions occurring in the solid state and which are absent in the free molecule. The difference EBnet  − EBmol  ∼ −6 kJ mol−1 is thus a direct measure of all the attractive intermolecular forces acting in the crystalline state. In this particular case, it is found to be rather weak (typical of van der Waals interactions) in agreement with the low molecular weight and low polarity of the CO molecule. The good news is now that this procedure is quite general and not limited to molecular networks. It can be easily applied in a systematic way to any crystalline network or isolated molecule. Errors in Evaluation of Electronic Signatures Another important aspect of the PACHA model concerns the systematic inclusion of errors in the electronic signature. First, one has to notice that, given structural Mij input, (4)–(8) lead to a unique electronic signature. If some errors are made concerning the determination of unit-cell parameters and/or atomic positions, the corresponding signature will be more or less affected depending on the accuracy of the structure determination. For experimental data coming from X-ray or neutron diffraction, the evaluation of errors is straightforward as these techniques give not only the structural parameters but also the estimated standard deviations (esd or ) on each optimized parameter. From a single input, it is then possible to generate N slightly different crystal structures by allowing random variations of the structural parameters within 3 (99.9% confidence level). By computing a Madelung matrix for each of these N crystal structures (typically N = 100), it is possible to perform a statistical analysis on the derived EN, GH, EB, GI, qi , and fi quantities. Corresponding errors on the PACHA parameters may then be reported as 3 . This systematic evaluation of errors allows us to know how many significant digits should be reported in the electronic signature. However, the same crystal structure may have been determined several times by different authors. In these cases, errors may not be computed from the individual esd, but rather from a statistical analysis performed over all available structural refinements. Such errors will be reported in boldface characters to distinguish them from the errors associated with a single refinement. Finally, if errors are reported in italics, they have been computed from an average over structural data of good quality obtained by rejecting from the statistics all structures with unknown R values or having R values typically higher than 10%.

Molecular Tectonics in Sol–Gel Chemistry

A direct and useful consequence of this systematic evaluation of errors in the electronic signature concerns the accuracy of the determination of the Madelung matrix. If structural data of the highest quality (R < 5%) is available, convergence would be reached as soon as the relative variation between two successive evaluations of the same matrix element is typically less than 10−4 . Increasing the accuracy beyond this point will increase severely the computation time for a statistically nonsignificant improvement of the electronic signature. Reciprocally, if the crystal structure has a huge unit cell, it will surely not be well refined (R > 10%). In such cases, it may be perfectly correct to use nonconverged Madelung matrices having a relative accuracy as low as 10−2 or higher in order to minimize the computation time. Situation Relative to ab initio Models Another interesting point concerns the accuracy of structural data derived from first-principles calculations with absolutely no experimental input. The use of the term “accurate” is here important, as it refers to the difference between a calculation and the true value of an observable. Because the true value of an observable is, in principle, unknowable, it is virtually impossible to judge the accuracy of a calculation. Such is not the case if we have some idea of the uncertainty (expressed as a standard deviation through a statistical analysis) attached to the measure of the observable. If this uncertainty is very low, we may safely identify the mean value measured with the true value of the observable. Now it is easy to check how many standard deviations separates the result of a calculation from a measured value. If theory lies within 3 of experience, the model can claim to reproduce accurately the experimental values; otherwise, it should be considered as not good enough to reproduce experimental trends. Consequently, the reported combined standard uncertainty on each electronic parameter (which depends on the crystalline short-range and long-range order) allows us to judge, in a quantitative and objective way, how far a theoretical structure is from the experimental one. A good agreement between theory and experiment should be claimed only when all electronic parameters of the theoretical structure lie within 3 of the experimental data. Figure 19 presents the PACHA model in relation to other quantum-mechanical tools. As can be seen, owing to the total absence of empirical parameters, it can be considered as an ab initio approach based on a spherical charge approximation of DFT equations. Its very high efficiency lies in the encapsulation of all the problematic electron–electron correlations into just two parameters per chemical element: the configuration energy identified with the electronegativity and an atomic radius identified with the chemical hardness. The interesting point is that the previously used PCM approach may be viewed as a particular case of the PACHA equations. The PCM is obtained by putting Mij = 0 and by using the Allred–Rochow scale to get electronegativities and hardnesses. In this case, the chemical hardness is approximated as the square root of the electronegativity through an empirical constant k in order to mimic the atomic radius dependence. This allows keeping just one parameter per chemical element instead of two in the PACHA approach. In the following, this PACHA model will be extensively used to

Molecular Tectonics in Sol–Gel Chemistry

755

Figure 19. PACHA model relative to other quantum-mechanical tools. The Hartree–Fock (HF) approaches based on the determination of the total wave function after resolution of the Schrödinger equation are represented on the left of the figure. Here n scales like the total number of electrons and gives an idea of the computational cost of each method. SCF, self-consistent field; MBPT, many-body perturbation theory; MP, Moller–Plesset development; CI, configuration interaction with S, single; D, double; T, triple; Q, quadruple excited configurations; FCI, full CI; QCI, quadratic CI; CC, coupled cluster; CEPA, coupled-electron-pair approximation; SCEP, self-consistent electron pair; CPF, coupled-pair functional approach. The approaches based on density functional theory (DFT) using the Kohn–Sham equations are represented on the right of the figure. GGA, generalized gradient-corrected approximation; B, Bethe exchange functional; LYP, Lee–Yang–Parr correlation functional; PW, Perdew–Wang; L(S)DA, local (spin) density approximation; PW, plane wave; PP, pseudo-potential; AE, all electrons; MTO, muffin-tin orbital; L, linearized; ASA, atomic sphere approximation; FP, full potential; APW, augmented PW; GTO, Gaussian-type orbital; LCAO, linear combination of atomic orbitals; U, correction for electron–electron repulsions.

discriminate between known TiO2 polymorphs or to understand the chemical properties of various complexes or building blocks that can be used in a rational design of hybrid organic–inorganic networks.

2.2.2. Application to TiO2 Polymorphs With at least six different known polymorphs, TiO2 provides a challenge for theoretical models devoted to chemical bonding in the solid state. Surprisingly enough, these crystalline TiO2 phases have never been systematically reviewed and compared using the same theoretical framework. Rutile This is the thermodynamically stable hightemperature polymorph. It is very well known that tetragonal crystal structure is based on linear chains of TiO6 octahedra sharing a pair of opposite edges and which are further linked by shared vertices to form a 3D structure of 6 ! 3 coordination (Fig. 20). In this structure, oxygen atoms are in an approximate hexagonal closest packing configuration with titanium atoms filling half of the available octahedral holes. Each TiO6 octahedron is in contact with 10 other ones (2 through edge sharing and 8 through corner sharing). The room-temperature rutile structure has been

refined several times [100–117], allowing us to compute the following low-accuracy electronic signature: Global
EN = 583 ± 023 V e2
GH = 304 ± 005 eV
EB = −235 ± 13 eV
GI = 4077 ± 088%

Local qTi = 1631 ± 0035 qO = −0815 ± 0018 f Ti = 1178 ± 0017 f O = −0089 ± 0009

(9)

In comparison with -quartz (EN = 1278 ± 007 V, e2 GH = 886 ± 006 eV, EB = −105 ± 04 eV, GI = 258 ± 04%, qSi = +103 ± 002, and qO = −0516 ± 0008) [118], rutile appears to be a much more ionic and less electronegative oxide material in agreement with common chemical knowledge. To match the experimental room-temperature band gap, Eg direct = 3062 eV and Eg indirect = 3101 eV [119], with the global hardness, we have to set G = 047 Å−1 . This value is very close to the optimum G value minimizing the computation time (G = 049 Å−1 ). The large frontier index found for titanium reflects the rather large orbital radius of the titanium 4s orbital (147.7 pm) used to approximate the chemical hardness of this atom. Limiting statistical analysis to the 20 structures

Molecular Tectonics in Sol–Gel Chemistry

756

Figure 20. Rutile crystal structure (space group P 42 /mnm). (a) Local geometry at Ti and O sites and ball-and-stick view of the chemical bond patterns. (b) Topology of the 3D framework is evidenced as corner sharing between chains of trans edge-sharing octahedra.

having R < 5% leads to the following much more accurate electronic signature: Global EN = 5838 ± 0014 V e2 GH = 3046 ± 0002 eV EB = −2341 ± 008 eV GI = 4072 ± 006%

Local qTi = 16286 ± 00022 qO = −08143 ± 00011 fTi = 11768 ± 00011 fO = −00884 ± 00005 (10)

[125] and ab initio [126] calculations lead to very similar values q(Ti) = −2 × q(O) = 2516 and 2.610, respectively. Consequently, it is clear that the rutile structure should have at least 40% covalent character, ruling out definitively the picture Ti4+ O2− for the Ti O bond. Knowing the room-temperature electronic signature of rutile, we may take a look at the effect of changing the temperature as crystal data are available from T = 15 K up to T = 1883 K [107, 112–114, 127]. Figure 21 shows that, with the exception of the T = 15 K point [113], smooth variations are obtained. Moreover, data points coming from different studies are found to be in rather close agreement. It is clear from these graphs that, above room temperature, higher temperatures mean higher EN, EB, q(O), f (O) and lower GH, GI, q(Ti), f (Ti). The absorption spectra of rutile crystals have shown that both band gaps, Eg (direct) and Eg (indirect), decrease on lowering the temperature [119]. At 1.6 K, Eg (direct) = 3033 eV (8Eg = −0029 eV) and Eg (indirect) = 3049 eV (8Eg = −0052 eV). A decrease in GH is also noted in Figure 21. However, it is so small (8Eg ∼ −0001 eV) that we cannot rule out an artifact coming from the experimental data used. Accordingly, for T = 16 K, the refinement of the structure was made using powder neutron diffraction data, while single-crystal X-ray diffraction has been used for other temperatures. On the other hand, between 298 and 100 K, we find that 8EN = −0050 eV, a value of the same order of magnitude as the experimental 8Eg . Concerning the high-temperature domain, a slight increase in the electric field gradient at titanium sites Vzz  with temperature Vzz  (V Å −2 ) = 21 + 6 × 10−4 T and a strong temperature dependence of the asymmetry parameter 1Q = 026 − 3 × 10−4 T were reported [128]. Using our charge distributions to compute these two parameters leads to a small decrease in Vzz  with temperature (0.5 V Å −2 between 300 and 1900 K). It also leads to a parabolic variation from 1Q = 035 at room temperature up to 1Q = 094 at 943 K and then down to 1Q = 049 at 1900 K. These

Finally, selecting one of the most recent and best crystal structure determinations (R = 11% [112]) leads to this very high accuracy signature: Global EN = 58354±00023 V e2 GH = 30464±00010 eV EB = −23420±0013 eV GI = 40725±0009%

Local qTi = 16290±00004 qO = −081449±000019 f Ti = 117700±000018 f O = −008850±000009 (11)

The 41% global ionicity found for this network may be compared to other ionicity indexes given in the literature. With (Ti) = 14 and (O) = 35, it is found that GI = 55% from the Pauling equation I(Ti O) = 1001− exp−018Ti − O 2  [120] against GI = −50 × q(O) = 374% from optical basicity–derived charges q(O) = −086/ Ti − 025) [121]. Accurate X-ray charge density studies of the rutile structure [109] have revealed a rather high degree of covalence but with q(Ti) = −2 × q(O)∼ +3, leading to GI ∼ 75%. This value is similar to that derived from LO–TO splitting [122] (GI = 66%) or from band structure calculations that show that the valence DOS has 2/3 O-2p character and 1/3 Ti-3d character [123, 124]. Semiempirical INDO

Figure 21. Evolution of the electronic signature of the rutile structure with temperature. Upon increasing temperature, EN, EB, q(O), and f (O) are found to increase in a parallel way with the following increments: 8EB = +2 eV, 8q(O) = +003, and 8f (O) = +0015. Conversely, GH, GI, q(Ti), and f (Ti) are decreasing functions of temperature with the following decrements: 8GI = −13% 8q(Ti) = −006, and 8f (Ti) = −003.

Molecular Tectonics in Sol–Gel Chemistry

variations are of the right order of magnitude for both Vzz  and 1Q but are at the opposite of the experimental findings (Vzz  increases and 1Q decreases with temperature). th reaches Interestingly enough, the temperature at which 1Q its maximum value (T = 943 K) is very close to the temexp perature (T = 980 K) at which 1Q ∼ 0. Consequently, if our electronic signatures are able to explain the amplitudes of the observed variations, they fail to reproduce the signs. More work is thus needed to get both amplitudes and signs. Figure 22 shows that increasing the pressure has the opposite effect of increasing the temperature, as higher pressure leads to higher GH, GI, q(Ti), f (Ti) and to lower EN, EB, q(O), f (O). The GH curve (not shown), however, displays an anomaly at P = 76 GPa, which parallels the nonlinear variation of the c parameter of the unit cell. The reported data were as follows: 2.959 Å (ambient pressure), 2.948 Å (3100 MPa), 2.946 Å (5000 MPa), 2.921 Å (7600 MPa), and 2.940 Å (8600 MPa) [129]. To conclude this section, we may note that at least four theoretical models have tried to reproduce the rutile crystal structure starting from first principles. Table 1 shows the results, taking the very accurate electronic signature (11) as the experimental reference for the esd. As can be seen, only the Car–Parinello method appears to be successful. All other methods are completely out of range by at least an order of magnitude. Anatase This is the other common tetragonal lowtemperature polymorph of titanium oxide displaying spiral chains of edge-sharing octahedra that are further linked by sharing edges and corners to form another 3D structure of 6 ! 3 coordination (Fig. 23). In contrast with rutile, oxygen atoms are found in an approximate cubic closest packing configuration. In this structure, each TiO6 octahedron is in contact with eight other ones (four through edge sharing and four through corner sharing). Among the six crystal structure determinations available [113, 115, 134–137], only

757 three are accurate enough (R < 5%) to compute a reasonable electronic signature: Global EN  = 5998±0008 V e2 GH = 31203±00015 eV EB = −2368±004 eV GI = 4091±003%

Local qT i = 16363±00011 qO = −08182±00005 fT i = 11647 ±00006 fO = −00824±00003 (12)

The best structural refinement (R = 23%) available for this anatase structure [136] leads to a very similar signature: Global EN = 5997 ± 0024 V e2 GH = 3120 ± 0025 eV EB = −2368 ± 004 eV GI = 4091 ± 009%

Local qTi = 16363 ± 00035 qO = −08182 ± 00018 f Ti = 11647 ± 00018 f O = −00824 ± 00009 (13)

Anatase is, then, slightly more ionic than rutile. The quite modest 8qTi = 0008 increase in ionicity from rutile to anatase is just slightly larger than that found by ab initio calculations qTi = −2 × qO = +2610 ⇒ 8qTi = 0003 [126]. As with the rutile structure, electron density studies have revealed strong covalent bonds between titanium and oxygen [138], while band structure calculations show considerable mixing between O(2p) and Ti(3d) orbitals in both the valence and the conduction bands [139]. Optical investigations have shown that the band gap is slightly wider in anatase (Eg = 32 eV at RT and Eg = 33 eV below 100 K) than in rutile [140, 141]. The 0.1-eV experimental increase in Eg is thus well in line with the 0.1-eV increase obtained for GH or GI. This result is also in line with the thermochemical value 8E = 12 kJ mol−1 ∼ 012 eV measured for the anatase → rutile transition [142]. This increase in Eg also explains the −195-ppm shielding observed in 47 49 TiNMR [143] and the 31-ppm shielding observed in 17 O-NMR [144]. To check this point, we may refer to the general theory of magnetic screening [145], allowing us to write on an absolute scale the isotropic part of the chemical shielding tensor of the 17 O nucleus in the following form [85]: iso ppm = dia ppm−966×R +;q×Pu /8E eV (14)

Figure 22. Evolution of the electronic signature of the rutile structure with pressure. Upon increasing pressure, EN, EB, q(O), and f (O) are found to decrease in a parallel way with the following decrements: 8EB = −2 eV, 8EN = −04 eV, and 8f (O) = −0015. Conversely, GH, GI, q(Ti), and f (Ti) are increasing functions of pressure with the following increments: 8GH = +003 eV, 8GI = +14%, and 8f (Ti) = +003. Note the mirror effect of pressure and temperature (cf. Fig. 21).

where dia is a diamagnetic contribution, 8E an average excitation energy, R the average value of the function a0 /r3  over the O-2p atomic orbital, q the electronic density around the nucleus, ; a parameter close to unity, and Pu an orbital contribution varying in a parabolic way with the atomic charge q. Referencing 17 O chemical shifts against water leads to the following relationship between screening constants and chemical shifts & [146]: &(17 O = 3240 − . The diamagnetic contribution may be evaluated directly from the crystal structure as [147]:  dia ppm = atdia q + 9393 × Z /r Å (15) 

Using Hartree–Fock–Slater wave functions, we can assume that for the 17 O nucleus atdia = 418 ppm, R = 503, and ; ∼ 1 [148, 149]. On the other hand, assuming isotropic p-orbital

Molecular Tectonics in Sol–Gel Chemistry

758

Table 1. Accuracy checking of theoretical rutile structures computed from first-principles methods against signature (11). Method esd NLPPMD PEG SCSPP SCSPP

Reference

EN

GH

GI

EB

q(Ti)

f (Ti)

q(O)

f (O)

Signature (2) [130] [131] [132] [133]

0.0047 4 32 47 62

0.0010 0 44 13 19

0.0185 3 21 43 57

0.0262 3 20 43 56

0.0007 4 22 46 60

0.0004 4 28 42 55

0.0004 3 19 40 53

0.0002 4 28 42 55

Note: SCSPP, self-consistent soft pseudo-potentials with LDA approximation; NLPPMD, nonlocal pseudo-potentials in molecular-dynamical density functional theory with LDA approximation; PEG, polarization-induced electron-gas model.

populations (Pxx = Pyy = Pzz ) and an s-orbital population close to 2 leads to Pu = 151 − qO − 12 /9] [85]. Now with qO = −081445 and 8E ∼ GH = 3046 eV for rutile [from signature (11)], Pu = 095127, (R + ;q = 42155, leading to &(rutile) = 324−7345−966×42155×095127/3046 = 861 ppm

(16)

Similarly, for anatase, qO = −08182 and 8E ∼ GH = 3120 eV [signature (13)], Pu = 094903, R + ;q = 42118, leading to &(anatase) = 324−7361−966×42118×094903/312 = 826 ppm

(17)

The ca + 270-ppm difference found between (16) or (17) and experimental chemical shifts reflects all the errors made by using atomic values for (R , ;) and approximate Pu

values. It also reflects the errors coming from the approximation 8E ∼ GH and from the deviation of signature (16) or (17) from experimental reality. With so many approximations in hand, finding values at 50% from experimental reality is by itself a very encouraging result. Moreover, assuming the same systematic errors between rutile and anatase leads to &(anatase)−&(rutile) = −35 ppm, which compares favorably with the −32-ppm experimental value. It may then be said that an increase in the global hardness difference of 0.074 eV between rutile and anatase is enough to explain to the 30-ppm shielding observed for the 17 O nucleus. Concerning the 47 Ti nucleus, the isotropic part of the shielding tensor may be written as iso ppm = dia ppm−966×R +;q×Du /8E eV (18) R is now the average value of the function a0 /r3  over the Ti-3d atomic orbitals (R = 2016343 a.u. and from Roothaan–Hartree–Fock atomic wave functions ; ∼ 063 [149]) with the population unbalance Du in titanium d orbitals approximated as [145]: Du ∼ 3P0 + P±1 + P±2  − 23 4P−2 P+2 + P0 P−1 + P+1  − 21 P−2 + P+2 P−1 + P+1  + P−1 P+1 

(19)

Here P0 , P−1 , P+1 , P−1 , and P−2 stand for populations of orbitals dz2 , dyz, dxz, dxy, and dx2 − y 2 , respectively. Assuming an empty 4s orbital, a t2g –eg splitting under an octahedral field (P−2 = P0 = 0), and an isotropic repartition of the (4 − qTi ) remaining electrons in the t2g set [P+1 = P−1 = P+2 = P = 4 − q/3] leads to Du ∼ P 9 − 3P /2 = 56 − qTi 10 + qTi /6. With atdia (Ti) = 1643 ppm [148], the absolute shielding of the titanium atom in the rutile phase (qTi = +16290 ⇒ Du = 6176, r −3  = 30426, and 8E ∼ GH = 3046 eV) may then be approximated as rutile = 18732 − 966 × 30426 × 6176/3046 = −4086 ppm

Figure 23. TiO2 anatase crystal structure (space group I41 /amd). (a) Local geometry at Ti and O sites and ball-and-stick view of the chemical bond patterns. (b) Topology of the cis edge sharing between TiO6 octahedra. (c) Topology of the 3D framework is evidenced as edge sharing between spiral octahedral chains.

(20)

On the other hand, for the absolute shielding of the titanium atom in the anatase polymorph (qTi = +16363 ⇒ Du = 6160 r −3  = 30472, and 8E ∼ GH = 3120 eV), it becomes anatase = 18742 − 966 × 30472 × 616/3120 = −3938 ppm

(21)

Molecular Tectonics in Sol–Gel Chemistry

759

According to these values, we predict that &anatase − &rutile = rutile − anatase ∼ −148 ppm, in reasonable agreement with the −195-ppm experimental value. As both 47 49 Ti and 17 O isotopes have nuclear quadrupole moments, it may be of interest to compare the electric field gradients in both structures. For the 17 O nucleus, experimental values are Vxx = +16 V Å−2 , Vyy = −238 V Å−2 , Vzz = +222 V Å−2 , 1Q = 089 in the rutile phase [151], 2 /31/2 = 15 and 1.1 MHz in and KQ = e2 Vzz Q/h1 + 1Q the rutile and anatase polymorphs respectively [144]. Let us now use signatures (11) and (13) with a Sternheimer antishielding factor 1 −   = 31 (adjusted value to reproduce the Vyy component of the rutile phase). We then predict Vxx = +190 V Å−2 , Vyy = −238 V Å−2 , Vzz = +48 V Å−2 , 1Q = 060 in the rutile phase (KQ = 166 MHz), and Vxx = −240 V Å−2 , Vyy = +229 V Å−2 , Vzz = +28 V Å−2 , 1Q = 090 in the anatase phase (KQ = 167 MHz). We are thus not able to explain the experimental 0.4-MHz decreases in the KQ of anatase relative to rutile. With reference to the general theory of the origin of electric field gradients [152], we may write: Vzz = 1 −

ext  Vzz

+ 1 − RVzzloc

Figure 24. Evolution of the electronic signature of the anatase structure with temperature. Upon increasing temperature, EN, EB, q(O), and f (O) are found to increase in a parallel way with the following increments: 8EB = +1 eV, 8q(O) = +0015, and 8f (O) = +0006. Conversely, GH, GI, q(Ti), and f (Ti) are decreasing functions of temperature with the following decrements: 8GI = −08% 8q(Ti) = −003, and 8f (Ti) = −0012.

(22)

Our failure to reproduce electric field gradient (efg) values may then be linked to the assumption that Vzzloc = 0. This just means that the local contribution that arises from the nonspherical filling of O-2p orbitals cannot be neglected in these phases. Similarly, concerning the efg at the 49 Ti nuclei, experiments [128] lead to Vxx = +86 V Å−2 , Vyy = +134 V Å−2 , Vzz = −220 V Å−2 , 1Q = 022 for the rutile phase (49 CQ = 139 ± 01 MHz, 1Q = 019 ± 01 [143]). For the anatase phase, 49 CQ = 479 ± 001 MHz, 1Q = 0 [143]. Using signatures (11), (13) and a Sternheimer antishielding factor 1 −   = 99 (adjusted value to reproduce the 49 CQ value of the anatase phase) leads to 49 CQ = 19 MHz, 1Q = 025 for the rutile polymorph. If the agreement on the 1Q value is good, the 9.1-MHz decrease observed on going from rutile to anatase is not reproduced. According to LAPW calculations, the very high CQ value of the rutile phase comes from the polarization of “semi-core” 3p orbitals [151], and it is thus not surprising that a model based on valence contributions failed in such a case. Consequently, our electronic signatures are able to explain on a semiquantitative basis chemical shift variations on all NMR-active nuclei, but fail to reproduce electric field gradients owing to the neglect of valence contributions and core polarization. It is then evident that, as in the case of silica polymorphs and in agreement with ab initio calculations, stoichiometry and local order (TiO6 octahedron and edge and/or corner sharing between octahedra) mainly govern charge distributions. Taking into account the long-range crystalline order (unit-cell repetition) leads only to rather small variations. As shown in Figure 24, the effect of temperature on the electronic signature of anatase is very similar to what has been found for the rutile structure. No pressure data appear to be available for this structure. Brookite This is the third natural form of titanium dioxide. Its orthorhombic structure is based on zigzag chains of edge-sharing octahedra that are further linked by sharing

corners to form a third type of 3D structure with 6 : 3 coordination (Fig. 25). As with the rutile structure, the idealized structure of brookite may be derived from hexagonal close-packed layers of oxygen atoms. However, in contrast with rutile, each TiO6 octahedron is in contact with nine other ones (three through edge sharing and six through corner sharing). Three refinements are available for this crystal structure [107, 153, 154], leading to the following electronic

Figure 25. TiO2 brookite crystal structure (space group Pbca). (a) Local C1 geometry at Ti and O sites. Atoms O1 and O2 are situated 8.8 pm and 8.3 pm, respectively, above the plane formed by the three Ti atoms. (b) Topology of the cis edge sharing between four TiO6 octahedra. (c) Topology of the 3D framework is evidenced as corner sharing between zigzag octahedral chains.

Molecular Tectonics in Sol–Gel Chemistry

760 signature: Global
EN = 5
919 ± 0
010 V e2
GH = 3
084 ± 0
008 eV
EB = −23
404 ± 0
013 eV
GI = 40
713 ± 0
009%

Local qTi = 1
6285 ± 0
0004
qO = −0
814 ± 0
006 f Ti = 1
1707 ± 0
0008
f O = −0
085 ± 0
005 (23)

The charge difference between the two crystallographically nonequivalent oxygen atoms being statistically insignificant, qO1 = −0813 ± 0004 and qO2 = −0816 ± 0004, only mean values have been reported in signature (23). The following electronic signature was computed from the best structural refinement available for this structure (R = 39% [107]): Global EN = 5914 ± 0022 V e2 GH = 3085 ± 0005 eV EB = −2343 ± 012 eV GI = 4073 ± 008%

Local qTi = 1629 ± 0003 qO = −0815 ± 0007 f Ti = 11711 ± 00017 f O = −0086 ± 0002 (24)

This shows that the rather low errors obtained in signature (23) come from the very limited set of data used (only 3) and thus cannot be considered as significant. This is not the case for signature (24) where averaging has been performed over 100 randomly generated structures. Brookite is, then, more electronegative and harder than rutile but less than anatase. It has, however, almost the same ionicity or electrostatic balance as rutile. To the best of our knowledge, a single band structure calculation has been performed for this crystal structure, using the orthogonalized LCAO method with the LDA approximation [139]. The results have shown very similar band structures and DOS and PDOS features among rutile, anatase, and brookite. This is in line with the close similarities of signatures (11), (13), and (24). According to these calculations, brookite should, however, have a direct band gap 0.42 eV higher than that of rutile and 0.16 eV higher than that of anatase [139]. Its static dielectric constant As = 789 should also be much higher than that of rutile exp exp = = 633) or anatase (Ath (Ath s = 604 and As s = 662 and As 562). This is not in agreement with the EN and GH parameters found for this polymorph, which suggests that brookite should have an electronic structure intermediate between rutile and anatase. Our result probably reflects the number of common edges found in these three phases that are rutile (two edges), brookite (three edges), and, finally, anatase (four edges). No 17 O-NMR data are available for brookite, but according to 47 49 Ti-NMR, this polymorph displays approximately the same chemical shift as rutile [143]. This experimental result would be very difficult to explain assuming a 0.4-eV band gap increase relative to the rutile polymorph. Assuming the same charge distribution in both phases would lead, according to (18), to brookite ∼ 18733 − 966 × 30426 × 6176/35 = −3313 ppm, that is, to a ca. 800-ppm shielding relative to rutile. Using signature (24) to compute the absolute shielding of brookite would predict brookite ∼ 18733 − 966 × 30426 × 6176/3085 = −4011 ppm, a much

more reasonable 75-ppm shielding relative to rutile and 63-ppm deshielding relative to anatase. Recent measurements have been made [155, 156], but the authors do not seem to agree on the reported values (brookite intermediate between anatase and rutile [155] and brookite more shielded than anatase [156]). Nevertheless, in both cases, chemical shift differences among the three polymorphs are found to be about 100 ppm, in good agreement with the above analysis. Concerning the electric field gradient at the titanium site, signature (24) would lead to 49 CQ = 29 MHz, 1Q = 054. This is a much lower value than in anatase and should be compared with the experimental values 47 CQ = 73 MHz [155], 49 CQ = 100 MHz [156], 1Q = 055 [155, 156]. Consequently, if the asymmetry parameter is well reproduced, problems remain with the absolute value of CQ as already noted for rutile and anatase. For 17 O nuclei, we would predict for the two crystallographically nonequivalent sites: &O1 = 846 ppm (15-ppm shielding from rutile), &O2 = 844 ppm (17-ppm shielding from rutile), CQ O1 = 154 MHz, CQ O2 = 144 MHz, 1Q O1 = 093 1Q O2 = 078. Experiments [156] have revealed a shielding of 12.5 and 44.5 ppm relative to rutile. Owing to the very similar partial charge on the O atom, one may conclude that the Pu contribution cannot be isotropic as assumed above (see Fig. 25 for a comparison of distortions around both sites). Brookite behaves exactly the same way as rutile or anatase concerning the variation of its electronic signature with temperature (Fig. 26). Again, as with anatase, no pressure data are available for this structure. TiO2 (B) This is a synthetic phase that may be obtained by proton exchange and subsequent dehydration of layered titanates having the formula A2 Tin O2n+1 (A = Na, K, Cs; 3 ≤ n ≤ 6) at temperatures below T = 350  C [157]. Above 550  C or by applying pressure (60 MPa at room temperature), this phase transforms into anatase [158]. Its monoclinic structure is very similar to that found for the covalent

Figure 26. Evolution of the electronic signature of the brookite structure with temperature. Upon increasing temperature, EN, EB, q(O), and f (O) are found to increase in a parallel way with the following increments: 8EB = +06 eV, 8q(O) = +0010, and 8f (O) = +0005. Conversely, GH, GI, q(Ti), and f (Ti) are decreasing functions of temperature with the following decrements: 8GI = −05% 8q(Ti) = −002, and 8f (Ti) = −0010.

Molecular Tectonics in Sol–Gel Chemistry

761

framework of the Nax Ti4 O8 bronze. It is based on double chains of edge-sharing octahedra, which are further linked by sharing corners to form a fourth type of 3D structure with oxygen atoms in fourfold, threefold, and twofold coordination (Fig. 27). In this structure, TiO6 octahedra are in contact either with nine other ones (four through corner sharing and five through edge-sharing for the Ti1 site) or with eight other ones (four through corner sharing and four through edge sharing for the Ti2 site). As with the anatase structure, the ideal structure of TiO2 (B) may be derived from a cubic close packing of oxygen atoms. In terms of ordered vacancies (
) within a NaCl-type network, anatase may be written as [Ti
][O2 ], whereas TiO2 -B may be written as [Ti4
5 ][O8
]. Only one crystal structure determination is available [156] leading to the following signature: Global EN = 615±033 V e2 GH = 332±028 eV EB = −235±10 eV GI = 409±06%

Local qTi = 163±016 qO = −082±011 f Ti = 115±013 f O = −008±013

(25)

The rather high errors reported for atomic coordinates explain the low accuracy of the reported signature. TiO2 (B) appears to be much more electronegative than anatase. If it also displays a high global hardness, its ionicity is found very close to that of other polymorphs. If the two symmetrically nonequivalent titanium atoms in the asymmetric cell are found to be not significantly different, this is not the case for oxygen atoms in twofold qO1[2 − Ti = −076 ± 007, and fourfold coordination, qO2[4 − Ti = −085 ± 003. Threefold coordinated oxygen atoms are very similar, qO3[3 − Ti = −083 ± 005 and qO4[3 − Ti =

−082 ± 002, and are not significantly different from O2. To the best of our knowledge, very few experimental and theoretical studies have been devoted to this phase. Table 2 shows the predicted NMR parameters for this phase if signature (25) is correct. TiO2 (R) This synthetic phase may be obtained after topotactic oxidation of the lithium titanate bronze Li05 TiO2 by acidic solutions of hydrogen chloride [159]. Its orthorhombic structure is based on double chains of edgesharing octahedra that are further linked by sharing corners to form a 3D structure similar to that of ramsdellite ( -MnO2 ) or of diaspore (-AlOOH) (Fig. 28). All oxygen atoms are found in threefold coordination with each TiO6 octahedron sharing four edges and four corners with eight other octahedra as in anatase. However, when heated above 640 K, TiO2 (R) transforms into brookite. As with the TiO2 (B) structure, only one crystal structure determination is available [159], leading to the following electronic signature: Global EN = 671 ± 004 V e2 GH = 3590 ± 0012 eV EB = −210 ± 02 eV GI = 3899 ± 018%

Local qTi = 1559 ± 0007 qO = −0780 ± 0024 f Ti = 1111 ± 0003 f O = −0055 ± 0013 (26)

TiO2 (R) appears, then, to be one of the most electronegative, hardest, and least ionic polymorphs of all the titanium oxides studied until now. Contrary to other titania polymorphs, there is a clear relationship between the network topology and the charge distribution. Concerning the two crystallographically nonequivalent oxygen atoms, they bear a very similar partial charge, qO1 = −0788 ± 0003 and qO2 = −0772 ± 0005, but they should be easily distinguished by 17 O-NMR. Taking rutile as the reference signature (26) would lead to &O1 = −165 ppm and &O2 = −150 ppm, with a very clear differentiation through the efg: CQ O1 = 148 MHz (1Q = 087) and CQ O2 = 058 MHz (1Q = 030). For 47 49 Ti-NMR, we predict a strong shielding of the titanium nucleus, &Ti = −851 ppm (rutile as the reference), with a rather large quadrupolar coupling constant, 49 CQ = 45 MHz and 1Q = 043. TiO2 (H) This synthetic phase may be obtained by topotactic oxidation of the potassium bronze K025 TiO2 [160]. Its tetragonal structure is based on the same double chains of edge-sharing octahedra found in TiO2 (R) but which are now further linked by sharing corners to form a 3D structure typical of the hollandite family (Fig. 29). The local environment of oxygen and titanium atoms in this structure is very similar to that found in TiO2 (R). All oxygen atoms are found Table 2. Theoretical predicted NMR parameters for the TiO2 (B) polymorph.

Figure 27. TiO2 (B) crystal structure (space group C2/m). (a) Local Cs geometry at all atomic sites. Atoms O3 and O4 are situated 0.0 pm and 0.9 pm, respectively, above the plane formed by the three Ti atoms. (b) Polyhedral view of the topology of the edge-sharing pattern between five TiO6 octahedra. (c) Topology of the 3D framework is evidenced as corner sharing between fused double octahedral chains.

Atomic site O1 O2 O3 O4 Ti1 Ti2 Charge q −0.7607 −0.8486 −0.8305 −0.8210 1.6071 1.6537 &/ppm (rutile) +46 −222 −122 −109 −459 −497 CQ (MHz) 2.4 1.2 1.8 1.5 1.6 3.2 1Q 0.04 0.17 0.71 0.96 0.51 0.66

762

Molecular Tectonics in Sol–Gel Chemistry

upon potassium removal, we have been able to compute the following electronic signature for this interesting phase: Global EN = 714 ± 005 V GH = 4517 ± 0012 eV EB = −211 ± 02 eV GI = 3908 ± 016%

Figure 28. TiO2 (R) crystal structure (space group Pbnm). (a) Local Cs geometry at all atomic sites. Atoms O1 and O2 are situated 4.1 pm and 93 pm, respectively, above the plane formed by the three Ti atoms. (b) Polyhedral view of the topology of the edge-sharing pattern between five TiO6 octahedra. (c) Topology of the 3D framework is evidenced as corner sharing between fused double octahedral chains.

in threefold coordination, with each TiO6 octahedron sharing four edges and four corners with eight other octahedra. However, contrary to TiO2 (R), heating TiO2 (H) above 410  C leads to the anatase polymorph and not to the brookite one. As with the TiO2 (B) and TiO2 (R) structures, only one crystal structure determination is available, involving some disordered potassium atoms [160]. Based on the assumption that the TiO2 framework would not be very much changed

Concerning the global ionicity, TiO2 (R) and TiO2 (H) are virtually indistinguishable. This result was foreseeable as both structures are built from the same double octahedral chains. The two structures are, however, completely different concerning the mean electronegativity and the global hardness, which display much higher values in TiO2 (H) than in TiO2 (R). This should mean that the NMR parameters of these phases should be completely different. Concerning the two crystallographically nonequivalent oxygen atoms, we get qO1 = −0766 ± 0005 and qO2 = −0796 ± 0002, leading to &O1 = −376 ppm and &O2 = −400 ppm (rutile as the reference). Nuclear quadrupolar coupling constants are expected to be very similar to those of TiO2 (R) with CQ O1 = 059 MHz (1Q = 021) and CQ O2 = 146 MHz (1Q = 081). For 47 49 Ti-NMR, the very high value found for GH means a very strong shielding of the titanium nucleus relative to the rutile phase, &Ti = −101 ppm. The nuclear quadrupolar coupling constant is expected to be much larger than in TiO2 (R), 49 CQ = 568 MHz, with a very low asymmetry parameter, 1Q = 002. TiO2 -II This metastable phase was first prepared from anatase, brookite, or rutile by heating at 450  C under 400 MPa [161]. It can also be prepared at room pressure by dissolving Ti3 O5 in sulfuric acid at elevated temperature (150–200  C) [162]. Upon heating at 600  C at atmospheric pressure, it transforms into rutile in a few hours. The phase boundary between rutile and TiO2 -II in a pressure– temperature diagram is not linear but changes from having a negative to having a positive slope with increasing temperature at about 6 GPa and 850  C [163]. TiO2 -II is isostructural with -PbO2 and displays zigzag chains of edge-sharing octahedra joined by common vertices to form a 3D structure with 6 : 3 coordination (Fig. 30). In this structure, each TiO6 octahedron is in contact with 10 other ones (2 through edge sharing and 8 through corner sharing). Two crystal structure refinements are available for this compound. Using the most recent one from X-ray powder diffraction (R = 25% [162]) leads to the following electronic signature: Global EN = 572 ± 002 V e2 GH = 2992 ± 0007 eV EB = −2361 ± 013 eV GI = 4086 ± 009%

Figure 29. TiO2 (H) crystal structure (space group I4/m). (a) Local Cs geometry at all atomic sites. Atoms O1 and O2 are situated 92.7 pm and 7.8 pm, respectively, above the plane formed by the three Ti atoms. (b) Polyhedral view of the topology of the edge-sharing pattern between five TiO6 octahedra. (c) Topology of the 3D framework is evidenced as corner sharing between fused double octahedral chains.

Local qTi = 1563 ± 0006 (27) qO = −078 ± 005 f Ti = 1078 ± 0003 f O = −004 ± 008

Local qTi = 1634 ± 0004 qO = −08172 ± 00018 f Ti = 11858 ± 00015 f O = −00929 ± 00008 (28)

This phase appears to be slightly less electronegative and slightly more ionic than rutile. Owing to its lower global hardness, this polymorph should appear deshielded relative to rutile, &17 O = +21 ppm and &47 49 Ti = +108 ppm. Asymmetric electric field gradients are expected at both sites, CQ 17 O = 141 MHz (1Q = 089) and CQ 49 Ti = 32 MHz (1Q = 035).

Molecular Tectonics in Sol–Gel Chemistry

Figure 30. TiO2 -II crystal structure (space group Pbcn). (a) Local geometry for Ti and O atoms. The O atom is situated 16.1 pm above the plane formed by the three Ti atoms. (b) Polyhedral view of the topology of the edge-sharing pattern between three TiO6 octahedra. (c) Topology of the 3D framework is evidenced as corner sharing between zigzag octahedral chains.

TiO2 -III At room temperature, rutile is stable up to 12 GPa, undergoing a direct transition to a structure displaying the same crystalline environment as ZrO2 (baddeleyite) [164], with titanium atoms in sevenfold coordination (Fig. 31). Upon the release of pressure, this baddeleyite-type phase converts to the -PbO2 -type polymorph. In this structure, the titanium atom is sandwiched between a square and a triangle of oxygen atoms defining a nonahedron. These nonahedra are linked into double sheets by sharing triangular edges. A dense stacking, through the remaining square edges, of these double sheets along the a axis leads to the 3D structure. Only unit-cell parameters are available for this phase [164]. However, it was possible to give an approximate electronic signature for this phase using the wellknown atomic positions for the zirconium compound [165]: Global EN = 4805 ± 0013 V e2 GH = 3230 ± 0006 eV EB = −2779 ± 007 eV GI = 4369 ± 004%

Local qTi = 1747 ± 0002 qO = −0874 ± 0040 f Ti = 12551 ± 00010 f O = −0128 ± 0033 (29)

This baddeleyite phase would thus be the most ionic and least electronegative of all the TiO2 polymorphs. Its global hardness should be close to that found for the TiO2 (B) polymorph. A shielding of the 17 O and 47 49 Ti nuclei relative to rutile is also anticipated. According to signature (29), a clear distinction between sites O1 (q = −08604 ± 00027 & = −132 ppm, CQ = 162 MHz, 1Q = 096) and O2 (q = −08869 ± 00016 & = −245 ppm, CQ = 069 MHz, 1Q = 069) is expected. The 113-ppm difference between both sites is well in line with the 77-ppm value found in

763

Figure 31. TiO2 -III crystal structure isostructural with baddeleyite (space group P 21 /c). (a) Seven-, three-, and fourfold coordination polyhedra for titanium and oxygen atoms. The O1 atom is situated 5.5 pm above the plane formed by the three Ti atoms. (b) Polyhedral view of the topology of the corner-sharing pattern within a single layer. (c) Topology of the 3D framework is evidenced as stacking of the layers displayed in (b).

ZrO2 –baddeleyite [144]. In 47 49 Ti-NMR a strong deshielding (+485 ppm) relative to rutile is expected with a moderately large efg, 49 CQ = 40 MHz (1Q = 029). Raman spectroscopy has shown that this baddeleyite phase may also be formed starting from the anatase polymorph between 13 and 17 GPa [166]. Between 4.5 and 7 GPa, anatase transforms into the -PbO2 network, while above 60 GPa, the baddeleyite polymorph seems to transform into a higher symmetry and coordination structure. As only one X-ray reflection is available for this new phase, its crystal structure remains unknown. General Discussion Using the previous results, we are ready to draw the electronegativity–hardness map [167] for all titania polymorphs (Fig. 32). Reading from left to right (increasing electronegativity), we find the following sequence of apparition: baddeleyite → rutile(P) → TiO2 (II) → rutile(T) → anatase → brookite → TiO2 (B) → TiO2 (R) → TiO2 (H). As can be seen in Table 3, this is virtually the order found by dividing the unit-cell volume V by the number of TiO2 formula units Z. The only exception concerns the phases TiO2 (B) and TiO2 (R). This correlation between EN and V /Z is easily explained by elementary quantummechanical considerations. Assuming that EN is a measure of the Fermi level of electrons −AF in the structure and treating a crystal as a three-dimensional box of volume V ∼ L3 filled with N electrons, we may write kF2 = 2E/L2 n2F = 2E/L2 n2x + n2y + n2z  = 3E 2 N /V 2/3 ⇒ AF =  2 /2me kF2 ∼ V −2/3

(30)

Molecular Tectonics in Sol–Gel Chemistry

764

Figure 32. Electronegativity–hardness map for titania polymorphs. Lines connecting points refer to the effect of changing pressure (rutile, TiO2 -II, and TiO2 -III) or temperature (rutile, anatase, and brookite). Labels B, R, and H refer to TiO2 (B), TiO2 (R), and TiO2 (H) networks, respectively.

Relation (30) tells us that −AF ∝ EN should decrease as V decreases in agreement with Figure 32 and Table 3. The inversion observed between TiO2 (B) and TiO2 (R) suggests that a crystal cannot always be assimilated to a box filled with electrons. The mode of linking of TiO6 polyhedra may thus have a nonnegligible effect (∼05 eV ∼ 50 kJ mol−1 ) on electronic parameters. Another sequence is found by reading the map from bottom to top (increasing chemical hardness): TiO2 (II) → rutile(T) → rutile(P) → anatase → brookite → TiO2 (B) ∼ baddeleyite → TiO2 (R) → TiO2 (H). Theoretically, this order should be related to the energy difference existing between the centers of gravity of valence and conduction band (average band gap). As chemical bonding studies in titania polymorphs have been mainly limited to rutile, anatase, and brookite, it is very difficult to check this point. Band structure calculations on rutile, anatase, and brookite structures lead to very similar DOS curves [139]. This is well in line with the very close charge distributions given above. Our review has, however, shown that the electronic structure of rutile, anatase, brookite, and TiO2 -II polymorphs should be quite different from that of TiO2 (B), TiO2 (R), TiO2 (H), or TiO2 -III. For rutile, anatase, and TiO2 -II, this Table 3. Classification of TiO2 polymorphs according to the volume occupied by one TiO2 formula unit (RTP means room temperature and pressure conditions). Phase

V Å3

Z(TiO2 )

V /ZÅ 3 

TiO2 (baddeleyite) TiO2 (II) Rutile (RTP) Brookite (RT) Anatase (RT) TiO2 (R) TiO2 (B) TiO2 (H)

10443 12233 6243 25684 13630 13716 28415 30749

4 4 2 8 4 4 8 8

2611 3058 3122 3211 3408 3429 3552 3844

result has been fully confirmed through Ti-2p and O-1s X-ray absorption studies [168]. For other polymorphs, experimental or theoretical data are still lacking. This review should then be considered as a very first step toward the characterization of chemical bonding in TiO2 polymorphs. In particular, it would have been interesting to extend this study to other rutile-based structures (M = Ti, Zn, V, Cr, or Ru with X = O or F) that have been fully investigated using FPLAPW calculations [169]. In view of Figure 32 and Table 3, there does not emerge a clear reason for the well-known thermodynamic stability of the rutile phase. Taking the full unit-cell volume V as an index of thermodynamic stability would lead to the correct identification of the most stable phase, that is, rutile, as it displays the smallest volume. However, one may also think that the volume occupied by one TiO2 formula unit V /Z would be a more logical choice, in which case the winner is the baddeleyite phase. Alternatively, most stable compounds are characterized by a large band gap (i.e., a high global hardness) and a low Fermi level (i.e., a high electronegativity), in which case the wheel turns in favor of TiO2 (H). This is in clear contrast with experimental data that show without any ambiguity that upon heating all polymorphs are transformed into the rutile phase. Similarly, upon release of pressure, TiO2 -II and TiO2 -III are again transformed into rutile. Experiments also show that at low temperature the rutile phase is seldom obtained and that most syntheses end up with the anatase network. Other polymorphs are usually obtained only under carefully controlled conditions or by increasing the pressure. Unfortunately, after a comprehensive review of the literature devoted to this stability problem, we have not been able to find a reasonable explanation for the dominant position of the anatase and rutile structures over other polymorphs. Worse, we have been faced with the puzzling glass paradox when we have tried to introduce entropy considerations. Accordingly, most thermodynamic textbooks state that, for a perfect crystal at T = 0 K, the absolute entropy S should be equal to 0 (Nernst theorem or third law of thermodynamics). From this principle and from the second principle stating that the entropy should be a positive quantity, it directly follows that, for any structural motif, a disordered arrangement (glass) should always have a higher entropy than a wellordered one (crystal). For example, let us call Sc the entropy of a 3D network like that of -quartz (crystal displaying a Dirac distribution of Si O Si bond angles). Similarly, let us call Sg the entropy of a static disordered array having an equivalent number of corner-sharing SiO4 tetrahedra (glass displaying a Gaussian distribution of Si O Si bond angles). According to the third law of thermodynamics, Sg > Sc , meaning that, for the transformation crystal → glass, we should have 8S = Sg − Sc > 0. Now, for any spontaneous process to occur, we must have a decrease in the Gibbs free energy, that is, 8G = 8H − T × 8S < 0. Consequently, if we want to avoid this “spontaneous” transformation, we must have 8G > 0, that is, 8H > T × 8S. Here lies the glass paradox. At the left of this inequality, we have a finite quantity, 8H, which can be either positive (endothermic process) or negative (exothermic process), as it depends on the way chemical bonds are rearranged during the transition. At the right, the situation is completely different as we have a

Molecular Tectonics in Sol–Gel Chemistry

strictly positive quantity, T × 8S (T > 0 8S > 0 according to established thermodynamic principles), which has absolutely no limits owing to its temperature dependence. Consequently, if at low temperature the crystal is in the stable thermodynamic state (8G > 0 because 8H > T × 8S), there will nevertheless always exist a finite temperature allowing the spontaneous disappearance of the crystalline order. In other words, if you start from a crystal and increase the temperature very slowly (to maintain equilibrium conditions at any time), you should always get a glass before fusing the sample! The amazing thing is that in the real world, to make a glass, you never proceed like that. First, you have to go to the liquid state and then quench your system very rapidly in order to avoid spontaneous crystallization. Moreover, even if you have succeeded to get a glass from a given material, it will be very hard to avoid crystallization between Tg and fusion. Obviously, Nature tells us that a crystal is more stable than a glass and that our starting theorem S = 0 for a perfect crystal should be urgently revised. Fortunately, if we switch to information theory [170–172] (Fig. 33), such a paradox is easily avoided. As a crystal is always more symmetric than a glass, one must have Sc > Sg , leading to a complete reversal of the above inequalities. With this more correct definition, an entropy increase is always correlated with an information loss or an increase in symmetry. Glasses, being less symmetric than crystals, are then systematically devitrified as soon as the temperature is raised, and if you want to obtain them, you have to be very clever in order to avoid crystallization. With the help of Figure 33, all we have to do is to compare the space-group orders of the eight TiO2 polymorphs. Moreover, as it is always possible to choose a primitive cell for describing a crystal structure, we can drop the Bravais symbol (A B C I F R) and focus on the remaining symmetry elements. The result is rutile = anatase (16) > brookite = ramsdellite = hollandite = TiO2 -II 8 > bronze = TiO2 -III (4). One may also use the number of refined parameters needed to obtain the atomic coordinates from the X-ray diffraction pattern to get a better discrimination, which becomes rutile = anatase (3) < TiO2 -II (7) < hollandite (8) < ramsdellite (9) < brookite (12) < TiO2 -III 13 < bronze (16). The situation is now perfectly clear. Rutile and anatase are the phases that display the lowest information content and thus the highest entropy. Consequently, at sufficiently high temperature, all other polymorphs are expected to end up in one of these two phases. To differentiate between these two polymorphs, one must go a step further by looking at the local symmetry elements. For rutile displaying D2h local symmetry for Ti atoms, eight and three bond angles are fixed by symmetry to be equal to 90 and 180 , respectively. Consequently, the full description of the TiO6 octahedron is achieved by the specification of just one arbitrary bond angle F, the three remaining ones being F and 2180 − F by symmetry. The situation is quite different in anatase with D4 symmetry for Ti atoms. Here, the full description of the TiO6 octahedron requires the specification of at least three bond angles F, G, and H, the 12 other bond angles being 180 , F, 3G 3H, and 4180 − H) by symmetry. As less information is required to describe the TiO6 octahedron in rutile, this last phase should have higher entropy than anatase. The anatase phase should then also

765

Figure 33. Relationships between entropy, symmetry, information, and thermodynamic stability. From the differential of the Gibbs free energy, dG = V dP − S dT < 0, it follows that any kind of matter will try to reduce its volume V and increase its entropy S after an increase in pressure and temperature, respectively. According to the fundamental  equation of information theory, S = −k i pi ln pi . In this relationship, k is the Boltzmann constant and pi is the probability of the occurrence of a microstate compatible with a set of macrovariables E N  V  T  P   and such that i pi = 1. From this definition, it follows that if the permutation symmetry is maximum (i.e., all the W possible microstates are degenerate in energy), then pi = 1/W and S = L = k ln W . Now, for a system to hold some information, an energetic difference between the various microstates is required. It then follows that the amount of information I contained in any material system displaying W microstates should be given by I = k ln W − S, where S denotes the entropy. A good rule of thumb to judge the entropy level of a material system is then to look at the group order G of all its symmetry elements. For a glass G = 1 (just identity as the symmetry element), entropy should be at a minimum and information at its maximum (about 1023 x y z triplets to describe the structure). On the other hand, a dilute gas G displays a fivefold infinity (most symmetric continuous group for translations, rotations, and reflections). As S = L, the information content here is I = 0 (full ignorance of the 1023 x y z triplets). With this diagram, it becomes obvious that, upon increasing the temperature, a glass should crystallize, a crystal should melt (with or without mesophase formation), and a liquid should vaporize. The amazing point is that most thermodynamic textbooks make no distinction between static disorder (glass) and dynamic disorder (gas), with the consequence that S is assumed to be 0 for a perfect crystal (Nernst theorem). This misconception leads to the “glass paradox” described in the text.

be transformed into rutile upon heating in agreement with experiments. After rutile and anatase, the phase that should display the highest entropy is TiO2 -II. The fact that this phase could be chemically synthesized without pressure is nice evidence of its good thermodynamic stability at moderate temperature [162]. The case of brookite deserves special attention. It is well known that this phase can be obtained only under hydrothermal conditions starting from aqueous solutions [173–175] or from organic solutions [176–179]. The rather low symmetry of brookite could help to explain the difficulty in obtaining it not mixed with rutile or anatase. Exactly the same conclusion may be drawn from the fact that at high pressure and temperature one obtains the TiO2 II polymorph rather than brookite. Similarly, at room temperature and above 12 GPa, rutile transforms directly into TiO2 -III (baddeleyite) and not into brookite. This clearly

766 shows that under a physical constraint low-symmetry phases may be obtained if they minimize their unit-cell volume. Consequently, the occurrence of the brookite phase cannot be related to the pressure increase coming from the use of hydrothermal conditions. It should rather be explained by the presence of a chemical constraint providing the necessary negative enthalpic contribution to overcome the loss of entropy relative to rutile or anatase. For example, structural defaults in the form of uncondensed Ti OH groups may be responsible for the stabilization of brookite. Similar considerations obviously apply to the TiO2 polymorphs (B, R, and H) synthesized after proton exchange and moderate heating of alkali-containing titanates. It may well be that in all these phases the true stoichiometry is not TiO2 but rather XA TiO2 . The foreign species X should then be responsible, through the introduction of structural defaults, for the stabilization of a particular network over that of rutile or anatase. The fact that TiO2 (R) transforms upon heating into brookite, a phase of lower symmetry, is also strong evidence that negative enthalpic contributions not linked to the TiO2 stoichiometry are lurking around.

2.3. Titanium Dioxide in Materials Chemistry In this section, we present a brief overview of the practical and potential applications of purely inorganic materials based on titanium oxides. The case of hybrid organic– inorganic materials will be treated after the section devoted to titanium(IV) coordination chemistry.

2.3.1. White Pigments One of the most important aspects of TiO2 compositions lies in their chemical inertness, associated with their nontoxicity to living matter. This nontoxicity has led, for example, to the replacement after 1920 of all previously used white pigments [ZnO, 2PbCO3 ·Pb(OH)2 , ZnS·BaS] by TiO2 owing to its large refraction index under the rutile (2.7 at 590 nm) or anatase (2.55 at 590 nm) form. These values are among the highest for a transparent inorganic material (e.g., diamond, ZnS, ZnO, and NaCl are characterized by 2.45, 2.38, 2.2, and 1.54). Moreover, as they are associated with a high reflectivity (a prerequisite for efficient light scattering), one may anticipate that TiO2 is a very attractive optical material. All these properties come, in fact, from a rather wide band gap (3.2 eV) [119], high enough to lead to transparent materials but low enough to provide a highly refractive solid medium. Since 1920, all white commercial materials (paints, plastics, paper, fabrics, rubber, pharmaceuticals, etc.) have been mainly of the rutile form (85%) and sometimes of the anatase form (15%). To fix the ideas, about 60% of the total production is devoted to paints, the remaining being equally distributed among plastics, papers, and fabrics. At an industrial scale, two processes are used. The older one involves leaching of poor ilmenite minerals (less than 60% TiO2 ) by sulfuric acid at moderate temperature (around 200  C). After thermolysis of the resulting solution at 110  C for several hours, the resulting precipitate is fired at 1000  C [180]. If no rutile seeds are added prior to heating, one ends up with the anatase polymorph [181, 182]. The growth mechanism of the anatase particles under such conditions has been well studied [183–186]. Alternatively, one may use

Molecular Tectonics in Sol–Gel Chemistry

hydrochloric acid as a leaching agent and add sulfate or fluoride anions to control the structure, size, and shape of the resulting particles [187, 188]. Around 1960, a new process was proposed involving carbochloration between 800 and 1000  C of ilmenites containing more than 60% TiO2 , giving rise to the formation of titanium chloride: TiO2 + 2C + 2Cl2 → TiCl4 ↑ + 2CO↑. TiCl4 may then be reacted with dioxygen above 1400  C to yield only the rutile polymorph: TiCl4 + O2 → TiO2 ↓ + 2Cl2 ↑. As a matter of fact, a direct interesting consequence of this is the easy detection of paint forgeries. If anatase is detected, the picture was probably painted between 1920 and 1953; if rutile is present, the picture cannot be older than 50 years. If TiO2 is not detected, the picture was surely painted before 1920. As a dense nonporous material, synthesis of bulk titania is also interesting for making high-refractive-index coatings on silica glasses [189]. The most striking feature of these coatings deposited from organic solutions is that their optical properties are dependent on the type of glass substrate. Thus, on alkalifree substrate, the anatase polymorph is always obtained, while, on a soda glass, a mixed Na2 O·xTiO2 phase is formed [189]. The organic precursor is also important as Ti(OEt)4 leads to anatase at a temperature as low as 150  C [190], while a TiCl2 (OEt)2 solution leads to brookite [189]. The addition of a mineral acid such as HNO3 or HCl [190] or of diethanolamine [191] has been described to obtain clear solutions from Ti(OEt)4 or Ti(OPri )4 precursors.

2.3.2. Photocatalysts and Gas Sensors It has long been recognized that an inherent drawback in the application of TiO2 in coatings is the “chalking” effect resulting from photoredox processes at the pigment surface [192]. Interestingly enough, these parasite reactions can be used to design efficient photoelectrochemical [193] cells or new photocatalysts [194] for the destruction of both organic and inorganic pollutants. For example, photocatalytic activity may be linked to the creation of active radical centers following generation of photocarriers that are able to perform interfacial redox processes. A good example of such a photocatalytic activity is provided by TiO2 thin films prepared by dip coating from Ti(OPri )4 dissolved in -terpineol in the presence of acetylacetone and acetic acid [195]. After calcination at 450  C for 1 h, 1-m-thick films of anatase were obtained that were able to perform the photooxidation of nitric oxide (1 ppm concentration) into nitrate ions NO− 3 under dry air conditions. Another example concerns the photocatalytic oxidation of organic pollutants during water treatment using TiO2 -based nanostructured sol–gel coatings [196]. It is noteworthy that anatase displays a far higher photocatalytic activity than rutile [197] and that the photoluminescence of anatase is quite different from that of rutile [192]. Consequently, the complete photoelectrolysis of water to H2 and O2 is thermodynamically possible on anatase only [198]. This stresses again the importance of controlling the anatase-to-rutile transformation, as rutile is desired for paints whereas anatase is preferred for photocatalysts. The presence of brookite, known to catalyze the anatase → rutile transformation, and the crystallite size (the bigger, the more stable) seem to be the key factors ruling the transition in the absence of doping ions [197].

Molecular Tectonics in Sol–Gel Chemistry

Closely related applications concern the elaboration of gas sensors for environmental purposes. It has been reported that nanosized TiO2 thin films were able to detect 20 ppm of NO2 at a temperature suitable for monitoring of exhaust gases from engines [199]. Undoped anatase thin films were also reported to display rapid responses to O2 , H2 , and ethanol [200]. Similarly, nanostructured thick films elaborated via screen-printing technology from sol–gel-derived anatase powders may be used for atmospheric pollutant monitoring such as carbon monoxide [201]. In all these applications, the thickness uniformity of these films should be very precisely controlled. Consequently, special coating techniques have been developed for that purpose such as atomic layer epitaxy using Ti(OR)4 (R = Et, Pri ) [202, 203] or TiCl4 [204] in the presence of water. Notice that a 2D sol–gel process has also been developed for the synthesis of oxide semiconductor nanofilms [205]. Accordingly, using the Langmuir–Blodgett technique and titanium butoxide, it was possible to form ultrathin TiO2 nanofilms exhibiting the quantum size effect [205]. However, care must be taken in the use of variations of optical properties of many forms of TiO2 -derived compounds as a straightforward probe of the particle size [206]. Finally, a very promising property of TiO2 surfaces is their amphiphilic character (both hydrophilic and oleophilic) upon ultraviolet irradiation, leading to antifogging and self-cleaning coatings [207]. The proposed explanation for such a remarkable fact lies in the creation of surface oxygen vacancies at bridging sites upon ultraviolet irradiation. This results in a conversion of relevant Ti4+ sites to Ti3+ sites that are more favorable for dissociative water adsorption. Consequently, without irradiation, the surface is completely hydrophobic, displaying contact angles with water of 72 ± 1 . After irradiation, hydrophilic domains surrounding the photogenerated defects appear, allowing the complete spreading of water droplets (contact angles of 0 ± 1 ) onto the surface. Self-cleaning properties are intimately linked to this amphiphilic character.

2.3.3. Photovoltaics Titanium oxide is also found at the very heart of dyesensitized solar cells, which provide a technically and economically credible alternative to present-day p–n junction photovoltaic devices [208–210]. Hydrothermal syntheses are here ideally suited to obtain the active nanocrystalline TiO2 colloids. A widely used method starts from TiCl4 or Ti(OR)4 precursors that are hydrolyzed under acidic (HNO3 , HCl, or MePhSO3 H) and moderate heating (60– 230  C) conditions [156, 211–213]. It was also reported [214, 215] that switching to base hydrolysis with tetramethylammonium hydroxide (Me4 NOH) allowed good control over the crystal structure, size, shape, and organization of TiO2 nanocrystals. Self-assembling processes of these nanocrystals into superlattices may then be exploited, leading to highly structured titania films [215]. In this process, it was also shown that the use of carboxylate-modified titanium alkoxides displaying a higher information content than unmodified alkoxides significantly influenced the final size and size distribution of the nanocrystals [216]. The transition from amorphous gels to the crystalline state in these systems was

767 followed by 47 49 Ti-NMR [156, 217] and 17 O-NMR [218] techniques. Quantification of the rutile-to-anatase ratio was thus possible [156], whereas detection of (3 -O, 4 -O) as core species and of (3 -O, 2 -O, Ti OH, Ti OH2 , Ti OR) as surface species was reported [217, 218]. Concerning the Ti atoms, XANES spectra are consistent with fivefold coordinated surface species in these nanocrystals. They have also confirmed that apparent band gaps do not vary in a simple way with particle size [219]. One may also notice that nonhydrolytic solution-based reactions involving [TiCl4 , Ti(OR)4 ] or (TiCl4 , R2 O) mixtures may also lead to the formation of TiO2 nanocrystals [220]. The underlying chemistry of these nonhydrolytic sol–gel routes has been reviewed [221]. Self-organized nanocrystalline anatase films are also prospective electrode materials for 2-V lithium ion batteries due to their convenient formal potential around 1.8 V (Li/Li+ ) [222]. Owing to the following insertion–extraction process TiO2 (s) + xLi+ + xe− = Lix TiO2 (s) with x < 05, the specific capacity of TiO2 -based electrodes is 170 mA h g−1 , allowing the realization of electrochromic devices [223] and of new types of intercalation batteries [224].

2.3.4. Ceramics Titania nanoparticles are also widely used for the preparation of ceramic-based microporous membranes [225] and are able to decrease significantly the sintering temperature of titania ceramics [226–228]. The mechanism of nucleation and growth of these nanoparticles has been studied for both Ti(OEt)4 [229] and Ti(OPri )4 [230] hydrolysis. With titanium tetraethoxide, it was shown that vnucl = k[H2 O]3 [Ti(OEt)4 ]−1 , the last ethoxy group being lost during growth [229]. With titanium isopropoxide, hydrolysis seems to be complete at low water concentration, resulting in the creation of nanosized nuclei [230]. Moreover, as the total mass of the nuclei seems to be conserved during the precipitation process, particle growth should involve nucleus aggregation. This difference in growth mechanism may explain why monodispersed powders are easily obtained with Ti(OEt)4 , while polydispersed powders are formed with Ti(OPri )4 . The PCM has been applied to this system and helps to explain these differences at the molecular level [231]. Interestingly enough, supercritical drying of titania gels [232] leads to highly porous aerogels based on a framework of connected fractal aggregates [233, 234]. These materials provide good supports for catalysis purposes. They may also be used as adsorbents or as thermal and phonic insulators [232] and are particularly useful for commercial applications in the elaboration of soft abrasives or of solar screens for cosmetics. With a melting point above 1800  C, TiO2 is also an attractive material to make protective coatings. Accordingly, in deep contrast with other transition metal alkoxides, the output of titanium alkoxides by the chemical industry can be reckoned in tons per annum. The origin of this remarkable difference may be traced back about 50 years ago when it was demonstrated that titanium butoxide could be used in making coatings stable for prolonged periods at 600  C (heat-resistant paints) [235]. Another application linked to this good thermal stability is refractory fiber drawing from solutions containing Ti(OPri )4 –H2 O–EtOH–HCl [236].

768

Molecular Tectonics in Sol–Gel Chemistry

2.3.5. Mixed SiO2 –TiO2 Oxides

2.3.6. Barium Titanate

We now focus our attention on some mixed systems based on TiO2 materials. In this field, titanium alkoxides are frequently used in conjunction with other metal alkoxides to get very useful multicomponent oxide materials. For example, interesting compositions are found in the SiO2 –TiO2 binary system. Below 10 wt% TiO2 , one may get ultralow thermal expansion SiO2 –TiO2 glasses. Such compositions may be readily prepared from Ti(OPri )4 –Si(OEt)4 –EtOH– HCl–H2 O mixtures [237]. Above 10 wt%, alkali-resistant SiO2 –TiO2 fibers may be directly drawn from these solutions [238]. Finally, using similar compositions, 30- to 95-mol% TiO2 amorphous oxide films can be obtained that display a refractive index ranging from 1.63 to 2.17, allowing the elaboration of antireflective coatings for silicon solar cells [239]. In catalysis, TiO2 –SiO2 systems are active compositions for acid-catalyzed reactions such as phenol amination, ethene hydration, butene isomerization, cumene dealkylation, 2propanol dehydration, and 1,2-dichloroethane decomposition [240]. The essential problem in the elaboration of these mixed SiO2 –TiO2 materials is the homogeneity of component mixing at the molecular level. Since Ti and Si alkoxide precursors do not hydrolyze at the same rate, small titania-rich domains may be formed in the mixed oxides [240]. Consequently, some fundamental studies have been devoted to the real chemical species that may be found in solutions after mixing Si(OR)4 with Ti(OR)4 with or without the addition of water. Concerning the possible transesterification reaction between both alkoxides in the absence of water Si(OEt)4 + Ti(OPri )4 → Si(OEt)4−x (OPri )x + Ti(OPri )4−x (OEt)x , it was shown using multinuclear NMR and X-ray absorption techniques that possible x values were mainly dependent on the relative ratio of the reactant [241]. For Si/Ti = 1, all possible species were detected and it was shown that the substitution of isopropoxy groups by ethoxy groups in the monomeric Ti(OPri )4 leads to the formation of oligomeric species Ti(OPri )4−x (OEt)x displaying pentacoordinated Ti atoms. The direct formation of Si O Ti bonds upon hydrolysis may be clearly evidenced using 17 O-NMR and seems to be favored when the alkoxide is added to a prehydrolyzed solution of tetraethoxysilane [242, 243]. Moreover, a careful study of molecular compounds has established the main spectroscopic features of such Si O Ti bridges [244]. By reference with wellknown Si O Si bridges characterized by NMR parameters &(Si O Si < 100 ppm, CQ (Si O Si > 40 MHz, it was found that CQ (Si O Ti) < 4.0 MHz, &(Si O TiO5  > 300 ppm, and &(Si O TiO3  > 200 ppm [244, 245]. The lowering of the quadrupolar constant is thus consistent with a more ionic Si O Ti bond, while the deshielding observed would be coherent either with a more anisotropic charge distribution in the p orbitals of O atoms or with a reduced HOMO–LUMO gap. Owing to the large deshielding observed and to the fact that Ti atoms have low-lying empty d levels, this last contribution seems more plausible. Concerning titanium atoms, an EXAFS study has shown that, for Ti contents below 10 mol%, Ti atoms were found in fourfold coordination, whereas, above 40 mol%, a majority of them were found in sixfold coordination [246]. At intermediate compositions, the TiO6 /TiO4 was found to increase with the TiO2 content and decrease upon increasing the temperature.

When TiO2 is mixed with an alkaline earth oxide (MgO, CaO, SrO, BaO) or with lead oxide (PbO), a wide array of ferroelectric, piezoelectric, and pyroelectric materials are obtained which may be structurally characterized by solidstate multinuclear NMR techniques [247]. The most studied one is obviously barium titanate (BaTiO3 ) owing to its high permittivity (K ∼ 6000 at 25  C for 0.7- to 1-m grain size), explaining its widespread use in ceramic multilayer capacitors [248]. At an industrial scale, BaTiO3 is prepared either by firing BaCO3 and TiO2 around 1000–1200  C or through the thermal decomposition above 800  C of barium titanyl oxalate salts (BaTiO[C2 O4 ]2 · 4H2 O) [248]. However, finely divided (5–15 nm) stoichiometric BaTiO3 agglomerated powders can be readily prepared at a temperature as low as 50  C after hydrolysis in isopropanol or benzene of an equimolar mixture of Ba(OPri )2 and Ti(OAmt )4 [249]. Consequently, there has been intensive research into the synthesis of mixed (Ba, Ti) alkoxides, which has led to the characterization of several complexes. One of the first isolated species, BaTiO(OPri )4 · 7/8Pri -OH, was obtained after refluxing Ba metal in a solution containing Ti(OPri )4 and isopropanol [250]. Two crystallographically different tetrameric bimetallic oxoalkoxides have been identified in the crystal structure of this compound [250, 251]. The first tetramer may be formulated as Ba4 Ti4 (4 -O)4 (3 -OPri )2 (OPri )8 (OPri )6 (Pri OH)4 (Fig. 34a) and is characterized by a distorted cube with alternating barium atoms and oxo groups. It may also be viewed as a [(Pri OH)Ba]4 tetrahedron capped on all its faces by fivefold coordinated TiO(OPri )4 groups. The second tetramer has a very similar structure (Fig. 34b) but should be formulated as Ba4 Ti4 (4 -O)4 (3 OPri )2 (-OPri )10 (OPri )4 (Pri OH)3 ]. Such a complex may also be obtained alone by reaction between barium and titanium isopropoxide (1 : 1 ratio) in the presence of toluene and acetone [252]. Similarly, for Ba(OEt)2 : Ti(OEt)4 = 1 : 2 in ethanol, the compound [Ba(OEt){Ti2 (OEt)9 }] · 5EtOH was isolated displaying the characteristic [Ti2 (OR)9 ]− building block made of two TiO6 octahedra sharing one face (Fig. 34c) [251, 253]. The same [Ti2 (OR)9 ]− building block was also evidenced in the complex Ba[Ti3 (3 -OPri )2 (2 OPri )5 (OPri )7 ] obtained with Ba(OPri )2 : Ti(OPri )4 = 1 : 3 in isopropanol/toluene solutions (Fig. 34d) [254] and in the complex Ba[Ti2 {(3 -OEt)(2 -OEt)3 (OEt)4 }2 ]2 obtained with Ba(OEt)2 : Ti(OEt)4 = 1 : 4 in ethanol (Fig. 34e) [253]. In all cases, the [Ti2 (3 -OR)2 (2 -OR)3 (OR)4 ]− unit was found to behave as a tetradentate ligand toward Ba2+ ions. On the other hand, two kinds of octahedral dimers, [Ti2 (-OMe)2 (OMe)8 ]2− (edge sharing) and [Ti2 O(-OMe)3 (OMe)5 ]2− (face sharing), have been characterized in the reaction product [Ba(MeOH)2 ][Ba(MeOH)5 ] [Ti2 O(OMe)8 ] [Ti2 (OMe)10 ]2 ·MeOH of Ba(OMe)2 with Ti(OMe)4 in a 1 : 2 ratio in methanol solutions (Fig. 34f) [255]. Interestingly, for the very similar Ca(OR)2 –Ti(OR)4 – ROH system, only one complex, [Ca{Ti2 (OR)9 }2 ], could be identified [253]. The transferability of the [Ti2 (OR)9 ]− building block to more complex ternary systems is also possible, as evidenced in the molecular structure of [{Cd(OPri )3 } Ba{Ti2 (OPri )9 }]2 (Fig. 34g) obtained by reaction between ICdTi2 (OPri )9 and KBa(OPri )3 in toluene [256].

Molecular Tectonics in Sol–Gel Chemistry

Figure 34. Crystal structures of some mixed barium–titanium(IV) alkoxides. (a) Fivefold coordination for Ti atoms in the molecular structure of tetrakis(4 -oxo)-bis(3 -isopropoxo)-octakis(2 -isopropoxo)-hexakis(isopropoxy)-tetrakis(isopropanol)-tetra-barium-tetra-titanium. (b) Fivefold coordination for Ti atoms in the molecular structure of tetrakis(4 -oxo)-bis(3 -isopropoxo)-decakis(2 -isopropoxo)-tetrakis(isopropoxy)-tris(isopropanol)-tetra-barium-tetra-titanium. (c) Face-sharing octahedral coordination for Ti atoms in the crystal structure of bis(3 -ethoxo)-tris(2 -ethoxo)-tetraethoxy-tetrakis(ethanol)-barium-dititanium(IV) ethoxide ethanol solvate. (d) Mixed (octehedral, trigonal bipyramidal) coordination for Ti atoms in the crystal structure of bis(3 -isopropoxo)-pentakis(2 -isopropoxo)-heptaisopropoxy-bariumtri-titanium. (e) Face-sharing octahedral coordination for Ti atoms in the crystal structure of bis[bis{(3 -ethoxo)-tris(2 -ethoxo)-tetraethoxy}-dititanium(IV)]-barium. (f) Mixed octahedral coordination for Ti atoms in the crystal structure of hexakis(3 -methoxo)-(3 -oxo)-bis(2 methoxo)-decakis(methoxy)-hepta(methanol)-di-barium-tetra-titanium di-methanol solvate. (g) Face-sharing octahedral coordination for Ti atoms in the crystal structure of bis[bis(3 -isopropoxo)-hexakis(2 isopropoxo)-tetrakis(isopropoxy)-barium-cadmium-di-titanium] toluene solvate.

The formation of BaTiO3 precursors is obviously not limited to bimetallic oxoalkoxides. Preparation of barium titanyl oxalate, BaTiO(C2 O4 )2 · 5H2 O, has thus been described from aqueous solutions containing barium nitrate and ammonium titanyl oxalate [257]. As already observed for other oxalates, the molecular structure of this complex is based on eight-membered Ti O rings composed of two pairs of nonequivalent [TiO(C2 O4 )2 ]2− moieties, which are related by an inversion center (Fig. 35a). Similarly, preparation of barium titanium citrate, BaTi(C6 H6 O7 )3 ·6H2 O, has been described in the literature [258], but the detailed molecular structures of this complex remain largely unknown. This is not the case for barium titanium glycolate, BaTi(C2 H4 O2 )3 · 4C2 H6 O2 · H2 O, that has been prepared by reaction between ethylene glycol, BaO, Ti(OPri )4 , and isopropanol [258]. As shown in Figure 35b, the structure may be described using two building-block units: a monomeric octahedral tris(glycolate) complex, [Ti(OCH2 CH2 O)3 ]2− , H-bonded to a nine-coordinate Ba atom [Ba(HOCH2 CH2 OH)4 (OH2 )]2+ .

769

Figure 35. Molecular structures of organometallic precursors of barium titanate (BaTiO3 ). (a) Tetrameric octahedral coordination in the crystal structure of barium titanyl oxalate pentahydrate. (b) Monomeric octahedral coordination in the crystal structure of aqua-tetrakis (ethylene glycol)-barium tris(ethylene glycolato)-titanium(IV). (c) Monomeric octahedral coordination in the crystal structure of tetrakis[(3 -phenoxo)(2 -phenoxo)-(phenoxy)-(dimethylformamide)]- di-barium-di-titanium dichloroethane solvate. (d) Monomeric octahedral coordination in the crystal structure of bis[(3 -ethoxo)-bis(2 -ethoxo)-bis(2,2,6,6tetramethylheptandionato-O,O ′ )-(ethoxy)-(ethanol)-barium-titanium].

Another kind of BaTiO3 precursor could be obtained by reacting barium metal with phenol and Ti(OPri )4 [259]. Recrystallization from DMF/Et2 O mixtures leads to a complex displaying the [BaTi(OC6 H5 )6 (DMF)2 ]2 stoichiometry with Ti atoms in octahedral coordination and Ba2+ ions adopting a bicapped trigonal prismatic coordination (Fig. 35c). A last precursor, Ba2 Ti2 (thd)4 (3 OEt)2 (-OEt)4 (OEt)2 (EtOH)2 , may be obtained by reacting Ti(OEt)4 with Ba(thd)2 (thd = 2,2,6,6-tetramethylheptane3,5-dione) in hexane [260]. This structure is built from neutral, centrosymmetrical, and tetranuclear units with a rhombus-shaped Ba2 Ti2 O6 core that are preserved in solution (Fig. 35d). The geometry is octahedral for titanium and monocapped trigonal prismatic for the Ba2+ ions. Obviously, if all these complexes lead to BaTiO3 powders upon hydrolysis and/or calcination, they should nevertheless promote different microstructures in the final powders.

2.3.7. Strontium and Lead Titanate Closely related to BaTiO3 is strontium titanate (SrTiO3 ), which may be used as a substrate for the deposition of hightemperature oxide superconductors, as symmetrical, voltagedependent varistors, and in many electronic devices, relays, and switching transistors. SrTiO3 nanocrystals with grain sizes ranging from 26 to 86 nm have been prepared by the stearic acid gel method [261]. Concerning mixed alkoxides, a SrTi4 (OEt)18 complex, isostructural with BaTi4 (OEt)18

770 (Fig. 34e), was characterized after reaction with Sr metal, EtOH, and Ti(OEt)4 under reflux [262]. Similarly, using the same procedure with Ti(OPri )4 and isopropanol leads to the complex [Sr2 Ti(OPri )8 (Pri OH)3 ] · 2Pri -OH with sixfold coordinated strontium and titanium atoms associated into a triangular unit (Fig. 36a) [262]. Another interesting compound for its piezoelectric properties is lead titanate (PbTiO3 ), which is widely used in microelectronics (actuators, sensors, and nonvolatile memories) [263]. It can be prepared under hydrothermal conditions [264] as most other perovskite-based titanates [265]. Here also, several mixed alkoxides have been described in the literature. The first isolated compound was Pb2 Ti4 O2 (CH3 COO)2 (OEt)14 obtained by reacting Pb(CH3 COO)2 · 3H2 O and Ti(OEt)4 in a 1 : 2 ratio in ethanol [266]. Its molecular structure is made of two [Ti2 (-O)(-OAc ·

Molecular Tectonics in Sol–Gel Chemistry

-OEt)(OEt)6 ]2− dimers bridged by two lead atoms in fourfold coordination (Fig. 36b). Attempts to get a complex with 1 : 1 stoichiometry were successful, and the compound Pb2 Ti2 O(OPri )10 was isolated after refluxing Pb(OPri )2 and Ti(OPri )4 in toluene [267]. This compound may be formulated as Pb2 Ti2 (4 -O)(3 -OPri )2 (-OPri )4 (OPri )4 and could be described as a corner-sharing [Ti2 (-O)(OPri )10 ]4− dimer in close association with two lead atoms in fourfold and fivefold coordination, respectively (Fig. 36c). Another possibility is to add Ti(OPri )4 to a suspension of lead acetate (3 : 1 ratio) in hexane, leading to the compound Pb2 Ti2 (4 -O)(-O2 CCH3 )2 (OPri )8 [268]. As shown in Figure 36d, the molecular structure of this complex may be described as [Ti2 (-O)(-OAc)(-OPri )(OPri )6 ]2− edgesharing dimers in strong association with [Pb2 (-OAc)(OPri )]2+ units. To increase the volatility of these mixed complexes, reactions between Ti(OPri )4 and lead amides such as Pb(NBut )2 SiMe2 have been investigated, leading to the isolation of Pb4 TiO(OPri )4 (NBut )3 [269]. Figure 36e shows the monomeric trigonal bipyramidal structure of this complex, which appears to be an addition product between Ti(OPri )4 and the lead-containing cage ligand Pb4 O(NBut )3 . Figure 36f shows another kind of addition product obtained by reacting SmI2 with NaTi(OPri )5 or Sm5 O(OPri )13 with Ti(OPri )4 [270]. The interesting feature of this complex [Sm4 Ti(5 -O)(3 -OPri )2 ( -OPri )6 (OPri )6 ] is the occurrence of a rather rare 5 -oxo bridge, which has also been characterized in the hydrolysis product of [LiTi(OPri )5 ] [271] (Fig. 36g). Other compositions based on ternary systems Pb(Zr, Ti)O3 , (Sr, Ba)TiO3 , and so on, or on other multicomponent systems [272, 273] will not be discussed here.

3. TITANIUM(IV) METALLO-ORGANIC COMPLEXES

Figure 36. Molecular structures of organometallic precursors of some miscellaneous titanates. (a) Monomeric octahedral coordination in the crystal structure of bis(3 -isopropoxy)-tris(2 -isoproproxy)-tris(isopropanolato)-tris(isopropoxy)-di-strontium-titanium isopropanol solvate. (b) Dimeric edge-sharing octahedral coordination for Ti atoms in the crystal structure of bis[(4 -oxo)-(2 -acetato-O,O ′ )-tetrakis(2 -ethoxo)triethoxy-lead(II)-di-titanium]. (c) Dimeric corner-sharing octahedral coordination for Ti atoms in the crystal structure of (4 -oxo)-bis(3 isopropoxo)-tetrakis(2 -isopropoxo)-tetrakis(isopropoxy)-di-lead-di-titanium. (d) Dimeric edge-sharing octahedral coordination for Ti atoms in the crystal structure of tetrakis(4 -oxo)-bis(2 -acetato)-pentakis(2 isopropoxo)-pentakis(isopropoxy)-di-lead-di-titanium. (e) Monomeric trigonal bipyramidal coordination for Ti atoms in the crystal structure of (4 -oxo)-tris(3 -tert-butylamine)-tetrakis(isopropoxy)-tetra-leadtitanium. (f) Monomeric trigonal bipyramidal coordination for Ti atoms in the crystal structure of (5 -oxo)-bis(3 -isopropoxo)-hexakis(2 -isopropoxo)-hexakis(isopropoxy)-tetra-samarium(III)-titanium. (g) Mixed (octahedral, trigonal bipyramidal) coordination of Ti atoms in the crystal structure of bis(5 -oxo)-tetrakis[(3 -isopropoxo)-(2 -isopropoxo)]bis(2 -oxo)-tetrakis(isopropoxy)-tetra-lithium-tetra-titanium.

The previous section has emphasized the widespread use of titanium(IV) alkoxides in materials chemistry. With so many potential applications in view for titanium alkoxides, a good understanding of their chemical reactivity is absolutely needed. A quick survey of the literature shows that, despite a very large number of publications referring to the use of these alkoxides, most published studies deliberately ignore that these compounds are oligomeric in solution and in the solid state. Worse, it seems rather amazing that the crystalline molecular structure of very basic compounds such as Ti(OPri )4 and Ti(OBun )4 remain completely unknown. Similarly, if numerous crystalline structures of the first hydrolysis products of Ti(OR)4 compounds are available, very few studies have been devoted to their mechanism of formation. The same situation holds for chemically modified (oxo)alkoxides. Several compounds have been synthesized and characterized by X-ray diffraction techniques. Their molecular structure or chemical reactivity has, however, never been really understood despite their extensive use in supramolecular or sol–gel chemistry for the design of hybrid organic–inorganic materials displaying new original physical properties. Consequently, it was thought that we could fill a real scientific gap by making this critical study of the coordination chemistry of titanium(IV) centers. It

Molecular Tectonics in Sol–Gel Chemistry

was hoped that by investigating in detail some well-selected hybrid organic–inorganic Ti(IV) complexes, very fundamental trends of the chemical reactivity of the Ti O C bond could be identified. This would provide very useful guidelines for anybody interested in the rational chemical design of hybrid TiO2 -based materials. Consequently, this section will begin by showing how our PACHA model could explain the chemical reactivity of titanium alkoxides toward protic species. This work is part of a systematic research program based on the molecular programming of titanium(IV) alkoxides that has been engaged in Strasbourg since 1993. Then, titanium(IV)-based complexes isolated in the crystalline state will be reviewed with a particular emphasis on their potential applications in homogeneous catalysis for example. Notice that for this review we have deliberately chosen to discard all organotitanium compounds (molecules with direct Ti C bonds). If we are fully aware of the importance of these complexes in homogeneous catalysis, their usefulness for the elaboration of stable hybrid organic– inorganic TiO2 -based materials has not yet been demonstrated. Consequently, it was thought that a better coherence could be reached by limiting this study to complexes displaying only Ti O C, Ti N C, or Ti O X (X = Si, P) bonds within their molecular structure.

3.1. Titanium(IV) Alkoxides It has long been known that titanium(IV) alkoxides are oligomeric compounds displaying various kind of Ti OR Ti bridges. When R is a primary aliphatic group, the basic structural unit is a compact edge-sharing tetramer [274–277] (Fig. 37). From a mechanistic point of view, the formation of a [Ti(OR)4 ]4 oligomer from tetrahedral Ti(OR)4 monomers may be rationalized by noticing that direct addition of two Ti(OR)4 tetrahedra leads to a dimer [(RO)4 Ti(OR)2 Ti(OR)4 ] displaying edge sharing between a Ti(OR)6 octahedron and a Ti(OR)4 tetrahedron (Fig. 37a). Repetition of this process may lead either to a tetramer Ti4 (OR)16 (smallest cyclic species containing only sixfold coordinated titanium atoms) or to an infinite edge-sharing octahedral chain [(RO)2 Ti(OR)4×1/2  ≡ Ti(OR)4 . Although for R = CH3 both structures have been characterized in the solid state [277], only in the case of the tetrameric unit was its structure elucidated by a single-crystal X-ray diffraction study [276]. Three kinds of OR groups (10 terminal OR positions, 4 2 -OR bridges, and 2 3 -OR bridges) may be identified in this tetrameric structure. This raises the question of their relative reactivity toward hydrolysis or substitution upon reaction with X OH molecules. To answer this question, this tetrameric structure was studied using the PACHA formalism and its electronic signature is given in Table 4. Several interesting features may be derived from these data. First, Ti atoms are found to be strongly electrophilic and thus highly prone to nucleophilic attack. This positive charge is counterbalanced by large negative charges on the methoxy groups. Interestingly enough, the negative charge distribution is quite anisotropic with Q3 -OMe) = −086, Q2 -OMe) = −071 (O7) and −070 (O6), and Q(OMe) = −054 (O1, O2), −050 (O3), −045 (O4), and −042 (O5). Bridging methoxy groups should, then, be better proton acceptors than terminal groups. Consequently,

771

Figure 37. Molecular structures of primary titanium(IV) alkoxides. (a) Formation of the planar tetramer Ti4 OR16  through successive addition of monomeric TiOR4 tetrahedra. (b) Labeling scheme for terminal and bridging OR groups. (c) Polyhedral view of the molecular structure of bis[(3 -methoxo)-bis(2 -methoxo)-heptamethoxy-dititanium]. (d) van der Waals 1D network for titanium tetramethoxide in the solid state.

Table 4. Electronic PACHA signature for the molecular crystal containing [Ti4 (OMe)16 ] tetramers. Atom O8 (3 -Ti) O6 (2 -Ti) O7 (2 -Ti) O1 (Ti2) O2 (Ti2) O3 (Ti1) O4 (Ti1) O5 (Ti1) C8 (O8) C6 (O6) C7 (O7) C3 (O3) C2 (O2) C1 (O1) C4 (O4) H81 (C8) H82 (C8) H61 (C6) C5 (O5) H40 (C4) H80 (C8)

Charge q

Index f

Atom

Charge q

Index f

−0740 −0665 −0663 −0583 −0580 −0527 −0495 −0484 −0128 −0088 −0082 −0048 −0042 −0041 −0021 −0003 +0003 +0005 +0006 +0006 +0007

−0013 −0004 −0003 0011 0012 0013 0018 0020 0014 0018 0018 0022 0023 0024 0021 0043 0045 0045 0020 0043 0047

H60 (C6) H71 (C7) H30 (C3) H50 (C5) H70 (C7) H20 (C2) H10 (C1) H52 (C5) H51 (C5) H72 (C7) H31 (C3) H41 (C4) H42 (C4) H22 (C2) H11 (C1) H12 (C1) H21 (C2) H62 (C6) H32 (C3) Ti1 (3-O) Ti2 (4-O)

+0007 +0008 +0008 +0008 +0011 +0013 +0020 +0021 +0024 +0025 +0026 +0027 +0028 +0031 +0031 +0032 +0034 +0034 +0038 +2250 +2485

0049 0052 0052 0041 0051 0055 0053 0056 0049 0050 0055 0055 0051 0054 0054 0052 0056 0049 0052 0299 0277

Note: Global parameters were EN = 1237 V, GH = 57 eV, EB = −1392 eV = −13435 kJ mol−1 , and GI = 313%. See Figure 3 for O- and Ti-atom numbering scheme. The symbol in parentheses refers to the immediate neighborhood.

772 one may understand that, faced with a molecule bearing a reactive hydroxy group X OH, Ti atoms should be easily attacked by nucleophilic oxygen centers. Following this attack, the bridging O atoms should also be preferentially protonated by the H atom residing on the hydroxo moiety of the attacking group. Titanium(IV) alkoxides thus display a rather high susceptibility toward hydrolysis with preferential attacks at the heart of their tetrameric core. To get a better visualization of this reactivity toward water, one may transform the partial charges found on O atoms into pKa values. The result clearly demonstrates a significantly higher basic character for bridging groups (pKa : O8 = 11.9, O6 = 9.0, and O7 = 8.9) relative to terminal groups (pKa : O1 = 5.7, O2 = 5.6, O3 = 3.5, O4 = 2.3, and O5 = 1.8). These considerations help to explain why Ti(OEt)4 hydrolysis products, heptameric [Ti7 (4 -O)2 (3 -O)2 (2 OEt)8 (OEt)12 ] [278–280], decameric [Ti10 (4 -O)4 (3 -O)2 (2 -O)2 (2 -OEt)10 (OEt)14 ] [279], and hexadecameric [Ti4 (4 -O)(3 -O)2 (2 -O)(2 -OEt)4 (OEt)4 ]4 [281] (Fig. 38), cannot be considered as condensation oligomers of tetrameric units. This would have happened only if terminal positions were more susceptible to hydrolysis than bridging positions. For the reverse situation (bridging positions more reactive than terminal positions), one may expect to find new compact structural units with oxo groups at the core (preferential hydrolysis) and unaffected terminal ligands. This is precisely what is observed experimentally. Another interesting aspect of this structure is the formation of a van der Waals chain of tetramers in the solid state (Fig. 37d). The very weak interactions responsible for the formation of this chain may be probed after isolation of a tetramer from its crystalline network, leading to EB = −134309 kJ mol−1 . Knowing that the full network was characterized by EB = −134350 kJ mol−1 , we got an in teraction energy of 8E = −134350 + 134309 =

Figure 38. Molecular structures of titanium(IV) tetraethoxide hydrolysis products. (a) Bis(4 -oxo)-bis(3 -oxo)-octakis(2 -ethoxo)dodecakis(ethoxy)-hepta-titanium. (b) Tetrakis(4 -oxo)-bis(3 -oxo)bis(2 -oxo)-decakis(2 -ethoxo)-tetradecakis(ethoxy)-deca-titanium toluene solvate. (c) Tetrakis[(4 -oxo)-bis(3 -oxo)-(2 -oxo)-tetrakis(2 ethoxo)-tetrakis(ethoxy)-tetra-titanium].

Molecular Tectonics in Sol–Gel Chemistry

−41 kJ mol−1 , a value typical of weak van der Waals attractions. Also notice that in the liquid state an alkoxide such as Ti(OEt)4 is no longer tetrameric but rather trimeric with a cyclic structure based on fivefold coordinated Ti atoms [282]. The reason for the occurrence of such a reduction in coordination number is still unclear and needs further theoretical investigations well beyond the scope of this review. Detailed structural crystalline data for nonhydrolyzed secondary or tertiary titanium(IV) alkoxides are still lacking. The only structural information available was obtained in solutions using XANES and EXAFS spectroscopy [282] or 47 49 Ti-NMR spectroscopy [283]. These techniques point to tetrahedral monomeric structures for Ti(OPri )4 , Ti(OBut )4 , and Ti(OAmt )4 . This is not, however, the case for hydrolyzed species (Fig. 39) where crystalline data have been reported for trimeric [Ti3 (3 -O)(3 -OMe)(2 -OPri )4 (OPri )6 ] [284], undecameric [Ti11 (3 -O)10 (2 -O)3 (2 -O Pri )4 (OEt)5 (OPri )6 ] [285], dodecameric [Ti12 (3 -O)14 (2 -O)2 (2 -OPri )4 (OEt)6 (OPri )6 ] [286, 287], heptadecameric [Ti17 (4 -O)4 (3 -O)16 (2 -O)4 (2 -OPri )4 (OPri )16 ] [288], and octadecameric [Ti18 (4 -O)4 (3 -O)20 (2 -O)3 (2 OH)(OBut )17 ] [289].

Figure 39. Molecular structures of titanium(IV) tetraisopropoxide hydrolysis products. (a) Octahedral coordination in the crystal structure of (3 -methoxy)-(3 -oxo)-tris(2 -isopropoxy)-hexakis(isopropoxy)-tri- titanium(IV). (b) Decakis(3 -oxo)- tris(2 -oxo)-heptakis(2 -isopropoxo)hexakis(isopropoxy)-pentakis(ethoxy)-undeca-titanium ethanol solvate. (c) Tetradecakis(3 -oxo)-bis(2 -oxo)-tetrakis(2 -isopropoxo)hexakis(ethoxy)-hexakis(isopropoxy)-dodeca-titanium. (d) Tetrakis[(4 oxo)-tetrakis(3 -oxo)-(2 -oxo)-(2 -isopropoxo)-tetrakis(isopropoxy)]heptadeca-titanium unknown solvate. (e) Tetrakis(4 -oxo)-icosakis(3 oxo)-tris(2 -oxo)(2 -hydroxo)-heptadecakis(tert-butoxy)-octadecatitanium tert-butanol solvate.

Molecular Tectonics in Sol–Gel Chemistry

773

3.2. Reaction with Tripodal Ligands Based on the above results, we have investigated the possibility of substituting all reactive bridging OR groups by suitable multidentate ligands. The planar geometry of the tetramer and the triangular disposition of the bridging OR groups suggested the use of tripodal ligands of the type XC(CH2 OH)3 . A survey of the Cambridge Structural Database showed that tris(hydroxymethyl)ethane or tris(hydroxymethyl)propane react with titanium isopropoxide to yield a tetrameric complex in the expected way [290], despite the fact that titanium isopropoxide is known to be monomeric in the liquid state [282, 283]. This result points to the high flexibility and lability of Ti OR bonds and the existence, in solution, of a chemical equilibrium between Ti(OR)4 monomers and Ti4 (OR)16 tetrameric forms, not only for R = Me, Et, but also for R = Pri . Upon addition of a suitable well-shaped molecule able to chemically recognize the spatial disposition of bridging OR groups, equilibrium is probably displaced toward the tetramer owing to its consumption by the complexation process. To clearly elucidate the influence of the OR group, we have undertaken a structural investigation of the products formed by reacting Ti(OR)4 (R = CH2 CH3 , CH(CH3 )2 , and CH2 CH2 CH2 CH3 ) with tris(hydroxymethyl)nitromethane (THMNM) [88]. This particular ligand was selected as it allows for the performance of 17 O- and 14 N-NMR studies and also displays a chemically reactive function allowing side-chain addition for forthcoming studies. The results of the study were as expected: conservation of the substituted tetrameric core in each case (Fig. 40). The fact that it was possible to change the OR group while maintaining the molecular structure clearly demonstrates the strong structuring role of the THMNM ligand. Similarly, the possibility of performing an oxolation reaction with minor changes to the tetrameric core is a good illustration of the protective role of multidentate ligands. Such reactions are obviously reminiscent of advanced organic synthesis, playing with the protective groups to obtain a better selectivity of the chemical reaction. Consequently, there is a clear benefit in this case for substituting bridging OR groups by multidentate ligands. However, the most interesting aspect is that we may have a deeper insight into the basic molecular mechanisms by looking at the electronic signatures of these substituted tetramers.

3.2.1. Reaction with Titanium(IV ) Ethoxide Table 5 gives the electronic signature for the ethoxy-based THMNM derivative (Fig. 40a). A comparison between EN and GH values shows that, from a MO point of view, the substituted tetramer is indeed more stable (higher EN and GH, i.e., lower HOMO and wider HOMO– LUMO gap) than the methoxy-based one. This increased stability is also confirmed by the lower EB term. Notice that, owing to the occurrence of strongly covalent N O bonds, the substituted tetramer has a more covalent character relative to the nonsubstituted one (lower GI). At an atomic scale, we may immediately notice the inversion of charge between atoms Ti1 and Ti2 and the significant higher electrophilic character of Ti atoms in the THMNM derivative. Moreover, the predicted pKa values for oxygen

Figure 40. Molecular structures of the reaction products of TiOEt4 (a), TiOPri 4 (b), and TiOBun 4 (c) with the tripodal ligand tris(hydroxymethyl)nitromethane (THMNM). Owing to its particular geometry, a perfect geometric match exists between the ligand and the six n -OR bridges n = 2 3 found on a Ti4 OR16  tetramer.

atoms of the ligand range from −8 for the nitro group to +110 for the 3 -OCH2 moiety of the THMNM ligand. Terminal OEt groups are more basic than OMe groups (4.7 ≤ pKa ≤ 5.6), while for the remaining 2 -OCH2 moieties a value around 8.6 is obtained. Consequently, and in agreement with experiment [290], these substituted titanium alkoxides should be as reactive toward hydrolysis as unmodified ones. A more contrasted view of the overall charge distribution in this molecule is provided by summing individual charges according to the ligand stoichiometry, leading to Q(OEt1) = −051, Q(OEt2) = −054, Q(OEt3) = Q(OEt10) = −049, Q(OEt9) = −047, and Q(THMNM) = −242. The strong accumulation of electronic density on the tripod ligand relative to the terminal ethoxy renders them highly prone to protonation, in agreement with the above pKa values.

3.2.2. Reaction with Titanium(IV ) Isopropoxide Table 6 shows the electronic effects associated with the replacement of OEt groups by OPri groups (Fig. 40b), while keeping intact the topology of the molecular object. As expected, these effects are rather weak and in coherence with the well-known better electron-donating properties of isopropoxy groups relative to ethoxy ones. Accordingly, lower positive charges are found on Ti atoms and a large decrease in the global ionicity index is observed. Surprisingly, if the HOMO is stabilized, the HOMO–LUMO gap is strongly reduced. This means that the isopropoxy-based tetramer should be slightly less reactive toward hydrolysis than the ethoxy-based derivative. Concerning pKa values for

Molecular Tectonics in Sol–Gel Chemistry

774 Table 5. Electronic PACHA signature for the molecular crystal containing [Ti4 (OEt)10 {(2 -OCH2 )2 (3 -OCH2 )C(NO2 )}2 ] tetramers.

Table 6. Electronic PACHA signature for the molecular crystal containing [Ti4 (OPri )10 {(2 -OCH2 )2 (3 -OCH2 )C(NO2 )}2 ] tetramers.

Atom

Charge q Index f

Atom

O5 (2Ti2, C9) O8 (C10, Ti1,Ti2) O4 (Ti1, Ti2,C7) O3 (Ti1, C5) O9 (Ti2, C11) O10 (Ti2, C13) O2 (Ti1, C3) O1 (Ti1, C1) O6 (N1) O7 (N1) C12 (C11) C6 (C5) C14 (C13) C2 (C1) C4 (C3) C9 (O5, C8) C10 (O8, C8) C7 (O4, C8) C3 (O2, C4) C1 (O1, C2) N1 C5 (O3, C6) C8 (N1) C13 (O10, C14) H7 (C3) C11 (O9, C12) H6 (C3) H2 (C1) H27 (C13)

−07176 −06574 −06541 −05801 −05789 −05777 −05680 −05564 −02382 −02287 −01918 −01734 −01729 −01587 −01575 −01012 −00885 −00880 −00335 −00287 −00117 −00090 −00044 −00003 +00083 +00196 +00253 +00259 +00312

−00046 −00005 −00003 00043 00045 00049 00053 00053 00197 00216 −00097 −00076 −00061 −00021 −00025 00021 00027 00023 00075 00073 00161 00059 00153 00077 00191 00083 00185 00185 00193

Atom H3 (C2) H11 (C5) H5 (C2) H19 (C9) H18 (C9) H23 (C11) H14 (C6) H22 (C11) H21 (C10) H4 (C2) H30 (C14) H8 (C4) H28 (C13) H10 (C4) H15 (C6) H26 (C12) H17 (C7) H13 (C6) H20 (C10) H25 (C12) H12 (C5) H31 (C14) H29 (C14) H9 (C4) H16 (C7) H1 (C1) H24 (C12) Ti2 (2OEt) Ti1 (3OEt)

Charge q Index f +00374 +00383 +00412 +00424 +00436 +00439 +00473 +00479 +00516 +00523 +00547 +00553 +00558 +00560 +00570 +00572 +00595 +00614 +00620 +00658 +00671 +00695 +00729 +00749 +00791 +00800 +00826 +23984 +25115

00215 00199 00223 00180 00180 00180 00245 00179 00193 00249 00259 00240 00183 00252 00242 00260 00203 00246 00211 00259 00194 00253 00238 00258 00221 00227 00246 01019 01118

Note: Global parameters were EN = 1303 V, GH = 61 eV, EB = −148746 kJ mol−1 , and GI = 257%. The symbol in parentheses refers to the immediate neighborhood.

the O atom, a slightly reduced range is spanned (from −78 for the nitro group up to 10.8 for the 3 -OCH2 moiety of the THMNM ligand). Terminal OPri groups are slightly less basic than OEt groups (43 ≤ pKa ≤ 54), while for the remaining 2 -OCH2 moieties a pKa value around 8.6 is obtained. This value is almost the same as that obtained for the ethoxy-based THMNM tetramer. The very similar character of both tetramers is further evidenced through the global charge repartition: Q(OPri 1 = −052, Q(OPri 2 = −049, Q(OPri 3 = −046, Q(OPri 9 = −051, Q(OPri 10 = −046, and Q(THMNM) = −244.

3.2.3. Reaction with Titanium(IV ) Butoxide Finally, Table 7 shows the electronic signature of the octameric species obtained after oxolation between two tetramers in the case of the n-butoxy ligand (Fig. 40c). As with the (Et → Pri ) substitution, the HOMO continues to be stabilized, though to a much lesser extent [8(EN) = 007 V versus 0.19 V previously], and the HOMO–LUMO gap is further reduced. Due to the existence of two 2 -oxo groups in the structure, a higher global ionicity is found relative to the isopropoxy-based tetramer. This ionicity remains, however, lower than that of the ethoxy-based tetramer. The remarkable feature of this structure is the occurrence of a strongly basic oxo ligand (pKa = 152). This obviously

O4 (-Ti3  O5 (-Ti2  O8 (-Ti2  O1 (Ti1) O9 (Ti2) O2 (Ti1) O10 (Ti2) O3 (Ti1) O7 (N) O6 (N) C8 (C7) C3 (C1) C19 (C17) C18 (C17) C5 (C4) C6 (C4) C15 (C14) C16 (C14) C9 (C7) C2 (C1) C10 (O4) C13 (O8) C12 (O5) N1 C11 (3 -C) C4 (O2) H8 (C4) C17 (O10) C1 (O1) C14 (O9) C7 (O3) H15 (C7) H35 (C17) H1 (C1) H22 (C10) H28 (C14) H6 (C3)

Charge q

Index f

Atom

Charge q

Index f

−0712 −0655 −0653 −0575 −0574 −0559 −0558 −0548 −0242 −0236 −0173 −0168 −0166 −0166 −0165 −0163 −0162 −0162 −0159 −0158 −0104 −0092 −0088 −0020 −0005 +0003 +0007 +0009 +0012 +0013 +0013 +0014 +0024 +0029 +0036 +0037 +0042

−0003 0000 −0000 0003 0003 0003 0004 0004 0018 0017 −0002 −0002 −0002 −0001 −0002 −0002 −0003 −0002 −0003 −0002 0002 0003 0002 0013 0012 0011 0012 0011 0011 0011 0011 0013 0015 0013 0015 0013 0017

H37 (C18) H18 (C8) H23 (C10) H31 (C15) H14 (C6) H7 (C3) H24 (C12) H19 (C9) H30 (C15) H32 (C16) H29 (C15) H2 (C2) H36 (C18) H12 (C6) H20 (C9) H34 (C16) H3 (C2) H10 (C5) H4 (C2) H16 (C8) H39 (C19) H13 (C6) H25 (C12) H33 (C16) H5 (C3) H38 (C18) H40 (C19) H11 (C5) H21 (C9) H9 (C5) H27 (C13) H26 (C13) H17 (C8) H41 (C19) Ti2 (4-O) Ti1 (3-O)

+0046 +0047 +0047 +0048 +0051 +0053 +0053 +0054 +0054 +0054 +0056 +0056 +0057 +0057 +0058 +0058 +0059 +0061 +0062 +0062 +0063 +0064 +0065 +0065 +0066 +0067 +0070 +0074 +0074 +0078 +0078 +0083 +0094 +0098 +2396 +2497

0016 0017 0015 0017 0019 0017 0015 0022 0018 0019 0020 0019 0017 0019 0019 0018 0018 0018 0021 0019 0019 0018 0016 0019 0020 0018 0019 0019 0021 0021 0015 0015 0020 0020 0079 0086

Note: Global parameters were EN = 1322 V, GH = 36 eV, EB = −1550 eV = −149502 kJ mol−1 , and GI = 218%. The symbol in parentheses refers to the immediate neighborhood.

means that such a 2 -oxo bridge should be stable only in aprotic solvents and would be immediately destroyed upon addition of water. As observed before, we found the logical sequence: pKa 3 -O C = 112 > pKa (2 -O C = 87 > pKa (Ti O C = 48 > pKa (NO2  = −81. Consequently, it appears obvious that the chemical nature of the OR chain plays a very minor role in fixing the acid–base properties of the tetramer. Concerning the global charge repartitions, we get the following distributions: Q(-OBu1) = −071, Q(OBu2) = −053, Q(OBu3) = −046, Q(OBu14) = −051, Q(OBu15) = −048, Q(OBu16) = −050, Q(OBu18) = −049, Q(OBu19) = −043, Q(THMNM14) = −253, and Q(THMNM18) = −220. If we exclude the OBu1 and THMNM14 ligands, we recover very similar values to those obtained with R = Et or Pri . This is completely in line with the fact that all these groups display exactly the same coordination mode in the three structures [terminal position for butoxy groups and fully bridging position (3 -O, 2 O′ , 2 -O′′ ) for the THMNM ligand]. For the butoxy chain

Molecular Tectonics in Sol–Gel Chemistry

775

Table 7. Electronic PACHA signature for the molecular crystal containing [Ti4 (OBun )7 (2 -OBun ){(2 OCH2 )2 (3 -OCH2 )C(NO2 )}{(OCH2 )(2 -OCH2 )(3 -OCH2 )C(NO2 )}O]2 octamers. Atom

Charge q

Atom

Charge q

Atom

O17 (2 -O) O8 (-Ti3 , C16) O9 (-Ti3 , C17) O1 (-Ti2 , C1) O4 (-Ti2 , C13) O10 (-Ti2 , C19) O5 (-Ti2 , C15) O19 (Ti4, C37) O2 (Ti1, C5) O15 (Ti3, C25) O16 (Ti3, C29) O3 (Ti1, C9) O14 (Ti3, C21) O13 (Ti2, C20) O18 (Ti4, C33) O7 (N1) O12 (N2) O11 (N2) O6 (N1) C40 (C39) C32 (C31) C28 (C27) C24 (C23) C36 (C35) C12 (C11) C8 (C7) C4 (C3) C16 (O8) C10 (C9, C11) C26 (C25, C27) C6 (C5, C7) C2 (C1, C3) C35 (C36, C34) C27 (C26, C28) C3 (C2, C4) C22 (C21, C23) C23 (C22, C24) C7 (C6, C8) C31 (C30, C32) C38 (C37, C39) C11 (C10, C12) C30 (C29, C31) C17 (O9) C34 (C33, C35) C39 (C38, C40) C15 (O5) C1 (O1) C13 (O4) C19 (O10) C20 (O13)

−0823 −0728 −0715 −0662 −0661 −0656 −0654 −0576 −0575 −0564 −0563 −0562 −0552 −0545 −0544 −0236 −0234 −0229 −0229 −0116 −0116 −0115 −0114 −0113 −0111 −0111 −0110 −0090 −0087 −0086 −0084 −0084 −0081 −0080 −0080 −0079 −0079 −0078 −0078 −0077 −0077 −0077 −0075 −0074 −0069 −0067 −0066 −0061 −0060 −0037

C33 (O18) C25 (O15) C37 (O19) C29 (O16) C21 (O14) C5 (O2) C9 (O3) N1 (O6, O7) N2 (O11, O12) C14 (N1) H89 (C16) C18 (N2) H66 (C1) H67 (C1) H103 (C25) H109 (C29) H114 (C33) H115 (C33) H79 (C9) H86 (C15) H96 (C21) H108 (C29) H92 (C17) H122 (C38) H97 (C21) H144 (C8) H77 (C7) H146 (C8) H94 (C19) H72 (C5) H143 (C4) H98 (C22) H125 (C39) H140 (C24) H83 (C11) H149 (C12) H113 (C31) H117 (C34) H93 (C17) H78 (C9) H100 (C23) H139 (C24) H70 (C3) H137 (C28) H145 (C8) H129 (C36) H121 (C37) H71 (C3) H73 (C5) H76 (C7)

−0031 −0030 −0026 −0024 −0016 −0013 −0012 −0010 −0010 −0009 −0006 −0003 +0001 +0006 +0007 +0011 +0014 +0014 +0015 +0016 +0017 +0021 +0023 +0024 +0025 +0029 +0030 +0031 +0033 +0035 +0035 +0036 +0036 +0036 +0036 +0037 +0037 +0037 +0038 +0038 +0038 +0038 +0038 +0038 +0039 +0039 +0039 +0039 +0039 +0039

H134 (C32) H81 (C10) H102 (C25) H130 (C36) H101 (C23) H110 (C30) H106 (C27) H124 (C39) H142 (C3) H107 (C27) H112 (C31) H133 (C32) H138 (C24) H74 (C6) H123 (C38) H131 (C36) H141 (C3) H127 (C40) H147 (C12) H69 (C2) H75 (C6) H135 (C28) H116 (C34) H87 (C15) H68 (C2) H84 (C13) H132 (C32) H118 (C35) H82 (C11) H99 (C22) H85 (C13) H104 (C26) H88 (C16) H148 (C12) H105 (C26) H120 (C37) H136 (C28) H119 (C35) H80 (C10) H128 (C40) H111 (C30) H126 (C40) H90 (C20) H95 (C19) H91 (C20) Ti2 (HMNM) Ti1 (2 × OBu) Ti4 (O3 × OBu) Ti3 (3 × OBu)

Charge q +0039 +0039 +0040 +0040 +0040 +0040 +0040 +0041 +0041 +0041 +0041 +0041 +0041 +0041 +0041 +0042 +0042 +0043 +0043 +0044 +0045 +0046 +0047 +0048 +0048 +0049 +0049 +0050 +0050 +0053 +0055 +0055 +0056 +0056 +0057 +0063 +0066 +0072 +0072 +0073 +0074 +0079 +0084 +0087 +0105 +2302 +2406 +2442 +2516

Note: Global parameters were EN = 1329 V, GH = 18 eV, EB = −288736 kJ mol−1 , and GI = 244%. The symbol in parentheses refers to the immediate neighborhood.

bonded to atom O1, we find a more negative charge owing to its bridging position. Reciprocally, the THMNM moiety based on atom C18 does not display a full bridging mode as before, but rather a (3 -O, 2 -O′ , -2O′′ ) coordination mode. Consequently, it bears less negative charge than the other one based on atom C14.

3.2.4. General Discussion We are now in a position to draw some conclusions from this series of three related crystal structures. Full substitution of bridging positions in Ti4 (OR)16 tetramers does not alter very much the acid–base properties of these complexes. With electronic density mainly localized on THMNM moieties,

776 protic reagents such as water are expected to react preferentially with these ligands and less favorably with the remaining terminal OR chains. However, the removal of such a ligand would require the simultaneous attack of three water molecules upon a single tetramer, a rather unlikely process for entropy reasons. Consequently, the tripod should remain bonded to the tetramer even after hydrolysis, preventing the destruction of the initial tetrameric core. The fact that water molecules effectively attack the THMNM ligand is demonstrated by the butoxy-based structure. The observed octamer may be obviously derived from two tetrameric species, after partial hydrolysis and further oxolation of four terminal butoxy groups. If the THMNM ligand were significantly inert in this process, the octamer would have displayed only terminal butoxy groups. As shown in Figure 40c, this is not the case as two butoxy ligands are found in bridging positions. The occurrence of these 2 -OBun groups may be explained if the 3 -OCH2 moiety has been first hydrolyzed as suggested by our charge distributions and predicted pKa values. Since the THMNM ligand is still linked to the tetramer by the two other arms, it cannot be eliminated. Consequently, the free arm is able to react with a neighboring terminal butoxy group, leading to the formation of a new link between the OCH2 moiety and the titanium atom. Now recall that, at room temperature, bridging and terminal positions are generally not distinguishable on the NMR time scale. Owing to the intrinsic lability of Ti O bonds in such compounds, a fast cyclic permutation between the three groups (2 -OCH2 → 3 -OH → 1 -OBun ) bonded to the same Ti atom may occur. This would then lead to a hydroxy group in the terminal position (1 -OH) ideally placed to undergo the final oxolation reaction and to the final observed structure: 2 -OBun and 3 -OCH2 .

3.3. Crystal Engineering of Hybrid Organic–Inorganic Networks Crystal engineering has been defined as the understanding of intermolecular interactions in the context of crystal packing and the use of such understanding in the design of new solids with desired physical and chemical properties [291]. Consequently, this field shares many concepts with molecular tectonics or sol–gel chemistry, and we thought it interesting to see to what extent titanium-based molecular precursors commonly used in sol–gel chemistry can be tailored to meet crystal engineering requirements. In fact, it soon appears that titanium alkoxides were much too flexible to be used in a reliable way for the rational design of hybrid organic–inorganic networks. Moreover, as our PACHA model is able to provide us with a direct measure of molecular interactions in the solid state, it is a rather easy job to classify the observed crystalline networks along a universal energy scale.

3.3.1. Titanium Methoxide Ti
OMe4 For example, let us go back to the crystal structure of titanium(IV) tetramethoxide. We have seen that the whole packing energy of Ti4 (OMe)16 tetramers into a 1D van der Waals chain (Fig. 37d) through methyl groups was indeed not very impressive (−41 kJ mol−1 ). But we can do more

Molecular Tectonics in Sol–Gel Chemistry

than that by looking at which kinds of methyl groups are involved in the stacking. Table 8 shows the retrosynthetic indexes [84] computed for the free tetramer after extraction from the network. Recall that these indexes are electronic probes defining which parts of a molecular fragment are deeply involved in the building of the lattice. They are simply defined as RI = 100 × qmol − qcryst /qcryst 0, where qmol is the charge of a given atom in the isolated fragment and qcryst its charge in the crystal. A low RI index means that the computed atomic charge is not under the control of the network, while a high value points to an atom strongly affected by the removal of the crystalline environment. For the methoxy-based tetramer, one may immediately see from Table 8 that stacking in the solid state involves interactions between bridging OMe groups. Assuming a reasonable threshold of at least 10% to define significant molecular interactions in the solid state, one gets an average H · · · H van der Waals interaction of −41/7 = −06 kJ mol−1 . This rather low value is in line with the fact that interactions between methyl groups are mainly responsible for the building of the network.

3.3.2. Tris
hydroxymethylnitromethane Derivatives If the above conclusions were correct, one would expect that after replacement of bridging OR groups by THMNM ligands (Fig. 40) a much stronger interaction should be found. This was indeed shown to be the case after comparison of the EB value for the full network (−149502 kJ mol−1 ) to the EB value of an isolated isopropoxy-based tetramer (−149227 kJ mol−1 ), leading to a difference 8E = −257 kJ mol−1 . As shown in Table 9, the networking interactions are found to involve now the nitro group with, by decreasing order of importance: Table 8. WinPacha retrosynthetic indexes after extraction of a [Ti4 (OMe)16 ] tetramer from its crystalline network. O10, O4 ⇔ O7 = −0.663 ⇒ 0% O5, O6 ⇔ O8 = −0.740 ⇒ 0% O3, O14 ⇔ O6 = −0.665 ⇒ 0% O1, O15 ⇔ O1 = −0.584 ⇒ 0% Ti3, Ti2 ⇔ Ti1 = +2.251 ⇒ 0% Ti4, Ti1 ⇔ Ti2 = +2.484 ⇒ 0% O2, O16 ⇔ O2 = −0.580 ⇒ 0% O9, O13 ⇔ O5 = −0.483 ⇒ 0% O8, O12 ⇔ O4 = −0.495 ⇒ 0% O7, O11 ⇔ O3 = −0.526 ⇒ 0% C4, C10 ⇔ C7 = −0.082 ⇒ 0% C2, C16 ⇔ C2 = −0.042 ⇒ 0% C5, C6 ⇔ C8 = −0.127 ⇒ 0% C11, C7 ⇔ C3 = −0.048 ⇒ 0% C12, C8 ⇔ C4 = −0.021 ⇒ 1% H6, H48 ⇔ H22 = +0.031 ⇒ 1% H12, H30 ⇔ H72 = +0.025 ⇒ 1% C15, C1 ⇔ C1 = −0.041 ⇒ 1% C14, C3 ⇔ C6 = −0.086 ⇒ 2% H2, H44 ⇔ H11 = +0.030 ⇒ 2% H3, H45 ⇔ H12 = +0.033 ⇒ 2%

H36, H24 ⇔ H42 = +0.028 ⇒ 2% H4, H46 ⇔ H20 = +0.014 ⇒ 3% H21, H33 ⇔ H32 = +0.039 ⇒ 3% H32, H20 ⇔ H31 = +0.027 ⇒ 5% H28, H10 ⇔ H70 = +0.011 ⇒ 5% H47, H5 ⇔ H21 = +0.032 ⇒ 6% C13, C9 ⇔ C5 = +0.006 ⇒ 7% H37, H25 ⇔ H50 = +0.009 ⇒ 7% H27, H39 ⇔ H52 = +0.022 ⇒ 8% H38, H26 ⇔ H51 = +0.026 ⇒ 8% H29, H11 ⇔ H71 = +0.009 ⇒ 8% H23, H35 ⇔ H41 = +0.030 ⇒ 8% H43, H1 ⇔ H10 = +0.018 ⇒ 10% H13, H16 ⇔ H80 = +0.006 ⇒ 10% H18, H15 ⇔ H82 = +0.004 ⇒ 15% H34, H22 ⇔ H40 = +0.005 ⇒ 20% H42, H9 ⇔ H62 = +0.027 ⇒ 20% H19, H31 ⇔ H30 = +0.010 ⇒ 30% H40, H7 ⇔ H60 = +0.004 ⇒ 39% H8, H41 ⇔ H61 = +0.007 ⇒ 43% H17, H14 ⇔ H81 = −0.005 ⇒ 47%

Note: The syntax is molecular labels ⇔ crystalline label = molecular charge ⇒ retrosynthetic index RI.

Molecular Tectonics in Sol–Gel Chemistry Table 9. WinPacha retrosynthetic indexes after extraction of a [Ti4 (OPri 10 (THMNM)2 ] tetramer from its crystalline network. O15, O2 ⇔ O2 = −0.559 ⇒ 0% O16, O3 ⇔ O3 = −0.548 ⇒ 0% Ti4, Ti1 ⇔ Ti1 = +2.497 ⇒ 0% O4, O10 ⇔ O4 = −0.712 ⇒ 0% Ti2, Ti3 ⇔ Ti2 = +2.395 ⇒ 0% O12, O8 ⇔ O9 = −0.574 ⇒ 0% O13, O9 ⇔ O10 = −0.558 ⇒ 0% O5, O11 ⇔ O5 = −0.654 ⇒ 0% O1, O14 ⇔ O1 = −0.574 ⇒ 0% C34, C8 ⇔ C3 = −0.168 ⇒ 0% C29, C23 ⇔ C19 = −0.167 ⇒ 0% C26, C24 ⇔ C15 = −0.163 ⇒ 0% O7, O6 ⇔ O8 = −0.654 ⇒ 0% C16, C28 ⇔ C18 = −0.165 ⇒ 0% C4, C19 ⇔ C10 = −0.104 ⇒ 1% C31, C2 ⇔ C4 = +0.003 ⇒ 1% H59, H41 ⇔ H39 = +0.064 ⇒ 1% C20, C5 ⇔ C12 = −0.089 ⇒ 1% H57, H30 ⇔ H37 = +0.045 ⇒ 2% C30, C1 ⇔ C1 = +0.012 ⇒ 2% C7, C33 ⇔ C2 = −0.161 ⇒ 2% C12, C38 ⇔ C9 = −0.162 ⇒ 2% C25, C27 ⇔ C16 = −0.165 ⇒ 2% C36, C10 ⇔ C6 = −0.167 ⇒ 2% O17, O19 ⇔ O6 = −0.231 ⇒ 2% H46, H52 ⇔ H31 = +0.047 ⇒ 2% H23, H77 ⇔ H16 = +0.061 ⇒ 3% C35, C9 ⇔ C5 = −0.159 ⇒ 3% H14, H69 ⇔ H6 = +0.043 ⇒ 3% H45, H51 ⇔ H30 = +0.056 ⇒ 4% C11, C37 ⇔ C8 = −0.166 ⇒ 4% C18, C21 ⇔ C14 = +0.013 ⇒ 4% N1, N2 ⇔ N1 = −0.019 ⇒ 5% H56, H29 ⇔ H36 = +0.059 ⇒ 5% H10, H65 ⇔ H2 = +0.059 ⇒ 5% C6, C17 ⇔ C13 = −0.087 ⇒ 5%

H44, H50 ⇔ H29 = +0.059 ⇒ 5% H5, H36 ⇔ H23 = +0.050 ⇒ 5% O20, O18 ⇔ O7 = −0.228 ⇒ 5% H28, H82 ⇔ H21 = +0.079 ⇒ 6% H70, H15 ⇔ H7 = +0.056 ⇒ 6% C15, C22 ⇔ C17 = +0.010 ⇒ 6% H72, H18 ⇔ H10 = +0.057 ⇒ 7% H38, H7 ⇔ H25 = +0.070 ⇒ 7% H1, H62 ⇔ H1 = +0.027 ⇒ 7% H49, H55 ⇔ H34 = +0.062 ⇒ 7% H42, H60 ⇔ H40 = +0.075 ⇒ 8% C3, C32 ⇔ C7 = +0.012 ⇒ 8% H39, H33 ⇔ H28 = +0.040 ⇒ 9% H73, H19 ⇔ H11 = +0.067 ⇒ 9% H37, H6 ⇔ H24 = +0.058 ⇒ 9% H67, H12 ⇔ H4 = +0.068 ⇒ 10% H25, H79 ⇔ H18 = +0.042 ⇒ 10% H11, H66 ⇔ H3 = +0.065 ⇒ 10% H68, H13 ⇔ H5 = +0.059 ⇒ 11% H16, H58 ⇔ H38 = +0.060 ⇒ 11% H27, H81,H74,H20 ⇔ H12 = +0.064 ⇒ 11% H4, H35 ⇔ H22 = +0.040 ⇒ 11% H43, H61 ⇔ H41 = +0.086 ⇒ 12% H75, H21 ⇔ H13 = +0.072 ⇒ 12% C13, C14 ⇔ C11 = −0.006 ⇒ 12% H76, H22 ⇔ H14 = +0.057 ⇒ 12% H26, H80 ⇔ H19 = +0.060 ⇒ 13% H48, H54 ⇔ H33 = +0.075 ⇒ 15% H53, H47 ⇔ H32 = +0.063 ⇒ 17% H2, H63 ⇔ H8 = +0.008 ⇒ 17% H3, H64 ⇔ H15 = +0.016 ⇒ 19% H9, H32 ⇔ H27 = +0.061 ⇒ 23% H71, H17 ⇔ H9 = +0.059 ⇒ 25% H8, H31 ⇔ H26 = +0.062 ⇒ 26% H24, H78 ⇔ H17 = +0.069 ⇒ 27% H40, H34 ⇔ H35 = +0.017 ⇒ 32%

777 −14 kJ mol−1 . This is 2.5 times stronger than the previously mentioned Me · · · Me interaction and is in full agreement with the well-known increase in strength of the van der Waals interaction with the atomic number. Figure 41 shows the hexagonal 2D packing resulting from these interactions between nitro and isopropoxy groups. One may also take a look at van der Waals interactions found in the very similar ethoxy-based tetramer. Comparison of the EB value for the full network (−148746 kJ mol−1 ) to the EB value of an isolated ethoxy-based tetramer (−148557 kJ mol−1 ), leads to a difference 8E = −189 kJ mol−1 . As shown in Table 10, the networking interactions are found to be completely different from the previous case. Again, by decreasing order of importance: 1. Interaction between four terminal OEt groups, one borne by the Ti2 atom and the three others by the Ti1 atom. The Ti2-OEt group is characterized by 952% for the C13 methine carbon, (27%, 20%) for the methine H atoms, and (19%, 12%) for the methyl H atoms. The large value (952%) found for the C13 atom comes from an almost null charge in the network associated with a change in sign of the charge on going from the crystal to the free state. The most involved Ti1-OEt moiety is based on atom C5: 71% for the methine carbon, (29%, 28%) for the methine H atoms, and (23%, 16%) for the methyl H atoms. The least involved is based on the C3 atom with 47% for just one H atom of the methylene group. The last Ti1-OEt group interacts mainly through its H atoms: (60%, 15%, 12%) for the H atoms of the methyl group, (29%, 14%) for the H atoms of the methylene group, and only 16% for the methine carbon.

Note: The syntax is molecular labels ⇔ crystalline label = molecular charge ⇒ retrosynthetic index RI.

1. The methine group (C17) of a terminal OPri group borne by the Ti2 atom (32%). Methyl groups of this moiety interact more weakly (11% and 12%). 2. The methyl group (C8) of a terminal OPri group borne by the Ti1 atom (27%). After come the methine group (19%) and the other methyl group (13%). 3. One methylene arm (C13, -Ti2 ) of the tripod ligand (26% and 23% for both H atoms). The other Ti2 arm (C12) displays negligible interaction ( 100 C) under

Molecular Tectonics in Sol–Gel Chemistry

autogeneous pressure. Thus, using ethylenediamine or 1,3diaminopropane, it was possible to prepare two new layered oxyfluorinated titanium(IV) phosphates, Ti2 (PO4 )2 F4 · H3 NCH2 CH2 NH3 and Ti2 (PO4 )2 F4 · H3 NCH2 CH2 CH2 NH3 · H2 O [459]. Using a similar procedure, a layered phase [H3 NCH2 CH2 NH2 ][TiOPO4 ] free of halogen atoms may be obtained [460]. As shown in Figure 83a, chains of trans corner-sharing TiO5 N octahedra linked through 3 phosphato bridges form these layers. The protonated amino group points to the interlayer space interacting with terminal P O groups by strong hydrogen bonds. A similar structure was also obtained starting from a mixture of Ti(OBun )4 , H3 PO4 , and ethylenediamine [461] in the presence of hydrogen peroxide [462]. Increasing the phosphoric acid concentration in this system leads to two titanium phosphates, [TiO(HPO4 )2 ][H3 NCH2 CH2 NH3 ] and [(TiO)3 (PO4 )6 ] · 5[H3 NCH2 CH2 NH3 ] · 2[H3 O] [463]. Figure 83b shows the one-dimensional chiral chains found in this last compound. They are built up from cis corner-sharing [TiO6 ] octahedra running along a 21 -screw axis and stabilized by 2 -phosphato bridges. Another kind of monodimensional chain is encountered in the crystal structure of [TiO(O3 PCH2 PO3 )] (NH4 )2 obtained from a mixture of hydrous TiO2 , methylenediphosphonic acid, and ammonia [464]. The chain is built up of trans corner-sharing TiO6 octahedra with (di-2 )methylenediphosphonato bridges (Fig. 84a). If HF replaces ammonia in this system, a quite different structure, [(Ti3 O2 )(H2 O)2 (O3 PCH2 PO3 )2 ] · 2H2 O, was obtained [465]. In this new titanium(IV) diphosphonate, trans corner-shared trimeric units of TiO6 octahedra are linked together via (di3 )-methylenediphosphonato bridges (Fig. 84b). This delimits a three-dimensional hybrid network with cross-linked 10-, 7-, and 6-membered ring tunnels along a, b, and c, respectively.

805

Figure 84. Crystalline structures of some hybrid organic–inorganic titanium(IV) diphosphonates. (a) Linear trans corner-sharing hybrid chain of TiO6 octahedra with (di-2 )-methylenediphosphonato bridges and H-bonded ammonium ions in the crystal structure of catena[diammonium (2 -oxo)-(methylenediphosphonato-O,O ′′ )titanium(IV)]. (b) Hybrid three-dimensional framework based on trans corner-shared trimeric units of TiO6 octahedra linked together via (di-3 )-methylenediphosphonato bridges in the crystal structure of catena-[bis(4 -methylenediphosphonato)-bis(2 -oxo)-diaqua-trititanium(IV) dihydrate].

4.4. Hybrid Materials Obtained in the Presence of Organic Templates Used in conjunction with surfactants or polymers, titanium compounds may yield very interesting new materials.

4.4.1. Sol–Gel Syntheses Using Surfactant Templates The most well known application of these hybrid materials was the elaboration of mesoporous molecular sieves assisted by the self-organization of surfactant molecules.

Figure 83. Crystalline structures of some hybrid organic–inorganic titanium phosphates. (a) Hybrid layer based on trans corner-sharing chain of TiO5 N octahedra linked together through 3 -phosphato bridges in the crystal structure of catena[(3 -phosphato)-(2 -oxo)-(2ammonio-ethylamino)-titanium(IV)]. (b) Hybrid helix based on cis corner-sharing chain of TiO6 octahedra with 2 -phosphato bridges and H-bonded ethylenediamine molecules in the crystal structure of catena-[pentakis(ethane-1,2-diammonium)-bis(hydroxonium)-bis(2 oxo)-hexakis(2 -phosphato-O,O ′ )-tri-titanium].

Mesoporous Titania The first example was the elaboration of Ti-MCM-41, a titanium-substituted derivative of hexagonal mesoporous silica MCM-41, from the basic hydrolysis of a mixture of Ti(OPri )4 , Si(OEt)4 , and CTAB, that is, cetyltrimethylammonium bromide, under hydrothermal conditions [466, 467]. A very similar material displaying a hexagonal arrangement of mesopores, Ti-HMS, may be obtained after gelation at room temperature of a Ti(OPri )4 , Si(OEt)4 , DDA (dodecylamine) mixture by alcoholic HCl solutions [467]. Such mesoporous phases were able to perform the selective catalytic oxidation of benzene

806 into phenol by H2 O2 . They were also active in the transformation of a much larger substrate such as 2,6-di-tertbutylphenol into quinone, a reaction not possible within the micropore structure of TS-1 (titanium silicalite). Soon after, using tetradecyl phosphate, a hexagonally packed mesoporous TiO2 called Ti-TMS1 was reported [468]. Later, it was shown [469] that this material may well be lamellar and better described as titanium oxo-phosphate. A new synthetic approach using DDA was then tried, leading to a rather unstable material [470]. Several other approaches have been described to get a thermally stable mesoporous TiO2 , such as the use of CTA[Ti(OCH2 CH2 O)3 ] [471], CTA mixed with soluble peroxytitanates [472], and the atrane route using triethanolamine complexes and CTAB [473]. The preparation of a titanium oxo-phosphate displaying a high surface area using a nonionic surfactant (polyethyleneoxide dodecanol + 5EO) has also been described [474]. The detailed mechanisms involved in the formation of these mesoporous phases from solute species remain unclear. Possible identified pathways involve the metallate rod assembly, the metallate layer puckering, the charge density matching, the folding of sheets around intercalated surfactant molecules, the metallatropic liquid crystal route, and the metallate rod clusters [475]. Among the catalytic applications of these Ticontaining mesoporous materials, one may cite oxidation of olefins, conversion of linalool into cyclic furan and pyran hydroxyl ethers, and hydroxylation of benzene derivatives [475]. Hollow Titania Fibers The use of surfactant molecules in the elaboration of porous materials is not limited to mesoporous phases. Thus, Ti(OPri )4 may be gelled through hydrogen-bonding interactions with the amine group of N -carbobenzyloxy-l-isoleucylaminooctadecane molecules [476]. After drying, a three-dimensional hybrid network was formed, displaying fibers 300–1500 nm in diameter. After calcination at 450  C, hollow TiO2 fibers 15–150 nm in diameter of both anatase and rutile structure (particle size, 15–30 nm) were obtained. TiO2 hollow fibers could also be prepared using supramolecular selfassemblies based on the sol–gel polymerization of Ti(OPri )4 with the surfactant trans-(1R,2R)-1,2-cyclohexane-di-(11aminocarbonylundecylpyridinium) hexafluorophosphate by ammonium hydroxide or HCl aqueous solutions [477]. In both cases, fibrous aggregates with diameters of 150–600 nm were obtained. However, owing to the positive charge present on the surfactant molecule, the fibrous structure could be preserved after calcination at 450  C only for the material synthesized under basic conditions.

4.4.2. Sol–Gel Syntheses Using Organic Polymers Mixing titanium alkoxides with polymeric materials is a very old idea that was used to produce water-repellent fabrics [478] or to promote rapid drying of oils, paints, and inks [293]. Titanium alkoxides have also been used as adhesion promoters in cellophane–polyethylene, mylar–polyethylene, and aluminum–polyethylene laminates [305]. Mesoporous Titania Most recent applications involve the use of amphiphilic block copolymers for the templating

Molecular Tectonics in Sol–Gel Chemistry

syntheses of mesoporous metal oxides with large ordering lengths and semicrystalline framework. The main advantage in using block copolymers instead of low-molecular-weight surfactants lies in the fine-tuning of the interactions between the inorganic and organic species. Such a control is obtained through variation of the chemical composition and/or variation of the chain lengths of the various blocks. For example, using triblock poly(alkylene) oxide polymers such as EO20 PO70 EO20 [EO = CH2 CH2 O, PO = CH2 CH(Me)O] as structure-directing agents, it was possible to obtain a 2D hexagonal mesophase of TiO2 by aerial hydrolysis of TiCl4 /EtOH mixtures [479]. A similar experiment performed with diblock polymers such as EO75 BO45 [BO = CH2 CH(Et)O] yielded instead a cubic Im3m mesophase of TiO2 . The mesoscopic order present in these hybrid materials is preserved after calcination at 400  C in air, yielding mesoporous titania with mean pore sizes of 65–70 Å and walls made of anatase nanocrystals of about 3 nm in size. The interactions between these PEO-based templates and metallic centers have been studied in some detail [480]. Briefly, in low-water-content media, strong chelation between metal centers and nonionic polar heads allows polymer unfolding, leading to wormlike phases. Larger quantities of water and acid seem to weaken the coordination bonds, leading to enhanced folding of the polymer and thus to more ordered mesophases. Another interesting aspect of these PEO-based systems lies in the possibility of using nano building blocks such as [Ti12 O16 (OPri )16 ] (Fig. 39c), [Ti16 O16 (OEt)32 ] (Fig. 38c), and [Ti18 O22 (OBun )26 (acac)2 ] (Fig. 58c) whose core structures can be preserved in the hybrid phase [481]. Another related strategy for assembling titanium oxo clusters into mesostructured hybrid materials is to use dendrimers as demonstrated by the reaction between [Ti16 O16 (OEt)32 ] and S P(p-OC6 H4 X)3 , where X stands for CH N N(Me)P(S)(p-OC6 H4 -R)3 and R for CH2 OH or CH2 CH COOH [482]. Extensions of this nanobuilding-block approach to other systems have recently been reviewed [483]. Polymerization of Nano Building Blocks Another strategy that has been used to obtain transition metal– based hybrid organic–inorganic materials was to use prefunctionalized metal oxo-alkoxides containing a polymerizable coordinating ligand located at the periphery. The radical-initiated polymerization of the ligand usually performed in nonprotic solvents then allows the assembly of nano building blocks into a coherent material [483– 486]. In this case, two different synthetic routes have been investigated. The first one (surface modification method) involves grafting a multidentate ligand (usually carboxylate or -diketonate derivative) to a preformed oxo-alkoxide. An obvious drawback of this method is the possible occurrence of molecular rearrangements during the grafting process, as evidenced in the case of the reaction between [Ti7 O4 (OEt)20 ] and benzoic acid [447]. The other route (in-situ assembly) involves the formation of the oxo-alkoxide in the presence of the polymerizable ligands. For example, polymerization of the oxo-titanate oligomers [Ti6 O4 (OEt)8 (OMc)8 ] (Mc = CO C(Me) CH2 ) or [Ti4 O2 (OPri )6 (OAcr)6 ] (Acr = CO CH CH2 ) with methylmethacrylate (MMA) or methacrylic acid (MA)

Molecular Tectonics in Sol–Gel Chemistry

co-monomers (1 ! 50–1 ! 200 molar ratio) in benzene or toluene resulted in polymers in which the polymer chains are efficiently cross-linked by the oxo-titanate complex [484]. A good way to check the integrity of the titanium-oxo core in this kind of polymerization is to rely on 17 O-NMR solid-state measurements [483]. Such hybrid polymeric materials generally display higher glass transition, improved mechanical properties, and insolubility in organic solvents, but are nevertheless able to undergo swelling, with a solvent uptake dependent on the proportion of oxo-metallate complexes [484]. Sometimes, the polymerizable ligand may be formed as a result of an aldol condensation as was observed by reacting Ti(OPri )4 with acetone, yielding the enolate derivative [Ti3 (3 -O)2 (OPri )5 (OCMe CH2 )3 (i PrOH)] [485]. As the crystallographic data of this compound were never published, the differences with the closely related and well-characterized trinuclear complex [Ti3 (3 O)(OPri )7 {Me2 C(O)CH C(O)CH2 C(O)Me2 }] obtained under similar conditions [285, 350] cannot be pointed out. Another side reaction is the possible cleavage of the C O bond by the alkoxide, leading to the loss of the polymerizable site as was observed in the reaction of titanium isopropoxide with 2-hydroxyethylmethacrylate (HEMA) [312]. A good solution was provided by the use of butenediol derivatives such as [Ti4 (OPri )8 (OCH2 CH CHCH2 O)4 ] that have been used for the synthesis of doped microcellular materials via copolymerization of polystyrene and divinylbenzene mixtures in biphasic media [324]. Such low-density microcellular foams have proven to be useful as deuterium and tritium sponges in direct-drive target designs for internal confinement fusion experiments. They may also be obtained using [Ti(OPri )2 (AAEMA)2 ] (HAAEMA = 2-(methacryloyl)oxyethyl acetoacetate) or [Ti(APO2 )2 ] (APO2 H2 = 3-allyloxypropane-1,2-diol) derivatives [324].

4.4.3. Nanocoating and Nanocasting Processes Another powerful way to make hybrid organic–inorganic materials is the nanocoating or nanocasting approach. This involves using the sol–gel process to cover a material (template) with a layer on the nanometer scale or to cover a nanoscale entity [487]. If the template is of an organic nature (emulsion droplets, polymer spheres, or gels), a truly organic–inorganic material is obtained, which, after calcination, may lead to three-dimensional structures displaying elaborate pore architectures. If the template is of an inorganic nature, a core–shell structure or a nanocomposite is obtained that may display optimized physical properties. Macroporous Titania The formation of ordered macroporous materials with periodicity in three dimensions and pore diameters comparable to optical wavelengths is an experimental challenge for catalysis, large-molecule separation processes, and elaboration of thermal, acoustic, or electrical insulators. The simplest synthetic route for such a TiO2 -based material involved the deposition, under vacuum, of millimeter-thick layers of latex spheres on filter paper in a Buchner funnel. Dropwise addition of titanium tetraethoxide while suction is being applied, followed by drying and calcination at 575  C, leads to anatase particles

807 (20–35 nm in diameter) [488]. These particles display highly ordered hexagonal packing with 320- to 360-nm voids over a range of hundreds of micrometers. Such a simple process is, however, not well suited for the preparation of photonic crystals made of air spheres in titania. Such materials are useful for creating photonic band gaps or optical stop bands (frequency ranges that will not propagate light owing to multiple Bragg reflections). A first route able to generate photonic band-gap materials involved the formation of a stable nonaqueous monodisperse emulsion. This emulsion may be obtained by mixing formamide and iso-octane in the presence of a symmetric triblock copolymer, poly(ethylene glycol)20 –poly(propylene glycol)70 –poly(ethylene glycol)20 , as a surfactant with silicone oil to prevent Ostwald ripening [489, 490]. Above a volume fraction of about 50%, such monodisperse emulsion droplets spontaneously order to form a close-packed structure. This droplet structure can then be permanently captured by gelation of the liquid in which the droplets are suspended. For TiO2 , the gelling agent may be ammonia. It was added to a sol obtained after hydrolysis by aqueous formamide of a titanium isopropoxide/acetylacetone mixture with all the isopropanol removed by a double extraction with a fivefold excess of hexanes [489]. The complete removal of the alcohol produced by the hydrolysis reaction was mandatory to avoid destabilization upon mixing this sol with the emulsion. After heat treatment at 1000  C of the hybrid gel, a macroporous rutile phase was obtained displaying highly uniform, spherical pores with sizes in the 50-nm to 10-m range and lattice porosities up to approximately 90%. Another route to large macroporous photonic titania crystals involved the growth of a colloidal crystal (opal-like material) by controlled sedimentation and drying of a 10 vol% colloidal suspension of polystyrene latex spheres in water [491, 492]. Then, the interstitial space present in these synthetic opals was infiltrated from 1 to 8 times with an ethanolic solution of titanium alkoxides, Ti(OR)4 (R = Et, Prn , Pri ), followed by hydrolysis with water from air. Calcination at 450  C yielded inverse opals made of anatase crystals with an average grain size of 202 ± 12 nm. The resulting material displays a nearly perfect hexagonal arrangement of macropores of radius between 322 ± 3 nm and 177 ± 2 nm and with a volume fraction between 5 and 12 vol% TiO2 [492]. A further refinement of this infiltration technique involved the use of polystyrene colloidal spheres coated with polyelectrolyte multilayers [493]. In this case, the pore morphology and the resulting macroporous structures depend on the nature of the multilayers deposited on the colloidal spheres, while the wall thickness of the pores can be tuned by altering the number of multilayers. One important limitation of this two-step procedure is, however, the quality of the colloidal crystal template before infiltration. Consequently, a simpler method involving the fabrication of the template and the infiltration at the same time has recently been described [494]. The basic idea was to infill ultrafine TiO2 particles into the voids of an ordered template directly by means of a local sucking capillary pressure. This could be easily realized by dipping a vertical substrate (glass, ITO, quartz slides) into a slurry containing polystyrene spheres and the ultrafine particles. Owing to the small size of the TiO2 particles (around 10 nm) compared with that of the polystyrene particles (several

808 hundred nanometers), the voids can be completely filled during the assembly. Consequently, most defects within the template can be immediately mended by the capillary pressure. Highly ordered three-dimensional porous TiO2 structures with macropores in the range of 300 to 600 nm were obtained using this cooperative method of assembly [494]. Polymer Gel Templates Another way to obtain highly porous oxide networks is to use a polymer gel template such as acrylamide/glycidyl methacrylate made of cross-linked thin fibers [495]. After exchange of the water contained within the gel by isopropanol, a titanium(IV) isopropoxide solution was permeated and further hydrolyzed by an isopropanol/water mixture (1 ! 1 by volume). Drying of the gel followed by calcination up to 1000  C then yielded corallike TiO2 networks. Depending on the calcination temperature, anatase or rutile phases are formed displaying pore sizes ranging from 100 nm to micrometers in diameter and with wall thickness of about 100–150 nm [495]. By playing with the chemical nature of the polymer template, TiO2 networks displaying porosities as high as 99% and surface areas from 5 to 100 m2 g−1 could be easily produced [496]. A closely related process concerns the use of a cellulose acetate (CA) membrane as the polymeric template [497]. It involves dipping the CA membrane in a closed vessel containing the titanium alkoxide, followed by hydrolysis with an isopropanol/water solution (50 ! 50 v/v). As before, drying and heating at 450  C produce a TiO2 material (particle size between 45 and 150 nm) with a thickness of about 80 m. This material closely resembles the tricontinuous pore structure of the initial CA membrane. A quicker process involves placing the membrane on a glass frit filter and applying vacuum. The metal alkoxide is then dripped onto the membrane, followed by the alcohol/water mixture [498]. Hollow Titania Spheres An alternative to the coating of a 1D, 2D, or 3D polymeric template by hydrolyzing titanium alkoxides is to use 0D templates such as polystyrene lattices in order to produce hollow spheres of TiO2 . Accordingly, mesoscale hollow spheres of ceramic materials are useful in many areas: encapsulation of drugs or biologically active agents, artificial cells, low-weight fillers, and so on [497]. Thus, submicrometer-sized anionic polystyrene lattices have been coated with uniform layers of amorphous TiO2 by hydrolysis of ethanolic solutions of Ti(OBun )4 containing the polymer cores and poly(vinylpyrrolidone) to prevent aggregation [499]. Calcination of these core–shell materials between 250 and 900  C led to hollow TiO2 particles of about 0.5 m in diameter. In such a simple method, it may, however, be difficult to control the homogeneity and thickness of the coating. Further refinements were then achieved following two different routes. In the first one, a crystalline array of polystyrene beads was fabricated between two glass substrates and infiltrated after drying by a solution of titanium isopropoxide in isopropanol (1 ! 19 v/v) through capillary action [497]. After gelation by moisture in air and partial drying, the cell is immersed in toluene to dissolve the polystyrene template, and the hollow spheres are released after sonication in a water bath of the disassembled cell. The voids of the resulting TiO2 hollow spheres were between 190 and 380 nm in diameter with a wall thickness of about 30–100 nm, depending

Molecular Tectonics in Sol–Gel Chemistry

on the concentration of the sol–gel solution [497]. The second route is based on the remarkable layer-by-layer (LbL) self-assembly technique [500]. It is based on the alternate adsorption of polycation and polyanion layers from their aqueous solutions, leading to multilayer films displaying a thickness controlled with a nanometer-scale precision [500]. This method has been very recently applied to the elaboration of titania nanosheet/polydiallyldimethylammonium composite films, where titania nanosheets were prepared from exfoliation of an acid-exchanged layered titanate [500]. Preparation of the template with this technique involved alternate deposition on negatively charged polystyrene (PS) spheres of a positively charged polymer such as poly(diallyldimethylammonium chloride) (PDADMAC) or poly(allylaminehydrochloride) (PAH) and of a negative polymer such as poly(sodium-4-styrenesulfonate) (PSS) [501]. Consequently, for a three-layer template (PS/PDADMAC/PSS/PDADMAC; PE3 ), one gets positively charged polymer particles, while for a PE4 structure (PS/PDADMAC/PSS/PDADMAC/PSS), the surface charge becomes negative. The role of these initial electrolyte layers is to produce a uniform and homogeneous surface for subsequent nanoparticle adsorption. Negatively charged TiO2 nanoparticles may be produced after a hydrothermal treatment of a titanium(IV) bis(ammonium lactato)dihydroxide solution, leading to a milky-white sol of TiO2 anatase nanoparticles (O potential of −40 mV for a diameter of about 5 nm) stabilized by lactate ions. On the other hand, a positively charged TiO2 anatase colloid (O potential of +42 mV for a diameter of about 6 nm) may be obtained by ammonia hydrolysis of TiCl4 after washing and redispersion by nitric acid under ultrasonic treatment [501]. When the negatively and positively charged sols are mixed with solutions containing PE3 - or PE4 -precoated PS spheres (diameter 200–700 nm), respectively, adsorption occurs, leading, on average, to a coating of about 1–3 monolayers of TiO2 nanoparticles. After washing by centrifugation, further deposition of three PE layers (PSS/PDADMAC/PSS for positively charged nanoparticles and PDADMAC/PSS/PDADMAC for a negatively charged sol) makes the surface available for a new deposition cycle. At least three TiO2 nanoparticles/PE3 layers are needed to get TiO2 hollow spheres that do not collapse after removal of the template by calcination at 500  C.

4.4.4. Core–Shell Structures The formation of core–shell structures is obviously not limited to polymeric materials. By using an inorganic template, other interesting materials could be obtained. Hybrids with Titania Shells First attempts in this domain involved the coating of ZnO [502] and copper(II) basic carbonate [503] monodisperse particles by the controlled hydrolysis of titanium butoxide in ethanol solutions. Moreover, owing to the considerable interest in catalytic, pigment, and photonic crystal applications, TiO2 -coated silica spheres were obtained using either titanium tert-butoxide in tetrahydrofuran [504] or TiOSO4 in sulfuric acid [505]. Later on, the process was optimized by hydrolyzing titanium nbutoxide in ethanol solutions, yielding titania coatings, ranging from sub-monolayer to 7 nm (∼20 monolayers) thick, on monodisperse silica spheres 270 nm in diameter [506].

Molecular Tectonics in Sol–Gel Chemistry

A further improvement of the method with silica spheres 550 nm in diameter allowed for an increase in the thickness of the TiO2 coating up to 46 nm (∼125 monolayers of titania) [507]. Metallic core–shell systems have also been investigated. For example, silver cores coated by a 1- to 2-nm layer of titanium oxide can be readily obtained by reduction of Ag+ ions by a DMF/ethanol mixture in the presence of Ti(OBun )4 and acetylacetone [508]. These positively charged core–shell nanoparticles can then be further assembled by the layer-by-layer assembly technique to form closely packed layers interlaced with polyelectrolytes [poly(acrylic acid) and poly(diallyldimethylammonium chloride) as negatively and positively charged polymers]. This stratified core– shell hybrid material was shown to display unique structure and catalytic properties associated with the original electrontransport properties [508]. Similarly, gold-titania core–shell nanoparticles have been obtained by treating gold particles with a surfactant such as sodium 10-mercaptodecane sulfonate, followed by the electrostatic layer-by-layer self-assembly of poly(diallyldimethylammonium chloride), poly(sodium-4-styrenesulfonate), and a negatively charged sol of TiO2 particles made from thermohydrolysis of titanium(IV) bis(ammonium lactato)dihydroxide solutions [509]. Anatase particles forming a shell thickness of about 10 nm around gold particles were evidenced in transmission electron micrographs of these organic–inorganic hybrid systems. A last original example of the templating process involves the use of an anodically grown aluminum oxide displaying a nanostructure consisting of long and narrow holes with diameters in the range of 10–200 nm according to the anodizing voltage used and subsequent etching treatments [510]. Using this template, an array of TiO2 nanotubes with inner diameter between 70 and 100 nm could be prepared by electrochemical deposition onto a poly(methyl methacrylate) (PMMA) replicated negatype of the porous alumina membranes. A much simpler method allowing for the synthesis of TiO2 tubules and fibrils from these membranes involved the dipping of the template into a milky-white TiO2 sol made after acid hydrolysis (HCl) of Ti(OPri )4 /EtOH solutions [511, 512]. Bundles of single-crystal anatase TiO2 nanofibrils with diameters of 22 nm were obtained after drying and calcination at 400  C of these membranes. Hybrids with Titania Cores Another class of hybrid materials is obtained when the surface of titania particles is modified by an organic or inorganic layer. For example, smart methods for polymerizing methylmethacrylate at the surface of nanometric titania particles have been developed in the paint and polymer industries [513]. In the domain of solar-energy conversion, nanocrystalline TiO2 – (MoO3 )x core–shell materials may be readily synthesized by a co-nucleation of polyoxometallates at the surface of surfactant micelles [514]. The synthesis involved mixing of aqueous solutions containing titanium(IV) bis(ammonium lactato)dihydroxide (NH4 )2 Ti(OH)2 (C3 H4 O3 )2 , cetyltrimethylammonium chloride, and Na4 Mo8 O26 at 70  C. The nanocrystalline core–shell material is obtained after washing, drying, and calcination at 450  C and displays a photoabsorption energy (PE) correlated with the nanoparticle size that can be readily adjusted from 8 nm down to 4

809 nm. Such core–shell particles showed a PE redshift from 2.88 to 2.60 eV with decreasing particle size [514]. This is in deep contrast with bulk TiO2 characterized by a mismatch between the band-gap energy (3.2 eV) and the most intense region of the solar spectrum centered at 2.6 eV. Still, in photovoltaic applications, electrochromic compounds are materials that change in color on application of a potential and are very interesting for large-segment static displays. TiO2 , being transparent to visible light and displaying electronic conductivity with a good affinity for defined ligands (bipyridinium salts, Prussian blue), is thus perfectly suited for these applications. Consequently, nanocrystalline electrodes derivatized by phosphonated triarylamines [515], mono-, di-, and trimeric N ,N ′ -dialkyl- or diphenyl-4,4′ bipyridinium salts [516, 517], and bis(2-phosphonoethyl)4,4′ -bipyridinium dichloride [518] have been synthesized. These hybrid nanocrystalline TiO2 layers can then be used for the elaboration of ultrafast electrochromic windows and displays. In this domain, nanocrystalline materials offer the opportunity to have fast interfacial electron transfer between the nanocrystal and the adsorbed modifier. They also provide high surface area of the support that amplifies optical phenomena by 2 or 3 orders of magnitude [516]. One then benefits from the long-term stability of solid-state devices as well as the sharp colors and fast switching of organic devices.

4.5. Hybrid Materials Involving Biological Matter Interactions between titanium alkoxides and biological matter have a quite old history. In this field, interest in titania mainly arises from its nontoxicity, high insolubility in the whole range of pH, and strong chemical inertness.

4.5.1. Cellulose Gelation and Enzyme Immobilization First applications in the textile industries include the gelation of cellulosics or proteinaceous materials such as wool or silk [519]. Since cellulose is a polymer of -1,4-linked dglucopyranose units, the 2- and 3-hydroxy vicinal diol groups are expected to be involved in chelate formation only. Consequently, the cross-linking of cellulose chains by Ti atoms should occur for steric reasons with the remaining 6-hydroxy group. On the other hand, for proteinaceous molecules, groups that may act as ligands toward Ti atoms are the free carboxy groups from the C terminus and acidic amino acids, the phenolic hydroxy groups from tyrosyl residues, the alcoholic hydroxy groups of seryl and threonyl residues, free sulfhydryl groups from any cysteinyl residues, and amino groups from the N terminus of A-amino groups of lysyl residues [520]. For enzymes carrying SH groups, one may also use Sn2+ as a chemical linking agent [512]. Enzymes are also protein-based materials. They have been used by man for hundreds of years in the preparation of food, drink, and clothing. Consequently, there is a considerable interest in immobilizing these enzymes onto an insoluble carrier for industrial purposes. Among the obvious advantages of insolubilized enzymes, one may cite: easy separation between the substrate and soluble products by filtration or centrifugation, packing into columns for continuous conversion processes,

Molecular Tectonics in Sol–Gel Chemistry

810 and changes in stability and kinetic properties upon immobilization [520]. Table 12 summarizes some bioencapsulates based on aqueous titania [520]. A very recent review of biodoped nanocomposite polymers involving sol–gel bioencapsulates is also available [521].

4.5.2. Blood and Hydroxyapatite Compatibility In the domain of titanium-based metallic implants, it was reported that the rutile form of TiO2 could be used to improve the blood compatibility of these materials [522]. On the contrary, the anatase form is characterized by low blood compatibility [523]. On the other hand, titania gels made from acid hydrolysis of Ti(OEt)4 and further treated by hydrogen peroxide were reported to display the highest blood compatibility [523]. Another important aspect of titanium-based metallic implants is their compatibility with hydroxyapatite (HAP) [Ca10 (PO4 )6 (OH)2 ] that have been widely used as bioceramics for clinical applications [524]. The preparation of functionally graded TiO2 /HAP coatings for Ti6 Al4 V implants, allowing the heterogeneous nucleation of HAP, was described starting from Ca(NO3 )2 · 4H2 O, H3 PO4 , CH3 OCH2 CH2 OH, Ti(OPri )4 , acetylacetone, and i PrOH was recently described [524].

4.5.3. Antitumor and Antiviral Agents Finally, one may also notice the low toxicity and high antitumor activities of biscyclopentadienyl- and bis(-diketonato)TiIV complexes against a wide range of murine and human tumors [525]. Moreover, Cp2 TiCl2 is known to exhibit pronounced antiviral, anti-inflammatory, and insecticidal activities [526]. Among such complexes, two of them, titanocene dichloride (Cp2 TiCl2 ) and budotitane [Ti(bzac)2 (OEt)2 ] (bzac = 1-phenylbutane-1,3-dionato ligand), are currently undergoing clinical trials [409]. An additional medical interest arises from the use of 45 Ti isotopes in radiopharmaceuticals [409]. In contrast with cisplatin-based drugs, the detailed mechanism of inhibition of DNA synthesis and mitotic activity by these complexes remains largely unknown.

Table 12. Biological materials (antibiotics, enzymes, bacteria) that have been used for immobilization on various organic or inorganic substrates. Biological material a

Antibiotics d-glucose oxidase Papain -Amylase, glucoamylase Dextranase Escherichia coli, Lactobacillus, Acetobacter

Support Cellulosics, paper, cotton, TiO2 , ZrO2 Chitin, alginic acid, glass, TiO2 Polypropylene, ZrO2 , glass, TiO2 Poly(4- and 5-acrylomidosalicylic acids), TiO2 TiO2 , ZrO2 TiO2 , ZrO2

a Ampicillin, chloramphenicol, gentamycin, kanamycin, neomycin, paromomycin, polymixin B, penicillin G, streptomycin, amphotericin B, natamycin. Note: Data gathered from [520]. For organic supports, coupling via hydrous titanium oxide was used.

5. CONCLUSION AND PERSPECTIVES Several conclusions may be drawn after this comprehensive review of titanium-based compounds and materials. (i) At a molecular scale, a large choice of monomeric complexes based on Ti O or Ti N bonds is already available. Most of these complexes have been characterized both in solution and in the solid state and display coordination numbers ranging from 4 to 8. The knowledge of their molecular structure is obviously of the utmost importance for mechanistic considerations particularly in the field of homogeneous catalysis. Surprisingly enough, their use in sol–gel syntheses was largely limited to titanium alkoxides. One may then hope that in the near future new TiO2 -based materials would be elaborated using the whole palette of TiIV coordination compounds and not only titanium alkoxides. Another neglected aspect of these complexes concerns their use in crystal engineering. With the considerable help provided by the PACHA formalism, it should be easier to set out the basic molecular interactions responsible for network formation in the solid state. This point is obviously of the utmost importance for a rational development of sol–gel syntheses and molecular tectonics approaches. (ii) At a nanometer scale, there have been considerable efforts to synthesize and characterize polynuclear titaniumbased complexes. The amount of well-characterized oxo complexes is, however, too limited as most of them are obtained through completely blind shake-and-bake processes. Worse, the detailed mechanistic pathways leading to their formation or to rearrangements of their core remain largely unknown. Unveiling these mechanisms would be of the utmost importance for a rational design of hybrid materials, and we think that titanium compounds should be used as a benchmark for the elucidation of nucleation and growth processes from solution. At this same scale, most TiO2 nanocrystals are elaborated after hydrolysis and condensation of titanium alkoxides. Here also, using the whole palette of TiIV complexes instead of just Ti(OR)4 derivatives would be of deep interest. The possible surface complexation, particularly by multidentate ligands, should be systematically studied and the resulting effect on size, shape, and morphology of the nanocrystals should be systematically investigated. Yet another largely neglected field concerns the mesostructure and mechanisms of formation of titania gels. If most past studies have focused on xerogels, the systematic use of atomic force microscopy should be particularly rewarding for the study of wet gels. (iii) At a macroscopic scale, eight TiO2 polymorphs have been isolated and characterized by X-ray diffraction. This observation raises the fascinating question of the possible existence of microporous TiO2 networks. Obviously, the problem of their stability relative to rutile or anatase phases for enthalpic and/or entropic reasons should be carefully studied. On the other hand, the meso- or macrostructuring of titania has been intensively developed in the past few years, but again only for rutile or anatase polymorphs. More effort is thus needed to apply these new techniques to other polymorphs. (iv) The lack of systematic studies devoted to the mesostructure of titania gels is probably responsible for the paucity of data concerning the biological applications of

Molecular Tectonics in Sol–Gel Chemistry

titania. This is rather surprising, as this oxide is perfectly suited (nontoxicity, insolubility in the full pH range, chemical inertness, etc.) to the elaboration of biocompatible materials. Consequently, it is anticipated that studies devoted to biomineralization processes involving titania will grow in importance in the next few years.

GLOSSARY Aquo cations Soluble cationic hydrated species [M(H2 O)N ]z+ displaying low electrical charge z < 3 and stable at low pH. Aquo ligand Formation of a coordination chemical bond between a water molecule and a cation (M OH2 type). Basic salt Crystalline phases containing hydrolyzed cationic species (see normal salt). Colloidal solution or sol Dispersion of solid particles (diameter 1–100 nm) in a liquid. Convergence parameter G Adjustable value in the reciprocal space (Å −1 unit) allowing to get the fastest convergence of a Madelung summation process for a given accuracy. Crystal Solid matter characterized by a well ordered atomic structure allowing X-ray diffraction. Crystal engineering Understanding of intermolecular interactions in the context of crystal packing and the use of this understanding in the design of new solids with desired physical and chemical properties. Density functional theory (DFT) Theoretical frame using the whole electronic density (r as basic variable instead of wave-functions ) r. Electric field gradient (efg) Second partial derivatives of a classical electrostatic potential V evaluated at a nuclear site. Electronegativity According to L. Pauling, “the power of an atom in a molecule to attract electrons to itself.” According to density functional theory, “the chemical potential of electrons in an atom or a molecule.” Electronic signature Set of parameters: mean electronegativity EN, global hardness GH, electrostatic balance EB, global ionicity GI, partial charges qi and frontier indexed fi computed using the PACHA formalism. Electrostatic balance
EB Summation over all possible atomic pairs (charges eqi and eqj at distance Rij ) of purely Coulombic contributions e2 qi qj /4EA0 Rij . Extended X-ray absorption fine structure (EXAFS) A spectroscopic technique for studying local order (first and second neighbors) in condensed matter. Frontier index Number f attached to an atomic site and ruling its chemical reactivity according to HSAB (hard and soft acids and bases) principle. The larger f , the higher the atomic polarizability of the site. Gel Dispersion of liquid droplets (diameter 1–100 nm) in a solid. Glass Solid matter displaying no crystalline order showing only X-ray diffusion. Global ionicity
GI Overall ionicity (ranging from 0 to 100%) of a given chemical compound in the PACHA formalism.

811 Global softness
GH Approximation of the HOMO– LUMO gap (I–A) in the PACHA formalism. Hardness Parameter inversely proportional to the polarizability (size) of the electronic cloud of an atom or a molecule (see softness). Hydrothermal synthesis Formation of crystalline phases from aqueous solutions at pressure higher than 1 atm. Hydroxo ligand Formation of a coordination chemical bond between a hydroxide ion OH− and a cation (M OH type). ICSD database Database located in Karlsruhe (Germany) gathering all published inorganic crystal structures displaying no C H bonds. LCAO-MO theory Theoretical frame using wave-functions based on linear combination of atomic orbitals (named molecular orbitals) and satisfying the time-independent Schrödinger equation H )  = E) . n -coordination mode Formation of n chemical bonds (bridges) between one single ligand and n cationic centers. Macroporous material Porous structure with pore diameters comparable to or larger than optical wavelengths. Madelung matrix A n × n square matrix whose nondiagonal elements are equal to 1/Rij (reciprocal of distance between atoms i and j) and whose diagonal elements are all equal to zero. This matrix may be contracted using strict mathematical rules for taking account the existence of symmetry elements and/or of periodic constraints. Mean electronegativity
EN Average common value for the electronic chemical potential reached by all atoms after addition q < 0 or removal q > 0 of electrons after atomic orbitals overlaps. Metal alkoxides Organometallic complexes of general formula M(OR)z R = Cn H2n+1  leading after hydrolysis and condensation to metallic oxides MOz/2 : M(OR)z + z/2 H2 O → MOz/2 : + z ROH. Mesoporous material Porous structure with pore diameters larger than 2 nm but smaller than optical wavelengths (less than ca 200 nm). Microporous material Porous structure with pore diameters smaller than 2 nm. Molecular tectonics Molecular-scale building of hybrid organic-inorganic materials using constructional processes based on supramolecular pre-organization, molecular recognition (templating) or cellular processing. Monodentate coordination mode Formation of a single chemical bond between a cation and an anion. Normal salt Crystalline phases containing non-hydrolyzed [M(H2 O)N ]z+ aquo-cations (see basic salt). Ostwald ripening Change upon aging of the size distribution of a collection of particles owing to the occurrence of redissolution/precipitation phenomena. Outer-sphere complex Stable association between a cation C+ and an anion A− mediated by a solvent molecule S: [C+ – S–A− ]. Oxo anions Soluble anionic species [MON ]2N −z− displaying high electrical charge z > 4 and stable at high pH. Oxo ligand Formation of a coordination chemical bond between an oxide ion O2− and a cation (M O type).

Molecular Tectonics in Sol–Gel Chemistry

812 PACHA model Non-empirical theoretical frame that uses Allen spectroscopic electronegativity scale and ab initio atomic radii for a fast and reliable evaluation of atomic partial charges from the sole knowledge of molecular or crystalline structures. Formally, it corresponds to a sphericalcharge approximation of density functional equations. Partial charge Number q attached to an atomic site in a chemical species equal to the difference between the atomic number Z and the actual total number of electrons N surrounding (on a time-average) this atom. Partial charge model (PCM) Empirical theoretical frame that uses the Allred-Rochow electronegativity scale for an ultra-fast evaluation of atomic partial charges from the sole knowledge of stoichiometry. It is particularly well suited for predicting chemical reactivity of solute chemical species whose detailed molecular structure remains unknown. Polyanions Small oligomeric species formed after adding an acid to oxo-anions. Polycations Small oligomeric species formed after adding a base to aquo-cations. Retrosynthetic index Number attached to an atomic site showing which parts of a molecular fragment are deeply involved in the building of a larger unit. This index may be obtained by comparing the partial charges computed when the fragment is embedded in its container and those computed for the same fragment isolated from its container. Softness Parameter proportional to the polarizability (size) of the electronic cloud of an atom or a molecule (see hardness). Sol See colloidal solution. Sternheimer anti-shielding factor Correction that should be applied to electric field gradients (efg) originating from sources external to an electron shell in order to account for the polarization of the charge distribution in the atomic core. THF Tetrahydrofurane. X-ray absorption near edge structure (XANES) A spectroscopic technique for studying nearest neighbors of an absorbing center in condensed matter.

REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9.

10. 11.

S. Mann, Nature 365, 499 (1993). H. Dislich, Angew. Chem., Int. Ed. Engl. 10, 363 (1971). K. S. Mazdiyasni, Ceram. Int. 8, 42 (1982). M. Henry, J. P. Jolivet, and J. Livage, Struct. Bonding 77, 153 (1992). J. P. Jolivet, M. Henry, and J. Livage, “Metal Oxide Chemistry and Synthesis.” Wiley, New York, 2000. H. Schmidt, J. Non-Cryst. Solids 100, 51 (1988). J. Livage, M. Henry, and C. Sanchez, Prog. Solid State Chem. 18, 259 (1988). C. J. Brinker and G. W. Scherer, “Sol–Gel Science.” Academic Press, San Diego, 1990. T. J. Barton, L. M. Bull, W. G. Klemperer, D. A. Loy, B. McEnaney, M. Misono, P. A. Monson, G. Pez, G. W. Scherer, J. C. Vartuli, and O. M. Yaghi, Chem. Mater. 11, 2633 (1999). M. Eddaoudi, D. B. Moler, H. Li, B. Chen, T. M. Reineke, M. O’Keefe, and O. M. Yaghi, Acc. Chem. Res. 34, 319 (2001). G. Férey, Chem. Mater. 13, 3084 (2001).

12. J. Livage and M. Henry, in “Ultrastructure Processing of Advanced Ceramics” (J. D. Mackenzie and D. R. Ulrich, Eds.), p. 183. Wiley, New York, 1988. 13. B. M. Gatehouse, S. N. Platts, and T. B. Williams, Acta Crystallogr., Sect. B 49, 428 (1993). 14. K. K. Wu and I. D. Brown, Acta Crystallogr., Sect. B 29, 2009 (1973). 15. C. F. Baes Jr. and R. E. Mesmer, “The Hydrolysis of Cations,” p. 148. Wiley, New York, 1976. 16. J. Kragten, “Atlas of Metal–Ligand Equilibria in Aqueous Solution,” p. 660. Ellis Horwood, Chichester, 1978. 17. I. A. Sheka and T. V. Pevzner, Russ. J. Inorg. Chem. 5, 1119 (1960). 18. T. C. W. Mak, Can. J. Chem. 46, 3491 (1968). 19. M. G. Reichmann, F. J. Hollander, and A. T. Bell, Acta Crystallogr., Sect. C 43, 1681 (1987). 20. W. Haase and H. Hoppe, Acta Crystallogr., Sect. B 24, 282 (1968). 21. J. Patarin, F. Marcuccilli-Hoffner, H. Kessler, and P. Daniels, Eur. J. Solid State Inorg. Chem. 31, 501 (1994). 22. S. Cohen, H. Selig, and R. Gut, J. Fluorine Chem. 20, 349 (1982). 23. D. Mootz, E. J. Oellers, and M. Wiebcke, Z. Anorg. Allg. Chem. 564, 17 (1988). 24. W. M. P. B. Menge and J. G. Verkade, Inorg. Chem. 30, 4628 (1991). 25. M. Fourati, M. Chaabouni, C. H. Belin, M. Charbonnel, J. L. Pascal, and J. Potier, Inorg. Chem. 25, 1386 (1986). 26. C. D. Garner and S. C. Wallwork, J. Chem. Soc. A 1496 (1966). 27. G. M. H. van de Velde, S. Harkema, and P. J. Gellings, Inorg. Chim. Acta 11, 243 (1974). 28. M. Haddad and F. Brisse, Can. Mineral. 16, 379 (1978). 29. A. Fester, W. Bensch, and M. Tromel, Acta Crystallogr., Sect. C 50, 850 (1994). 30. A. Fester, W. Bensch, and M. Tromel, Inorg. Chim. Acta 193, 99 (1992). 31. G. Lundgren, Ark. Kemi 10, 397 (1956). 32. M. A. K. Ahmed, H. Fjellvag, and A. Kjekshus, Acta Chem. Scand. 50, 275 (1996). 33. I. E. Grey and R. Stranger, J. Solid State Chem. 101, 331 (1992). 34. S. Krimi, I. Mansouri, A. El Jazouli, J. P. Chaminade, P. Gravereau, and G. Le Flem, J. Solid State Chem. 105, 561 (1993). 35. Yu. A. Ivanov, E. L. Belokoneva, Yu. K. Egorov-Tismenko, N. V. Simonov, and Yu. A. Ivanov, Dokl. Akad. Nauk SSSR 252, 1122 (1980). 36. J. L. Rodrigo, P. Carrasco, and J. Alamo, Mater. Res. Bull. 24, 611 (1989). 37. E. S. Lunezheva, B. A. Maksimov, and O. K. Mel’nikov, Kristallografiya 34, 674 (1989). 38. R. Duhlev, Acta Crystallogr., Sect. C 50, 1525 (1994). 39. R. M. Hazen, D. C. Palmer, L. W. Finger, G. D. Stucky, W. T. A. Harrison, and T. E. Gier, J. Phys.: Condens. Matter 6, 1333 (1994). 40. A. N. Christensen, E. K. Andersen, I. G. K. Andersen, G. Alberti, M. Nielsen, and M. S. Lehmann, Acta Chem. Scand. 44, 865 (1990). 41. S. Bruque, M. A. G. Aranda, E. R. Losilla, P. Olivera-Pastor, and P. Maireles-Torres, Inorg. Chem. 34, 893 (1995). 42. M. A. Salvado, P. Pertierra, S. Garcia-Granda, J. R. Garcia, J. Rodriguez, and M. T. Fernandez-Diaz, Acta Crystallogr., Sect. B 52, 896 (1996). 43. E. R. Losilla, M. A. G. Aranda, and S. Bruque, J. Solid State Chem. 125, 261 (1996). 44. A. M. K. Andersen, P. Norby, and T. Vogt, J. Solid State Chem. 140, 266 (1998). 45. D. M. Poojary, A. I. Bortun, L. N. Bortun, and A. Clearfield, J. Solid State Chem. 132, 213 (1997). 46. M. A. Salvado, P. Pertierra, S. Garcia-Granda, J. R. Garcia, M. T. Fernandez-Diaz, and E. Dooryhee, Eur. J. Solid State Inorg. Chem. 34, 1237 (1997).

Molecular Tectonics in Sol–Gel Chemistry 47. C. Serre and G. Férey, C. R. Acad. Sci. Paris, Sér. IIc 2, 85 (1999). 48. W. T. A. Harrison, T. E. Gier, J. C. Calabrese, and G. D. Stucky, J. Solid State Chem. 111, 257 (1994). 49. B. A. Maximov, N. E. Klokova, I. A. Verin, and V. A. Timofeeva, Kristallografiya 35, 847 (1990). 50. P. G. Nagornyi, A. A. Kapshuk, N. V. Stus’, N. S. Slobodyanik, and A. N. Chernega, Zh. Neorg. Khim. 36, 2766 (1991). 51. A. Robertson, J. G. Fletcher, J. M. S. Skakle, and A. R. West, J. Solid State Chem. 109, 53 (1994). 52. I. N. Geifman, N. G. Furmanova, P. G. Nagornyi, Li Don Yun, and M. V. Rotenfel’d, Kristallografiya 38, 88 (1993). 53. P. G. Nagornyi, A. A. Kapshuk, N. V. Stus’, and N. S. Slobodyanik, Russ. J. Inorg. Chem. 34, 1731 (1989). 54. M. L. F. Phillips, W. T. A. Harrison, G. D. Stucky, E. M. McCarron, J. C. Calabrese, and T. E. Gier, Chem. Mater. 4, 222 (1992). 55. P. G. Nagornyi, A. A. Kapshuk, N. V. Stus’, and N. S. Slobodyanik, Kristallografiya 35, 634 (1990). 56. I. Tordjman, R. Masse, and J. C. Guitel, Z. Kristallogr. 139, 103 (1974). 57. I. V. Voloshina, R. G. Gerr, M. Yu. Antipin, V. G. Tsirel’son, N. I. Pavlova, Yu. T. Struchkov, R. P. Ozerov, and I. S. Rez, Kristallografiya 30, 668 (1985). 58. P. A. Thomas, A. M. Glazer, and B. E. Watts, Acta Crystallogr., Sect. B 46, 333 (1990). 59. N. K. Hansen, J. Protas, and G. Marnier, Acta Crystallogr., Sect. B 47, 660 (1991). 60. E. L. Belokoneva, O. L. Slovokhotova, M. Yu. Antipin, V. G. Tsirel’son, and Yu. T. Struchkov, Dokl. Akad. Nauk SSSR 322, 520 (1992). 61. S. Dahaoui, N. K. Hansen, and B. Menaert, Acta Crystallogr., Sect. C 53, 1173 (1997). 62. P. A. Thomas, S. C. Mayo, and B. E. Watts, Acta Crystallogr., Sect. B 48, 401 (1992). 63. J. A. Kaduk and R. H. Jarman, Z. Kristallogr. 204, 285 (1993). 64. A. S. Lyakhov, A. F. Selevich, and A. I. Verenich, Zh. Neorg. Khim. 38, 1121 (1993). 65. H. Nyman, M. O’Keeffe, and J. O. Bovin, Acta Crystallogr., Sect. B 34, 905 (1978). 66. Y. K. Egorov-Tismenko, M. A. Simonov, and N. V. Belov, Dokl. Akad. Nauk SSSR 240, 78 (1978). 67. A. Ziadi, G. Thiele, and B. Elouadi, J. Solid State Chem. 109, 112 (1994). 68. A. Ziadi, H. Hillebrecht, G. Thiele, and B. Elouadi, J. Solid State Chem. 123, 324 (1996). 69. W. H. Zachariasen, Z. Kristallogr. 73, 7 (1930). 70. R. Mongiorgi and L. Riva di Sanseverino, Mineral. Petrol. Acta 14, 123 (1968). 71. J. A. Speer and G. V. Gibbs, Am. Mineral. 61, 238 (1976). 72. M. Taylor and G. E. Brown, Am. Mineral. 61, 435 (1976). 73. C. L. Hollabaugh and F. F. Foit Jr., Am. Mineral. 69, 725 (1984). 74. V. S. Urusov, N. N. Eremin, and O. V. Yakubovich, Kristallografiya 40, 485 (1995). 75. S. Kek, M. Aroyo, U. Bismayer, C. Schmidt, K. Eichhorn, and H. G. Krane, Z. Kristallogr. 212, 9 (1997). 76. W. T. A. Harrison, T. E. Gier, and G. D. Stucky, Zeolites 15, 408 (1995). 77. E. A. Behrens, D. M. Poojary, and A. Clearfield, Chem. Mater. 8, 1236 (1996). 78. M. S. Dadachov and W. T. A. Harrison, J. Solid State Chem. 134, 409 (1997). 79. D. M. Poojary, A. I. Bortun, L. N. Bortun, and A. Clearfield, Inorg. Chem. 35, 6131 (1996). 80. P. Pertierra, M. A. Salvado, S. Garcia-Granda, A. I. Bortun, and A. Clearfield, Inorg. Chem. 38, 2563 (1999). 81. M. Henry, C. Gérardin, and F. Taulelle, Mater. Res. Soc. Symp. Proc. 271, 243 (1992). 82. M. Henry, Mater. Sci. Forum 152–153, 355 (1994).

813 83. 84. 85. 86. 87. 88. 89. 90. 91. 92. 93. 94. 95. 96. 97. 98. 99. 100. 101. 102. 103. 104. 105. 106. 107. 108. 109. 110. 111. 112. 113. 114. 115. 116. 117. 118. 119. 120. 121. 122. 123. 124. 125. 126. 127.

M. Henry, Top. Mol. Org. Eng. 15, 273 (1997). M. Henry, Coord. Chem. Rev. 180, 1109 (1998). M. Henry, Am. Chem. Soc. Symp. Ser. 732, 277 (1999). T. M. Alam and M. Henry, Phys. Chem. Chem. Phys. 2, 23 (2000). A. Rammal, F. Brisach, and M. Henry, J. Am. Chem. Soc. 123, 5612 (2001). S. Weymann-Schildknecht and M. Henry, J. Chem. Soc., Dalton Trans. 2425 (2001). K. Gigant, A. Rammal, and M. Henry, J. Am. Chem. Soc. 123, 11632 (2001). M. Henry, Chem. Phys. Chem., 3, 561 (2002). J. Dubuc and M. Henry, Inorg. Chem., submitted. F. Biechel and M. Henry, Inorg. Chem., submitted. R. P. Feynman, Phys. Rev. 56, 340 (1939). P. Hohenberg and W. Kohn, Phys. Rev. B 136, 864 (1964). J. B. Mann, T. L. Meek, and L. C. Allen, J. Am. Chem. Soc. 122, 2780 (2000). J. B. Mann, T. L. Meek, E. T. Knight, J. F. Capitani, and L. C. Allen, J. Am. Chem. Soc. 122, 5132 (2000). J. T. Waber and D. T. Cromer, J. Chem. Phys. 42, 4116 (1965). L. Vegard, Z. Phys. 61, 185 (1930). R. Fischer and H. Ludwiczek, Monatsh. Chem. 106, 223 (1975). F. Schossberger, Z. Kristallogr. 104, 358 (1942). W. H. Baur, Naturwissenschaften 42, 295 (1955). S. Andersson, B. Collen, U. Kuylenstierna, and A. Magneli, Acta Chem. Scand. 11, 1641 (1957). W. H. Baur, Acta Crystallogr. 14, 493 (1961). W. H. Baur and A. A. Khan, Acta Crystallogr., Sect. B 27, 2133 (1971). S. C. Abrahams and J. L. Bernstein, J. Chem. Phys. 55, 3206 (1971). V. I. Khitrova, M. F. Bundule, and Z. G. Pinsker, Kristallografiya 22, 1253 (1977). E. P. Meagher and G. A. Lager, Can. Mineral. 17, 77 (1979). T. M. Sabine and C. J. Howard, Acta Crystallogr., Sect. B 38, 701 (1982). W. Gonschorek, Z. Kristallogr. 160, 187 (1982). W. Gonschorek and R. Feld, Z. Kristallogr. 161, 1 (1982). H. Seki, N. Ishizawa, N. Mizutani, and M. Kato, J. Ceram. Assoc. Jpn. 92, 219 (1984). R. Restori, D. Schwarzenbach, and J. R. Schneider, Acta Crystallogr., Sect. B 43, 251 (1987). J. K. Burdett, T. Hughbanks, G. J. Miller, J. W. Richardson, and J. V. Smith, J. Am. Chem. Soc. 109, 3639 (1987). K. Sugiyama and Y. Takeuchi, Z. Kristallogr. 194, 305 (1991). C. J. Howard, T. M. Sabine, and F. Dickson, Acta Crystallogr., Sect. B 47, 462 (1991). R. J. Swope, J. R. Smyth, and A. C. Larson, Am. Mineral. 80, 448 (1995). I. E. Grey, C. Li, C. M. MacRae, and L. A. Bursill, J. Solid State Chem. 127, 240 (1996). M. Henry, Solid State Sci., submitted. J. Pascual, J. Camassel, and H. Mathieu, Phys. Rev. B 18, 5606 (1978). L. Pauling, J. Phys. Chem. 56, 361 (1952). J. H. Binks and J. A. Duffy, J. Chem. Soc., Faraday Trans. 2 81, 473 (1985). F. Gervais, personal communication. L. A. Grunes, R. D. Leapman, C. N. Wilker, R. Hoffmann, and A. B. Kunz, Phys. Rev. B 25, 7157 (1982). B. Poumellec, P. J. Durham, and G. Y. Guo, J. Phys.: Condens. Matter 3, 8195 (1991). A. Stashans, S. Lunell, and R. W. Grimes, J. Phys. Chem. Solids 57, 1293 (1996). A. Fahmi, C. Minot, B. Silvi, and M. Causa, Phys. Rev. B 47, 11717 (1993). H. Shintani, S. Sato, and Y. Saito, Acta Crystallogr., Sect. B 31, 1981 (1975).

Molecular Tectonics in Sol–Gel Chemistry

814 128. O. Kanert and H. Kolem, J. Phys. C: Solid State Phys. 21, 3909 (1988). 129. Y. Kudoh and H. Takeda, Physica B and C 139, 333 (1986). 130. D. C. Allan and M. P. Teter, J. Am. Ceram. Soc. 73, 3247 (1990). 131. D. J. Lacks and R. G. Gordon, Phys. Rev. B 48, 2889 (1993). 132. K. M. Glassford and J. R. Chelikowsky, Phys. Rev. B 46, 1284 (1992). 133. K. M. Glassford, N. Troullier, J. L. Martins, and J. R. Chelikowsky, Solid State Commun. 76, 635 (1990). 134. F. Schossberger, Philos. Mag. 32, 505 (1916). 135. R. L. Parker, Z. Kristallogr. 59, 1 (1924). 136. M. Horn, C. F. Schwerdtfeger, and E. P. Meagher, J. Am. Ceram. Soc. 53, 124 (1970). 137. V. I. Khitrova, M. F. Bundule, and Z. G. Pinsker, Kristallografiya 22, 1253 (1977). 138. M. Sakata, M. Takagi, M. Takata, and C. J. Howard, Physica B 213–214, 384 (1995). 139. D.-D. Mo and W. Y. Ching, Phys. Rev. B 51, 13023 (1995). 140. H. Tang, H. Berger, P. E. Schmid, and F. Lévy, Solid State Commun. 87, 847 (1993). 141. N. Hosaka, T. Sekiya, M. Fujisawa, C. Sakoto, and S. Kurita, J. Electron Spectrosc. Relat. Phenom. 78, 75 (1996). 142. J. K. Burdett, Inorg. Chem. 24, 2244 (1985). 143. T. J. Bastow, M. A. Gibson, and C. T. Forwood, Solid State Magn. Reson. 12, 201 (1998). 144. T. J. Bastow and S. N. Stuart, Chem. Phys. 143, 459 (1990). 145. C. J. Jameson and H. S. Gutowsky, J. Chem. Phys. 40, 1714 (1964). 146. J. Vaara, J. Lounila, K. Ruud, and T. Helgaker, J. Chem. Phys. 109, 8388 (1998). 147. W. H. Flygare and J. Goodisman, J. Chem. Phys. 49, 3122 (1968). 148. K. M. S. Saxena and P. T. Narasimhan, Int. J. Quantum. Chem. 1, 731 (1967). 149. G. Malli and S. Fraga, Theor. Chim. Acta 6, 54 (1966). 150. C. F. Bunge, J. A. Barrientos, and A. V. Bunge, Atomic Data and Nuclear Data Tables 53, 113 (1993). 151. P. Blaha, D. J. Singh, P. I. Sorantin, and K. Schwarz, Phys. Rev. B 46, 1321 (1992). 152. E. N. Kaufmann and R. J. Vianden, Rev. Mod. Phys. 51, 161 (1979). 153. R. Weyl, Z. Kristallogr. 68, 239 (1928). 154. W. H. Baur, Acta Crystallogr. 14, 214 (1961). 155. T. J. Bastow, G. Doran, and H. J. Whitfield, Chem. Mater. 12, 436 (2000). 156. C. Gervais, M. E. Smith, A. Pottier, J.-P. Jolivet, and F. Babonneau, Chem. Mater. 13, 462 (2001). 157. T. P. Feist and P. K. Davies, J. Solid State Chem. 101, 275 (1992). 158. L. Brohan, A. Verbaere, M. Tournoux, and G. Demazeau, Mater. Res. Bull. 17, 355 (1982). 159. J. Akimoto, Y. Gotoh, Y. Oosawa, N. Nonose, T. Kumagai, K. Aoki, and H. Takei, J. Solid State Chem. 113, 27 (1994). 160. M. Latroche, L. Brohan, R. Marchand, and M. Tournoux, J. Solid State Chem. 81, 78 (1989). 161. P. Y. Simons and F. Dachille, Acta Crystallogr. 23, 334 (1967). 162. I. E. Grey, C. Li, I. C. Madsen, and G. Braunshausen, Mater. Res. Bull. 23, 743 (1988). 163. J. S. Olsen, L. Gerward, and J. Z. Jiang, J. Phys. Chem. Solids 60, 229 (1999). 164. H. Sato, S. Endo, M. Sugiyama, T. Kikegawa, O. Shimomura, and K. Kusaba, Science 251, 786 (1991). 165. C. J. Howard, R. J. Hill, and B. E. Reichert, Acta Crystallogr., Sect. B 44, 116 (1988). 166. K. Lagarec and S. Desgreniers, Solid State Commun. 94, 519 (1995). 167. S. Shankar and R. G. Parr, Proc. Natl. Acad. Sci. U.S.A. 82, 264 (1985). 168. R. Ruus, A. Kikas, A. Saar, A. Ausmees, E. Nommiste, J. Aarik, A. Aidla, T. Uustare, and I. Martinson, Solid State Commun. 104, 199 (1997).

169. 170. 171. 172.

173. 174. 175. 176. 177. 178. 179. 180. 181. 182. 183. 184. 185. 186. 187. 188. 189. 190. 191. 192. 193. 194. 195. 196. 197. 198. 199. 200. 201.

202. 203. 204. 205. 206. 207.

208.

P. I. Sorantin and K. Schwarz, Inorg. Chem. 31, 567 (1992). S.-K. Lin, J. Chem. Inf. Comput. Sci. 36, 367 (1996). S.-K. Lin, Int. J. Mol. Sci. 2, 10 (2001). E. T. Jaynes in “Maximum Entropy and Bayesian Methods” (C. R. Smith, G. J. Erickson, and P. O. Neudorfer, Eds.), p. 1. Kluwer Academic, Dordrecht, 1992. T. Nagase, T. Ebina, T. Iwasaki, H. Hayashi, Y. Onodera, and M. Chatterjee, Chem. Lett. 9, 911 (1999). Y. Zheng, E. Shi, S. Cui, W. Li, and X. Hu, J. Am. Ceram. Soc. 83, 2634 (2000). A. Pottier, C. Chanéac, E. Tronc, L. Mazerolles, and J.-P. Jolivet, J. Mater. Chem. 11, 1116 (2001). S. Komarneni, E. Breval, and R. Roy, J. Non-Cryst. Solids 79, 195 (1986). I. P. Saraswat, S. K. Srivasta, G. Bhattacharjee, and Sharadanand, J. Mater. Sci. Lett. 5, 795 (1986). P. Arnal, R. J. P. Corriu, D. Leclercq, P. H. Mutin, and A. Vioux, J. Mater. Chem. 6, 1925 (1996). H. Kominami, M. Khono, and Y. Kera, J. Mater. Chem. 10, 1151 (2000). C. Ligorio and L. T. Work, Ind. Eng. Chem. 29, 213 (1937). H. B. Weiser and W. O. Milligan, J. Phys. Chem. 38, 513 (1934). H. B. Weiser, W. O. Milligan, and E. L. Cook, J. Phys. Chem. 45, 1227 (1941). Z. Jerman, Collect. Czech. Chem. Commun. 31, 3180 (1966). O. Sönhel, Collect. Czech. Chem. Commun. 40, 2560 (1975). J. F. Duncan and R. G. Richards, New Zealand J. Sci. 19, 171 (1976). E. Matijevic, M. Budnik, and L. Meites, J. Colloid Interface Sci. 61, 302 (1977). L. I. Bekkerman, I. P. Dobrovol’skii, and A. A. Ivakin, Russ. J. Inorg. Chem. 21, 223 (1976). E. Narita, H. Tajeuchi, N. Horiguchi, and T. Okabe, Bull. Chem. Soc. Jpn. 57, 1388 (1984). H. Schroeder, in “Physics of Thin Films,” Vol. 5, p. 87. Academic Press, New York, 1969. B. E. Yoldas, J. Mater. Sci. 21, 1087 (1986). Y. Takahashi and Y. Matsuoka, J. Mater. Sci. 23, 2259 (1988). R. Janes, M. Edge, J. Rigby, D. Mourelatou, and N. S. Allen, Dyes Pigments 48, 29 (2001). M. Grätzel, Nature 414, 338 (2001). A. Fujishima and K. Honda, Nature 238, 37 (1972). N. Negishi and T. Takeuchi, J. Sol–Gel Sci. Technol. 22, 23 (2001). M. Zaharescu, M. Crisan, A. Szatvanyi, and M. Gartner, J. Optoelectron. Adv. Mater. 2, 618 (2000). J. Ovenstone and K. Yanagisawa, Chem. Mater. 11, 2770 (1999). L. Kavan, M. Grätzel, S. E. Gilbert, C. Klemenz, and H. J. Scheel, J. Am. Chem. Soc. 118, 6716 (1996). M. Ferroni, V. Guidi, G. Martinelli, G. Faglia, P. Nelli, and G. Sberveglieri, Nanostruct. Mater. 7, 709 (1996). H. Tang, K. Prasad, S. Sanjinés, and F. Lévy, Sens. Actuators, B 26, 71 (1995). E. Traversa, M. L. Di Vona, S. Licoccia, M. Sacerdoti, M. C. Carotta, L. Crema, and G. Martinelli, J. Sol–Gel Sci. Technol. 22, 167 (2001). J. Aarik, A. Aida, V. Sammelselg, T. Uustare, M. Ritala, and M. Leskelä, Thin Solid Films 370, 163 (2000). A. Rahtu, K. Kukli, and M. Ritala, Chem. Mater. 13, 817 (2001). R. Matero, A. Rahtu, and M. Ritala, Chem. Mater. 13, 4506 (2001). I. Moriguchi, H. Maeda, Y. Teraoka, and S. Kagawa, J. Am. Chem. Soc. 117, 1139 (1995). S. Monticone, R. Tufeu, A. V. Kanaev, E. Scolan, and C. Sanchez, Appl. Surf. Sci. 162–163, 565 (2000). R. Wang, K. Hashimoto, A. Fujishima, M. Chikuni, E. Kojima, A. Kitamura, M. Shimohigoshi, and T. Watanabe, Nature 388, 431 (1997). B. O’Regan and M. Grätzel, Nature 353, 737 (1991).

Molecular Tectonics in Sol–Gel Chemistry 209. A. Hagfeldt and M. Grätzel, Acc. Chem. Res. 33, 269 (2000). 210. M. Grätzel, J. Sol–Gel Sci. Technol. 22, 7 (2001). 211. D. Duonghong, J. Ramsden, and M. Grätzel, J. Am. Chem. Soc. 104, 2977 (1982). 212. A. Leaustic, F. Babonneau, and J. Livage, Chem. Mater. 1, 248 (1989). 213. E. Scolan and C. Sanchez, Chem. Mater. 10, 3217 (1998). 214. T. Moritz, J. Reiss, K. Diesner, D. Su, and A. Chemseddine, J. Phys. Chem. B 101, 8052 (1997). 215. A. Chemseddine and T. Moritz, Eur. J. Inorg. Chem. 235 (1999). 216. A. Rammal, F. Brisach, and M. Henry, C. R. Acad. Sci. Paris, Sér IIc 5, 59 (2002). 217. T. J. Bastow and H. J. Whitfield, Chem. Mater. 11, 3518 (1999). 218. E. Scolan, C. Magnenet, D. Massiot, and C. Sanchez, J. Mater. Chem. 9, 2467 (1999). 219. V. Luca, S. Djajanti, and R. F. Howe, J. Phys. Chem. B 102, 10650 (1998). 220. T. J. Trentler, T. E. Denler, J. F. Bertone, A. Agrawal, and V. L. Colvin, J. Am. Chem. Soc. 121, 1613 (1999). 221. A. Vioux, Chem. Mater. 9, 2292 (1997). 222. P. Krtil, D. Fattakhova, L. Kavan, S. Burnside, and M. Grätzel, Solid State Ionics 135, 101 (2000). 223. A. Hagfeldt, N. Vlachopoulos, and M. Grätzel, J. Electrochem. Soc. 142, L82 (1994). 224. S. Y. Huang, L. Kavan, I. Exnar, and M. Grätzel, J. Electrochem. Soc. 142, L142 (1995). 225. Q. Xu and M. A. Anderson, J. Am. Ceram. Soc. 77, 1939 (1994). 226. M. Visca and E. Matijevic, J. Colloid Interface Sci. 68, 308 (1979). 227. E. A. Barringer and H. K. Bowen, J. Am. Ceram. Soc. 65, C199 (1982). 228. T. A. Ring, Mater. Res. Soc. Bull. 15, 34 (1990). 229. E. A. Barringer and H. K. Bowen, Langmuir 1, 414 (1985). 230. A. Soloviev, R. Tufeu, C. Sanchez, and A. V. Kanaev, J. Phys. Chem. B 105, 4175 (2001). 231. J. Livage, M. Henry, J.-P. Jolivet, and C. Sanchez, Mater. Res. Soc. Bull. 15, 16 (1990). 232. S. J. Teichner, G. A. Nicolaon, M. A. Vicarini, and G. E. E. Gardes, Adv. Colloid Interface Sci. 5, 245 (1976). 233. O. Masson, V. Rieux, R. Guinebretière, and A. Dauger, Nanostruct. Mater. 7, 725 (1996). 234. F. Meng, J. R. Schlup, and L. T. Fan, Chem. Mater. 9, 2459 (1997). 235. I. Kraitzer, K. McTaggart, and G. Winter, J. Oil Colour Chem. Assoc. 31, 405 (1948). 236. K. Kamiya, K. Tanimoto, and T. Yoko, J. Mater. Sci. Lett. 5, 402 (1986). 237. T. Hayashi, T. Yamada, and H. Saito, J. Mater. Sci. 18, 3137 (1983). 238. K. Kamiya, S. Sakka, and S. Ito, J. Ceram. Soc. Jpn. 85, 599 (1977). 239. C. J. Brinker and M. S. Harrington, Sol. Energy Mater. 5, 159 (1981). 240. R. J. Davis and Z. Liu, Chem. Mater. 9, 2311 (1997). 241. S. Diré and F. Babonneau, J. Non-Cryst. Solids 167, 29 (1994). 242. P. E. Dirken, M. E. Smith, and H. J. Whitfield, J. Phys. Chem. 99, 395 (1995). 243. L. Delattre and F. Babonneau, Chem. Mater. 9, 2385 (1997). 244. C. Gervais, F. Babonneau, D. Hoebbel, and M. E. Smith, Solid State NMR 17, 2 (2000). 245. C. Gervais, F. Babonneau, and M. E. Smith, J. Phys. Chem. B 105, 1971 (2001). 246. R. Anderson, G. Mountjoy, M. E. Smith, and R. J. Newport, J. Non-Cryst. Solids 232–234, 72 (1998). 247. S. F. Dec, M. F. Davis, G. E. Maciel, C. E. Bronnimann, J. J. Fitzgerald, and S.-S. Han, Inorg. Chem. 32, 955 (1993). 248. D. Hennings, M. Klee, and R. Waser, Adv. Mater. 3, 334 (1991). 249. K. S. Mazdiyasni, Ceram. Int. 8, 42 (1982). 250. A. I. Yanovsky, M. I. Yanovskaya, V. K. Limar, V. G. Kessler, N. Ya. Turova, and Yu. T. Struchkov, J. Chem., Soc. Chem. Commun. 1605 (1991).

815 251. A. I. Yanovsky, E. P. Turevskaya, M. I. Yanovskaya, V. G. Kessler, N. Ya. Turova, A. P. Pisarevskii, and Yu. T. Struchkov, Zh. Neorg. Khim. 40, 355 (1995). 252. B. Gaskins, J. J. Lannutti, D. C. Finnen, and A. A. Pinkerton, Acta Crystallogr., Sect. C 50, 1387 (1994). 253. E. P. Turevskaya, V. G. Kessler, N. Ya. Turova, A. P. Pisarevsky, A. I. Yanovsky, and Yu. T. Struchkov, J. Chem. Soc., Chem. Commun. 2303 (1994). 254. M. Veith, S. Mathur, and V. Huch, Inorg. Chem. 36, 2391 (1997). 255. Z. A. Starikova, A. I. Yanovsky, N. M. Kotova, M. I. Yanovskaya, N. Y. Turova, and D. Benlian, Polyhedron 16, 4347 (1997). 256. M. Veith, S. Mathur, and V. Huch, Inorg. Chem. 35, 7295 (1995). 257. W. E. Rhine, R. B. Hallcock, W. R. Davis, and W. Wong-Ng, Chem. Mater. 4, 1208 (1992). 258. V. W. Day, T. A. Eberspacher, M. H. Frey, W. G. Klemperer, S. Liang, and D. A. Payne, Chem. Mater. 8, 330 (1996). 259. V. W. Day, T. A. Eberspacher, W. G. Klemperer, and S. Liang, Chem. Mater. 7, 1607 (1995). 260. V. G. Kessler, L. G. Hubert-Pfalzgraf, S. Daniele, and A. Gleizes, Chem. Mater. 6, 2336 (1994). 261. W.-F. Zhang, Q. Xing, and Ya.-B. Huang, Mod. Phys. Letts. B 14, 709 (2000). 262. I. Baxter, S. R. Drake, M. B. Hursthouse, K. M. A. Malik, D. M. P. Mingos, J. C. Plakatouras, and D. J. Otway, Polyhedron 17, 625 (1998). 263. C. D. Chandler and M. J. Hampden-Smith, Chem. Mater. 4, 1137 (1992). 264. M. Lencka and R. E. Riman, J. Am. Ceram. Soc. 76, 2649 (1993). 265. M. M. Lencka and R. E. Riman, Ferroelectrics 151, 159 (1994). 266. H. K. Chae, D. A. Payne, Z. Xu, and L. Ma, Chem. Mater. 6, 1589 (1994). 267. S. Daniele, R. Papiernik, L. G. Hubert-Pfalzgraf, S. Jagner, and M. Hakansson, Inorg. Chem. 34, 628 (1995). 268. L. G. Hubert-Pfalzgraf, S. Daniele, R. Papiernik, M.-C. Massiani, B. Septe, J. Vaissermann, and J.-C. Daran, J. Mater. Chem. 7, 753 (1997). 269. R. Papiernik, L. Hubert-Pfalzgraf, M. Veith, and V. Huch, Chem. Ber. 130, 1361 (1997). 270. S. Daniele, L. G. Hubert-Pfalzgraf, J.-C. Daran, and S. Halut, Polyhedron 13, 927 (1994). 271. R. Kuhlman, B. A. Vaartstra, W. E. Streib, J. C. Huffman, and K. G. Caulton, Inorg. Chem. 32, 1272 (1993). 272. C. D. Chandler, C. Roger, and M. J. Hampden-Smith, Chem. Rev. 93, 1205 (1993). 273. K. van Werde, G. Vanhoyland, D. Nelis, D. Mondelaers, M. K. Van Bael, J. Mullens, and L. C. van Poucke, J. Mater. Chem. 11, 1192 (2001). 274. J. A. Ibers, Nature 197, 686 (1963). 275. R. D. Witters and C. N. Caughlan, Nature 205, 1312 (1965). 276. D. A. Wright and D. A. Williams, Acta Crystallogr., Sect. B 24, 1107 (1968). 277. R. W. Adams and G. Winter, Aust. J. Chem. 20, 171 (1967). 278. K. Watenpaugh and C. N. Caughlan, J. Chem. Soc., Chem. Commun. 76 (1967). 279. V. W. Day, T. A. Eberspacher, W. G. Klemperer, C. W. Park, and F. S. Rosenberg, J. Am. Chem. Soc. 113, 8190 (1991). 280. R. Schmid, A. Mosset, and J. Galy, J. Chem. Soc., Dalton Trans. 1999 (1991). 281. A. Mosset and J. Galy, C. R. Acad. Sci. Paris, Sér. II 307, 1747 (1988). 282. F. Babonneau, S. Doeuff, A. Leaustic, C. Sanchez, C. Cartier, and M. Verdaguer, Inorg. Chem. 27, 3166 (1988). 283. N. Hao, B. G. Sayer, G. Denes, D. G. Bickley, C. Detellier, and M. J. McGlinchey, J. Magn. Reson. 50, 50 (1982). 284. V. W. Day, T. A. Eberspacher, Y. Chen, J. Hao, and W. G. Klemperer, Inorg. Chim. Acta 229, 391 (1995).

816 285. N. Steunou, F. Ribot, K. Boubekeur, J. Maquet, and C. Sanchez, New J. Chem. 23, 1079 (1999). 286. V. W. Day, T. A. Eberspacher, W. G. Klemperer, and C. W. Park, J. Am. Chem. Soc. 115, 8469 (1993). 287. N. Steunou, F. Robert, K. Boubekeur, F. Ribot, and C. Sanchez, Inorg. Chim. Acta 279, 144 (1998). 288. N. Steunou, G. Kickelbick, K. Boubekeur, and C. Sanchez, J. Chem. Soc., Dalton Trans. 3653 (1999). 289. C. F. Campana, Y. Chen, V. W. Day, W. G. Klemperer, and R. A. Sparks, J. Chem. Soc., Dalton Trans. 691 (1996). 290. T. J. Boyle, R. W. Schwartz, R. J. Doedens, and J. W. Ziller, Inorg. Chem. 34, 1110 (1995). 291. G. R. Desiraju, “Crystal Engineering.” Elsevier, Amsterdam, 1989. 292. H. Meerwein, B. von Bock, B. Kirschnick, W. Lenz, and A. Migge, J. Prakt. Chem. 147, 113 (1937). 293. D. C. Bradley, Adv. Chem. Ser. 23, 10 (1959). 294. T. J. Boyle, T. M. Alam, E. R. Mechenbier, B. L. Scott, and J. W. Ziller, Inorg. Chem. 36, 3293 (1997). 295. G. W. Svetich and A. A. Voge, Acta Crystallogr., Sect. B 28, 1760 (1972). 296. S. C. James, N. C. Norman, and A. G. Orpen, Acta Crystallogr., Sect. C 54, 1261 (1998). 297. L. D. Durfee, S. F. Latesky, I. P. Rothwell, J. C. Huffman, and K. Folting, Inorg. Chem. 24, 4569 (1985). 298. R. T. Toth and D. W. Stephan, Can. J. Chem. 69, 172 (1991). 299. A. V. Firth, J. C. Stewart, A. J. Hoskin, and D. W. Stephan, J. Organomet. Chem. 591, 185 (1999). 300. L. D. Durfee, P. E. Fanwick, I. P. Rothwell, K. Folting, and J. C. Huffman, J. Am. Chem. Soc. 109, 4720 (1987). 301. J. E. Hill, P. E. Fanwick, and I. P. Rothwell, Inorg. Chem. 28, 3602 (1989). 302. J. E. Hill, P. E. Fanwick, and I. P. Rothwell, Acta Crystallogr., Sect. C 47, 541 (1991). 303. J. E. Hill, R. D. Profilet, P. E. Fanwick, and I. P. Rothwell, Angew. Chem., Int. Ed. Engl. 29, 664 (1990). 304. C. H. Zambrano, R. D. Profilet, J. E. Hill, P. E. Fanwick, and I. P. Rothwell, Polyhedron 12, 689 (1993). 305. J. H. Haslam, Adv. Chem. Ser. 23, 272 (1959). 306. L. Peng-Ju, H. Sheng-Hua, H. Kun-Yao, W. Ru-Ji, and T. C. W. Mak, Inorg. Chim. Acta 175, 105 (1990). 307. N. W. Mitzel, S. Parsons, A. J. Blake, and D. W. H. Rankin, J. Chem. Soc., Dalton Trans. 2089 (1996). 308. K. Wieghardt, I. Tolksdorf, J. Weiss, and W. Swiridoff, Z. Anorg. Allg. Chem. 490, 182 (1982). 309. G. J. Gainsford, T. Kemmitt, C. Lensik, and N. B. Milestone, Inorg. Chem. 34, 746 (1995). 310. R. E. Reeves and L. W. Mazzeno, J. Am. Chem. Soc. 76, 2533 (1954). 311. D. M. Puri and R. C. Mehrotra, Indian J. Chem. 5, 448 (1967). 312. N. Pajot, R. Papiernik, L. G. Hubert-Pfalzgraf, J. Vaisserman, and S. Paraud, J. Chem. Soc., Chem. Commun. 1817 (1995). 313. D. Wang, R. Yu, N. Kumada, and N. Kinomura, Chem. Mater. 11, 2008 (1999). 314. I. D. Williams, S. F. Pedersen, K. B. Sharpless, and S. J. Lippard, J. Am. Chem. Soc. 106, 6430 (1984). 315. D. P. Steinhuebel and S. J. Lippard, Organometallics 18, 109 (1999). 316. D. P. Steinhuebel and S. J. Lippard, J. Am. Chem. Soc. 121, 11762 (1999). 317. L. T. Armistead, P. S. White, and M. R. Gagné, Organometallics 17, 4232 (1998). 318. I. Kim, Y. Nishihara, R. F. Jordan, R. D. Rogers, A. L. Rheingold, and G. P. A. Yap, Organometallics 16, 3314 (1997). 319. P. H. Bird, A. R. Fraser, and C. F. Lau, Inorg. Chem. 12, 1322 (1973). 320. H. Mimoun, M. Postel, F. Casabianca, J. Fischer, and A. Mitschler, Inorg. Chem. 21, 1303 (1982).

Molecular Tectonics in Sol–Gel Chemistry 321. M. Postel, F. Casabianca, Y. Gauffreteau, and J. Fischer, Inorg. Chim. Acta 113, 173 (1986). 322. L. D. Durfee, J. E. Hill, P. E. Fanwick, and I. P. Rothwell, Organometallics 9, 75 (1990). 323. D. Seebach, D. A. Plattner, A. K. Beck, Y. M. Wang, D. Hunziker, and W. Petter, Helv. Chim. Acta 75, 2171 (1992). 324. N. Miele-Pajot, L. G. Hubert-Pfalzgraf, R. Papiernik, J. Vaissermann, and R. Collier, J. Mater. Chem. 9, 3027 (1999). 325. B. A. Borgias, S. R. Cooper, Y. B. Koh, and K. N. Raymond, Inorg. Chem. 23, 1009 (1984). 326. H. Honda, K. Suzaki, and Y. Sugahara, J. Sol–Gel Sci. Technol. 22, 133 (2001). 327. T.-B. Wen, B.-S. Sheng, C.-Y. Su, D. X. Wu, L.-G. Wang, S. Liao, and H.-Q. Liu, Bull. Chem. Soc. Jpn. 71, 2339 (1998). 328. T. P. Vaid, E. B. Lobkovsky, and P. T. Wolczanski, J. Am. Chem. Soc. 119, 8742 (1997). 329. T. P. Vaid, J. M. Tanski, J. M. Pette, E. B. Lobkovsky, and P. T. Wolczanski, Inorg. Chem. 38, 3394 (1999). 330. J. M. Tanski, T. P. Vaid, E. B. Lobkovsky, and P. T. Wolczanski, Inorg. Chem. 39, 4756 (2000). 331. J. M. Tanski and P. T. Wolczanski, Inorg. Chem. 40, 2026 (2001). 332. J. M. Tanski, E. B. Lobkovsky, and P. T. Wolczanski, J. Solid State Chem. 152, 130 (2000). 333. N. W. Eilerts, J. A. Heppert, M. L. Kennedy, and F. Takusagawa, Inorg. Chem. 33, 4813 (1994). 334. M. Terada, Y. Matsumoto, Y. Nakamura, and K. Mikami, Inorg. Chim. Acta 296, 267 (1999). 335. M. H. Chisholm, J. H. Huang, J. C. Huffman, W. E. Streib, and D. Tiedtke, Polyhedron 16, 2941 (1997). 336. P. V. Rao, C. P. Rao, E. K. Wegelius, E. Kolehmainen, and K. Rissanen, J. Chem. Soc., Dalton Trans. 4469 (1999). 337. D. C. Bradley and C. E. Holloway, J. Chem. Soc., Chem. Commun. 284 (1965). 338. D. C. Bradley and C. E. Holloway, J. Chem. Soc. A 282 (1969). 339. R. C. Fay and A. F. Lindmark, J. Am. Chem. Soc. 105, 2118 (1983). 340. A. Leaustic, F. Babonneau, and J. Livage, Chem. Mater. 1, 240 (1989). 341. R. J. Errington, J. Ridland, W. Clegg, R. A. Coxall, and J. M. Sherwood, Polyhedron 17, 659 (1998). 342. G. D. Smith, C. N. Caughlan, and J. A. Campbell, Inorg. Chem. 11, 2989 (1972). 343. A. Yamamoto and S. Kambara, J. Am. Chem. Soc. 79, 4344 (1957). 344. P. D. Moran, C. E. F. Rickard, G. A. Bowmaker, R. P. Cooney, J. R. Bartlett, and J. L. Woolfrey, Inorg. Chem. 37, 1417 (1998). 345. P. Toledano, M. In, and C. Sanchez, C. R. Acad. Sci. Paris, Ser. II 313, 1247 (1991). 346. U. Schubert, H. Buhler, and B. Hirle, Chem. Ber. 125, 999 (1992). 347. J. L. Wang, F. M. Miao, X. J. Fan, X. Feng, and J. T. Wang, Acta Crystallogr., Sect. C 46, 1633 (1990). 348. S. I. Troyanov and O. Yu. Gorbenko, Polyhedron 16, 777 (1997). 349. A. R. Siedle and J. C. Huffman, Inorg. Chem. 29, 3131 (1990). 350. J. P. Corden, W. Errington, P. Moore, M. G. Partridge, and M. G. H. Wallbridge, J. Chem. Soc., Dalton Trans. 2647 (1999). 351. J. V. Barkley, J. C. Cannadine, I. Hannaford, M. M. Harding, A. Steiner, J. Tallon, and R. Whyman, J. Chem. Soc., Chem. Commun. 1653 (1997). 352. T. Kemmit, N. I. Al-Salim, and G. J. Gainsford, Eur. J. Inorg. Chem. 1847 (1999). 353. S. Doherty, R. J. Errington, N. Housley, J. Ridland, W. Clegg, and M. J. Elsegood, Organometallics 18, 1018 (1999). 354. A. A. Diamantis, M. Manikas, M. A. Salam, M. R. Snow, and R. T. Tiekink, Aust. J. Chem. 41, 453 (1988). 355. A. Caneschi, A. Dei, and D. Gatteschi, J. Chem. Soc., Chem. Commun. 630 (1992). 356. H. Hefele, E. Ludwig, E. Uhlemann, and H. Nöth, Z. Anorg. Allg. Chem. 621, 1431 (1995). 357. D. Schwartzenbach, Helv. Chim. Acta 55, 2990 (1972).

Molecular Tectonics in Sol–Gel Chemistry 358. H. Manohar and D. Schwartzenbach, Helv. Chim. Acta 57, 1086 (1974). 359. D. Schwartzenbach, Inorg. Chem. 9, 2391 (1970). 360. P. Jeske, G. Haselhorst, T. Weyermüller, K. Wieghardt, and B. Nuber, Inorg. Chem. 33, 2462 (1994). 361. A. Bodner, P. Jeske, T. Weyhermüller, K. Wieghardt, E. Dubler, H. Schmalle, and B. Nuber, Inorg. Chem. 31, 3737 (1992). 362. P. Jeske, K. Wieghardt, and B. Nuber, Z. Naturforsch., B: Chem. Sci. 47, 1621 (1992). 363. K. Wieghardt, D. Ventur, Y. H. Tsai, and C. Krüger, Inorg. Chim. Acta 99, L25 (1985). 364. L. Porri, A. Ripa, P. Colombo, E. Miano, S. Capelli, and S. V. Meille, J. Organomet. Chem. 514, 213 (1996). 365. J. Okuda, S. Fokken, T. Kleinhenn, and T. P. Spaniol, Eur. J. Inorg. Chem. 1321 (2000). 366. S. F. Pedersen, J. C. Dewan, R. E. Eckman, and K. B. Sharpless, J. Am. Chem. Soc. 109, 1279 (1987). 367. E. J. Corey, C. L. Cywin, and M. C. Noe, Tetrahedron Lett. 35, 69 (1994). 368. S. Bott, A. W. Colman, and J. L. Atwood, J. Chem. Soc., Chem. Commun. 610 (1986). 369. P. D. Hampton, C. E. Daitch, T. M. Alam, Z. Bencze, and M. Rosay, Inorg. Chem. 33, 4750 (1994). 370. W. Clegg, M. R. J. Elsegood, S. J. Teat, C. Redshaw, and V. C. Gibson, J. Chem. Soc., Dalton Trans. 3037 (1998). 371. M. M. Olmstead, G. Sigel, H. Hope, X. J. Hu, and P. P. Power, J. Am. Chem. Soc. 107, 8087 (1985). 372. G. E. Hofmeister, F. E. Hahn, and S. F. Pedersen, J. Am. Chem. Soc. 111, 2318 (1989). 373. M. Albrecht and S. Kotila, Angew. Chem., Int. Ed. Engl. 34, 2134 (1995). 374. M. Albrecht and S. Kotila, Angew. Chem., Int. Ed. Engl. 35, 1208 (1996). 375. M. Albrecht and S. Kotila, J. Chem. Soc., Chem. Commun. 2309 (1996). 376. M. Albrecht, H. Rötteleand, and P. Burger, Chem. Eur. J. 2, 1264 (1996). 377. M. Albrecht, M. Schneider, and R. Fröhlich, New J. Chem. 753 (1998). 378. M. Scherer, D. L. Caulder, D. W. Johnson, and K. N. Raymond, Angew. Chem., Int. Ed. Engl. 38, 1588 (1999). 379. D. L. Caulder and K. N. Raymond, J. Chem. Soc., Dalton Trans. 1185 (1999). 380. R. L. Harlow, Acta Crystallogr., Sect. C 39, 1344 (1983). 381. A. A. Naiini, W. M. P. B. Menge, and J. G. Verkade, Inorg. Chem. 30, 5009 (1991). 382. A. A. Naiini, S. L. Ringrose, Y. Su, R. A. Jacobson, and J. G. Verkade, Inorg. Chem. 32, 1290 (1993). 383. G. Boche, K. Möbus, K. Harms, and M. Marsch, J. Am. Chem. Soc. 118, 2770 (1996). 384. K. Wieghardt, U. Quilitzsch, J. Weiss, and B. Nuber, Inorg. Chem. 19, 2514 (1980). 385. D. Schwartzenbach and K. Girgis, Helv. Chim. Acta 58, 2391 (1975). 386. S. M. Harben, P. D. Smith, R. L. Beddoes, D. Collison, and C. D. Garner, Angew. Chem., Int. Ed. Engl. 36, 1897 (1997). 387. S. M. Harben, P. D. Smith, M. Helliwell, D. Collison, and C. D. Garner, J. Chem. Soc., Dalton Trans. 4517 (1997). 388. H. Chen, P. S. White, and M. R. Gagné, Organometallics 17, 5358 (1998). 389. J. M. McInnes, D. Swallow, A. J. Blake, and P. Mountford, Inorg. Chem. 37, 5970 (1998). 390. F. Francheschi, E. Solari, C. Floriani, M. Rosi, A. Chiesi-Villa, and C. Rizzoli, Chem. Eur. J. 5, 708 (1999). 391. K. M. Carroll, J. Schwartz, and D. M. Ho, Inorg. Chem. 33, 2707 (1994).

817 392. F. Francheschi, E. Gallo, E. Solari, C. Floriani, A. Chiesi-Villa, C. Rizzoli, N. Re, and A. Sgamellotti, Chem. Eur. J. 2, 1466 (1996). 393. E. Gallo, E. Solari, F. Francheschi, C. Floriani, A. Chiesi-Villa, and C. Rizzoli, Inorg. Chem. 34, 2495 (1995). 394. S. J. Coles, M. B. Hursthouse, D. G. Kelly, A. J. Toner, and N. M. Walker, Can. J. Chem. 77, 2095 (1999). 395. P. R. Woodman, N. W. Alcock, I. J. Munslow, C. J. Sanders, and P. Scott, J. Chem. Soc., Dalton Trans. 3340 (2000). 396. Y. N. Belokon, S. Caveda-Cepas, B. Green, N. S. Ikonnikov, V. N. Khrustalev, V. S. Larichev, M. A. Moscalenko, M. Morth, C. Orizu, V. I. Tararov, M. Tasinazzo, G. I. Timofeeva, and L. V. Yashkina, J. Am. Chem. Soc. 121, 3968 (1999). 397. S. Pritchett, D. H. Woodmansee, P. Gantzel, and P. J. Walsh, J. Am. Chem. Soc. 120, 6423 (1998). 398. R. Guilard, J.-M. Latour, C. Lecomte, J.-C. Marchon, J. Protas, and D. Ripoll, Inorg. Chem. 17, 1228 (1978). 399. S. De Angelis, E. Solari, C. Floriani, A. Chiesi-Villa, and C. Rizzoli, Angew. Chem., Int. Ed. Engl. 34, 1092 (1995). 400. C. E. Housmekerides, R. S. Pilato, G. L. Geoffroy, and A. L. Rheingold, J. Chem. Soc., Chem. Commun. 563 (1991). 401. C. E. Housmekerides, D. L. Ramage, C. M. Kretz, J. T. Shontz, R. S. Pilato, G. L. Geoffroy, A. L. Rheingold, and B. S. Haggerty, Inorg. Chem. 31, 4453 (1992). 402. A. J. Blake, J. M. McInnes, P. Mountford, G. I. Nikonov, D. Swallow, and D. J. Watkin, J. Chem. Soc., Dalton Trans. 379 (1999). 403. F. E. Hahn, S. Rupprecht, and K. H. Moock, J. Chem. Soc., Chem. Commun. 224 (1991). 404. T. B. Karpishin, T. D. P. Stack, and K. N. Raymond, J. Am. Chem. Soc. 115, 182 (1993). 405. C. Brückner, R. E. Powers, and K. N. Raymond, Angew. Chem., Int. Ed. Engl. 37, 1837 (1998). 406. J. P. Fackler Jr., F. J. Kristine, A. M. Mazany, T. M. Moyer, and R. E. Shepherd, Inorg. Chem. 24, 1857 (1985). 407. N. Klouras, N. Tzavellas, and C. P. Raptopoulou, Monatsh. Chem. 128, 1201 (1997). 408. D. F. Evans, J. Parr, S. Rahman, A. M. Z. Slawin, D. J. Williams, C. Y. Wong, and J. D. Woollins, Polyhedron 12, 337 (1993). 409. M. Guo, H. Sun, S. Bihari, J. A. Parkinson, R. O. Gould, S. Parsons, and P. J. Sadler, Inorg. Chem. 39, 206 (2000). 410. H. Hefele, E. Ludwig, W. Bansse, E. Uhlemann, Th. Lügger, E. Hahn, and H. Mehner, Z. Anorg. Allg. Chem. 621, 671 (1995). 411. U. Auerbach, T. Weyhermüller, K. Wieghardt, B. Nuber, E. Bill, C. Butzlaff, and A. X. Trautwein, Inorg. Chem. 32, 508 (1993). 412. G. Schottner, Chem. Mater. 13, 3422 (2001). 413. G. Philipp and H. Schmidt, J. Non-Cryst. Solids 63, 283 (1984). 414. P. Innocenzi, G. Brusatin, M. Guglielmi, R. Signorini, R. Bozio, and M. Maggini, J. Non-Cryst. Solids 265, 68 (2000). 415. D. Hoebbel, M. Nacken, H. Schmidt, V. Huch, and M. Veith, J. Mater. Chem. 8, 171 (1998). 416. T. Gunji, T. Kasahara, A. Fujii, Y. Abe, and M. Kawano, Bull. Chem. Soc. Jpn. 68, 2975 (1995). 417. M. A. Hossain, M. B. Hursthouse, M. A. Mazid, and A. C. Sullivan, J. Chem. Soc., Chem. Commun. 1305 (1988). 418. M. A. Hossain, M. B. Hursthouse, A. Ibrahim, M. Mazid, and A. C. Sullivan, J. Chem. Soc., Dalton Trans. 2347 (1989). 419. M. Lazell, M. Motevalli, S. A. A. Shah, C. K. S. Simon, and A. C. Sullivan, J. Chem. Soc., Dalton Trans. 1449 (1996). 420. D. B. Dell’Amico, F. Calderazzo, S. Ianelli, L. Labella, F. Marchetti, and G. Pelizzi, J. Chem. Soc., Dalton Trans. 4339 (2000). 421. M. Crocker, R. H. M. Herold, A. G. Orpen, and T. A. Overgaag, J. Chem. Soc., Dalton Trans. 3791 (1999). 422. B. F. G. Johnson, M. C. Klunduk, C. M. Martin, G. Sankar, S. J. Teate, and J. M. Thomas, J. Organomet. Chem. 596, 221 (2000). 423. M. B. Hursthouse and M. A. Hossain, Polyhedron 3, 95 (1984).

818 424. M. Crocker, R. H. M. Herold, and A. G. Orpen, J. Chem. Soc., Chem. Commun. 2411 (1997). 425. A. Voigt, R. Murugavel, V. Chandrasekar, N. Winkhofer, H. W. Roesky, H.-G. Schmidt, and I. Uson, Organometallics 15, 1610 (1996). 426. T. Mashmeyer, M. C. Klunduk, C. M. Martin, D. S. Shepard, J. M. Thomas, and B. F. G. Johnson, J. Chem. Soc., Chem. Commun. 1847 (1997). 427. F. T. Edelmann, S. Giessmann, and A. Fischer, J. Organomet. Chem. 620, 80 (2001). 428. A. Voigt, R. Murugavel, M. L. Montero, H. Wessel, F.-Q. Liu, H. W. Roesky, I. Uson, T. Albers, and E. Parisini, Angew. Chem., Int. Ed. Engl. 36, 1001 (1997). 429. Z. Duan, A. A. Naiini, J.-H. Lee, and J. G. Verkade, Inorg. Chem. 34, 5477 (1995). 430. C. Sanchez and F. Ribot, New J. Chem. 18, 1007 (1994). 431. P. Judenstein and C. Sanchez, J. Mater. Chem. 6, 511 (1996). 432. J. N. Hay and H. M. Raval, Chem. Mater. 13, 3396 (2001). 433. S. Doeuff, M. Henry, and C. Sanchez, Mater. Res. Bull. 25, 1519 (1990). 434. H. Barrow, D. A. Brown, N. W. Alcock, H. J. Clase, and M. H. Wallbridge, J. Chem. Soc., Chem. Commun. 1231 (1995). 435. G. Kickelbick and U. Schubert, Eur. J. Inorg. Chem. 159 (1998). 436. I. Gautier-Luneau, A. Mosset, and J. Galy, Z. Kristallogr. 180, 83 (1987). 437. S. Doeuff, Y. Dromzee, and C. Sanchez, C. R. Acad. Sci. Paris, Ser. II 308, 1409 (1989). 438. S. Doeuff, Y. Dromzee, F. Taulelle, and C. Sanchez, Inorg. Chem. 28, 4439 (1989). 439. I. Laaziz, A. Larbot, C. Guizard, J. Durand, L. Cot, and J. Joffre, Acta Crystallogr., Sect. C 46, 2332 (1990). 440. U. Schubert, E. Arpac, W. Glaubitt, A. Helmeric, and C. Chau, Chem. Mater. 4, 291 (1992). 441. A. Rammal and M. Henry, to be published. 442. X. Lei, M. Shang, and M. Fehlner, Organometallics 15, 3779 (1996). 443. T. J. Boyle, C. J. Tafoya, and B. L. Scott, Abstr. Pap.-Am. Chem. Soc. 211, 62-INOR (1996). 444. R. Papiernik, L. G. Hubert-Pfalzgraf, J. Vaissermann, and M. C. H. B. Goncalves, J. Chem. Soc., Dalton Trans. 2285 (1998). 445. T. J. Boyle, T. M. Alam, C. J. Tafoya, and B. L. Scott, Inorg. Chem. 37, 5588 (1998). 446. A. Pandey, V. D. Gupta, and H. Nöth, Eur. J. Inorg. Chem. 1351 (2000). 447. I. Mijatovic, G. Kickelbick, and U. Schubert, Eur. J. Inorg. Chem. 1933 (2001). 448. C. Sanchez, J. Livage, M. Henry, and F. Babonneau, J. Non-Cryst. Solids 100, 65 (1988). 449. S. Doeuff, M. Henry, C. Sanchez, and J. Livage, J. Non-Cryst. Solids 89, 206 (1987). 450. U. Schubert, S. Tewinkel, and F. Möller, Inorg. Chem. 34, 995 (1995). 451. X. Lei, M. Shang, and M. Fehlner, Organometallics 16, 5289 (1996). 452. C. Guerrero, P. H. Mutin, and A. Vioux, Chem. Mater. 12, 1268 (2000). 453. C. Guerrero, M. Mehring, P. H. Mutin, F. Dahan, and A. Vioux, J. Chem. Soc., Dalton Trans. 1537 (1999). 454. M. Mehring, G. Guerrero, F. Dahan, P. H. Mutin, and A. Vioux, Inorg. Chem. 39, 3325 (2000). 455. M. Mehring, M. Schurmann, P. H. Mutin, and A. Vioux, Z. Kristallogr. 215, 591 (2000). 456. R. J. Errington, J. Ridland, K. J. Willett, W. Clegg, R. A. Coxall, and S. L. Heath, J. Organomet. Chem. 550, 473 (1998). 457. C. G. Lugmair and T. D. Tilley, Inorg. Chem. 37, 1821 (1998). 458. D. L. Thorn and R. L. Harlow, Inorg. Chem. 31, 3917 (1992). 459. C. Serre and G. Férey, J. Mater. Chem. 9, 579 (1999). 460. M. Riou-cavellec, C. Serre, and G. Férey, C. R. Acad. Sci. Paris, Sér IIc 2, 147 (1999).

Molecular Tectonics in Sol–Gel Chemistry 461. K. O. Kongshaug, H. Fjellvag, and K. P. Lillerud, J. Chem. Soc., Dalton Trans. 551 (2000). 462. Y. Zhao, G. Zhu, X. Jiao, W. Liu, and W. Pang, J. Mater. Chem. 10, 463 (2000). 463. Y. Guo, Z. Shi, J. Yu, J. Wang, Y. Liu, N. Bai, and W. Pang, Chem. Mater. 13, 203 (2001). 464. C. Ninclaus, C. Serre, D. Riou, and G. Férey, C. R. Acad. Sci. Paris, Sér. IIc 1, 551 (1998). 465. C. Serre and G. Férey, Inorg. Chem. 38, 5370 (1999). 466. P. T. Tanev, M. Chibwe, and T. J. Pinnavaia, Nature 368, 321 (1994). 467. A. Corma, M. T. Navarro, and J. Perez-Pariente, J. Chem. Soc., Chem. Commun. 147 (1994). 468. D. M. Antonelli and J. Y. Ying, Angew. Chem., Int. Ed. Engl. 34, 2014 (1995). 469. R. L. Putnam, N. Nakagawa, K. M. McGrath, N. Yao, I. A. Aksay, S. M. Gruner, and A. Navrotsky, Chem. Mater. 9, 2690 (1997). 470. D. M. Antonelli, Micropor. Mesopor. Mater. 30, 315 (1999). 471. D. Khushalani, G. A. Ozin, and A. Kuperman, J. Mater. Chem. 9, 1491 (1999). 472. D. T. On, Langmuir 15, 8561 (1999). 473. S. Cabrera, J. E. Askouri, C. Guillem, J. Latorre, A. BeltranPorter, D. Beltran-Porter, M. D. Marcos, and P. Amoros, Solid State Sci. 2, 405 (2000). 474. M. Thieme and F. Schüth, Micropor. Mesopor. Mater. 27, 193 (1999). 475. J. Y. Ying, C. P. Mehnert, and M. S. Wong, Angew. Chem., Int. Ed. Engl. 38, 57 (1999). 476. S. Kobayashi, K. Hanabusa, M. Suzuki, M. Kimura, and H. Shirai, Chem. Lett. 1077 (1999). 477. S. Kobayashi, H. Hanabusa, N. Hamasaki, M. Kimura, and H. Shirai, Chem. Mater. 12, 1523 (2000). 478. J. K. Speer and D. R. Carmody, Ind. Eng. Chem. 42, 251 (1950). 479. P. Yang, D. Zhao, D. I. Margolese, B. F. Chmelka, and G. D. Stucky, Chem. Mater. 11, 2813 (1999). 480. G. J. A. A. Soler-Illia and C. Sanchez, New J. Chem. 24, 493 (2000). 481. G. J. A. A. Soler-Illia, E. Scolan, A. Louis, P. A. Albouy, and C. Sanchez, New J. Chem. 25, 156 (2001). 482. G. J. A. A. Soler-Illia, L. Rozes, M. K. Boggiano, C. Sanchez, C. O. Turrin, A. M. Caminade, and J. P. Majoral, Angew. Chem., Int. Ed. Engl. 39, 4250 (2000). 483. C. Sanchez, G. J. A. A. Soler-Illia, F. Ribot, T. Lalot, C. R. Mayer, and V. Cabuil, Chem. Mater. 13, 3061 (2001). 484. U. Schubert, Chem. Mater. 13, 3487 (2001). 485. L. G. Hubert-Pfalzgraf, Coor. Chem. Rev. 178–180, 967 (1998). 486. U. Schubert, N. Hüsing, and A. Lorenz, Chem. Mater. 7, 2010 (1995). 487. R. A. Caruso and M. Antionetti, Chem. Mater. 13, 3272 (2001). 488. B. T. Holland, C. F. Blanford, and A. Stein, Science 281, 538 (1998). 489. A. Imhof and D. J. Pine, Nature 389, 948 (1997). 490. A. Imhof and D. J. Pine, Adv. Mater. 10, 697 (1998). 491. J. E. G. Wijnhoven and W. L. Vos, Science 281, 802 (1998). 492. J. E. G. Wijnhoven, L. Bechger, and W. L. Vos, Chem. Mater. 13, 4486 (2001). 493. D. Wang, R. A. Caruso, and F. Caruso, Chem. Mater. 13, 364 (2001). 494. Q.-B. Meng, C.-H. Fu, Y. Einaga, Z.-Z. Gu, A. Fujishima, and O. Sato, Chem. Mater. 14, 83 (2002). 495. R. A. Caruso, M. Giersig, F. Willig, and M. Antonietti, Langmuir 14, 6333 (1998). 496. R. A. Caruso, M. Antonietti, M. Giersig, H.-S. Hentze, and J. Jia, Chem. Mater. 13, 1114 (2001). 497. Z. Zhong, Y. Yin, B. Gates, and Y. Xia, Adv. Mater. 12, 206 (2000). 498. R. A. Caruso and J. H. Schattka, Adv. Mater. 12, 1921 (2000). 499. H. Shiho and N. Kawahashi, Colloid Polym. Sci. 278, 270 (2000). 500. T. Sasaki, Y. Ebina, T. Tanaka, M. Harada, M. Watanabe, and G. Decher, Chem. Mater. 13, 4661 (2001).

Molecular Tectonics in Sol–Gel Chemistry 501. R. A. Caruso, A. Susha, and F. Caruso, Chem. Mater. 13, 400 (2001). 502. M. Ocana, W. P. Hsu, and E. Matijevic, Langmuir 7, 2911 (1991). 503. I. Haq and E. Matijevic, Colloids Surf., A 81, 153 (1993). 504. S. Srinivasan, A. K. Datye, M. Hampden-Smith, I. E. Wachs, G. Deo, J. M. Jehng, A. M. Turek, and C. F. H. Peden, J. Catal. 131, 260 (1991). 505. W. P. Hsu, R. Yu, and E. Matijevic, J. Colloid Interface Sci. 156, 56 (1993). 506. A. Hanprasopwattana, S. Srinivasan, A. G. Sault, and A. K. Datye, Langmuir 12, 3173 (1996). 507. X.-C. Guo and P. Dong, Langmuir 15, 5535 (1999). 508. I. Pastoriza-Santos, D. S. Koktysh, A. A. Mamedov, M. Giersig, N. A. Kotov, and L. M. Liz-Marzan, Langmuir 16, 2731 (2000). 509. K. S. Mayya, D. I. Gittins, and F. Caruso, Chem. Mater. 13, 3833 (2001). 510. P. Hoyer, Langmuir 12, 1411 (1996). 511. B. B. Lakshmi, P. K. Dorhout, and C. R. Martin, Chem. Mater. 9, 857 (1997). 512. B. B. Lakshmi, C. J. Patrissi, and C. R. Martin, Chem. Mater. 9, 2544 (1997). 513. C. H. M. Hoffman-Caris, New J. Chem. 18, 1087 (1994).

819 514. S. H. Elder, F. M. Cot, Y. Su, S. M. Heald, A. M. Tyryshkin, M. K. Bowman, Y. Gao, A. G. Joly, M. L. Balmer, A. C. Kolwaite, K. A. Magrini, and D. M. Blake, J. Am. Chem. Soc. 122, 5138 (2000). 515. P. Bonhôte, E. Gogniat, M. Grätzel, and P. V. Ashrit, Thin Solid Films 350, 269 (1999). 516. F. Campus, P. Bonhôte, M. Grätzel, S. Heinen, and L. Walder, Sol. Energy Mater. Sol. Cells 56, 281 (1999). 517. P. Bonhôte, E. Gogniat, F. Campus, L. Walder, and M. Grätzel, Displays 20, 137 (1999). 518. D. Cummins, G. Boschloo, M. Ryan, D. Corr, N. Rao, and D. Fitzmaurice, J. Phys. Chem B 104, 11449 (2000). 519. H. H. Beacham, Adv. Chem. Ser. 23, 282 (1959). 520. J. K. Kennedy, Chem. Soc. Rev. 8, 221 (1982). 521. I. Gill, Chem. Mater. 13, 3404 (2001). 522. H. Nan, C. Y. Ru, L. J. Ming, Y. J. Lu Rong, X. Z. Nan, and L. X. Huai, J. Biomater. Appl. 8, 404 (1994). 523. S. Takemoto, K. Tsuru, S. Hayakawa, A. Osaka, and S. Takashima, J. Sol–Gel Sci. Technol. 21, 97 (2001). 524. Y.-M. Lim, K.-S. Hwang, and Y.-J. Park, J. Sol–Gel Sci. Technol. 21, 123 (2001). 525. P. J. Sadler, Adv. Inorg. Chem. 36, 1 (1991). 526. P. Köpf-Maier and H. Köpf, Struct. Bonding 70, 105 (1988).

Encyclopedia of Nanoscience and Nanotechnology

www.aspbs.com/enn

Molecular Wires and Switches Chen Wang, Chunli Bai The Chinese Academy of Sciences, Beijing, People’s Republic of China

CONTENTS 1. Introduction 2. Molecular Wires 3. Molecular Switches 4. Molecules for Data Storage 5. Molecular Machines 6. Summary Glossary References

1. INTRODUCTION Molecular nanostructures with dimensions below 100 nm are considered important constituents in the pursuit of nanotechnology. The advances in supramolecular chemistry, self-assembly, and microlithography technology have laid the foundation for nanotechnology. It is reasoned that the structures at nanometer scale can introduce novel functions leading to new devices, and the assembling can improve the stringent demands on lithographic techniques at this scale. With the wealth of knowledge acquired in past decades in the field of supramolecular chemistry and self-assembly [1–3], as well as synthetic chemistry, molecular nanostructures can produce vast diversity in device functionality and enhanced performance [4–6]. The molecular structures can function either in the form of an individual unit, such as single molecules, or in a coherent way through self-assembling. The understanding of self-assembling at various scales has enriched the study of molecular crystallization, as well as new lithographic venues. This work aims at providing a summary of the widely reported molecular wires and switches, with experimental evidence on their device applications. There have been numerous research reports and review articles as well as books on this fast-evolving front. Owing to the enormous literature in the relevant fields, some of the excellent advances in this work may have been overlooked. We intend to limit the scope of discussion of this work to the areas that are more relevant to nanometer-scale devices, such as molecular ISBN: 1-58883-061-6/$35.00 Copyright © 2004 by American Scientific Publishers All rights of reproduction in any form reserved.

wires and switches [4
5], although there are also structures with great importance in fields such as catalysis, materials sciences, and biological sciences, where nanometer-scale effects have also been extensively studied. The pursuit of device applications of the molecular wires and switches also can be reflected in the design considerations for molecular memory designs, as well as molecular motors. These latter aspects are briefly discussed at the end of this work.

2. MOLECULAR WIRES Molecular wires are one-dimensional electrical conductive molecular structures. The effort in constructing molecular wires can be one of the representatives in combining chemistry with proposed nanodevices. Motivated by the conceptual inspiration of molecular electronics and other devices, the design and synthesis of electrical conductive one-dimensional molecular structures attract extensive interest. This effort, together with the effort in nanolithography techniques, is aimed at obtaining functional structures with electronic functions in the length scale below 100 nm. A chemical approach to this scale regime has its uniqueness owing to the diverse molecular functions. The consideration for transportation processes in molecular wires can be described in electron transfer formalism: KET = k0 exp−d or

R = R0 expd

where KET represents the efficiency for electron transfer, k0 is the preexponential factor, and  is the decay length of the transfer that describes the electronic coupling between the donor and acceptor. The formalism was developed and tested in a solution, and applied successfully in solid junction studies [7–9]. So far, only limited species have been subjected to direct characterizations on a single molecular level. The development of self-assembling and the Langmuir–Blodget technique, scanning probe microscopy (SPM), and so on, has enabled the experimental realization of direct characterization of single molecules, greatly enhancing the feasibility of constructing molecular devices based on carrier transportation processes.

Encyclopedia of Nanoscience and Nanotechnology Edited by H. S. Nalwa Volume 5: Pages (821–834)

822 The other approach in designing molecular wires is derived from conjugated molecules, generally represented by the family of conductive polymers. Polymeric molecules have demonstrated appreciable carrier mobility when properly doped with donors or acceptors, and have already attained commercial device applications. The effort in studying this category of molecules can lead to improved mobility at a single molecular level and a larger carrier transportation range. The third family of wires can be seen in the columnar structure of discotic liquid crystal molecules connected by ligands. The columns are formed by a stacking of molecules, leading to a conductive core with a typical diameter of a few nanometers, separated by a less conductive sheath of similar dimension. The coherence length of the columns can be in the range of a few tens of nanometers. This category of one-dimensional columns can be either electronic or ionic conductive. Some of the species have also demonstrated photoelectric responses. Carbon nanotubes (CNTs) and other nanotube structures are also pursued as candidates for molecular wires. By controlling the tube structure and composition, we demonstrate properties from semiconducting to metallic, and the rectifying behavior of hybrid tubes. In particular, single-walled carbon nanotubes (SWCNTs) can be a promising component of future molecular electronic devices. Probably one of the most interesting wire structures of natural existence is DNA molecules. The abundance and accessibility are highly attractive when it comes to applications. There have been uncertainties in characterizing the electron conductivity of this category of molecules. However, interest still remains in pursuing highly desirable molecular wire structures.

Molecular Wires and Switches

2.2. Conjugated Molecules As mentioned previously, the conjugated molecules have a higher carrier mobility than aliphatic molecules due to the nature of the delocalized electronic states. There are a large number of one-dimensional molecules that have been vigorously studied [29
30], and that can be considered as potential candidates for conductive wires. The resistance of a number of different-sized molecules (monomers, oligomers) with aromatic components was measured. The resistance of double-ended aryl dithiols (xylyldithiol) was estimated as 18 ± 12 M [31], and benzene–1,4–dithiol as about 22 M [32]. One should note that the resistance measurements include the metal–molecule–metal junction, and the contact between the molecule and metal electrode could greatly affect the measured resistance [20]. Oligomers with linearly conjugated double and triple bonds are also typical for conductive molecules, as illustrated in Schemes 1 and 2. The effective conjugation length for poly (triacetylenes) 1 was determined in the range of 7–10 monomer units [34
35]. There have been extensive studies on thiophene–ethynylene and phenylene–ethynylene oligomer-based molecular wires 2–5 [36], substituted with -active groups. In addition, molecules with ferrocene as terminal groups were also studied for oligo (phenylethynyl) 6–10 [37] and oligo (phenylvinylene) 11 [38]. The wire structure was further expanded to branched structures of three-terminal and four-terminal systems 12– 14, as shown in Scheme 3, intended for molecular transistor designs [39]. The oligomers of oligothiophenes and porphyrins have also been widely studied [40]. In the case of fused porphyrins

2.1. Linear Alkane Derivatives Studies on this group of aliphatic molecules (exemplified by alkanethiols) are focused on constructing devices directly based on single molecule conductivity. The pursuit spanned nearly three decades, from the early study on stearic acetate [10], which was recently revisited by several groups [11–16]. The SPM method also contributed to the study [17]. The results revealed the effects of tunneling barriers, terminal groups, and so on, and helped examine the electron transfer mechanism. The resistance of chemically bonded octanedithiol is determined at 900 ± 50 M, while nonbonded molecules have a resistance at least four orders of magnitude higher [17]. This value is significantly higher than the molecules containing phenylene groups (for example, the resistance of benzene–1,4–dithiol is about 22 M [18]). Recent studies obtained the tunneling characteristics of alkane derivatives formed on indium oxide [19], indicating the possible effect of functional groups on the tunneling behavior as theoretically predicted [20]. Typical values of the decay length of the transfer  for alkanethiolate obtained on gold and mercury surfaces are in the range of 0.8–1.5 Å−1 [21–28], and 0.4–0.6 Å−1 , respectively, for the phenyl group [21–28]. The decay lengths for nitro-based molecules were found to depend on the tip bias [28].

Scheme 1. Molecular wire structures. The molecular structure (1) is reprinted with permission from [35], R. E. Martin et al., Angew. Chem. Int. Ed. 38, 817 (1999). © 1999, Wiley-VCH. The molecular structures (2–5) are reprinted with permission from [36], J. M. Tour, Acc. Chem. Res. 33, 791 (2000). © 2000, American Chemical Society.

Molecular Wires and Switches

823

Scheme 4. Molecular wire structures. The molecular structure (15) is reprinted with permission from [41], N. Aratani et al., Angew. Chem. Int. Ed. 39, 1458 (2000). © 2000, Wiley-VCH. The molecular structure (16) is reprinted with permission from [43], R. Dembinski et al., J. Am. Chem. Soc. 122, 810 (2000). © 2000, American Chemical Society. Scheme 2. Ferrocene-terminated molecular wire structures. The molecular structures (6–10) are reprinted with permission from [37], S. Creager et al., J. Am. Chem. Soc. 121, 1059 (1999). © 1999, American Chemical Society. The molecular structure (11) is reprinted with permission from [38], S. P. Dudek et al., J. Am. Chem. Soc. 123, 8033 (2001). © 2001, American Chemical Society.

15 [41
42] (Scheme 4), the UV absorption results prove enhanced delocalization of electrons with increased porphyrin units (up to 128-mer), while direct measurements on electrical conductivity are yet to be performed. A different wire-like structure formed by unsaturated elemental carbon chains was also studied as carbon-based polyynediyl molecular wires 16 [43] (Scheme 4). Polymerization of the diacetylene compound R–C C– C C–R′ (R CH3 (CH2 11 , R′ (CH2 8 COOH) with high spatial precision was realized by using a scanning tunneling microscope (STM) [44]. The as-generated conjugated polymeric nanowires are in the range of 5–300 nm.

Scheme 3. Branched molecular wire structure [39]. The molecular structures (12–14) are reprinted with permission from [36], J. M. Tour, Acc. Chem. Res. 33, 791 (2000). © 2000, American Chemical Society.

2.3. Conductive Polymers It is of natural interest to expand the achievements of conductive polymers such as oligothiophenes 17 (Scheme 5) to the pursuit of conductive wires [40, 45–47]. In particular, with the realization of single molecule manipulation with the SPM method, it is now feasible to measure the properties of single molecules, such as elasticity [48
49]. The delocalized electronic states are also shown to enhance the chemosensory sensitivity. An example of such

Scheme 5. Polymeric molecular wire structures. The molecular structures (18–21) are reprinted with permission from [47], Q. Zhou and T. M. Swager, J. Am. Chem. Soc. 117, 12593 (1995). © 1995, American Chemical Society.

824

Molecular Wires and Switches

enhancement can be found in both polythiophenes and poly (phenyleneethynylene) 18–21 [47] (Scheme 5). This is beneficial in realizing high-sensitivity polyreceptor fluorescent chemosensors.

2.4. Rectification Molecular Wires The concept of an electronic rectification wire was first explored with the donor–spacer–acceptor (D–S–A) model in the early 1970s, and became extensively tested in the study of molecular wire structures [50]. The study can be considered in a broader scope of research in electron transfer within molecules. The characteristic linear molecular structures of D–S–A are studied for conductive wires. These molecules formed ideal examples to test the electron transfer formalism. A number of the wire structures manifested appreciable rectifying behavior which could be utilized for transistors. The well-documented molecular wire structure with rectification behavior is represented by –hexadecylquinolinium tricyanoquinomethanide 22 (C16 H33 Q–3CNQ) [51–53] (Scheme 6). The rectification behavior of the molecule is demonstrated in the asymmetric current–voltage characteristic measurements shown in Figure 1.

2.5. Carbon Nanotubes Carbon nanotubes can be thought of as graphite sheets with a hexagonal lattice that have been wrapped up into a seamless cylinder. Both single-walled and multiwalled carbon nanotubes have been examined for electron and hole transportation. The substitutional doping of boron and nitrogen in multiwalled carbon nanotubes (MWCNTs) has shown to change the electric conductive behavior in the range from semiconducting to metallic [54]. The inclusion of alkali and halogen in single-walled carbon nanotubes enhances the electrical conductivity [55
56]. Hybrid carbon nanotubes have been shown to possess excellent rectifying behavior [57]. The conductance of the SWCNT was shown to be affected by the chemical environment, such as NH3 and NO2 [58], which could be applicable to chemical sensing. In addition, it has been found that nanotubes can be made from a variety of materials, including carbon, ceramics, metals, and organic polymers. The control of size, especially the diameter, is a key factor in the success of nanotube synthesis. C60 nanotubes with a monodisperse size distribution and uniform orientation can be directly made by evaporating

Scheme 6. Rectification molecular wire structures. The molecular structure (22) is reprinted with permission from [51], R. M. Metzger et al., J. Am. Chem. Soc. 119, 10455 (1997). © 1997, American Chemical Society.

Figure 1. Schematic and I–V curve of (C16 H33 Q–3CNQ). Both (a) a linear plot and (b) a logarithmic plot are presented. Reprinted with permission from [51], R. M. Metzger et al., J. Am. Chem. Soc. 119, 10455 (1997). © 1997, American Chemical Society.

a toluene solution of C60 from an ordered porous alumina template with a narrow pore size distribution [59].

2.6. Columnar Molecular Structures In the columnar phase of discotic liquid crystals, the molecules form stacks, via ligand bonding or – interaction, extending tens of nanometers in coherence length. Such structures have been studied for the potential of onedimensional electron transportation [60]. For the species with alkyl substituents, the side chains interdigitate to form a separating region between molecular cores. The STM observation revealed various assembling behaviors of alkylsubstituted phthalocyanines 23 and porphyrins 24 on a graphite surface [61] (Scheme 7 and Fig. 2). Alongwith the effort in transferring electrons or holes using low-dimensional molecular nanostructures, there have also been studies on ionic transportation which is important for both biological and chemical processes [62–65]. An example is illustrated by the columnar structure consisting of cyclic D,L––peptides 25 [63] (Scheme 8). Low-generation dendrimers are also known to form columnar structures via nonbonding interactions [66–68]. The assemblies of low-generation dendrimers with nanometer diameter cavity channels were directly observed by an STM [69].

Molecular Wires and Switches

825

Scheme 8. Columnar molecular structure. The molecular structure (25) is reprinted with permission from [63], S. Fernandez-Lopez et al., Nature 412, 452 (2001). © 2001, Macmillan Magazines Limited.

Scheme 7. Molecular structures of alkyl-substituted phthalocyanine and porphyrin.

to be as long as 40 Å, with the aid of covalently linked donor and acceptor intercalators [70]. A number of mechanisms have been pursued to understand the charge-transfer pathways under various conditions [71
72]. The ongoing extensive exploration will help to clarify the nature of the charge migration process in DNA with respect to intercalators, sequence, and so on [70–74]. Apart from one-dimensional molecular wires, attaching specific sticky ends to a DNA-branched junction enables the construction of stick figures, whose edges are doublestranded DNA. This approach has been used to assemble a cube, a truncated octahedron, specific 2-D structural features on the nanometer scale, and nanomechanical devices by self-assembly techniques [75].

2.7. DNA Molecules The quest to use DNA as an electron conducting wire has been pursued in the past decade. The quest is rooted in the one-dimensional and well-defined helical structure that is composed of uniformly spaced base pairs which is electron rich. The range for electron transfer was proposed

3. MOLECULAR SWITCHES There is a large variety of molecules that can be effectively and reversibly affected by chemical, optical, and electrical means [1
76]. Such behavior has been extensively exploited as molecular switches for various applications.

3.1. Molecular Switches Based on Interlocked Supramolecules

Figure 2. 2-D assembly of CuPcOC8 on a graphite surface. Reprinted with permission from [61], X. H. Qiu et al., J. Am. Chem. Soc. 122, 5550 (2000). © 2000, American Chemical Society.

The family of cantenane-based interlocked molecules 26 (Scheme 9) has shown drastic UV–vis spectrum changes in the redox process [77] (Fig. 3). As an example, an electrochemical cell formed by a molecular monolayer of [2]– cantenane displayed bistable behavior [78
79]. The behavior led to the design of current-driven molecular logic circuits and addressable memory [80–82]. It was further pointed out that the molecular domains, rather than individual molecules, are responsible for the observed switching behavior [83]. In addition, it has been known that pseudorotaxanes can dissociate into rotaxanes at elevated temperatures or light irradiation, leading to thermal or photomediated molecular switches [84]. The lifetime of the light-triggered excitation state is shown to be as long as a few hundred microseconds for [2]–catenane consisting of a bipyridium cyclophane and a dioxybenzene [85].

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Molecular Wires and Switches

Scheme 9. Molecular structure of [2]–cantenane. The molecular structure (26) is reprinted with permission from [82], A. R. Pease et al., Acc. Chem. Res. 34, 433 (2001). © 2001, American Chemical Society.

3.2. Conjugated Aromatic Molecular Switches This category of molecular structures possesses rich functions in response to external conditions. The redox activity of a number of electrode-bound species, such as phenoxynaphthacene quinone 27, nitrospiropyran 28, rotaxane 29, and so on, were shown to be reversibly switched through photoisomerization [86]. The molecule 30, consisting of anthracene and acylated diaminopyridin as receptors, can undergo a redox process under electrochemical conditions [87] (Fig. 4). The electrochromic effect in macrocyclic derivatives can be exploited for molecular switches. A recent example can be found in the octamethoxytetraphenylene compound 31

Figure 4. Molecular switches based on the photoisomerization process. Reprinted with permission from [86], A. N. Shipway and I. Willner, Acc. Chem. Res. 34, 421 (2001). © 2001, American Chemical Society.

[88] (Scheme 10). The dimerization of the conjugated aromatic species 1,3,5–tripyrrolidinobenzene 32 was also suggested as a venue for realizing molecular switching [89]. Anthracene-based molecules can be fluorescent in the presence of a proton [90]. These switches lead to a novel design of logic circuits based on supramolecular structures, especially interlocked molecules [91]. The concept of (D–S–A) has been widely utilized to design various photosensitive as well as electricalinduced molecular switches, as shown in a series of systems exemplified by D = zinc 5–phenyl–10,15,20–tri(n– pentyl)porphyrin, S = perylene–3,4–dicarboimide, and A = 1,8:4,5–naphthalenediimide 33, 34 [92
93] (Scheme 11). A comparison of the conformation dynamics and chargetransfer effect was analyzed in detail using phenothiazine– (phenyl)n –pyrene (n = 0
1) dyads 35–40 [94] (Scheme 12). It is also shown that, under electrode potential control, the molecular orientation of adsorbed 4,4′ –bipyridine 41 changes reversibly from perpendicular to the electrode surface to nearly parallel [95
96] (Fig. 5).

3.3. Oligomer-Based Switches

Figure 3. Schematic of switching behavior of a [2]–cantenane-based switch. Reprinted with permission from [82], A. R. Pease et al., Acc. Chem. Res. 34, 433 (2001). © 2001, American Chemical Society.

Direct measurement of conductive polymers using microfabricated electrodes revealed a much faster switching behavior compared with bulk material under electrochemical control (polyaniline) [97]. The oligophenylenevinylenes (OPVs) 42 (Scheme 13) having a protonable phenathroline group can also be tuned by acidition [98]. Photochromic oligothiophene-substituted chromenes 43– 46 (Scheme 14) displayed a structural change that can be associated with a change in electrical polarization [99].

Molecular Wires and Switches

Scheme 10. Molecular switches. The molecular structure (30) is reprinted with permission from [87], R. Deans et al., J. Am. Chem. Soc. 119, 10863 (1997). © 1997, American Chemical Society. The molecular structure (31) is reprinted with permission from [38], R. Rathore et al., Angew. Chem. Int. Ed. 39, 809 (2000). © 2000, Wiley-VCH. The molecular structure (32) is reprinted with permission from [84], J. Heinze et al., Angew. Chem. Int. Ed. 40, 2861 (2001). © 2001, Wiley-VCH.

827

Scheme 11. D–S–A type of molecular switches. The molecular structure (33) is reprinted with permission from [92], R. T. Hayes et al., J. Am. Chem. Soc. 122, 5563 (2000). © 2000, American Chemical Society. The molecular structure (34) is reprinted with permission from [93], D. Gosztola et al., J. Am. Chem. Soc. 120, 5118 (1998). © 1998, American Chemical Society.

3.4. Nuclear-Compound-Based Molecular Switches A series of mononuclear, dinuclear, and heteronuclear ruthenium complexes of 4,4′ –azo–(2,2′ –bipyridine)(L) 47–50 (Scheme 15) is shown to be redox responsive [100
101]. The redox-driven translocation of copper cations was shown in double-stranded mononuclear cupric and cuprous complexes 51 [102] (Scheme 15). The photoirradiation is also shown to induce structural changes in iron (II) molecular complexes, [Fe(phen)2 (NCS)2 ](phen = 1,10-phenanthroline) 52 (Scheme 16), leading to a transition between high-spin and low-spin states [103]. The concept of a molecular switch has been applied to control chemical reactions. It was shown that a molecule 53 (Scheme 17) consisted of aluminum porphyrin, and an olefin could be reversibly tuned by UV and visible light through photoisomerization of the olefin, and thus used to control the reaction of carbondioxide and epoxide [104].

3.5. Chiral-Molecule-Based Switches In a recent review, the switching behavior of chiral molecules was also described [105]. The representative examples of chiral optical molecular switches can be

Scheme 12. Molecular switches. The molecular structures (35–40) are reprinted with permission from [94], J. Daub et al., J. Phys. Chem. A 105, 5655 (2001). © 2001, American Chemical Society.

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828

Figure 5. Orientation of bpy under electrochemical control. Reprinted with permission from [96], Th. Wandlowski et al., Langmuir 18, 4331 (2002). © 2002, American Chemical Society.

illustrated by a compound of unsymmetrically sterically overcrowded thiolxan-thenes 54–56 [105] (Scheme 18). These molecules consist of a static part and a rotary part that can be turned under light irradiation. Their potential applications in molecular motor designs were also explored. In a separate work, the effect of molecular chirality was demonstrated on the directional motion of rotaxane-based molecular motors [106].

3.6. Fullerene-Based Molecular Switches A conformation change of fullerene molecules can lead to drastically different responses in electronic behavior, such as C60 under deformation by an STM tip [107
108] or by controlling the gate potential in a three-terminal geometry [109]. A significant negative differential resistance (NDR) effect can be observed in a junction formed by two C60 molecules, due to the local density distribution at the Fermi level of C60 molecules [110] (Fig. 6).

Scheme 14. Molecular switches. The molecular structures (43–46) are reprinted with permission from [99], A.Yassar et al., Eur. Phys. J. AP 18, 3 (2002). © 2002, EDP Sciences.

components that are photoisomerized and proton sensitive, respectively, a molecular switch 57 (Scheme 19) was realized that can be controlled by both pH and light [111]. A scheme for an optical communication network was proposed based on the photoisomerization of a spiropyran derivative 58 [112]. The spiropyran derivative was shown to be tunable (by ultraviolet light, visible light, and pH) to three distinctive states, namely, the colorless spiropyran state (SP) and two types of colored merocyanine forms (ME and MEH, respectively), as shown in Figure 7.

3.7. Multifunction Molecular Switches

3.8. Biological Switches

In addition to the above-discussed single-function molecular-switched structures, others that consist of different functional groups have also been studied. By combining

A vital aspect of biological activities is regulation at all levels. There are numerous examples in biological systems where the regulation or switching functions involve individual protein molecules. A comprehensive summary is beyond the scope of this work, and dedicated literature [113–119] would be appropriate for interested investigators.

4. MOLECULES FOR DATA STORAGE

Scheme 13. Polymeric molecular switch. The molecular structure (42) is reprinted with permission from [98], N. Armaroli et al., Chem. Commun. 2105 (2000). © 2000, Royal Society of Chemistry.

Along with the effort to develop nanostructures to construct prototype electronic circuits, there are studies to develop molecule-based storage structures. This is also an essential part of integrated nanometer-scale devices. The molecular species reported in this category can be triggered by an external field consisting of an electric field, light, and a magnetic field.

Molecular Wires and Switches

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Scheme 18. Chiral molecular switches. The molecular structures (54– 56) are reprinted with permission from [105], B. L. Feringa, Acc. Chem. Res. 34, 504 (2001). © 2001, American Chemical Society.

Scheme 15. Molecular switches. The molecular structures (47–50) are reprinted with permission from [101], J. Otsuki et al., J. Am. Chem. Soc. 119, 7895 (1997). © 1997, American Chemical Society. The molecular structure (51) is reprinted with permission from [102], D. Kalny et al., Chem. Commun. 1426 (2002). © 2002, Royal Society of Chemistry.

Figure 6. Negative differential resistance of C60 . Reprinted with permission from [110], C. G. Zeng et al., Appl. Phys. Lett. 77, 3595 (2000). © 2000, American Institute of Physics.

Scheme 16. Molecular switch. The molecular structure (52) is reprinted with permission from [103], M. Marchivie et al., J. Am. Chem. Soc. 124, 194 (2002). © 2002, American Chemical Society.

Scheme 17. Molecular switch. The molecular structure (53) is reprinted with permission from [104], H. Sugimoto et al., J. Am. Chem. Soc. 121, 2325 (1999). © 1999, American Chemical Society.

Scheme 19. Multifunction molecular switch. The molecular structure (57) is reprinted with permission from [111], L. Gobbi et al., Angew. Chem. Int. Ed. 38, 674 (1999). © 1999, Wiley-VCH.

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Molecular Wires and Switches

Figure 7. Schematic of optical communication system based on a molecular switch. Reprinted with permission from [112], F. M. Raymo and S. Giordani, J. Am. Chem. Soc. 124, 2004 (2002). © 2002, American Chemical Society.

4.1. Electric-Driven Molecular Storage The switching behavior of a number of molecules that lead to different resistance states are important candidates for molecular memory designs. The nanopore experiments [120
121] indicated that the nitroamino compound 59 (Scheme 20) has two distinct conduction states (conducting and non conducting). It was also suggested that the charged state of dinitro compounds, 2′ –nitro–4–ethynylphenyl–4′ ethynylphenyl–5′ -nitro– 1–benzene thiolate 60 (Scheme 20), can also be considered for a type of molecular switch [122]. The switching behavior is associated with the ensemble of approximately 1000 molecules in the nanopore junction region. Another study on the complex of 3–nitrobenzal malononitril and 1,4–phenylenediamine(NBMN–pDA), p– nitrobenzonitrile (PNBN) demonstrated distinctively different conductive states which could be reversibly controlled by an electric field [123–125].

Scheme 21. Examples of single molecular magnetic molecules. The molecular structures (61
62) are reprinted with permission from [121], K. Park et al., J. Appl. Phys. 91, 7167 (2002). © 2002, American Institute of Physics. The molecular structure (63) is reprinted with permission from [132], E.-C. Yang et al., J. Appl. Phys. 91, 7382 (2002). © 2002, American Institute of Physics.

4.2. Molecular Magnets for Data Storage Molecules with paramagnetic transition metal centers have been pursued as magnetic materials. These species could provide potentials for designing data storage strategies on a single molecular level. A family of molecules exemplified by Mn12 [Mn12 O12 (O2 CMe)16 (H2 O)4 ] · 4H2 O · 2MeCOOH [126– 129] 61 (Scheme 21) and Fe8 [Fe8 O2 (OH)12 (tacn)6 ]+8 62 [129–131] (Scheme 21) has been studied. Due to the weak intermolecular interactions between magnetic centers (12 Mn atoms), these species are widely pursued as single molecular magnets (SMMs). Other examples of molecular magnets include Co4 [Co4 (hmp)4 (MeOH)4 Cl4 63 (Scheme 21), where hmp− = anion of hydroxymethylpyridine] [132], Fe4 [Fe4 (OCH3 )(dmp)6 , dpm = dipivaloylmethane] [133
134]. Organic radicals (such as tetracyanoethylene (TCNE), nitroxide derivatives) provide another category of molecular magnets. The examples are M(TCNE)x · y(solvent) (M = V, Fe, Mn, Co, Ni; TCNE = tetracyanoethylene) [135], together with the family of radical-based molecular magnets [136]. ML × 4
4′ –bipyridine) (M = Fe, Co, Ni, Zn; IV L = C2 O2− 4 or Cl2 ) [137–139]. V15 (K6 [V 15 As6 O42 (H2 O)] · 8H2 O) [140–142].

4.3. Molecular Memory in Biological Systems Scheme 20. Molecules for molecular memory device. The molecular structures (59
60) are reprinted with permission from [122], J. M. Seminario et al., J. Chem. Phys. 116, 1671 (2002). © 2002, American Institute of Physics.

The understanding of the memory function of the brain has a profound impact on all aspects of life. Memory function is exhibited by storing and retrieving information for both long and short periods of time.

Molecular Wires and Switches

The extensive studies in the past several decades have remarkably advanced the knowledge of molecular memory in biological systems [143–145]. The proposition and confirmation of long-term potentiation is one of the major achievements in this field [146
147]. This process is characterized by the sustained increase in synaptic strength generated by an action potential in the presynaptic axon [148
149]. The mechanism of the information encoding process is identified by molecules such as Ca2+ /calmodulindependent protein kinase II (CaMKII) and the NMDA (N–methyl–D–aspartate) subtype of the glutamate receptor [150].

5. MOLECULAR MACHINES 5.1. Supramolecule-Based Molecular Motor The interest in constructing nanometer-scale machines with dynamic functions has led to extensive efforts evidenced by the diverse designs of molecular nanostructures stemming from supramolecular chemistry. The function-oriented synthesis and assembling have provided rich options for mechanical parts, such as brakes, shuttles, and so on. The advances are summarized in a special issue of Accounts of Chemical Research, volume 34, issue 6 (2001). The fascinating results shed light on the possibility of conversion of the photo and chemical potential difference into mechanical motion of various artificially designed molecular machines. The illustrated examples include triptycene 61based molecular brakes and ratchet [151] (Fig. 8). A number of cyclic components, such as rotaxane and cyclodextrin, could display rotational or translational motion, once threaded through a rigid rod-like structure (such as a polymer chain). The general principle of the driving force is based on the redox activity of the electroactive parts of the assembly. Rotational motion was shown in a

831 chiral, helical alkene with the irradiation of ultraviolet light [152].

5.2. Biological Molecular Motors Proteins that function as molecular motors are important parts of biological activities, typically driven by energy via the hydrolysis of adenosine triphosphate (ATP). With the characteristic size in the range of nanometers, these proteins can function either in single molecules or in large ensembles. A number of protein families have been extensively studied in this category, including actin-based myosins with more than ten different family types [153
154], the microtubulebased kinesin family [155
156, dyneins [157], and the membrane motor protein of prestin [158]. Prototype artificial molecular machines were proposed and explored based on a single molecule configuration [159–162].

6. SUMMARY The surge of interest in nanoscience and technology has generated a vast expansion in research activities. The outcome of the endeavor may go much beyond the goal of device miniaturizations, to new perspectives and novel properties which are not prevalent in bulk materials. Studies of molecular nanostructures can contribute as well as benefit greatly during the process. The interface between nanometer-scale molecular structures with a macroscopic environment is another field that needs to be explored. The interaction between molecules and the solid support, a combination of the assembling process with state-of-art lithography technology, are important issues that need to be vigorously addressed in future research. The advances in self-assembly, especially the assembly processes involving multiple components and directional assembly, will have an important impact on the fabrication routes for devices. Extensive explorations of the molecular properties (conductivity, etc.) on a single molecular level are also essential to the realization of high-performance molecular devices. As the major body of current knowledge is based on the results obtained on the molecular assemblies, progress in the detection techniques would greatly facilitate the understanding of single molecules in various environments.

GLOSSARY

Figure 8. Examples of motions performed by molecular motor parts. (a) Schematic of the braking motion. (b) Corresponding molecular structures. Reprinted with permission from [151], T. R. Kelly, Acc. Chem. Res. 34, 514 (2001). © 2001, American Chemical Society.

Aliphatic molecule Molecule that can be generally regarded as a methane derivative. Chiral molecules Molecules containing asymmetric components that are mirror images of each other. They are also defined optically as right- and left-handed structures. Conjugated polymer Polymer containing sequential double bonds. Dendrimer Highly branched polymer of controlled branching structure. Ionic transportation Movement of charged particles under the influence of an electric field.

832 Liquid crystal Anisotropic liquid state that possesses crystalline structures. Oligomer Polymer with a degree of polymerization up to a value of 10–20. Rectification Switching behavior of abrupt discontinuity in electrical resistance.

REFERENCES 1. J.-M. Lehn, “Supramolecular Chemistry: Concepts and Perspectives.” VCH, Weinheim, Germany, 1995. 2. G. M. Whitesides and B. Grzybowski, Science 295, 2418 (2002). 3. G. M. Whitesides, J. P. Mathias, and C. T. Seto, Science 254, 1312 (1991). 4. F. L. Carter (Ed.), “Molecular Electronic Designs I.” Marcel Dekker, New York, 1987. 5. F. L. Carter (Ed.), “Molecular Electronic Designs II,” Marcel Dekker, New York, 1987. 6. A. J. Bard, “Integrated Chemical Systems: A Chemical Approach to Nanotechnology.” Wiley, New York, 1994. 7. M. A. Fox, Acc. Chem. Res. 32, 201 (1999). 8. M. N. Paddon-Row, Acc. Chem. Res. 27, 18 (1994). 9. S. N. Yalikari, A. E. Roitberg, C. Gonzalez, V. Mujica, and M. Ratner, J. Chem. Phys. 111, 6997 (1999). 10. B. Mann and H. Kuhn, J. Appl. Phys. 42, 4398 (1971). 11. M. A. Rampi, O. J. A. Schueller, and G. M. Whitesides, Appl. Phys. Lett. 72, 1781 (1998). 12. R. Haag, M. A. Rampi, R. E. Holmlin, and G. M. Whitesides, J. Am. Chem. Soc. 121, 7895 (1999). 13. R. E. Holmlin, R. Haag, M. L. Chabinyc, R. F. Ismagilov, A. E. Cohen, A. Terfort, M. A. Rampi, and G. M. Whitesides, J. Am. Chem. Soc. 123, 5075 (2001). 14. K. Slowinski, H. K. Y. Fong, and M. Majda, J. Am. Chem. Soc. 121, 7257 (1999). 15. K. Slowinski, K. U. Slowinski, and M. Majda, J. Phys. Chem. B 103, 8544 (1999). 16. K. Slowinski and M. Majda, J. Electroanal. Chem. 491, 139 (2000). 17. X. D. Cui, A. Primak, X. Zarate, J. Tomfohr, O. F. Sankey, A. L. Moore, T. A. Moore, D. Gust, G. Harris, and S. M. Lindsay, Science 294, 571 (2001). 18. M. A. Reed, C. Zhou, C. J. Muller, T. P. Burgin, and J. M. Tour, Science 278, 252 (1997). 19. X. L. Fan, C. Wang, D. L. Yang, L. J. Wan, and C. L. Bai, Chem. Phys. Lett. 361, 465 (2002). 20. S. N. Yaliraki, M. Kemp, and M. A. Ratner, J. Am. Chem. Soc. 121, 3428 (1999). 21. M. A. Rampi, O. J. A. Schueller, and G. M. Whitesides, Appl. Phys. Lett. 72, 1781 (1998). 22. K. Slowinski, H. K. Y. Fong, and M. Majda, J. Am. Chem. Soc. 121, 7257 (1999). 23. D. J. Wold and C. D. Frisbie, J. Am. Chem. Soc. 123, 5549 (2001). 24. D. J. Wold and C. D. Frisbie, J. Am. Chem. Soc. 122, 2970 (2000). 25. L. A. Bumm, J. J. Arnold, T. D. Dunbar, D. L. Allara, and P. S. Weiss, J. Phys. Chem. B 103, 8122 (1999). 26. D. J. Wold, R. Haag, M. A. Rampi, and C. D. Frisbie, J. Phys. Chem. B 106, 2813 (2002). 27. R. E. Holmlin, R. Haag, M. L. Chabinyc, R. F. Ismagilov, A. E. Cohen, A. Terfort, M. A. Rampi, and G. M. Whitesides, J. Am. Chem. Soc. 123, 5075 (2001). 28. F. R. F. Fan, J. P. Yang, L. T. Cai, D. W. Price, Jr., S. M. Dirk, D. V. Kosynkin, Y. X. Yao, A. M. Rawlett, J. M. Tour, and A. J. Bard, J. Am. Chem. Soc. 124, 5550 (2002). 29. C. K. Chiang, C. R. Fincher, Y. W. Park, A. J. Heeger, H. Shirakawa, E. J. Louis, S. C. Gau, and A. G. MacDiarmid, Phys. Rev. Lett. 39, 1098 (1977).

Molecular Wires and Switches 30. T. A. Skotheim, J. R. Reynolds, and R. L. Elsenbaumer (Eds.), “Handbook of Conducting Polymers,” 2nd ed. Marcel Dekker, New York, 1997. 31. R. P. Andres, T. Bein, M. Dorogi, S. Feng, J. I. Henderson, C. P. Kubiak, W. Mahoney, R. G. Osifchin, and R. Reifenberger, Science 272, 1323 (1996). 32. M. A. Reed, C. Zhou, C. J. Muller, T. P. Burgin, and J. M. Tour, Science 278, 252 (1997). 33. C. Joachim, J. K. Gimzewski, and A. Aviram, Nature 408, 541 (2000). 34. R. E. Martin, U. Gubler, C. Boudon, V. Gramlich, C. Bosshard, J. P. Gisselbrecht, P. Gunter, M. Gruss, and F. Diederich, Chem. Eur. J. 3, 1505 (1997). 35. R. M. Martin, T. Mader, and F. Diederich, Angew. Chem. Int. Ed. 38, 817 (1999). 36. J. M. Tour, Acc. Chem. Res. 33, 791 (2000). 37. S. Creager, C. J. Yu, C. Bamdad, S. O’Connor, T. MacLean, E. Lam, Y. Chong, G. T. Olsen, J. Y. Luo, M. Gozin, and J. F. Kayyem, J. Am. Chem. Soc. 121, 1059 (1999). 38. S. P. Dudek, H. D. Sikes, and C. E. D. Chidsey, J. Am. Chem. Soc. 123, 8033 (2001). 39. J. M. Tour, M. Kozaki, and J. M. Seminario, J. Am. Chem. Soc. 120, 8486 (1998). 40. D. Fichou (Ed.), “Handbook of Oligo- and Polythiophenes,” Wiley-VCH, Weiheim, Germany, 1999. 41. N. Aratani, A. Osuka, Y. H. Kim, D. H. Jeong, and D. Kim, Angew. Chem. Int. Ed. 39, 1458 (2000). 42. A. Tsuda and A. Osuka, Science 293, 79 (2001). 43. R. Dembinski, T. Bartik, B. Bartik, M. Jaeger, and J. A. Gladysz, J. Am. Chem. Soc. 122, 810 (2000), and references therein. 44. Y. Okawa and M. Aono, J. Chem. Phys. 115, 2317 (2001). 45. R. D. McCullough, Adv. Mater. 10, 93 (1998). 46. D. O. Cowan and F. M. Wiygyl, Chem. Eng. News 29, (1986). 47. Q. Zhou and T. M. Swager, J. Am. Chem. Soc. 117, 12593 (1995). 48. M. Rief, F. Oesterhelt, B. Heymann, and H. E. Gaub, Science 275, 1295 (1997). 49. R. M. Overney, D. P. Leta, C. F. Pictroski, M. H. Rafailovich, Y. Liu, J. Quinn, J. Sokolov, A. Eisenberg, and G. Overney, Phys. Rev. Lett. 76, 1272 (1996). 50. A. Aviram and M. A. Ratner, Chem. Phys. Lett. 29, 277 (1974). 51. R. M. Metzger, B. Chen, U. Hopfner, M. V. Lakshmikantham, T. V. Hughes, H. Sakurai, J. W. Baldwin, C. Hosch, M. P. Cava, L. Brehmer, and G. J. Ashwell, J. Am. Chem. Soc. 119, 10455 (1997). 52. R. M. Metzger, Acc. Chem. Res. 32, 950 (1999). 53. T. Xu, I. R. Peterson, M. V. Lakshmikatham, and R. M. Metzger, Angew. Chem. Int. Ed. 40, 1749 (2001). 54. D. L. Carroll, X. Blase, J.-C. Charlier, S. Curran, Ph. Redlich, P. M. Ajayan, S. Roth, and M. Ruhle, Phys. Rev. Lett. 81, 2332 (1998). 55. A. M. Rao, P. C. Eklund, S. Bandow, A. Thess, and R. E. Smalley, Nature 388, 257 (1997). 56. R. S. Lee, H. J. Kim, J. E. Fischer, A. Thess, and R. E. Smalley, Nature 388, 255 (1997). 57. C. W. Zhou, J. King, W. Yenilmez, and H. J. Dai, Science 290, 1552 (2000). 58. J. Kong, N. R. Franklin, C. W. Zhou, M. G. Chapline, S. Peng, K. Cho, and H. J. Dai, Science 287, 622 (2000). 59. H. B. Liu, Y. L. Li, H. Y. Luo, S. Q. Xiao, H. J. Fang, H. M. Li, D. B. Zhu, D. P. Yu, J. Xu, and B. Xiang, J. Am. Chem. Soc. 124, 13370 (2002). 60. S. Roth, “One-Dimensional Metals: Physics and Materials Science.” Wiley, New York, 1995. 61. X. H. Qiu, C. Wang, Q. D. Zeng, B. Xu, S. X. Yin, H. N. Wang, S. D. Xu, and C. L. Bai, J. Am. Chem. Soc. 122, 5550 (2000). 62. T. Kato, Science 295, 2414 (2002).

Molecular Wires and Switches 63. S. Fernandez-Lopez, H. S. Kim, E. C. Choi, M. Delgado, J. R. Granja, A. Khasanov, K. Kraehenbuehl, G. Long, D. A. Weinberger, K. M. Wilcoxen, and M. R. Ghadiri, Nature 412, 452 (2001). 64. O. Ikkala and G. ten Brinke, Science 295, 2407 (2002). 65. G. W. Gokel and O. Murillo, Acc. Chem. Res. 29, 425 (1996). 66. G. R. Newkome, C. N. Moorefield, and F. Vögtl, “Dendritic Molecules. Concepts, Synthesis, Perspectives.” VCH, Weinhem, 1996. 67. S. M. Grayson and J. M. J. Fréchet, Chem. Rev. 101, 3819 (2001). 68. A. W. Bosman, H. W. Janssen, and E. W. Meijer, Chem. Rev. 99, 1665 (1999). 69. P. Wu, Q. D. Zeng, S. L. Xu, C. Wang, S. X. Yin, and C. L. Bai, Chem. Phys. Chem. 12, 751 (2001). 70. C. J. Murphy, M. R. Arkin, Y. Jenkins, N. D. Ghatlia, S. H. Bossmann, N. J. Turro, and J. K. Barton, Science 262, 1025 (1993). 71. For example, A. Harriman, Angew. Chem. Int. Ed. 38, 945 (1998). 72. G. B. Schuster, Acc. Chem. Res. 33, 253 (2000); B. Giese, Acc. Chem. Res. 33, 631 (2000); M. Bixon and J. Jortner, J. Am. Chem. Soc. 123, 12556 (2001) and references. 73. U. Diederichsen, Angew. Chem. Int. Ed. 36, 2317 (1997). 74. M. W. Grinstaff, Angew. Chem. Int. Ed. 38, 3629 (1999). 75. N. C. Seeman, Annu. Rev. Biophys. Biomol. Struct. 27, 225 (1998). 76. J. F. Stoddart, Acc. Chem. Res. 34, 433 (2001). 77. For example, B. L. Feringa, “Molecular Switches.” Wiley-VCH, Weinheim, 2001. 78. C. P. Collier, G. Mattresteig, E. W. Wong, Y. Luo, K. Beverly, J. Sampaio, F. M. Raymo, J. F. Stoddart, and J. R. Heath, Science 289, 1172 (2000). 79. C. P. Collier, E. W. Wong, M. Belohradsky, F. M. Raymo, J. F. Stoddart, P. J. Kuekes, R. S. Williams, and J. R. Heath, Science 285, 391 (1999). 80. C. L. Brown, U. Jonas, J. A. Preece, H. Ringsdorf, M. Seitz, and J. F. Stoddart, Langmuir 16, 1924 (2000). 81. C. P. Collier, J. O. Jeppesen, Y. Luo, J. Perkins, E. W. Wong, J. R. Heath, and J. F. Stoddart, J. Am. Chem. Soc. 123, 12632 (2001). 82. A. R. Pease, J. O. Jeppesen, J. F. Stoddart, Y. Luo, C. P. Collier, and J. R. Heath, Acc. Chem. Res. 34, 433 (2001). 83. Y. Luo, C. P. Collier, J. O. Jeppesen, K. A. Nielsen, E. Delonno, G. Ho, J. Perkins, H. R. Tseng, T. Yamamoto, J. F. Stoddart, and J. R. Heath, Chem. Phys. Chem. 3, 519 (2002). 84. F. M. Raymo and J. F. Stoddart, Chem. Rev. 99, 1643 (1999). 85. M. Alvaro, M. N. Chretien, B. Ferrer, V. Fornes, H. Garcia, and J. C. Scaiano, Chem. Commun. 2106 (2001). 86. A. N. Shipway and I. Willner, Acc. Chem. Res. 34, 421 (2001). 87. R. Deans, A. Niemz, E. C. Breinlinger, and V. M. Rotello, J. Am. Chem. Soc. 119, 10863 (1997). 88. R. Rathore, P. Le Magueres, S. V. Lindeman, and J. K. Kochi, Angew. Chem. Int. Ed. 39, 809 (2000). 89. J. Heinze, C. Willmann, and P. Bauerle, Angew. Chem. Int. Ed. 40, 2861 (2001). 90. A. P. de Silva, Nature 364, 42 (1993). 91. F. M. Raymo, Adv. Mater. 14, 401 (2002). 92. R. T. Hayes, M. R. Wasielewski, and D. Gosztola, J. Am. Chem. Soc. 122, 5563 (2000). 93. D. Gosztola, M. P. Niemczyk, and M. R. Wasielewski, J. Am. Chem. Soc. 120, 5118 (1998). 94. J. Daub, R. Engl, J. Kurzawa, S. E. Miller, S. Schneider, A. Stockmann, and M. R. Wasielewski, J. Phys. Chem. A 105, 5655 (2001). 95. L. J. Wan, H. Noda, C. Wang, C. L. Bai, and M. Osawa, Chem. Phys. Chem. 10, 617 (2001). 96. Th. Wandlowski, K. Ataka, and D. Mayer, Langmuir 18, 4331 (2002). 97. H. X. He, J. S. Zhu, N. J. Tao, L. A. Nagahara, I. Amlani, and R. Tsui, J. Am. Chem. Soc. 123, 7730 (2001). 98. N. Armaroli, J. F. Eckert, and J. F. Nierengarten, Chem. Commun. 2105 (2000).

833 99. A. Yassar, H. Jaafari, N. Rebiere-Galy, M. Frigoli, C. Moustrou, A. Samat, and R. Gugliemetti, Eur. Phys. J. AP 18, 3 (2002). 100. J. Otsuki, K. Sato, M. Tsujino, N. Okuda, K. Araki, and M. Seno, Chem. Lett. 847 (1996). 101. J. Ostuki, M. Tsujino, T. Iizaki, K. Araki, M. Seno, K. Takatera, and T. Watanabe, J. Am. Chem. Soc. 119, 7895 (1997). 102. D. Kalny, M. Elhabiri, T. Moav, A. Vaskevich, I. Rubinstein, A. Shanzer, and A. M. Albrecht-Gary, Chem. Commun. 1426 (2002). 103. M. Marchive, P. Guionneau, J. A. K. Howard, G. Chastanet, J. F. Letard, A. E. Goeta, and D. Chasseau, J. Am. Chem. Soc. 124, 194 (2002). 104. H. Sugimoto, T. Kimura, and S. Inoue, J. Am. Chem. Soc. 121, 2325 (1999). 105. B. L. Feringa, Acc. Chem. Res. 34, 504 (2001). 106. C. A. Schalley, K. Beizai, and F. Vogtle, Acc. Chem. Res. 34, 465 (2001). 107. C. Joachim, J. K. Gimzewski, R. R. Schlittler, and C. Chavy, Phys. Rev. Lett. 74, 2102 (1995). 108. C. Joachim, J. K. Gimzewski, and H. Tang, Phys. Rev. B 58, 16407 (1998). 109. J. Taylor, H. Guo, and J. Wang, Phys. Rev. B 63, 121104 (2001). 110. C. G. Zeng, H. Q. Wang, B. Wang, J. L. Yang, and J. G. Hou, Appl. Phys. Lett. 77, 3595 (2000). 111. L. Gobbi, P. Seiler, and F. Diederich, Angew. Chem. Int. Ed. 38, 674 (1999). 112. F. M. Raymo and S. Giordani, J. Am. Chem. Soc. 124, 2004 (2002). 113. M. Yan, L. C. Wang, S. G. Hymowitz, S. Schilbach, J. Lee, A. Goddard, A. M. de Vos, W. Q. Gao, and V. M. Dixit, Science 290, 523 (2000). 114. H. T. Kao, H. J. Song, B. Porton, G. L. Ming, J. Hoh, M. Abraham, A. J. Czernik, V. A. Pieribone, M. M. Poo, and P. Greengard, Nature Neurosci. 5, 431 (2002). 115. J. Lisman, H. Schulman, and H. Cline, Nat. Rev. Neurosci. 3, 175 (2002). 116. T. Cheng, N. Rodrigues, H. M. Shen, Y. G. Yang, D. Dombkowski, M. Sykes, and D. T. Scadden, Science 287, 1804 (2000). 117. S. E. Ross, N. Hemati, K. A. Longo, C. N. Bennett, P. C. Lucas, R. L. Erickson, and O. A. MacDougald, Science 289, 950 (2000). 118. J. P. Zha, S. Weiler, K. J. Oh, M. C. Wei, and S. J. Korsmeyer, Science 290, 1761 (2000). 119. A. Wittinghofer and H. Waldmann, Angew. Chem. Int. Engl. 39, 4192 (2000). 120. J. Chen, M. A. Reed, A. M. Rawlett, and J. M. Tour, Science 286, 1550 (1999). 121. J. Chen, W. Wang, M. A. Reed, A. M. Rawlett, D. W. Price, and J. M. Tour, Appl. Phys. Lett. 77, 1224 (2000). 122. J. M. Seminario, A. G. Zacarias, and P. A. Derosa, J. Chem. Phys. 116, 1671 (2002). 123. H. J. Gao, K. Sohlberg, Z. Q. Xue, H. Y. Chen, S. M. Hou, L. P. Ma, X. W. Fang, S. J. Pang, and S. J. Pennycook, Phys. Rev. Lett. 84, 1780 (2000). 124. D. X. Shi, Y. L. Song, D. B. Zhu, H. X. Zhang, S. S. Xie, S. J. Pang, and H. J. Gao, Adv. Mater. 13, 1103 (2001). 125. D. X. Shi, Y. L. Song, H. X. Zhang, P. Jiang, S. T. He, S. S. Xie, S. J. Pang, and H. J. Gao, Appl. Phys. Lett. 77, 3203 (2000). 126. R. Sessoli, D. Gatteschi, and M. Novak, Nature 365, 149 (1993). 127. R. Sessoli, H. L. Tsai, A. R. Schake, S. Wang, J. B. Vincent, K. Folting, D. Gatteschi, G. Christou, and D. N. Hendrickson, J. Am. Chem. Soc. 115, 1804 (1993). 128. T. Lis, Acta Crystall. Sect. B: Struct. Crystall. Cryst. Chem. 36, 2042 (1980). 129. K. Park, M. A. Novotny, N. S. Dalal, S. Hill, and P. A. Rikvold, J. Appl. Phys. 91, 7167 (2002).

Molecular Wires and Switches

834 130. K. Wieghart, K. Pohl, I. Jibril, and G. Huttner, Angew. Chem. Int. Ed. 23, 77 (1984). 131. A. Caneschi, D. Gatteschi, C. Sangregorio, R. Sessoli, L. Sorace, A. Cornia, M. A. Novak, C. Paulsen, and W. Wernsdorfer, J. Magn. Magn. Mater. 200, 182 (1999). 132. E. C. Yang, D. N. Hendrickson, W. Wernsdorfer, M. Nakano, L. N. Zakharov, R. D. Sommer, A. L. Rheingold, M. L. Gairaud, and G. Christou, J. Appl. Phys. 91, 7382 (2002). 133. A. Barra, A. Caneschi, A. Cornia, F. F. de Biani, D. Gatteschi, C. Sangregorio, R. Sessoli, and L. Sorace, J. Am. Chem. Soc. 121, 5302 (1999). 134. A. Bouwen, A. Caneschi, D. Gatteschi, E. Goovaerts, D. Schoemaker, L. Sorace, and M. Stefan, J. Phys. Chem. B 105, 2658 (2000). 135. K. R. Dunbar (Ed.), “Proceedings of the 7th International Conference on Molecular-Based Magnets,” San Antonio, TX; Polyhedron 20 (2001). 136. J. S. Miller and A. J. Epstein, Angew. Chem. Int. Ed. 33, 385 (1994). 137. J. Y. Lu, M. A. Lawandy, J. Li, T. Yuen, and C. L. Lin, Inorg. Chem. 38, 2695 (1999). 138. M. A. Lawandy, X. Huang, R. Wang, J. Li, J. Y. Lu, T. Yuen, and C. Lin, Inorg. Chem. 38, 5410 (1999). 139. T. Yuen, C. L. Lin, T. W. Milhalisin, M. A. Lawandy, and J. Li, J. Appl. Phys. 87, 6001 (2000). 140. A. Muller and J. Doring, Angew. Chem. Int. Ed. 27, 1721 (1991). 141. D. Gatteschi, L. Pardi, A. L. Barra, and A. Muller, Mol. Eng. 3, 157 (1993). 142. D. Gatteschi, L. Pardi, A. L. Barra, A. Muller, and J. Doring, Nature 354, 465 (1991).

143. 144. 145. 146. 147. 148. 149. 150. 151. 152. 153. 154. 155. 156. 157. 158. 159. 160. 161. 162.

J. E. Lisman and J. R. Fallon, Science 283, 339 (1999). R. C. Malenka and R. A. Nicoll, Science 285, 1870 (1999). T. V. Bliss and G. L. Collingridge, Nature 361, 31 (1993). D. O. Hebb, “The Organization of Behavior.” Wiley, New York, 1949. T. V. Bliss and T. Lomo, J. Physiol. 232, 331 (1973). For example, see J. E. Lisman and C. C. McIntyre, Curr. Biol. 11, R788 (2001). D. G. Wells and J. R. Fallon, Cell. Mol. Life Sci. 57, 1335 (2000). F. Gardoni, A. Caputi, M. Cimino, L. Patorino, F. Cattabeni, and M. Di Luca, J. Neurochem. 71, 1733 (1998). T. R. Kelly, Acc. Chem. Res. 34, 514 (2001). N. Koumura, R. W. J. Zijlstra, R. A. van Delden, N. Harada, and B. L. Feringa, Nature 401, 152 (1999). J. A. Spudich and R. S. Rock, Nature Cell Biol. 4, E8 (2001). M. Schliwa, Nature 401, 431 (1999). G. Bloom and S. Endow, Prot. Profiles 1059 (1994). S. A. Endow, Nature Cell Biol. 1, E163 (1999). N. Hirokawa, Science 279, 519 (1998). P. Dallos and B. Fakler, Nat. Rev. Mol. Cell. Biol. 3, 104 (2002). J. T. Finer, R. M. Simmons, and J. A. Spudich, Nature 368, 113 (1994). J. E. Molloy, J. E. Burns, J. Kendrick-Jones, R. T. Tregear, and D. S. C. White, Nature 378, 209 (1995). A. Ishijima, H. Kojima, T. Funatsu, M. Tokunaga, H. Higuchi, and T. Yanagida, Cell 92, 161 (1998). K. Visscher, M. J. Schnitzer, and S. M. Block, Nature 400, 184 (1999); A. E. Knight and J. E. Molloy, Nature Cell Biol. 1, E87 (1999).

Encyclopedia of Nanoscience and Nanotechnology

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Monolayer-Assisted Electrochemical Nanopatterning O. Azzaroni, P. L. Schilardi, R. C. Salvarezza INIFTA, UNLP—CONICET, La Plata, Argentina

CONTENTS 1. Introduction 2. Alkanethiol Self-Assembled Monolayers (SAMs) on Metals 3. Metal Electrodeposition on Alkanethiolate SAMs 4. Applications 5. Conclusions Glossary References

1. INTRODUCTION Self-assembled monolayers (SAMs) consist in a single layer of molecules adsorbed on a substrate, with the particularity of being highly oriented, ordered, and packed. In particular, SAMs of thiols on metals have attracted considerable scientific interest because they provide a method for creating well-defined surfaces with controllable chemical functionality [1, 2]. The possible application of SAMs ranges from nanotechnology to fundamental surface science. Selfassembled monolayers can be used to prevent corrosion [3–5], modify wetting and wear properties [6–8] of solid surfaces, develop nano-devices for electronics [9], and for pattern formation [10–12]. In particular, by anchoring specific chemical groups to these molecular self-assemblies, wellordered structures with controlled chemical features can be achieved in order to be employed in molecular recognition [13], protein adsorption [14], and templates for crystallization of inorganic salts [15]. Otherwise, the fabrication of nanostructures is one of the most relevant topics in modern technologies. Nanofabrication has been defined as a technique capable of generating structures with at least one lateral dimension between 1–100 nm [16, 17]. Nano- and micro-fabrication is based mainly on photolithography [18] and its immediate implications are related to the fabrication of microelectronic devices that have new architectures [19], biomimetic structures [20], fiber optic communications [21],

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and microfluidic systems [22]. The development of novel methods, in particular to build three-dimensional patterned microstructures, enables new options for microfabrication and creates the possibility of choosing the most convenient method considering several factors such as complexity, cost, and elapsed time of fabrication. Several strategies have been developed for fabricating micrometer- and nanometer- scale patterns [23–25]. The method of fabrication often involves several steps of various degrees of complexity depending on the desired structure. In the case of patterned organic polymer surfaces using elastomeric masters [26], intermediate steps include elastomer curing, peeling off, organic polymer curing, compressing, bending, and stretching. In the case of patterned metallic nano-microstructures, common intermediate stages are electroplating [24], etching [26], surface pretreatment and electroless deposition [27]. In particular, micropatterned metal surfaces are considered very interesting in the electronic materials research field due to potential applications on printed wiring boards (PWB), magnetic recordings materials, microwave conductors, contact materials, display devices, and optical disks [28]. In some cases nano and microfabrication has been made by patterning the substrate with self-assembled monolayers (SAMs) of thiol by using contact printing or photopatterning [29]. The printed pattern can protect the underlying substrate acting as a mask against etchants [12] or for metal deposition. Recently, Ag films covered by patterned SAMs formed by microcontact printing have been used to fabricate thin film transistors [30]. Electrodeposition is used to produce materials and architectures that cannot be built by traditional techniques. By means of this method, different materials, such as nanometer-scale crystallites [31], nanocomposites [32], epitaxially deposited metal films [33], compositional superlattices [34], and ceramic materials [35] have been prepared. Electrodeposition is an intrinsically fast technique that is compatible with patterning and large scale production. Here the electrodeposition of metals on self-assembled alkanethiol monolayers (alkanethiol SAMs) is reviewed in relation to nano/microtechnology applications. Based on

Encyclopedia of Nanoscience and Nanotechnology Edited by H. S. Nalwa Volume 5: Pages (835–850)

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2. ALKANETHIOL SELF-ASSEMBLED MONOLAYERS (SAMs) ON METALS Schemes showing the structure of typical alkanethiol molecules that self-assemble on metal surfaces are shown in Figure 1. All these molecules exhibit an active sulfur head that anchors the molecules on the substrate and long hydrocarbon chains consisting of n methylene (CH2 ) units. The terminal group could be a hydrophobic group such as methyl groups (CH3 ), or a hydrophilic group such as H2 N, OH, or COOH. The number of CH2 units and the nature of the terminal group (hydrophobic or hydrophilic) determine the solubility of the alkanethiol molecules in a given solvent. The introduction of conjugated bonds in the hydrocarbon chain increases markedly the electronic conduction of these molecules [36]. When dealing with oxide-covered surfaces other kind of molecules, different from alkanethiols, are used in order to build up self-assembled molecular films. That is the case of the hydrolysis and polymerization of alkyltrichlorosilanes on hydrated surfaces such as SiO2 /Si or Al2 O3 surfaces or the adsorption of carboxilic, hydroxamic, or phosphonic acids on native oxides like CuO/Cu, AgO/Ag, or TiO2 /Ti [37–43].

O C

C H

2.1. SAMs Preparation Self-assembly of alkanethiol molecules on clean metal surfaces takes place through a redox process that can be represented by the following reaction [44] X(CH2 )n SH + Me = [X(CH2 )n S-Me] + 1/2H2 + e

Dodecanethiol

S 2p

Hexanethiol

S-Octomers

H 170

S hexanethiol

(1)

where Me stands for the metal substrate, X represents the terminal group, brackets stand for the adsorbed alkanethiolate-Me species. This reaction implies the formation of a strong thiolate bond similar to that formed for adsorbed S as revealed by XPS measurements (Fig. 2) and the formation of molecular hydrogen [45]. The selfassembly process represented by Eq. (1) can be made in both gas-phase and liquids environments (for methyl terminated alkanethiols usually ethanolic or toluenic solutions, pure alkanethiols, etc.). Self-assembled alkanethiol monolayers preparation from alkanethiol-containing solution is the most popular because it is extremely simple, and accordingly, accessible to all laboratories. In this case, the self-assembly process is made by immersion of the clean metal substrate in an alkanethiolate-containing ethanolic or toluene solution during a time ti as schematically shown in Figure 3. The SAMs quality strongly depends on ti values and hydrocarbon chain lengths. A scheme showing possible mechanisms for alkanethiol self-assembly is shown in Figure 4. In mechanism A, disordered phases are formed before islands of vertically oriented molecules nucleate and grow on the substrate. This mechanism has been observed in liquids media. In fact, for short alkanethiol (n < 6), self-assembly on Au(111) immersion times in the order of 24 hr result in a mixture of unstable ordered phases (the so-called p(n × 1) phases) and disordered domains (Fig. 5). On the other hand, for alkanethiols with n > 6, good quality SAMs (Fig. 6) have been obtained for immersion times in the 1–24 hr range. A scheme showing the temporal evolution of alkanethiol surface structures in liquids is shown in Figure 7. The size of the ordered domains can be increased and defect density decreased after annealing of the self-assembled monolayer for 4–6 hr at 60  C in the alkanethiol containing solution [46]. On the other hand, mechanism B (Fig. 5) involves the formation of

Intensity (arb. units)

recent results, it can be concluded that electrodeposition on these surface-modified substrates is a powerful tool not only in producing standing-free thin metal and alloy films but also results in an easy way to fabricate nano/micro patterned masters, molds, and replicas in different materials. In contrast to other methods, which requires contact printing, masking, or photopatterning, the substrate treatment needed before electrodeposition on alkanethiol-covered surfaces involves only a simple immersion of the masters on the alkanethiol “ink.” This review is organized in the following order. First, we review SAM preparation, SAM quality (surface structural, defects), and SAM stability (interaction forces acting at SAMs). Second, underpotential and overpotential deposition of metals on SAM-covered metal substrates is reviewed. In a third part, the applicability of electrodeposition to prepare standing-free films of different metals and alloys, and the possibility of transferring nano/microstructures to the thin metallic films is presented. Finally, the fabrication of masters, molds, and replicas by electrodeposition techniques is described.

S 6-mercaptohexanoic acid

Figure 1. Schemes of the molecular structure of (a) hexanethiol and (b) 6-mercaptohexanoic acid.

168

166

164

162

160

158

Binding energy/ eV Figure 2. X-ray photoelectron spectroscopy (XPS) spectra (S 2p) for sulfur, hexanethiolate, and dodecanethiolate monolayers on Au(111). Reprinted with permission from [50], C. Vericat et al., Langmuir 17, 4919 (2001). © 2001, American Chemical Society.

Monolayer-Assisted Electrochemical Nanopatterning

837

Figure 5. Self-assembly of butanethiol on Au(111) after 24 hr of immersion time. Ordered and disordered domains coexit on the Au(111) surface.

Figure 3. Scheme showing self-assembling of alkanethiol molecules on a metallic substrate from liquid solution.

ordered domains of lying flat alkanethiol molecules before the formation of the ordered islands of vertically oriented molecules takes place. This mechanism has been observed by in-situ scanning tunneling microscopy (STM) in gas phase preparation [47].

2.2. Stable Surface Structures Alkanethiolates adsorbed on Au(111) have been taken as a model system for SAM studies. Because of this possible use in many interesting technological applications, SAMs have been characterized by using different techniques as shown in Table 1. It is well known that the surface structure consists of monoatomic√high√vacancy islands and ordered domains (Fig. 6) of the 3 × 3 R30  lattice and its related c(4 × 2) superlattice in both gas phase [48] and liquid environments [49], irrespective of the X-terminal group and hydrocarbon chain length as shown in Figure 6 for hexadecanethiol and

mercaptoundecanoic acid (MUA). In these lattices, the alkanethiolate molecules are chemisorbed on the Au surface by the S-heads forming the thiolate bond [50] and they are  with respect to the substrate normal [51]. The tilted 20–40 √ √ 3 × 3 R30  lattice exhibits nearest neighbor distances d ≈ 0 5 nm (Fig. 8a crosssection), while the c(4 × 2) lattice exhibits some pairing of the S atoms as revealed by GIXD data [52]. Besides, STM measurements have shown d = 0 45 nm between the bright and dark spots (interrows distance) (Fig. 8b) and d = 0 5 nm inside the row (intrarow distance) of the c(4 × 2) superlattices [48]. Recent density functional theory calculations have shown that the best sites for alkanethiol adsorption on the Au(111) surface is at fccbridge and hcp-bridge sites (Fig. 9). Lower adsorption energies are involved for fcc, hcp, bridge, and top sites. Reports

mechanism B

mechanism A Figure 4. Two mechanisms for alkanethiol self-assembly. In mechanism A, islands of vertically oriented molecules are formed from a disordered phase; this mechanism has been observed in SAMs prepared from liquid media. Mechanism B involves the formation of ordered domains with alkanethiol molecules lying parallel to the surface before the formation of vertically oriented molecule domains.

Figure 6. STM images of ordered alkanethiol domains produced on Au(111) after 24 hr of immersion in alkanethiol containing solutions. (a) hexanethiol (b) mercaptoundecanoic acid. The typical stable phases √ √ 3 × 3 R30  and c(4 × 2) (rectangular and zig-zag) are shown as insets. Reprinted with permission from [141], O. Azzaroni et al., Langmuir 17, 6647 (2001). © 2001, American Chemical Society.

838

Monolayer-Assisted Electrochemical Nanopatterning

Surface structure evolution in SAMs in liquid media

(a)

0.50 nm

disordered phases

p(nx1)

(b)

0.45 nm

Stable phases √3x√3 R30˚

c(4x2)

(c)

Figure 7. Scheme showing the possible temporal evolution of the surface structure of SAMs produced in liquid media.

on alkanethiol adsorption on the other faces of Au are scarcely found in the literature [53]. In the case of Au(100) c(10 × 10) (large hydrocarbon chain length) and c(2 × 2) (small hydrocarbon chain length), surface structures [54] have been reported [55]. In the case of alkanethiolate adsorption on Ag(111), chemisorbed molecules are also bonded by the S head to the Ag surface through a thiolate bond, although their tilt with respect to the substrate normal ranges from 0 to 15 [56]. Scanning tunneling microscopy studies have shown that alkanethiolates with large hydrocarbon chains (n > 8) Table 1. Techniques used to characterize self-assembled monolayers. Diffraction-based techniques Low energy electron diffraction (LEED) Grazing incidence X-ray diffraction (GIXD) Low-energy atom diffraction (LEAD) X-ray reflectivity (XR) Helium atom reflectivity (HAR) Spectroscopy-based techniques Infrared spectroscopy (IR) Second harmonic generation (SHG) Sum frequency generation (SFG) Surface-enhanced Raman scattering (SERS) High-resolution electron energy loss spectroscopy (HREELS) Near-edge X-ray adsorption fine structure spectroscopy (NEXAFS) X-ray photoelectron spectroscopy (XPS)

0.46 nm

0

1

4

organize on Ag(111) forming an incommensurate hexagonal layer (Fig. 8) with d = 0 46 nm (Fig. 8c) [57], which is a value√slightly √ greater than d = 0 44 nm found in the distorted 7 × 7 R19.1  lattice observed for S on Ag(111) at a high surface coverage, and for short alkanethiols on the same substrate [58]. In this lattice, the S atom is bonded at hollow and top sites, the unit cell involving one fcc, one hcp, and one top site. It should be noted that the value d = 0 46 nm has been observed in close-packed bulk alkanes, because this distance optimizes hydrocarbon chain interactions. Also note that the atomic size of the methyl group is 0.45 nm. Vibrational spectroscopic data (Raman, Fourier transform infrared spectroscopy (FTIR), and sum frequency

fcc fcc-bridge bridge hcp-bridge

fcc

Scanning tunneling microscopy (STM) Atomic force microscopy (AFM) Thermally-programmed desorption (TPD) Ellipsometry Quartz crystal microbalance (QCM) Electrodesorption curves

3

Figure 8. Cross-sections corresponding to dodecanethiolate SAMs √ √ adsorbed on (a) Au(111), 3 × 3 R30 , (b) Au(111), c(4×2), and √ √  (c) Ag(111), 7 × 7 R19 .

Microscopy-based techniques

Other techniques

2

hcp top

hcp (a)

(b)

Figure 9. (a) fcc and hcp hollow sites on a (111) face. (b) Possible sites for alkanethiol adsorption on a (111) surface.

839

Monolayer-Assisted Electrochemical Nanopatterning

generation (SFG)) for alkanethiol monolayers on Au and Ag have also shown that the molecular chains are in a mostly trans configuration [59]. Alkanethiols strongly adsorb on Cu(111) at hollow site surfaces promoting a surface layer reconstruction [60]. Ultra high vacuum (UHV) X-ray standing wave (NIXSW) and near edge X-ray adsorption fine structure (NEXAFS) recent studies have shown that the alkanethiol molecules are almost normal (tilt angle 12  ) to the substrate surface, similar to alkanethiols on Ag(111) [61]. During adsorption of methanethiol on the Cu(111) face at room temperature, certain amounts of S atoms have been also produced [62]. In aqueous media, no surface structural data for alkanethiol adsorption on Cu have been reported [63]. Self-assembled alkanethiol monolayers can be also formed on Pt surfaces as judged from surface-sensitive techniques [64]. In addition, self-assembly of alkanetiols molecules have been recently reported on Pd [65, 66], although, in relation to Au, Ag, and Cu, little information is available. Using vibrational spectroscopy, ordered/ disordered transitions in aqueous solutions have been observed. Other more reactive metals, such as Ni and Fe, have also been investigated in relation to the alkanethiol self-assembly in the frame of corrosion prevention [67–70]. However, for these metals, even small amounts of oxides result in poor quality SAMs. Therefore, they can be handled in ultra-high vacuum conditions reducing considerably their potential use for technological applications.

2.3. Stabilizing Forces at SAMs The self-assembly and stability of these two-dimensional structures implies alkanethiolate-metal, alkanethiolatealkanethiolate, alkanethiolate-environment, and metalenvironment interactions. Previous studies for the alkanethiolate electrodesorption from Au surfaces in hexadecane have reported activation energies that increase 0.84 kJ/mol per C unit [71]. Stabilization energies in the order of 1.5 kJ/mol per C unit have also been proposed from the analysis of different adsorption/desorption data [72]. In the case of electrolyte solutions, the most important environment for nano/microtechnology applications, reductive electrodesorption curves have been used to estimate the magnitude √ √of these interactions [73]. In aqueous 0.1 M NaOH 3 × 3 R30  and c(4 × 2), alkanethiolate lattices on Au(111) are desorbed in sharp voltammetric peaks (Fig. 10) according to the reaction

Figure 10. Typical electrodesorption curve for hexanethiolate electrodesorption from Au(111) in 0.1 M NaOH recorded at 0.05 V s−1 . (solid line) first scan; (dashed line) second scan. Region 1 corre√ √ sponds to the potential region were the 3 × 3 R30 and c(4 × 2) surface structure at terraces are stable. Peak D corresponds to the electrodesorption of these surface structures from terraces. Region 2 corresponds to the potential region where Au(111) and hexanethiol molecules adsorbed at step edges coexits. Peak D corresponds to the electrodesorption of hexanethiol molecules from step edges. Reprinted with permission from [76], C. Vericat et al., J. Chem. Phys. 115, 6672 (2001). © 2001, American Institute of Physics.

alkanethiolate molecules remain adsorbed at step edges (Fig. 12). Complete desorption of these molecules takes place in the potential region where the hydrogen evolution reaction (her) takes place. However, in aqueous solutions for n > 6, micelle formation have been also reported (Fig. 13) [75, 76]. The peak potential (Ep ) related the electrodesorption peak shifts in the negative potential (E) direction as the number of C units in the hydrocarbon chain (n) of alkanethiolate molecules increases (Fig. 14). From the slopes of peak potential (Ep ) versus n plots

(CH3 )(CH2 )n S-Au + solvent + e = [(CH3 )(CH2 )n S− ]solv + Ausolv

(2)

where solv indicates solvated species. In fact, at potential values more positive than those related √ to√the electrodesorption peak, the c(4 × 2) and the 3 × 3 R30  surface structures are stable although they exhibit potential-independent transitions and defect fluctuations, that is, they are repaired and reformed in the time range of a few seconds (Fig. 11a–f). It has also been shown [74] that in the potential range of the electrodesorption peak, the ordered surface structures are completely removed from the Au(111) terraces although

Figure 11. (20 × 20 nm2 ) STM images (raw data) of hexanethiolate covered Au(111) surface in 0.1 M NaOH taken at E values within region 1. √ √ 3 × 3 R30  and c(4 × 2) reversible transitions and nanometer-sized defects are observed. Defects are continously created and repaired. Reprinted with permission from [76], C. Vericat et al., J. Chem. Phys. 115, 6672 (2001). © 2001, American Institute of Physics.

840

Monolayer-Assisted Electrochemical Nanopatterning -0.60 -0.75

Ep /V vs SCE

Au(111)aq

-0.90

Au(111)met

-1.05 -1.20

Cu(111)??

-1.35

Ag(111)met

-1.50 2

4

6

8

10

12

14

16

18

n Figure 14. Ep versus n plots for different alkanethiolates adsorbed on Au(111) and Ag(111) derived from the electrodesorption curves recorded at 0.1 V s−1 . (
) Au(111), aqueous 0.1 M NaOH, () Au(111), 0.1 M NaOH 95% methanol + 5% H2 O, (•) Ag(111), 0.1 M NaOH 95% methanol + 5% H2 O. Figure 12. (9 × 9 nm2 ) STM image (raw data) and crosssection (upper) taken in region 2 (before the potential reached peak D′ ) showing a monoatomic high Au(111) step. (6 5 × 6 5 nm2 ) STM image. Bright spots at the step edges correspond to hexanethiol molecules.

the stabilizing interactions, van der Waals and hydrophobic forces have been estimated in 3–4 kJ/mol per C unit [77]. The use of methanol reduces interactions forces to 1.8–2 kJ/mol per C unit, then indicating the important role

Figure 13. (12 5 × 12 5 nm2 ) STM images (raw data). (a) Au(111) surface in 0.1 M NaOH covered by an ordered hexanethiolate lattice, E = −0 90 (region 1). (b) physisorbed micelles resulting from the fast electrodesorption of the hexanethiol lattice, E = −0 99 V (region 2). The central hole observed in (a) and (b) indicate that the same region was imaged before and after electrodesorption. Reprinted with permission from [76], C. Vericat et al., J. Chem. Phys. 115, 6672 (2001). © 2001, American Institute of Physics.

of the hydrophobic forces on SAMs stability. All the abovementioned data have been obtained in alkaline solutions. Conversely, little information has been reported for alkanethiol electrodesorption from metal surfaces in acid solutions. For etanethiol-covered Au(111) in H2 SO4 solutions, the Ep value is strongly shifted in the positive direction with respect to that observed in the alkaline media, then reducing the stability range of the alkanethiol layer [78]. Similar results have been obtained for dodecanethiol-covered Au(111). In the case of ethanethiolate-covered Au(100) in 0.1 M H2 SO4 , potential-dependent reversible structural transitions have been reported [79]. It should be noted that polycrystalline Au exhibits the same electrodesorption behavior than those described for the single crystalline Au surfaces. A detailed study on the reductive electrodesorption of SAMs on Ag(111) in aqueous and methanolic solutions has also been performed (Fig. 15a) [80, 81]. In aqueous solutions, the Ep versus n plots (Fig. 14) gives similar results for hydrocarbon chain-chain and hydrocarbon chainsolvent interactions than those found for alkanethiolates on Au(111). It has also been shown that for a constant n, the alkanethiolate molecules are desorbed from Ag (111) at more negative potential values than those corresponding to the desorption from Au(111). This difference has been explained by the smaller work function value of Ag than Au (12a) or to the stronger Lewis acid behavior of Ag than Au [82]. However, all electrochemical STM data and quantum density functional theory calculations have shown that the difference in peak potentials experimentally observed for the reductive desorption of a given alkanethiolate from the Ag(111) and Au(111) surfaces is determined by the energy to introduce an electron into the adsorbed alkanethiolatemetal species, the desorption energy of the alkanethiolate anion, and the solvent/metal interaction energy [83]. In the case of alkanethiolate covered-Cu, no voltammetric peaks related to the electrodesorption process can be observed in alkaline media (Fig. 15b). In fact, the alkanethiol-Cu interaction is so strong that the hydrogen evolution reaction takes place (probably at SAM defects) before the alkanethiolate electrodesorption takes place. The same behavior is observed in acid media (Fig. 15b) so that

841

Monolayer-Assisted Electrochemical Nanopatterning

3.1. Bulk Metal Electrodeposition

(a)

j / µA.cm-2

-30 -60 -90 -120 -150 -1.6

-1.4

-1.2

-1.0

-0.8

-0.6

-0.4

-0.3

0.0

E / V vs SCE

0

(b)

j / µA.cm-2

-30 -60 -90 -120 -150 -180 -1.8

-1.5

-1.2

-0.9

-0.6

E / V vs SCE Figure 15. (a) Electrodesorption curves recorded at 0.1 V s−1 in 0.1 M NaOH for dodecanethiolate on: (solid line) Au(111), (dashed line) Ag(111). (b) Electrodesorption curves at 0.1 V s−1 for dodecanethiolate on Cu(111) in: (solid line) 0.1 M NaOH, (dashed line) 0.5 M H2 SO4 .

alkanethiolates on Cu form more stable SAMs than those formed on Ag(111) and Au(111). In the case of SAMs on Cu, the quality can be markedly improved by SAMs preparation on toluene solutions rather than ethanolic solutions [84]. Finally, the importance of the peak potential values should be stressed because alkanethiol electrodesorption determines the stability range of SAMs when they are used for modifying the physical chemistry of metal surfaces for metal electrodeposition. Thus, alkanethiolate SAMs on Cu appear as the best candidate for technological applications due to the high stability and low cost. In addition, long hydrocarbon chain alkanethiols and aqueous media should also be preferred due to the stabilizing effect of van der Waals and hydrophobic forces. In the next section, the information about metal electrodeposition (from the submonolayer to the multilayer level) on alkanethiolate-covered substrates is reviewed.

Bulk metal electrodeposition on self-assembled monolayers has been studied under galvanostatic (constant current) conditions [85, 86]. It has been observed that bulk electrodeposition is strongly affected by the presence of the self-assembled layer. The alkanethiolate self-assembled monolayer introduces an additional resistance to charge transfer from solution; thus the chain length determines the overpotential for copper electrodeposition Figure 16. The electrodeposit morphology is markedly influenced by the monolayer; in some cases the formation of lowadherence hemispherical copper deposits has been reported, in contrast to the uniform deposits electroformed on monolayer-free electrodes. Otherwise, it has been suggested that defects and pinholes play a determining role in the early stages of electrodeposition because they act as electrocrystallization nuclei [87]. When long-chain thiolates (n < 12) are used at low current density, a few large crystallites are generated, but at higher current densities a high number of small crystallites are obtained. These facts indicate that large defects in the thiolate layer act as preferred sites for electrocrystallization at low-current densities, whereas at high-current densities, crystallites nucleate at minor defects. This fact is consistent with potential induced defects on selfassembled monolayers recently reported [88], considering that higher cathodic galvanic conditions require more negative electrode potentials. The mechanism to describe the electrodeposition on SAMs is a matter of apparent controversy. Two different mechanisms of electrodeposition on thiolates SAMs have been suggested [85], depending on the length of the thiol chain. In the case of short chains, the charge transfer occurs on top of the monolayer by tunneling through the hydrocarbon chain. On the other hand, if a long chain thiolates monolayer is assembled on the electrode, the charge transfer takes place mainly at defects of the SAM. Despite this, a monolayer-defect-mediated mechanism has been proposed in which electrodeposition is done through defects on the monolayer making no differences between short and -0.4

-0.3

η /V

0

-0.2

-0.1

0.0

3. METAL ELECTRODEPOSITION ON ALKANETHIOLATE SAMs The key role played by metal/metal and metal/organic interfaces in several technological fields is well known, ranging from molecular electronics to industrial electroplating. From this aspect, alkanethiolate self-assembled monolayers were taken as model systems to study the metallization of organic surfaces under different experimental conditions.

0

20

40

60

80

t /s Figure 16. Overpotential ( = E − Er ) versus electrodeposition time for Cu electrodeposition on: (solid line) dodecanethiolate-covered polycrystalline Cu; (dashed line) polycrystalline Cu. E: applied potential; Er : reversible potential for the Cu2+ /Cu reaction. Note that larger 3 are needed to deposit Cu on the SAM. Electrolyte: 0.6 M CuSO4 ·5H2 O + 0.5 M H2 SO4 + 0.025 mM thiourea.

842 long-chain thiols [86]. At late stages of metal electrodeposition, the deposit morphology is independent of surface hydrophilicity (i.e., independent of the terminal group of the alkanethiol chain) of the tailored electrodes. Metal electrodeposition on alkanethiolate-covered metal substrates has also been studied under potentiostatic conditions at potential values slightly negative than the reversible potential of the Me+z /Me redox couple (overpotential deposition, (OPD) conditions). While three-dimensional growth takes place on a bare Au(111) substrate, a two-dimensional growth (layer-by-layer) is observed for short alkanethiolate covered-Au(111) [89]. However, for long-chain alkanethiols (n > 12), no further growth of initially deposited nanoclusters is observed at room temperature. At higher temperatures, the SAM act as a surfactant, even for longchain alkanethiolates showing layer-by-layer growing in the OPD regime. This interesting behavior has been assigned to thermal-induced defects in the SAM, which allow rapid copper electroreduction due to an enhanced copper penetration in the disordered monolayer and surface diffusion [90]. Concerning defects, a recent Second Harmonic Generation (SHG) study showed that copper deposition is not accompanied by a strong conformational disorder of the SAM, but it can induce structural changes that differ from the wellknown gauche defects [91].

3.2. Underpotential Deposition Underpotential deposition (UPD) takes place when metal ions (Me+z ) can be deposited at potentials more positive than the equilibrium potential of the Me+z /Me redox couple. The combination of metal UPD and alkanethiolate selfassembled monolayers has brought useful routes for building up metal surfaces with well-defined physicochemical properties on the nanometer range or even at the molecular scale [92]. Metal UPD on alkanethiolate self-assembled monolayers has been performed in order to image individual defect structures contained on the SAM. By imaging the metal nanoislands underpotentially deposited at SAM defects, it has been possible to obtain information about self-assembly kinetics [93]. In the case of Cu UPD on alkanethiolate SAMs, it has been shown that the self-assembled layer has a striking influence on the growth morphology. In contrast to Cu UPD on bare Au(111), in the presence of decanethiolate self-assembled monolayers, Cu underpotential deposition proceeds by homogeneous and instantaneous nucleation of nanosized clusters on flat terraces, with no preferences for step edges or other sorts of surface defects [87]. The morphological evolution of the metal nanoclusters to dendritic-shape nanoislands resembles the metal epitaxy in UHV environments. In-situ STM and electrochemical measurements have shown that the absence of a clear UPD signal on the electrochemical response does not imply the absence of underpotentially deposited metal [87]. This finding has been attributed to kinetic effects introduced by the self-assembled film even for short-chain alkanethiolates. Several electrochemical studies have shown that the SAM acts as surfactants in the UPD regime, the metal is underpotentially deposited through the defects, and the deposited nanoisland is then covered by alkanethiolates

Monolayer-Assisted Electrochemical Nanopatterning

diffusing from surroundings. This mechanism is quite similar to place-exchange reactions used to describe the surfactant action of metal monolayers in UHV experiments [94]. This place-exchange reaction can be associated to a well-defined voltammetric signal in the case of Cu UPD on ethanethiolate-modified Au(111) electrodes [95]. In spite of the chain length of the SAM as a relevant factor in different SAM-related processes, it has been observed that the growth of nanoislands in the UPD region is a chain length independent phenomena in contrast to results reported for Cu OPD on SAM-modified Au(111) [96]. Silver UPD has also been performed on different thiolates-covered Au [97, 98]. It has been observed that short-chain alkanethiolates introduce changes in the UPD behavior of Ag, but this effect is considerably lower than in the case of Cu UPD. This can be explained considering that blocking effects of the SAM in electrochemical reactions increase with increasing Stokes radius of metal ions. Otherwise, it should be noted that Ag UPD on shortchain alkanethiolates may be affected by the electrochemical stability of these adsorbates, since anodic potentials could induce oxidative desorption of alkanethiolates. The mechanism proposed for Ag UPD on Au involves Ag deposition at defects of SAM, crawl under the SAM and lateral grow, which induces further defects at which Ag UPD can proceed, resulting in a preferential lateral growth of Ag monolayers [99, 100]. At present, metal electrodeposition involving SAMs is a very active research field [101–106] due to their potential applications in several technological areas.

4. APPLICATIONS 4.1. Patterning Alkanethiol-Masked Substrates The viability of patterning SAMs by photo-oxidation [107–109], contact printing [110–112], pen writing [113–115], electron beam lithography [116], and SPM-based [117, 118] methods have recently been reported in the literature. A simple way to patterning an alkanethiolate monolayer on a metal surface by STM consist in repetitive scanning on a desired surface area (Fig. 17) at a high tip-sample interaction (high tunneling current, low bias voltage). The patterned film on the metal surface can be used as a resist for subsequent etching or metal electrodeposition.

Figure 17. Scanning tunneling microscopy image and crosssection showing a square region “written” by repetitive scanning of a STM tip on a dodecanethiolate-covered Cu substrate. Reprinted with permission from [140], O. Azzaroni et al., Langmuir 17, 1483 (2001). © 2001, American Chemical Society.

843

Monolayer-Assisted Electrochemical Nanopatterning

that metal electrodeposition on alkanethiolate SAMs takes place at the nanometer-sized defects present in the monolayer (Fig. 11), that is, it results in the nucleation and growth of nanoparticles confined in the alkanethiolate layer. After deposition, the SAM can be easily removed by UV. Nickel nanocrystales (6 nm average size and 0.7–1 nm height) on Au(111) have been prepared using this method (Fig. 19).

4.3. Preparation of Nanocrystalline Standing-Free Films

Figure 18. Patterned surface consisting in a Ag plate with Pd hexagonal features. An alkanethiolate-covered Ag surface was marked with a metal grid and exposed to UV radiation. The photo-oxidized alkanethiolate areas are chemically reactive and Pd is deposited by a redox reaction involving Pd+2 ion reduction and Ag oxidation.

Patterning can also be performed by photo-oxidation by applying a short-time (20 min) UV exposure of SAMcovered metal masked with a metallic grid. The nonexposed areas to the UV act as a resist for subsequent deposition as shown in Figure 18. Ultraviolet radiation produces O3 that rapidly oxides alkanethiol molecules to alkylsulfonates [119]. It has been shown that patterning Au or Cu substrates by contact printing with a long-chain alkanethiol (n = 16) as a resist material allows selective electrodeposition of iron group metals [120]. In this way, ordered Ni microstructures can be electrodeposited on these metals. The size of the structures that can be prepared by this technique depends on the resolution limit of the contact printing method due to the diffusion of the alkanethiol “ink” [121], and in this case, it results in the micrometer range. Other problems associated with metal electrodeposition on patterned alkanethiol monolayer is related to the lateral growth of the deposited island films when the thickness of the metal electrodeposit exceeds the length of the hydrocarbon chain. Monolayer-covered metals can also be patterned by using electron beam nanolithography [122]. Well-defined regions of the self-assembled monolayer are removed selectively by dosing them with electron beams, and then copper nanostructures can be deposited on the exposed areas. With this approach, it is possible to nanofabricate metallic patterns as small as 75 nm.

Other interesting properties of adsorbed alkanethiols is dramatically increasing the antiadherent properties of the solid surface [124]. This property and the enhanced lateral growth when the deposit thickness exceeds the length of the hydrocarbon chain length [120], have been exploited for the fabrication of standing-free thin metal and alloy films by electrodeposition. Standing-free films have many technological uses and several methods have been developed in order to obtain metal thin films [125]. The method that uses SAMs to fabricate standing-free films has the advantages of simplicity and low cost, in contrast to other techniques previously developed, such as chemical vapor deposition, physical vapor deposition, sputtering, etc., which involve complicated and expensive equipment and need other methods to eliminate the substrate. Figure 20(upper) shows STM images of a polished Cu substrate derivatized with a dodecanethiol monolayer for an immersion time ta = 1 h and a Cu electrodeposit grown on it from 0.6 M CuSO4 · 5H2 O + 0 5 M H2 SO4 aqueous solution (Fig. 20 left). The electrodeposit surface consists of micrometer-sized Cu grains that form an irregular surface. Following the time (t) dependence of the root mean square roughness (W ), the growth mode of the deposit can be elucidated [126]. W increases with time as W ∝ t with

= 0 7, as it has been reported for Cu electrodeposition on nonderivatized Cu substrates [127]. It means that the growth

4.2. Nanocrystal Preparation Metallic nanoparticles supported on conducting substrates are of interest due to their unique physical chemistry properties, which result from the perturbations introduced by the large area/volume atom ratio in relation to bulk metals. These nanoparticles are important in dealing with heterogeneous catalysis and electrocatalysis. They also exhibit interesting properties such as giant magneto resistances and high saturation moments [123]. Metal electrodeposition on alkanethiolate SAMs can be used to prepare nanometersized metallic crystals. This method is based on the fact

Figure 19. (100 × 100 nm2 ) STM image of Ni nanoclusters grown by electrodepositon on a hexanethiolate-covered Au(111). Electrolyte: 1 M NiSO4 · 7H2 O + 0.25 M NiCl2 6H2 O + 0.61 M H3 BO3 , E = −0 6 V (vs SCE).

844

Figure 20. STM image of copper substrate (upper). STM images of Cu electrodeposits grown at 20 mA cm−2 from 0.6 M CuSO4 · 5H2 O + 0 5 M H2 SO4 (left). The same electrolyte but containing 0.025 M thiourea (right). Reprinted with permission from [131], P. L. Schilardi et al., Langmuir 17, 2748 (2001). © 2001, American Chemical Society.

mode of the Cu deposit does not change under the presence of the SAM. However, the electrodeposited Cu samples detach spontaneously or they are easily removed from the Cu substrate with tweezers without deformations. The easy detachment of the Cu deposits is not observed when electrodeposition is made on nonderivatized Cu substrates, indicating that it is related to the presence of the dodecanethiol SAM. Similar results were obtained from the same plating bath using a derivatized Au(111) as substrate. On the other hand, when Cu electrodeposition is made from the plating bath containing 0.025 mM thiourea, the growth mode of the Cu deposits is changed leading to smoother Cu films (Fig. 20 right) formed by nanometersized grains (20 nm in average size). In the presence of thiourea, Cu is preferentially deposited at valleys rather than at protrusions [128]. In this case, after detachment, the inner face of the electrodeposit resembles the morphology of the derivatized Cu substrate reproducing its polishing lines (Fig. 20 upper). These facts—substrate replication and easy detachment from the substrate—indicate the possible use for pattern transfer. This fact arises from the nanostructured nature of the deposited material that could replicate nano/microstructures larger than the 20 nm average grain size. The possibility of using this method to fabricate standingfree films with complex chemical composition, such as magnetic alloys, have been recently explored. In principle, electrodeposition on alkanethiolate-covered substrates would be inadequate when alkanethiol adsorption is stronger on the surface of the metal to be deposited than on the surface of the metal used as the template. For example, when Ag is electrodeposited on a alkanethiolate-covered Au electrode, a place exchange process between the adsorbed alkanethiolate and the depositing Ag atom takes place [100].

Monolayer-Assisted Electrochemical Nanopatterning

Place exchange occurs because the adsorption energy of alkanethiolates on the Ag surface is greater than on the Au surface. Thus, the adsorbed layer floats on the surface of the deposited metal film proving the method inapplicable. On the other hand, chemical reactions among the alkanethiolates adsorbed on the template (used as the cathode in the electrochemical cell) and the ionic metal species of the plating bath could produce partial oxidation of the alkanethiolate layer [129]. Finally, and more important, the alkanethiolate layer could be electrodesorbed from the template at the high negative potential values required to electrodeposit active metals such as Fe, Co, and Ni for which E < −1 2 V are needed. However, recent experimental results have demonstrated that alkanethiol-assisted electrodeposition can be used to produce standing-free films of CoNiFe alloys (these films have an interesting low coercivity Hc ≈ 3 Oe) by simple electrodeposition on a dodecanethiolate-covered Cu substrate [130]. The easy detachment and good quality of the alloy film show that neither flotation, nor desorption, nor damage of the dodecanethiolate layer, take place during the thiol-assisted electrodeposition. Therefore, this method has also been used to prepare Ni, Bi, Co standing-free films from different plating baths (Table 2) in an easy and simple way.

4.4. Patterning Metallic Films: Molding and Replication The best route for serial fabrication of nano/micrometersized structures is molding and replication. Electrodeposition on alkanethiolate-covered metal substrates has been successfully used for both mold and replica fabrication in the nano/micrometer range. The method consists of metal electrodeposition onto a conducting patterned master which is previously derivatized with an alkanethiol self-assembled monolayer. In this procedure, the inner face of the electrodeposited sample is the mold of the master. By changing the electrodeposition time, the thickness of the mold can vary from micrometer to millimeter range in order to obtain a desired mechanical stability. After the preset thickness has been reached, the mold spontaneously detaches or it is easily removed from the master. Once the metallic mold is obtained, it is derivatized again with a SAM and a new metal electrodeposit is grown on it. After detaching the metal film, a replica of the master is obtained on the inner face of the electrodeposit. A scheme showing the steps to fabricate a mold and a replica of a given pattern by using Table 2. Different plating baths used to prepare metallic standing-free films by electrodeposition. Metal Cu Ni Bi Co

Plating bath 0.6 M CuSO4 · 5H2 O + 0.5 M g/l H2 SO4 + 2 5 × 10−5 M thiourea 1.1 M NiSO4 · 7H2 O + 0.25 M NiCl2 · 6H2 O + 0.6 M H3 BO3 0.14 M Bi(NO3 )3 + 1.3 M glycerol + 0.33 M tartaric acid + HNO3 (pH = 2) 0.42 M CoCl2 · 6H2 O + 0.9 M NH4 F · HF + 0.7 M H3 BO3

j (mA · cm−1 ) T (K) 10

298

40

327

5

298

20

298

Monolayer-Assisted Electrochemical Nanopatterning

845

metal electrodeposition on alkanethiol-covered masters is shown in Figure 21. Figure 22 shows a Cu mold and a Cu replica obtained from a dodecanethiol-covered Cu master by using this procedure. The master is a grid of 500 nm wide Cu rows separated by 900 nm wide and 90 nm deep channels as shown in the STM image and crosssection (Fig. 22a–b). The master was then subjected to the procedure indicated in Figure 21. After depositing a 7 m thick Cu film from 0.6 M CuSO4 · 5H2 O + 0 5 M H2 SO4 + 0 025 mM thiourea, the copper sample was easily removed from the Cu master with tweezers. The STM image of the inner face of the 7 m thick electrodeposited Cu film now shows a pattern consisting of 900 nm wide Cu rows separated by 500 nm wide and 90 nm in depth channels (Fig. 22c–d), that is, this face is a mold of the original Cu master. In order to obtain replicas, this mold is again derivatized with the SAM, and then a Cu electrodeposit is grown following the same procedure described above. After removing the electrodeposited film from the mold, STM imaging of the inner face shows a replica of the original gridmaster (Fig. 22e–f).

(a)

(b)

(c)

(d)

(e)

(f) Figure 21. Scheme showing the different steps involved in molding and replication: a) micropatterned conducting master, b) micropatterned conducting master derivatized with an alkanethiolate monolayer (black, not in scale), c) electrodeposit grown on the derivatized conducting master, d) detachment of the electrodeposit, the inner face is a mold of the master, e) derivatized mold with an alkanethiol monolayer (black, not in scale), f) electrodeposition on the derivatized mold, the inner face is a replica of the master. Reprinted with permission from [131], P. L. Schilardi et al., Langmuir 17, 2748 (2001). © 2001, American Chemical Society.

Figure 22. 10 m × 10 m STM image of the micropatterned Cu master grid (a) and crosssection (b). 10 m × 10 m STM image of the Cu mold obtained after electrodeposition and detachment from the derivatized Cu master grid (c) and crosssection (d). 10 m × 10 m STM image of the micropatterned Cu replica after electrodeposition and detachment (e) and crosssection (f). Reprinted with permission from [131], Schilardi et al., Langmuir 17, 2748 (2001). © 2001, American Chemical Society.

The mechanical stability of the metallic molds is good. In fact, many (more than 20) Cu, Ni, CoNiFe, and polymermade replicas (the polymer replicas prepared by the procedure described next) can be been fabricated by using the same derivatized-Cu mold without modification of the mold architecture [131]. This means that the wear of master caused by replica removal is not significant possibly due to the high mechanical stability of the Cu mold. Another route for patterning metallic films has been recently proposed using triglyceride as an intermedium layer of resistant molecules [132]. In this method, a macromolecular membrane is used as an antiadherent layer and, like techniques using dodecanethol SAMs, allows the fabrication of metal thin films with bendable properties. Its main disadvantage is that it does not permit the reusage of molds because part of the membrane is left on the thin film. The physical properties of the patterned sample depend markedly on the morphology and size of the grains that

846 constitute the building blocks of the system. Therefore, the study of possible routes for modifying grain size without changing the nano/micropattern is a crucial point for the fabrication of metallic samples with specific structural and physical properties. It has been shown that controlled postdeposition thermal annealing of nano/micropatterned standing free copper samples at temperatures T < 0 5Tm , Tm the melting temperature, increases grain size and improves the electric conductivity of the sample by Otswald ripening without changing the nano/micro pattern [133].

Monolayer-Assisted Electrochemical Nanopatterning (a)

(b)

Thiol Assisted Templated Electrdeposition

(c)

Self Assembly of a Thiol Monolayer on the Mold

(d)

The Mold is Pressed Against the Liquid Polymer Film

(e)

Easy Mold Release After Polymer Curing

4.5. Patterning Polymeric Films with Alkanethiolate-Covered Metallic Molds The derivatized molds can be used directly for microtransfer molding (TM) to polymeric materials. The use of metallic rigid molds improves the resolution limit of the conventional TM method and eliminates the restrictions present on the other modified versions of this technique [134]. By using rigid dodecanethiolate-covered metallic mold patterns with ratio l/d, l being the lateral size and d the depth of the feature equal to 7, can be prepared and the resolution limit could move from 1 m to sub-100 nm. The alkanethiolate layer modifying the metallic-made mold enables a complete release of the mold from the polymeric film producing defect-free patterns irrespective of the adhesive properties of the polymer; thus this method eliminates the severe restrictions present in TM [135]. The versatility of the method is demonstrated by the fabrication of glasssupported gratings of polymer materials having very different adhesive and mechanical properties and with architecture similar to those fabricated by laser ablation. The method for fabricating the polymer-made grating involves a few very simple steps (Fig. 23). The dodecanethiol-modified mold is placed about 30 min in pure toluene to remove the physisorbed molecules forming multilayers. Then, the liquid polymer is poured on the glass support (Fig. 23c), and the thiol-modified copper mold is immediately pressed on the glass-supported liquid polymer film (Fig. 23d), controlling the applied pressure by using a micrometer screw. The use of metallic molds, in contrast to polydymethylsiloxane (PDMS) molds, allows the application of high pressures without introducing significant deformations. Once the polymer is cured, the thiol-modified mold is easily released from the polymeric film (Fig. 23e). In this method, the release procedure requires only a minimum mechanical effort producing no damages to the polymer-made grating or to the copper-made mold. The low adherence properties of methylterminated self-assembled monolayers have been previously exploited for micropatterning-conducting polymers on gold surfaces [136]. Atomic force microscopy (AFM) images of the copper-made master (Fig. 24a), the copper-made mold (Fig. 24b), and high impact polystyrene (HIPS)-made (Fig. 24c) and poly(isobutylcyanoacrylate)-made (Fig. 24d) replicas show the accurate form in which track periodicity and channel depth were reproduced in the polymeric gratings. Therefore, this method allows the fabrication of ordered gratings irrespective of the adhesive and mechanical properties of the polymers. In fact, HIPS exhibits a relatively poor adherence and is an easily deformed material,

Figure 23. Schematic illustration of the complete procedure for fabrication of polymeric nanostructures by the microtransfer molding method. a) thiol-modified metallic master; b) mold fabrication by thiol-assisted templated electrodeposition, followed by mold modification by thiol adsorption; c) polymer film on the glass substrate; d) the thiol-modified mold is pressed on the liquid polymer film supported on the glass substrate; e) after casting, high impact polystyrene, or polymerization, poly(isobutylcyanoacrylate), the mold is easily released from the polymer-made film. The polymer face in contact with the mold is a replica of the template.

Figure 24. 20 × 20 m2 AFM images. (a) copper-made master, (b) copper made mold, (c) high impact polystyrene-made replica, and (d) poly(isobutylcyanoacrylate)-made replica.

Monolayer-Assisted Electrochemical Nanopatterning

847

whereas poly(isobutylcyanoacrylate) is an extremely adhesive and rigid polymer. The importance of the surface chemistry modification introduced by the alkanethiol layer is clearly revealed by performing control experiments, where the polymer deposition was directly made onto a bare Cu mold. In these cases the polymer films cannot be released from the Cu mold. The resolution of the method was also explored by using an dodecanethiolate-modified Au(111) surface as template for poly(isobutylcyanoacrylate) embossing [134]. After the template was released, AFM imaging of the polymer inner face shows triangular terraces and steps that intersect forming 60  angles, that is, the typical pattern of the Au(111) surface. The crosssection analysis shows steps 0.6 nm in height. Typical monoatomic high steps with 0.24 nm have been lost in the transfer process. The smallest terraces that have been transferred are 40 nm in width. Therefore, considering the smallest features replicated from the Au(111) surface, it is believed that the method allows 40 nm lateral and 0.6 nm vertical resolutions.

4.6. Fundamental Aspects of Electrodeposition on SAMs Now we focus on the mechanism involved in monolayerassisted electrodeposition. Recently, it has been shown that when metal electrodeposition is made on a Cu electrode covered by a dodecanethiolate SAM, nucleation of the depositing material takes places only at defective sites allowing the growth of isolated crystals outwards [131]. This is clearly demonstrated in Figure 19, where Ni has been electrodeposited on a hexanethiol covered Au. The number of small Ni clusters (6 nm in size) observed in the STM image is 1011 cm−2 in agreement with the defect density calculated from the STM image shown in Figure 11. Therefore, it is proposed that the initial step (Fig. 25a and b) is the nucleation of metal particles at defect sites. These particles grow outwards forming nanometer-sized columns Figure 25c. The column width should be close to defect size in the SAM, which is in the nanometer range, and its maximum height close to the molecular length, that is, ≈1 7 nm for dodecanethiol monolayers [137]. After the column tips reach the outer limit of the SAM, they can coarsen closely following the substrate morphology as schematically shown in Figures 25d–e. The presence of organic additives such as thiourea (TU) in the plating bath plays a key role in this method. In fact, TU molecules adsorb at the tip of the growing columns enhancing lateral growth [138]. This results in smooth films required for molding and replication. As shown in Figure 20, the average grain size (d) in the presence of TU is d = 20 nm, much smaller than d = 500 nm, produced in the plating bath without TU. The value of d of the Cu deposit grown in the presence of TU allows the replication of nanometer-sized features. The decrease in grain size has been assigned to a decrease in the diffusion length of metal adatoms due to the adsorption of the organic additive at the electrodeposit surface [139]. Detailed studies on the effect of TU in Cu deposit morphology have been reported

Figure 25. Scheme showing the steps involved in Cu electrodeposition on a derivatized Cu substrate: (a) The derivatized substrate in contact with the plating bath. Defects of the SAM are shown. (b) Cu crystals are formed at the defective sites of the SAM. The crystals grow outwards. (c–e) The presence of thiourea (TU) molecules in the bath enhances lateral growth leading to smooth and flat metal films. Reprinted with permission from [131], P. L. Schilardi et al., Langmuir 17, 2748 (2001). © 2001, American Chemical Society.

[127, 138]. The experimental conditions indicated in this work can be considered as the optimum conditions for molding and replication of Cu nanostructures in the case of SAMmodified Cu electrode. The deposited sample is connected to the substrate only by the nanometer-sized columns. They can be easily broken allowing the detachment of the deposit, that is, the deposit adherence has been dramatically decreased. This poor adherence is an interesting interfacial property of metal electrodeposits on SAMs which is exploited in this method for molding and replication purposes. This phenomenon is not unexpected since SAMs act as

848 lubricant/antistick layer. Contact angle measurements show that the SAM remains on the derivatized electrode surface (the master or the mold) due to the strong binding energy that exists between the S atom of the alkanethiol head and the Cu surface. Also, it has been verified by derivatizing the Cu master for ta = 2 days. In this case a multilayer is formed on the metal surface. After Cu electrodeposition and film detachment, the master surface was imaged with STM. Repetitive STM scanning over a given area of the master results in window formation due to the removal of the alkanethiol multilayer by the tip. When the inner face of the electrodeposited metal film in contact with the master was subjected to the same procedure, no window formation was observed. These results also demonstrate that the alkanethiol layer remains absorbed on the derivatized metal surface. In principle, it should be expected that multilayer formation should frustrate the plating process. However, the fraction of the surface covered by defects, that is, a fraction of the Cu surface exposed to the plating bath, decreases only from 1 7 × 10−2 to 4 8 × 10−3 as ta increases from 1 hr to 16 h [140]. Then, the defect density decreases very slowly with the adsorption time. Therefore, even for a long adsorption time, there are enough defects in the dodecanethiol multilayer to allow Cu electrodeposition. As previously mentioned, electrodeposition from the plating bath is possible even on derivatized Au(111) substrates, where the density of defects is expected to be much lower than that present on Cu. As expected, the decrease in the defect number favors the sample detachment but hinders the replication process because the growth centers are very separated. Note that the best conditions for molding and replication involves ta = 1 hs, that is, the fraction of Cu substrate noncovered by dodecanethiol is ≈2%.

5. CONCLUSIONS Electrodeposition of different metals on alkanethiolatecovered metallic substrates have been reviewed under a wide range of experimental conditions. The information available at present strongly suggests that this procedure can be used as a fast and inexpensive route to produce thin metallic standing-free films and/or to fabricate nano/micropatterned masters, molds, and replicas of different materials including a variety of polymers. The elapsed time of fabrication is about 2 hr and no hazardous reagents are involved in the preparation. This procedure is easily carried out using basic electrochemical instrumentation and facilities disposable at any laboratory.

GLOSSARY Alkanes Organic molecules with general formulae Cn Hn+2 . Electrodeposition Deposition of substances on a conducting substrate from an electrolyte by applying an electric potential or current. Electrodesorption Desorption of species from a conducting substrate by applying an electric potential or current. Nanofabrication Technique capable of generating structures with at least one lateral dimension less than 100 nm.

Monolayer-Assisted Electrochemical Nanopatterning

Overpotential deposition (OPD) Electrodeposition process carried out at potentials more negative than the equilibrium potential of the electrochemical reaction. Self-assembled monolayer (SAM) Single layer of molecules that self-assembles on a substrate. Standing-free films Self-supported deposited films that remain stable after removal from the substrate. Thiol Organic molecules containing a -SH group. Underpotential deposition (UPD) Electrodeposition of substances carried out at potentials more positive than the equilibrium potential of the electrochemical reaction.

ACKNOWLEDGMENTS The authors thank Agencia Nacional de Promoción Científica y Tecnológica (PICT 99-5030) and CONICET (PIP-0897) (Argentina). O. A. is thankful for a grant from Fundación Antorchas.

REFERENCES 1. H. O. Flinkea, in “Electroanalytical Chemistry” (A. J. Bard and I. Rubinstein, Eds.), Vol. 19, pp. 109–335. Marcel Dekker, New York, 1996. 2. H. O. Finklea, in “Encyclopedia of Analytical Chemistry: Theory and Instrumentation” (R. A. Meyers, Ed.), John Wiley & Sons, Chichester, 2000. 3. G. K Jennings, J. C. Munro, T.-H. Yong, and P. E. Laibinis, Langmuir 14, 6130 (1998). 4. F. P. Zamborini and R. M. Crooks, Langmuir 14, 3779 (1998). 5. E. Boubour and R. B. Lennox, Langmuir 16, 4222 (2000). 6. R. Maboudian and R. T. Howe, J. Vac. Sci. Technol. B 15, 1 (1997). 7. T. M. Mayer, M. P. de Boer, N. D. Shin, P. J. Clews, and T. A. Michalske, J. Vac. Sci. Technol. B 18, 2433 (2000). 8. R. Maboudian, W. R. Ashurst, and C. Carraro, Sensors and Actuators A 82, 219 (2000). 9. R. Haag, M. A. Rampi, R. E. Holmlin, and G. M. Whitesides, J. Am. Chem. Soc. 121, 7895 (1999). 10. M. Geissler, A. Bernard, A. Bietsch, H. Schmid, B. Michel, and E. Delamarche, J. Am. Chem. Soc. 122, 6303 (2000). 11. C. S. Chen, M. Mrksich, S. Huang, G. M. Whitesides, and D. E. Ingber, Biotechnol. Prog. 14, 356 (1998). 12. Y. Xia, E. Kim, M. Mrksich, and G. M. Whitesides, Chem. Mater 8, 601 (1996). 13. O. Chailapakul and R. M. Crooks, Langmuir 9, 884 (1993). 14. S. Kidoaki and T. Matsuda, Langmuir 15, 7639 (1999). 15. J. Küther, R. Seshadri, G. Nelles, W. Assenmacher, H.-J. Butt, W. Mader, and W. Tremel, Chem. Mater. 11, 1317 (1999). 16. Y. Xia, J. A. Rogers, K. Paul, and G. M. Whitesides, Chem. Rev. 99, 1823 (1999). 17. H. I. Smith and H. G. Craighead, Phys. Today 24 (1990). 18. W. M. Moreau, in “Semiconductor Lithography,” Plenum Press, New York, 1988. 19. C. S. Lent, P. D. Tougaw, W. Porod, and G. H. Bernstein, Nanotechnology 4, 49 (1993). 20. W. Gopel, Biosens. Bioelectron. 10, 35 (1995). 21. L. Y. Lin, E. L. Goldstein, and R. W. Tkach, IEEE J. Selected Top. Quantum Electron. 5, 4 (1999). 22. M. A. Unger, H.-P. Chou, T. Thorsen, A. Scherer, and S. R. Quake, Science 288, 113 (2000). 23. Y. Xia, E. Kim, X.-M. Zhao, J. A. Rogers, M. Prentiss, and G. M. Whitesides, Science 273, 347 (1996).

Monolayer-Assisted Electrochemical Nanopatterning 24. R. J. Jackman, S. T. Brittain, A. Adams, M. G. Prentiss, and G. M. Whitesides, Science 280, 2089 (1998). 25. W. T. S. Huck, J. Tien, and G. M. Whitesides, J. Am. Chem. Soc. 120, 8267 (1998). 26. A. Kumar, H. A. Biebuyck, and G. M. Whitesides, Langmuir 10, 1498 (1994). 27. P. C. Hidber, W. H. Helbig, E. Kim, and G. M. Whitesides, Langmuir 12, 1375 (1996); C. S. Dulcey, J. H. Georger Jr., V. Krauthamer, D. A. Stenger, T. L. Fare, and J. M. Calvert, Science, 252, 551 (1991); W. J. Dressick and J. M. Calvert, Jpn. J. Appl. Phys. 32, 5829 (1993). 28. M. Masuko, T. Osaka, and Y. Ito (Eds.) “Electrochemical Technology-Innovations and New Developments.” Gordon and Breach Publishers, Amsterdam 1996. 29. M. J. Tarlov, D. R. F. Burguess, and G. Gillen, J. Am. Chem. Soc. 15, 5305 (1993). 30. J. A. Rogers, J. Tate, W. Li, Z. Bao, and A. Dodabalapur, Isr. J. Chem. 40, 139 (2000). 31. L. Lu, M. L. Sui, and K. Lu, Science 287, 1463 (2000). 32. J. A. Switzer, H.-J. Hung, E. W. Bohannan, M. G. Shumsky, and D. C. Van Aken, Adv. Mat. 9, 334 (1997). 33. F. Y. Yang, K. Liu, K. Hong, D. H. Reich, P. C. Searson, and C. L. Chien, Science 284, 1335 (1999). 34. J. A. Switzer, M. J. Shane, and R. P. Phillips, Science 247, 444 (1990). 35. J. A. Switzer, M. G. Shumsky, and E. W. Bohanna, Science 284, 293 (1999). 36. J. H. Schön, H. Meng, and Z. Bao, Adv. Mater. 14, 323 (2002). 37. A. Kumar, H. Biebuyck, and G. M. Whitesides, Langmuir 10, 1498 (1994). 38. J. P. Folkers, C. B. Gorman, P. E. Laibinis, S. Buchholz, G. M. Whitesides, and R. G. Nuzzo, Langmuir 11, 813 (1995). 39. J. Sagiv, J. Am. Chem. Soc. 102, 92 (1980). 40. R. Maoz and J. Sagiv, J. Colloid. Interface. Sci. 100, 465 (1984). 41. S. R. Wasserman, Y.-T. Tao, and G. M. Whitesides, Langmuir 5, 1074 (1989). 42. H. Lee, L. J. Kepley, H. G. Hong, S. Akhter, and T. E. Mallouk, J. Phys. Chem. 92, 2597 (1988). 43. B. L. Frey, D. G. Hanken, and R. M. Corn, Langmuir 9, 1815 (1993). 44. C. A Widrig, C. Chung and M. D. Porter, J. Electroanal. Chem. 310, 335 (1991). 45. C.-J. Zhong, N. T. Woods, G. B. Dawson, and M. C. Porter, Electrochem. Comm. 1, 17 (1999). 46. L. A. Bumm, J. J. Arnold, L. F. Charles, T. D. Dunbar, D. L. Allara, and P. S. Weiss, J. Am. Chem. Soc. 121, 8017 (1999). 47. G. Poirier, Chem. Rev. 97, 1117 (1997). 48. D. Anselmetti, A. Baratoff, H. J. Guntherodt, E. Delamarche, B. Michel, Ch. Gerber, H. Kang, H. Wolf, and H. Ringsdorf, Europhys. Lett. 27, 365 (1994). 49. F. Terán, M. E. Vela, R. C. Salvarezza, A. J. Arvia, J. Chem. Phys. 109, 5703 (1998). 50. C.-J. Zhong, R. C. Brush, J. Anderegg, M. D. Porter, Langmuir 15, 518 (1999); C. Vericat, M. E. Vela, G. Andreasen, R. C. Salvarezza, L. Vázquez, and J. A. Martín-Gago, Langmuir 17, 4919 (2001). 51. A. Ulman, Chem. Rev. 96, 1533 (1996). 52. F. Schreiber, Prog. Surf. Sci. 65, 151 (2000). 53. Y. Akinaga, T. Najajima, and K. Hirao, J. Chem. Phys. 114, 8555 (2001); J. Gottschalck and B. Hammer, J. Chem. Phys. 116, 784 (2002). 54. L. Strong and G. M Whitesides, Langmuir 4, 546 (1988). 55. L. H. Dubois, B. R. Zegarski, and R. G. Nuzzo, J. Phys. Chem. 98, 678 (1993). 56. A. Nemetz, T. Fischer, A. Ulman, and W. Knoll, J. Chem. Phys. 98, 5912 (1993). 57. K. S. Dhirani, M. A. Hines, A. J. Fischer, O. Ismail, and P. GuyotSionnest, Langmuir 11, 2609 (1995).

849 58. G. D. Aloisi, M. Cavallini, M. Innocenti, M. L. Foresti, G. Pezzatini, and R. Guidelli, J. Phys. Chem. B 101, 4774 (1997); H. Rieley, G. K. Kendall, R. G. Jones, and D. P. Woodruff, Langmuir 15, 8856 (1999). 59. M. A. Hines, J. A. Todd, and P. Guyot-Sionnest, Langmuir 11, 493 (1995). 60. G. J. Jackson, D. P. Woodruff, R. G. Jones, N. K. Singh, A. S. Y. Chan, B. C. C. Cowie, and V. Formoso, Phys. Rev. Lett. 84, 119 (1999). 61. H. Rieley, G. K. Kendall, R. G. Jones, and D. P. Woodruff, Langmuir 15, 8856 (1999). 62. S. Volmer, G. White, and C. Wöll, Langmuir 17, 7560 (2001). 63. J. Scherer, M. R. Vogt, O. M. Magnussen, and R. J. Behm, Langmuir 13, 7045 (1997). 64. L. Dreseen, C. Humbert, M. Celebi, J. J. Lemaire, A. A. Mani, P. A. Thiry, and A. Peremans, Appl. Phys. B 74, 621 (2002). 65. A. Carvalho, M. Geissler, H. Schmid, B. Michel, and E. Delamarche, Langmuir 18, 2406 (2002). 66. J. C. Love, D. B. Wolfe, M. L. Chabinyc, K. E. Paul, and G. M. Whitesides, J. Am. Chem. Soc. 124, 1576 (2002). 67. Z. Mekhalif, J. Delhalle, J.-J. Pireaux, S. Noël, F. Houze, and L. Boyer, Surf. Coat. Technol. 100–101, 463 (1998). 68. Z. Mekhalif, J. Riga, J.-J. Pireaux, and J. Delhalle, Langmuir 13, 2285 (1997). 69. M. Volmer-Uebing and M. Stratmann, Appl. Surf. Sci. 55, 19 (1992). 70. M. Volmer, B. Czodrowski, and M. Stratmann, Ber. Bunsenges. Phys. Chem. 92, 1335 (1988). 71. C. D. Bain, E. B. Troughton, Y. Tao, J. Evall, G. M. Whitesides, and R. G. Nuzzo, J. Am. Chem. Soc. 111, 321 (1989). 72. D. Schwartz, Annu. Rev. Phys. Chem. 52, 107 (2001). 73. M. Walczak, C. A. Alves, B. D. Lamp, and M. D. Porter, J. Electroanal. Chem. 396, 103 (1995). 74. H. Martín, C. Vericat, G. Andreasen, M. E. Vela, and R. C. Salvarezza, J. Chem. Phys. 117, 2293 (2002). 75. D. Hobara, K. Miyake, S. Imabayashi, K. Niki, and T. Kakiuchi, Langmuir 14, 2293 (1998). 76. C. Vericat, G. Andreasen, M. E. Vela, H. Martín, and R. C. Salvarezza, J. Chem. Phys. 115, 6672 (2001). 77. M. E. Vela, H. Martín, C. Vericat, G. Andreasen, A. HernándezCreus, and R. C. Salvarezza, J. Phys. Chem. B 104, 11878 (2000). 78. H. Hagenström, M. A. Schneeweiss, and D. M. Kolb, Langmuir 15, 2435 (1999). 79. M. Schweizer, H. Hagenström, and D. M. Kolb, Surf. Sci. 490, L627 (2001). 80. D. W. Hatchett, K. J. Stevenson, W. B. Lacy, J. M. Harris, and H. S. White, J. Am. Chem. Soc. 119, 6596 (1997). 81. D. W. Hatchett, R. H. Uibel, K. J. Stevenson, J. M. Harris, and H. S. White, J. Am. Chem. Soc. 120, 1062 (1998). 82. N. Mohtat, M. Byloos, M. Soucy, S. Morin, and M. Morin, J. Electroanal. Chem. 484, 120 (2000). 83. O. Azzaroni, M. E. Vela, G. Andreasen, P. Carro, and R. C. Salvarezza, J. Phys. Chem. B 106, 12267 (2002). 84. H. Ron, H. Cohen, S. Matlis, M. Rappaport, and I. Rubinstein, J. Phys. Chem. B. 102, 9861 (1998). 85. J. A. M. Sondag-Huethorst, and L. G. J. Fokkink, Langmuir 11, 4823 (1995). 86. E. D. Eliadis, R. G. Nuzzo, A. A. Gewirth, and R. C. Alkire, J. Electrochem. Soc. 144, 96 (1997). 87. S. E. Gilbert, O. Cavalleri, and K. Kern, J. Phys. Chem. 100, 12123 (1996). 88. E. Boubour and R. B. Lennox, J. Phys. Chem. B 104, 9004 (2000). 89. O. Cavalleri, S. E. Gilbert, and K. Kern, Chem. Phys. Lett. 269, 479 (1997). 90. O. Cavalleri, H. Kind, A. M. Bittner, and K. Kern, Langmuir 14, 7292 (1998).

850 91. M. Epple, A. M. Bittner, K. Kuhnke, K. Kern, W.-Q. Zheng, and A. Tadjeddine, Langmuir 18, 773 (2002). 92. K. Shimazu, T. Kawaguchi, and T. Isomura, J. Am. Chem. Soc. 124, 652 (2002). 93. L. Sun and R. M. Crooks, J. Electrochem. Soc. 138, L23 (1991). 94. J. Camarero, J. Ferrón, V. Cros, L. Gómez, A. L. Angel de Parga, J. M. Gallego, J. E. Prieto, J. J. de Miguel, and R. Miranda, Phys. Rev. Lett. 81, 850 (1998). 95. H. Hagenström, M. A. Schneweiss, and D. M. Kolb, Langmuir 15, 7802 (1999). 96. O. Cavalleri, A. M. Bittner, H. Kind, K. Kern, and T. Greber, Z. Phys. Chem. 208, 107 (1999). 97. H. Hagenström, M. J. Esplandiú, and D. M. Kolb, Langmuir 17, 839 (2001). 98. M. J. Esplandiú and H. Hagenström, Solid State Ionics 150, 39 (2002). 99. D. Oyamatsu, S. Kubawata, and H. Yoneyama, J. Electroanal. Chem. 473, 59 (1999). 100. D. Oyamatsu, M. Nishizawa, S. Kubawata, and H. Yoneyama, Langmuir 14, 3298 (1998). 101. M. Nishizawa, T. Sunagawa, and H. Yoneyama, Langmuir 13, 5215 (1997). 102. C. M. Whelan, M. R. Smyth, and C. J. Barnes, J. Electroanal. Chem. 441, 109 (1998). 103. H. Hagenström, M. A. Schneweiss, and D. M. Kolb, Electrochim. Acta 45, 1141 (1999). 104. C. M. Whelan, M. R. Smyth, and C. R. Barnes, Langmuir 15, 116 (1999). 105. M. A. Scheneweiss and D. M. Kolb, Phys. Stat. Sol. (A) 173, 51 (1999). 106. X. G. Zhang, X. H. Li, and H. L. Li, J. Colloid. Interface. Sci. 234, 68 (2001). 107. M. J. Tarlov, D. R. F. Burguess, and G. Guillen, J. Am. Chem. Soc. 115, 5305 (1993). 108. G. Gillen, J. Bennett, M. J. Tarlov, and D. R. F. Burguess, Anal. Chem. 66, 2170 (1994). 109. J. Huang and J. C. Hemminger, J. Am. Chem. Soc. 115, 3342 (1993). 110. Y. Xia, E. Kim, M. Mrksich, and G. M. Whitesides, Chem. Mater. 8, 601 (1996). 111. A. Kumar, H. A. Biebuyck, and G. M. Whitesides, Langmuir 10, 1498 (1994). 112. Y. Xia, X.-M. Zhao, and G. M. Whitesides, Microelectron. Eng. 32, 255 (1996). 113. R. D. Piner, J. Zhu, F. Xu, S. Hong, and C. A. Mirkin, Science 283, 661 (1999). 114. S. Hong, J. Zhu, and C. A. Mirkin, Science 286, 523 (1999). 115. S. Hong and C. A. Mirkin, Science 288, 1808 (2000).

Monolayer-Assisted Electrochemical Nanopatterning 116. C. S. Whelan, M. J. Lercel, H. G. Craighead, K. Seshadri, and D. L. Allara, Appl. Phys. Lett. 69, 4245 (1996). 117. G. Y. Liu, S. Xu, and Y. Qian, Acc. Chem. Res. 33, 457 (2000). 118. J. K. Schoer and R. M. Crooks, Langmuir 13, 2323 (1997). 119. D. A. Hutt and G. J. Leggett, J. Phys. Chem. 100, 6657 (1996). 120. T. P. Moffatt and H. Yang, 142, L220 (1995). 121. Y. Xia and G. M. Whitesides, J. Am. Chem. Soc. 117, 3274 (1995). 122. J. A. M. Sondag-Huethorst, H. R. J. van Helleputte, and L. G. J. Fokkink, Appl. Phys. Lett. 63, 285 (1994). 123. C. Binns, Surf. Sci. Rep. 44, 1 (2001). 124. O. Azzaroni, P. L. Schilardi, and R. C. Salvarezza, Nano Lett. 1, 291 (2001). 125. A. Nobuyoshi, K. Toshio, M. Katsuyuki, K. Oku, and H. Akihiko, JP Patent JP10321621, 1998; T. P. Howard, US Patent US6171712, 2001. 126. R. C. Salvarezza and A. J. Arvia, in “Electrochemical Nanotechnology: In-Situ Local Techniques at Electrochemical Interfaces,” (W. J. Lorenz and W. Plieth, Eds.) p. 57. Wiley-VCH, Weinheim, 1998. 127. S. Méndez, G. Andreasen, P. L. Schilardi, M. Figueroa, L. Vázquez, R. C. Salvarezza, and A. J. Arvia, Langmuir 14, 2515 (1998). 128. P. L. Schilardi, O. Azzaroni, and R. C. Salvarezza, Phys. Rev. B 62, 13098 (2000). 129. G. Capozzi and G. Modena, in “The Chemistry of the Thiol Group” (S. Patai, Ed.), John Wiley & Sons, New York, 1974. 130. O. Azzaroni, P. L. Schilardi, and R. C. Salvarezza, Appl. Phys. Lett. 80, 1061 (2002). 131. P. L. Schilardi, O. Azzaroni, and R. C. Salvarezza, Langmuir 17, 2748 (2001). 132. J. Feng, B. Cui, Y. Zhan, and S. Y. Chou, Electrochem. Comm. 4, 102 (2002). 133. G. Andreasen, P. L. Schilardi, O. Azzaroni, and R. C. Salvarezza, Langmuir 18, 10430 (2002). 134. M. Cavallini, M. Murgia, and F. Biscarini, Nano Lett. 1, 193, (2001). 135. E. Delamarche, H. Schmid, H. A. Biebuyck, and B. Michel, Adv. Mater. 9, 741 (1997). 136. Z. Huang, P.-C. Wang, A. G. MacDiarmid, Y. Xia, and G. M. Whitesides, Langmuir 13, 6480 (1997). 137. T. Kondo, M. Yanagida, K. Shimazu, and K. Uosaki, Langmuir 14, 5656 (1998). 138. P. L. Schilardi, S. Méndez, R. C. Salvarezza, and A. J. Arvia, Langmuir 14, 4308 (1998). 139. L. Vázquez, R. C. Salvarezza, and A. J. Arvia, Phys. Rev. Lett. 79, 709 (1997). 140. O. Azzaroni, M. Cipollone, M. E. Vela, and R. C. Salvarezza, Langmuir 17, 1483 (2001). 141. O. Azzaroni, M. E. Vela, H. Martin, A. Hernandez Creus, R. C. Salvarezza, Langmuir 17, 6647 (2001).

Encyclopedia of Nanoscience and Nanotechnology

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Monolayer-Based Scanning Probe Lithography Ryan R. Fuierer, Christopher B. Gorman North Carolina State University, Raleigh, North Carolina, USA

CONTENTS 1. Introduction 2. Negative Pattern Scanning Probe Lithography (SPL) 3. Positive Pattern SPL—“Dip-Pen Nanolithography” 4. SPL on Self-Assembled Monolayers (SAMs) via Modification of Terminal Chemical Functionality 5. Closing Remarks Glossary References

1. INTRODUCTION The requirement to fabricate at the meso- and nanometer (10−7 to 10−9 m) length scales will be essential for the future miniaturization of electronic and sensing devices. With that, the spatial arrangement of functional materials on solid surfaces with artificial control has attracted attention for the construction of novel surface bound chemical systems. Potential applications range from fundamental scientific research in micro- and nanoscale surface chemistry, to practical applications, such as chemical sensors and electronic or optical devices. One very promising candidate material for the further miniaturization of electronics is the use of molecules that self-assemble. Molecular self-assembly is a chemical process in which amphiphilic precursor molecules chemisorb to surfaces, producing films of monomolecular thickness, that are chemically bonded to those substrates. These materials are often organic in nature and are frequently termed soft materials.

1.1. Self-Assembled Monolayers Self-assembled monolayers (SAMs) have attracted considerable attention as patterning materials because of their spontaneous adsorption on certain substrates, their excellent ISBN: 1-58883-061-6/$35.00 Copyright © 2004 by American Scientific Publishers All rights of reproduction in any form reserved.

uniformity in molecular order, and their resistivity to various types of chemical etching. Self-assembling monomers can be considered bifunctional molecules that can bond to the substrate at one end (head) and an organic group (R) that imparts the desired functionality to the modified surface at the other end (tail) [1]. The surface reactions are thermodynamically driven to completion, lowering the free energy of the system when chemisorbed to the surface. Organothiol molecules (R-SH) self-assemble on coinage metal surfaces (Au, Ag, Cu, Pt) through the formation of chemisorbed bonds [2, 3]. Any surface that has exposed hydroxyl ( OH) groups can react with organosilanes (R SiX3 , X = Cl, OCH3 , OCH2 CH3 ) to form siloxane (Si O Si substrate) linkages. The amphiphilic nature of these self-assembling molecules has allowed them to be chemically tailored to perform specific functions on a variety of substrates. Self-assembled monolayers are excellent candidates for preparing template architectures at the molecular scale or as resist layers; however, spatial resolution and rational placement at the molecular scale is often considered very challenging. Speculation exists that photolithography will not be able to create patterned features cheaply at the nanoscale (1 to 100 nm). Electron beam lithography is an alternative but does not permit definition of chemistry without subsequent processing steps. Microcontact printing [4] offers a promising alternative to parallel lithography of self-assembling materials; however, it has only begun to reach sub-50-nm length scales at the present day. Probe microscopy techniques appear particularly well suited for surface nanopatterning.

1.2. Scanning Probe Microscopy Scanning probe microscopy (SPM) is a family of surfacebased interface techniques for investigating and manipulating these materials (SAMs) at the molecular and nanometer scales. SPM techniques have emerged as a premier surface analysis methodology, and have been employed in many surface and materials modification studies. Surface science on the submicro-to-atomic scale has certainly been driven forward because of these tools. It was not long after

Encyclopedia of Nanoscience and Nanotechnology Edited by H. S. Nalwa Volume 5: Pages (851–859)

Monolayer-Based Scanning Probe Lithography

852 their initial development that microscope probe tips were used for lithographic applications on the atomic scale [5], which was one of the earliest demonstrations of scanning probe lithography (SPL). The patriarch of the SPM family is the scanning tunneling microscope (STM) [6] (Fig. 1A). A sharp metal probe tip is attached to a computer-controlled piezo-positioning element, which allows the tip to be moved independently in three dimensions with atomic scale precision. The metal probe, typically made of tungsten or platinum/iridium alloy, is brought within several angstroms (Å, 1 × 10−10 m) of a conducting or semiconducting sample. As a voltage is applied between the tip and sample, a small electrical current is measured between the two electrodes (tip and substrate). The current flow is a result of electrons tunneling through the tip–substrate gap, called the tunneling current. The feedback loop adjusts the height of the tip (in z-direction) by monitoring the tunneling current. If the measured current is smaller than a user set reference current, the tip is moved closer to the sample, to reestablish the set point current. Likewise, if the measured tunneling current is too large, the tip is moved away from the sample. To generate an image of the surface, the tip is scanned in a raster pattern across the sample in the x- and y-dimensions, systematically recording how much the tip was moved (in the z-direction) to maintain a constant set point current value along the scan pattern. A three-dimensional surface relief map is generated representing a convolution of the topography and electronic properties of the surface. Background material can be found in [7–13].

A

x

Setpoint current

y Feedback Loop

z

y x

Itunneling

Tip raster pattern

z

V

Electronics controller

x y

Conductive sample Photo segmented diode

B x y

Cantilever

Tip raster pattern

Piezo Electronics controller

Laser

Sample z x y

Figure 1. Schematics showing the operation of (A) the scanning tunneling microscope (STM), (B) the atomic force microscope (AFM).

Shortly after the invention of the STM, the atomic force microscope (AFM) was conceived [14]. In this new class of SPMs, the surface morphology is tracked by monitoring the forces imparted on a probe tip attached at the end of a flexible cantilever, rather than a current detection motif. Height information is deduced from the deflection of the cantilever as the tip scans the sample surface in a raster pattern (parallel to the length of the beam), while maintaining contact with the surface (Fig. 1B). The deflection of the cantilever is monitored by reflecting a laser beam off the back side of the cantilever, to a positron sensitive diode (PSD), which monitors the laser beam’s coordinates to produce a three-dimensional relief of the surface morphology. Because of this optical detection scheme, cantilever-forcebased SPM techniques are commonly referred to as scanning force microscopy (SFM). There are two basic AFM modes that make SFM techniques so versatile for imaging and manipulation purposes: contact mode, and noncontact mode. Operation in contact mode involves tracking surface morphology by rastering the tip across the sample in its scan pattern, analogous to how a record player needle is dragged along its grooved track. A noncontact imaging mode is termed tapping mode AFM (TMAFM™), in which the cantilever is oscillated close to its resonant frequency, intermittently “tapping” the surface as it scans the surface. Differences in surface morphology cause damping in these oscillations detected by the PSD to generate a topographical image. This mode is very good at imaging softer surfaces that may normally be damaged by the forces applied to a cantilever in contact mode imaging. This mode was a common technique reported in the papers described within to survey the chemical pattern structures generated, or subsequent chemical binding event. Many of the SPLs described within employed other popular SFM techniques and image the lithography generated. Lateral force microscopy (LFM) is a useful contact mode technique that can detect the friction (stickiness) between multiple chemical functionalities or components on a surface [15]. In this mode, the torsion that is imparted on the tip when scanning perpendicularly to the length of the cantilever beam is monitored by the left and right PSD segments, concomitantly monitoring the z-deflection in the cantilever, to give a morphological representation of a surface, viewed in two separate data images (friction and topography). SFM can also detect currents, or apply bias, when equipped with a potentiostat and conductive cantilever. The commonly termed “conducting AFM” (cAFM) measures surface morphology with conventional AFM optical detection, with the added ability to measure current similar to the two-electrode configuration used in STM, which makes this technique well suited for current–voltage measurements. In all the AFM techniques briefly described above, there are cantilever force ranges with specific properties for different modes that are commercially available for optimal imaging results. It is also noted that STM was often employed in the fabrication for smaller studies (