Encyclopedia of Nanoscience and Nanotechnology 9781588830647, 1588830640

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Encyclopedia of Nanoscience and Nanotechnology Volume 8 Number 1 2004 Near-Field Optical Properties of Nanostructures

1

Nicolas Richard Noble Metal Nanoparticles

9

Yiwei Tan; Yongfang Li; Daoben Zhu Noble Metal Nanocolloids

41

Ichiro Okura Nonlinear Optical Materials by Sol-Gel Method

49

Wenyan Li; Sudipta Seal Nonlinear Optics of Fullerenes and Carbon Nanotubes

67

Rui-Hua Xie; Qin Rao; Lasse Jensen Nonlinear Optics of Nanoparticles and Nanocomposites

101

Quandou Wang; Jianfeng Xu; Rui-Hua Xie Nucleation Kinetics of Nanofilms

113

S. A. Kukushkin; A. V. Osipov Nucleoprotein Assemblies

137

Steven S. Smith One-Dimensional Metal Oxide Nanostructures

147

Lionel Vayssieres; Arumugam Manthiram Optical Fibers for Nanodevices

167

Jenny M. Tam; Sabine Szunerits; David R. Walt Optical Properties of Gallium Nitride Nanostructures

179

Annamraju Kasi Viswanath Optical Properties of Oligophenylenevinylenes

219

Johannes Gierschner; Dieter Oelkrug Ordered Mesoporous Materials

239

Sebastian Polarz Ordered Nanoporous Particles

259

Ferry Iskandar; Mikrajuddin; Kikuo Okuyama Organic Nanofilm Growth

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Serkan Zorba; Yongli Gao

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Organic Polyradical Magnetic Nanoclusters

285

Andrzej Rajca Organic Thin Film Deposition Techniques

295

M. C. Petty Organic/Inorganic Nanocomposite Colloids

305

Elodie Bourgeat-Lami Oxide Nanoparticles

333

K. P. Jayadevan; T. Y. Tseng Oxide Nanowires and Nanorods

377

Guozhong Cao; Steven J. Limmer Palladium Nanoparticles

397

Chia-Cheng Yang; Chi-Chao Wan; Chien-Liang Lee Patterned Magnetic Nanostructures

415

Jian-Ping Wang; Tie-Jun Zhou Pb-Based Ferroelectric Nanomaterials

435

Ki Hyun Yoon; Dong Heon Kang Peptide Nanotubes

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Hiroshi Matsui Periodic Nanostructures with Interfering Femtosecond Lasers

457

Masahiro Hirano; Ken-ichi Kawamura; Hayato Kamioka; Taisuke Miura; Hideo Hosono Pharmaceutical Nanotechnology

469

Paul A. McCarron; Maurice Hall Phase Mixture Models for Metallic Nanomaterials

489

Yuri Estrin; Hyoung Seop Kim; Mark B. Bush Phonon Confinement in Nanostructured Materials

499

Akhilesh K. Arora; M. Rajalakshmi; T. R. Ravindran Phonons in GaN-AlN Nanostructures

513

J. Frandon; J. Gleize; M. A. Renucci Photochemical Molecular Devices

527

Alberto Credi Photochemistry in Zeolite Nanocavities

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Masanobu Kojima Photoconductivity of Carbon Nanotubes

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Akihiko Fujiwara

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Photodynamics of Nanoclusters

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M. Belkacem; M. A. Bouchene; P.-G. Reinhard; E. Suraud Photoexcitation Dynamics of Fullerenes

593

Mamoru Fujitsuka; Osamu Ito Photonic Crystal Lasers

617

John D. O'Brien; Wan Kuang; Po-Tsung Lee; Jiang Rong Cao; Cheolwoo Kim; Woo Jun Kim Phthalocyanine Nanostructures

629

Eunkyoung Kim Plasma Chemical Vapor Deposition of Nanocrystalline Diamond

691

Katsuyuki Okada Polyacetylene Nanostructures

703

Kevin K. L. Cheuk; Bing Shi Li; Ben Zhong Tang Polyaniline Fractal Nanocomposites

715

Reghu Menon; A. K. Mukherjee Polymer Electrolyte Nanocomposites

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Mikrajuddin Abdullah; Wuled Lenggoro; Kikuo Okuyama Polymer Nanostructures

763

Liming Dai Polymer/Clay Nanocomposites

791

Masami Okamoto Polymeric Nano/Microgels

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Piotr Ulanski; Janusz M. Rosiak Polymeric Nanoparticles

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Bobby G. Sumpter; Donald W. Noid; Michael D. Barnes; Joshua U. Otaigbe Copyright © 2004 American Scientific Publishers

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Encyclopedia of Nanoscience and Nanotechnology

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Near-Field Optical Properties of Nanostructures Nicolas Richard Thomson Tubes and Displays, Genlis, France

CONTENTS 1. Introduction 2. Depolarization Effects in the Near-Field Optics 3. Optical Properties of Subwavelength Objects Deposited on a Surface 4. Analysis of the Polarization Near Subwavelength Objects 5. Conclusion Glossary References

1. INTRODUCTION During these last years, scanning near-field optical microscopy (SNOM) has become an extremely powerful technique for the analysis of surface structures with a resolution far beyond the diffraction limit [1, 2]. The role of the incident polarization associated with the incoming light is important for the understanding of optical images under the condition of total internal reflection in the nearfield optics using a photon scanning tunneling microscope (so-called PSTM or STOM) [3–8] or under the illumination in normal incidence (SNOM configuration) [9]. These techniques tend to elucidate the optical properties of mesoscopic and nanoscopic particles in the near-field. The mesoscopic regime corresponds to optical properties of the system where the size of the objects is of the order of the incident wavelength. For the visible range, it means that the object has a lateral size between 100 nm and 1000 nm. The nanoscopic regime corresponds to structures smaller than 100 nm. On the other hand, when the size of the object is much greater compared to the incident wavelength, one usually speaks of the macroscopic regime. Geometrical optics and Kirchhoff diffraction can be treated on a macroscopic scale. Near-field optics deals with behaviors occurring with evanescent electromagnetic waves which become important

ISBN: 1-58883-064-0/$35.00 Copyright © 2004 by American Scientific Publishers All rights of reproduction in any form reserved.

when the size of the object is of the order or lower compared to the incident wavelength. The actual theory well describes the interaction between objects and light in the microscopic or in the macroscopic regimes. A numerical approach based on Maxwell equations is needed to know the optical response of such systems in the mesoscopic range. Many approaches were realized to model optical microscopy in the near-field optics for objects deposited on perfectly flat and rough surfaces [10–12]. Different experimental devices were used for the study of near-field optical microscopy according to the properties in transmission [13]. To understand the optical properties of mesoscopic and nanoscopic objects, many studies were performed on periodic structures in the near-field optics [14]. Main problems come from the understanding of tip detection for the electromagnetic field at a given distance from the surface and many theroretical models try to understand the basic properties of an optical microscope [15]. Optical contrasts produced by nanoscopic or mesoscopic dielectric objects according to the incident polarization associated with the incoming light for nanoscopic or mesoscopic dielectric objects are presented. First, we will describe the notion of depolarization for nanoscopic objects in the nearfield optics and the impact of the object size and of the wavelength in the optical images. Second, the impact of the polarization in the near-field optics will be discussed showing optical images under several conditions of illumination and detection. The incident polarization is chosen rectilinear under the condition of total internal reflection and in the air [16]. Circular polarization is also chosen to see the optical behaviors in normal incidence [17]. These two configurations will show effects related to the impact of the incident polarization on the optical response of the dielectric object in the near-field optics. In both configurations (PSTM and SNOM), the probe is the main tool for the detection of the electromagnetic field or the illumination of the sample at the nanometer scale. In near-field optical microscopy, the local detection of the optical signal relies on the use of nanometer-sized probes. In the SNOM configuration, the probe acts as a local source

Encyclopedia of Nanoscience and Nanotechnology Edited by H. S. Nalwa Volume 8: Pages (1–8)

2 of evanescent optical fields whereas in the PSTM setup, the probe behaves as a local detector of light. In these devices, SNOM and PSTM tips are usually coated with a thin metal layer in order to achieve a narrow localization of the incident light on the sample (SNOM configuration) or to improve the resolution in detection for the PSTM configuration. However, Al-coated tips showed limited improvement due to the degradation of the signal-to-noise ratio related to the very low transmission through such coating in the PSTM configuration. The scattering effects are the main problems which occur strongly in the near-field optics because these waves damage the resolution of the optical images. Scattering of the electromagnetic waves by a sphere (Mie theory) and an ellipsoid has been extensively studied in both microscopic and mesoscopic regimes [18–23]. This problem has a known solution in an analytical way. More complicated shapes involving objects with sharp edges could not be solved analytically. Far-field expressions were detailed to understand the scattering cross-section behaviors but analytical nearfield expressions could not be given in the same way. Mainly, backward and forward scattering were found in the different scattering diagrams according to the size of the sphere and to the refractive index of the material. In order to eliminate the scattering behaviors which occur in the near-field optics, polarization studies are thus necessary to understand the scattered field behaviors in the analysis of near-field optical images. This outlines effects relative to the confinement of the electric field near the objects. Main problems are involved in the diffraction pattern of the forward and backward waves scattered by the objects. The study of the different components will reject this problem and only the objects’ response is taken into account.

1.1. Green’s Dyadic Technique The calculations are based on the Green’s dyadic technique using Lippmann–Schwinger and Dyson equations for all numerical computations [24, 25]. This method is proven to be an efficient computation technique for the typical parameters of near-field optics (size of the object, height of detection, wavelength, dielectric permittivity of materials). This numerical method is reliable to solve the Maxwell equations and it is based on the knowledge of the Green’s dyadic associated with a reference system which is a flat surface or vacuum in our case. The procedure considers any object deposited on the surface or placed in the air as a perturbation discretized in direct space. The electric field is determined self-consistently inside the perturbations; a renormalization associated with the depolarization effect is taken into account for the self-interaction of each discretization cell. The Huygens–Fresnel principle uses the values of the field inside the perturbations to compute the electric field or the optical magnetic field elsewhere [26]. This method for the calculation of both optical electric and magnetic fields can treat any kind of nanoscopic and mesoscopic objects in the near-field optics. The shape and the dielectric constant of the particles can be arbitrarily taken. Moreover, this numerical technique can treat anisotropic objects in near-field and in far-field optics [27]. As the discretization is performed in direct space, this

Near-Field Optical Properties of Nanostructures

method can be thus extended to experimental samples using the topography of the surface, that is, any input geometry of the computations according to a given AFM (atomic force microscopy) data file recorded on the sample. This capability gives the opportunity to better understand the experimental images in the near-field optics.

1.2. Optical Initial Conditions in the Near-Field We choose glass for the use of a dielectric material and we consider that the index of refraction of the glass, fixed to 1.5, does not depend on the incident wavelength. Other materials used for the optical properties in different wavelength ranges could be taken into account but the main physical principles are explained in the following sections. In the case of other materials, spectroscopic behaviors are important for the understanding of the near-field optical images in order to take into account resonance behaviors according to the optical response of a given structure [28–30]. Here, we will detail the case of dielectric particles deposited on a dielectric glass substrate or illuminated in the air. For the first case, the objects are bidimensional structures which are illuminated in the air. In the second case, these ones are tridimensional and illuminated under the condition of total internal reflection as in the PSTM configuration beyond the glass–air critical angle. For the circular polarization, the objects lying on a dielectric surface will be illuminated in normal incidence. We show numerical simulations which take account of the analysis for the intensity associated with the total electric field and with the optical magnetic field scattered by nanoscopic objects in transmission at constant height in the total internal reflection configuration. In the case of a surface separating two dielectric media (glass–air interface), two modes of polarization are associated with the incoming light: TE and TM modes. The z-direction being perpendicular to the glass–air interface, as we chose the incident light to be linearly polarized, the TE mode (s polarization) corresponds to an incident electric field perpendicular to the plane of incidence (y-z plane). The TM mode (p polarization) corresponds to a field parallel to the plane of incidence. In the case of bidimensional objects, the direction of the incident light is perpendicular to the infinite z-direction of the structure. In both cases, the detection is performed in the x-y plane at a constant height in the case of the surface using three-dimensional structures.

2. DEPOLARIZATION EFFECTS IN THE NEAR-FIELD OPTICS To understand the optical effects produced by subwavelength objects, it is important to introduce the notion of depolarization. In order to explain this behavior, one considers a bidimensional object which is illuminated along its smaller dimensions in the air; no surface is included for this model and the incident electric field is applied perpendicularly to the lateral sides of the particle. One can see that, for subwavelength objects, the negative contrast which occurs inside the object is a result of the depolarization effect which

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is related to the conservation of the components normal to the object faces according to the displacement vector [31] (Fig. 1a). Moreover, a higher intensity can thus be found around the lateral sides of the object close to its edges (Fig. 1a). This high-intensity effect borders the structure along the direction of the applied incident electric field (x-direction). This depolarization effect is mostly related to the size of the object which belongs to the nanometer scale (100 nm) according to the incident wavelength (633 nm). One can observe that, when the size of the object is relatively small compared to the incident wavelength, which is the present case, the field intensity distribution around the object tends to reproduce its profile. This conclusion can be extended to any nanoscopic isolated objects in the near-field optics. We took the two-dimensional case; therefore, no depolarization effect appears along the infinite z-direction. In Section 3, we will show the importance of depolarization in different directions by using a tridimensional object deposited on a dielectric glass substrate.

2.1. Influence of the Particle Size on the Optical Image Let us now consider a 200 × 200 nm2 dielectric squared structure illuminated in the same conditions as in the previous section. By doubling the object size, one can obtain an optical image including not only depolarization effects but also scattering waves near the structure because we switch from the nanoscopic regime (previous section) to the mesoscopic

range at the optical scale. One can see that a back reflected wave occurs in the optical image y < 0 and also a forward scattering in the direction of the incident light y > 0 (see Fig. 1b). By this change, one can see the strong influence of the particle size on the resolution of the optical image. When we consider an object which has a size compared to the incident wavelength, the structure has not only depolarization properties but also scattering effects around the particle; these optical waves degrade considerably the resolution of the optical image.

2.2. Influence of the Incident Wavelength The results presented in this section are a consequence of the different effects found in the previous one. To understand the impact of the wavelength in the optical image, let us consider a squared dielectric particle (100 × 100 nm2 ) illuminated as previously but with a different wavelength lower than 633 nm. If one turns to a wavelength dependence, the use of a particle size (100 nm) which can be compared to the wavelength of the incident light (400 nm) shows scattering effects in the optical image (see Fig. 1c). One can see the similar behaviors shown in the previous section: backward and forward scattering can be clearly seen in the optical image as we turned to the mesoscopic regime. Consequently, these effects show the main differences between the nanoscopic regime and the mesoscopic one in the optical images when dealing with nanometric objects in the near-field and by only changing the wavelength in the visible range. Therefore, one has to be aware that the illumination wavelength and the lateral size of the particle have a strong impact on the resolution of the optical images in the nearfield optics for the visible range as one can switch from the nanoscopic regime to the mesoscopic one.

3. OPTICAL PROPERTIES OF SUBWAVELENGTH OBJECTS DEPOSITED ON A SURFACE (a)

(b)

(c) Figure 1. For  = 633 nm, variation of the intensity associated with the total electric field for a glass squared rod of 100 × 100 nm2 section (a) and of 200 × 200 nm2 section (b). For  = 400 nm, variation of the intensity associated with the total electric field for a glass squared rod of 100 × 100 nm2 section (c). The object is illuminated along the y-direction and the incident polarization direction is along the x-axis.

In this section, the influence of the polarization associated with the incident light on the object is shown. The index of refraction of the substrate as well as the refractive index of the object is fixed to 1.5. Depending on the size of the object and on the incident wavelength, such a protrusion can behave more or less as a obstacle to the propagation of the surface wave. For the condition of total internal reflection, the object is illuminated with an angle of incidence of 60 and the detection is performed in the near-field optics at constant height above the object. It is also important to see what the tridimensional case will bring to the optical image. As the object will become three-dimensional, the other direction will give more insight for the depolarization effect along this direction.

3.1. Optical Electric Field For the condition of total internal reflection, the 100 × 100 × 40 nm2 dielectric object is illuminated with an angle of incidence of 60 and the detection is performed in the near-field

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Near-Field Optical Properties of Nanostructures

optics at a constant height of 10 nm above the object (see Fig. 2a and b). When the detection of the electromagnetic field is closer to the objects, one can find the same basic optical properties explained in the previous sections. Consequently, the backward and forward scattering effects cannot be seen in the optical images for both modes of polarization. The depolarization effect occurs in the lateral sides of the particle in the TE mode as we had previously (Fig. 2a). However, this effect happens at the top of the object in the TM mode. In this mode, the incident electric field is parallel to the plane of incidence. Therefore, this field has components in both directions: parallel (y-direction) and perpendicular to the surface (z-axis). The angle of incidence (60 ) is taken in such a way that the component which is perpendicular to the surface is larger compared to the parallel one. Consequently, the depolarization effect occurs in the z-direction, which produces the bright contrast in the near-field optical image (Fig. 2b). Moreover, an inverse contrast similar to the TE polarization cannot show up in the TM mode because at short distances the vertical z-component of the electric field dominates. The matching condition of the vertical component of the displacement vector leads to a confined optical electric field close to the upper face of the pad. Therefore, in the three-dimensional case, the depolarization effect in the near-field optics could occur in the three axis according to the direction of application of the incident electric field. A striking difference of behavior was found depending on the polarization state of the traveling wave along the

(a)

(b)

(c)

(d)

Figure 2. For  = 633 nm, variation of the intensity associated with the total electric field for the TE mode (a) and for the TM mode (b) at a constant height of 50 nm above the dielectric surface. Variation of the intensity associated with the total magnetic field for the TE mode (c) and for the TM mode (d) for a 100 × 100 × 40 nm3 glass pad at a height of 100 nm above the surface. The object is illuminated by the glass substrate under the condition of total internal reflection with an angle of incidence of 60 .

surface. In the subwavelength range, the TM polarization mode allows to reproduce the shape of the objects, whereas a TE polarized wave can be used to extract information on the contours of the objects themselves.

3.2. Optical Magnetic Field Tip detection is important according to the optical properties of the sample surfaces. In the PSTM configuration, the detection performed with dielectric tips or with dielectric tips covered by a thin noble metal film shows different optical images in the near-field. In the first case, one detects an intensity associated with the optical electric field and in the other case, one can detect a signal proportional to the optical magnetic field associated with the optical wave for wavelengths in the visible range. This behavior is mainly related to the surface plasmon effect occurring in the thin metal film which covers the dielectric tip. Therefore, this proves that the optical images depend strongly on the tip response. We will discuss later the optical image patterns obtained with the electric field associated with the optical wave and also those of the magnetic field obtained in the same conditions. In order to achieve a better resolution in the optical images, dielectric tips coated by a thin gold film can be used. But the optical images obtained using such tips show inverted contrasts compared to the ones obtained with uncoated dielectric tips. These results indicated that the detected signal may reveal different physical behaviors according to the probe composition [32, 33]. While the dielectric tip always collects a signal proportional to the square modulus of the electric near-field, using the same initial conditions, the optical images obtained with a coated gold tip display the same patterns as the theoretical maps of the square modulus of the magnetic field associated with the optical near-field. These images can be obtained under several conditions: the use of a defined gold film thickness which corresponds to a given excitation wavelength has to be achieved to obtain a signal proportional to the optical magnetic field associated with the scattered light in transmission. These conditions have to sustain a plasmon resonance mode in the thin metal film which covers the dielectric tip. These studies show another way to detect a signal proportional to the optical magnetic field for wavelengths corresponding to the visible range. In order to show this purpose, one can compute the optical magnetic field associated with the lightwave in transmission (Fig. 2c and d). The object is illuminated as in Section 2 under the condition of total internal reflection. The height of detection is chosen to be 60 nm above the top of the dielectric object. One can see that the depolarization effects occur at the top of the object in the TE mode while these occur on the lateral sides of the structure in the TM polarization for the optical magnetic field images (see Fig. 2c and d). These results show different behaviors compared to those found for the electric field intensities in both modes of polarization. All the optical responses are inverted for the detection of the magnetic field compared to the electric field signals: the dark contrast in the TE mode for the signal associated with the electric field gives a bright one for the optical

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Near-Field Optical Properties of Nanostructures

4. ANALYSIS OF THE POLARIZATION NEAR SUBWAVELENGTH OBJECTS

(a)

(b)

As shown previously, one can detect experimentally the optical magnetic field associated with the scattered light. Using crossed polarizers, one can detect the different cartesian components associated with the electric field or with the optical magnetic field using coated gold dielectric tips at the resonance of the thin metal film or out of resonance. Choosing a proper incident polarized wave, one can detect the scattered wave obtained by eliminating the incident wave using another crossed polarizer at the fiber exit. This could give more information on the size and shapes of the objects as the behaviors are not the same when using nanometric or mesoscopic objects compared to the incident wavelength. The cartesian components could give more insight about the shape of the object rising on the surface.

4.1. Detection of the Different Cartesian Components in the TE Mode (c)

(d)

Figure 3. For  = 633 nm, variation of the intensity associated with the total electric field (a), the x-component (b), the y-component (c), and the z-component (d) for a 100 × 100 × 40 nm3 glass pad. The incident polarization direction is along the x-axis (TE or s mode). The object is illuminated under the same conditions described in Figure 2. The dectection is performed at a height of 100 nm above the surface.

magnetic field (Fig. 2c and Fig. 3a). Similarly, a bright contrast for the TM mode for the intensity associated with the electric field leads to a dark one for the optical magnetic field (Fig. 2d and Fig. 4a).

(a)

(b)

(c)

(d)

Figure 4. For  = 633 nm, variation of the intensity associated with the total electric field (a), the x-component (b), the y-component (c), and the z-component (d) for a 100 × 100 × 40 nm3 glass pad. The incident polarization direction is along the y- and z-axis (TM or p mode). The object is illuminated under the same conditions described in Figure 3.

The detection is not performed close to the objects in order to show scattering effects along the dielectric surface. The aim of the following section is to show the possibility to suppress these optical waves in the near-field optics. We illuminate a dielectric glass object at a wavelength of 633 nm through a glass substrate under the condition of total internal reflection with an angle of incidence of 60 . The lateral size of the dielectric pad is 100 nm and its height is 40 nm, placing it in the nanoscopic regime. The detection of the electromagnetic field is performed at 60 nm above the pad of dielectric permittivity of 2.25 which is equal to the one of the substrate. This detection height involves scattering behaviors around the object in the near-field optics. The computation of the total intensity associated with electric field and to each cartesian component is realized for the TE mode (Fig. 3). The intensities are normalized according to the incident light. It is known that in the near-field optics, a strong z-component of the electric field exists since this one does not appear in reflectivity or in transmission for thin films in the far-field. Moreover, it is also important to see its evolution with the incident polarization; this will be shown for the TM mode in the next section. In this polarization mode, the electric field associated with the incident light is perpendicular to the plane of incidence. As shown previously, the negative contrast above the object is the depolarization effect and this can be seen in the optical images for the intensity associated with the total electric field (Fig. 3a) and also according to the x-component (Fig. 3b) which corresponds to the direction of application for the incident electric field. In this mode, one can see first that the intensity associated to the total electric field shows a confinement of the electric field close to the lateral sides of the pad along the x-direction (Fig. 3a) which is displayed by an increase of intensity in the optical image. Nevertheless, interference phenomena due to the backward scattering effects of the incident light on the object are more accentuated in the near-field optical image (Fig. 3a) for y < 0. Moreover, the forward scattering appears on the optical image for y > 0.

6 Second, we can see that the x-component of the electric field, which is the incident one, is major (Fig. 3b) compared to the others (y- and z-components in Fig. 3c and d) as expected. One can see in Figure 3c that the interferences on the images due to the backscattering reflected wave on the object disappeared and only the effects due to the confinement of the field around the object show up. These ones are related to the topography of the object on the surface. The same behavior can be seen in Figure 3d for the z-component of the electric field which shows optical effects due to the topography of the object. However, the intensities are greater for this component (Fig. 3d) compared to the other one (Fig. 3c). This shows the predominance of the z-component of the electric field compared to the one parallel to the surface (y-component) in the near-field optical images. The image associated with the total electric field shows a negative optical response (dark contrast) above the nanoscopic object (Fig. 3a). Moreover, the y-component shows an electric field which is well confined at the corners of the dielectric pad (Fig. 3c), whereas the z-component displays the same strong effects on the lateral sides of the pad along the x-direction (Fig. 3d). By these optical patterns, one can distinguish the x-component of the electric field from the parallel y-component.

4.2. Detection of the Different Cartesian Components in the TM Mode In this mode, one can see first that the optical images for the intensity associated with the total electric field and for each cartesian component are different compared to the TE mode. Consequently, the polarization plays an important role when analyzing the effects in the near-field optics. For this mode of polarization, we can see first that the intensity associated with the total electric field shows a confinement of the electric field above the upper side of the dielectric pad along the z-direction (Fig. 4a), as shown in Section 3.1. As in the TE mode, interference phenomena on the surface due to the backward scattering effect of the incoming light on the dielectric object show up in the optical image (Fig. 4a). Second, the y-component and more particularly, the z-component of the electric field which are associated to the incident one are major (Fig. 4c and d) compared to the other one (x-component in Fig. 4b) because they are associated with the incident electric field. The z-component is the strongest in the near-field optics, as discussed previously. We can see in Figure 4b that the interferences on the images due to the backscattering reflected wave on the object disappeared and only the effects due to the confinement of the field around the object show up in the optical images. These are related to the topography of the object on the surface as in the TE mode. We also show in this case that the z-component of the electric field is stronger in the near-field optical images compared to the y-component. Moreover, the x-component shows an electric field which is well confined on lateral sides of the pad (along the x-direction) whereas the ycomponent and the z-component display both interferences due to the incident light and a confinement of the electric

Near-Field Optical Properties of Nanostructures

field respectively on the lateral sides along the y-direction and on the top of the pad along the z-direction (Fig. 4c and d). It is thus possible to distinguish these three components in the near-field optics. Moreover, the forward scattering (y > 0) shows up in the optical images (Fig. 4a, c, and d). Thanks to this study, we show that the analysis of polarization in the near-field optics shows that one can eliminate interference behaviors on the surface. Moreover, this analysis also shows the weight of each cartesian component in the near-field optical images. Similar effects can be found for any kind of material of real positive dielectric permittivity. The behaviors are thus accentuated as the dielectric permittivity increases raising the intensities associated with each component. Nevertheless, the intensity variations associated with the component which was not in the polarization of the incoming light (for the TE mode: y- and z-components; for the TM mode: x-component) can be detected experimentally under the condition of a good signal-to-noise ratio. Other studies show that these intensities could get higher values using other materials. In this case, it is necessary to make spectroscopy computations by varying the incident wavelength in the visible range showing for which one the exaltation of the electric field in the near-field optics appears. This intensity enhancement is mainly due to the basic properties of matter from which the object is based [34].

4.3. Dealing with Different Objects In order to complete the previous discussion, we use several structures of different sizes and shapes. The sizes are arbitrary, taken in order to create a group which belongs to the mesoscopic regime. Using different object sizes, one can see that scattering waves occur in the image providing difficulties to see the confinement of the electric field around each object. The case of bidimensional objects is chosen. Using different objects sizes and shapes, it is important to see the optical signal associated with the component which is not in the incident electric field. One can see that the electric field is well confined on the edges of the different structures although surrounded by interference behaviors (see Fig. 5a). Using different sizes of the structures in the mesoscopic regime, backward and forward scattering can be clearly seen in the optical images. One is aware that these effects

(a)

(b)

Figure 5. For  = 633 nm, variation of the intensity associated with the total electric field (a) and the y-component (b) for several dielectric bidimensional objects.

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Near-Field Optical Properties of Nanostructures

degrade strongly the resolution of the optical images in the near-field optics. The detection of the y-component shows that one can detect with a better accuracy the positions of the objects as the scattered waves are almost eliminated (see Fig. 5b). This analysis shows a new technique to eliminate interference behaviors occurring in the near-field optics, bringing to the fore only optical effects relative to the topography of the objects on the surface.

4.4. Circular Polarization The use of circular polarized light has been developed for the case of dichroism in order to understand the optical properties of magnetic materials at the microscopic level. Circularly polarized light emitted from a scanning tunneling microscope was observed when the sample surface of a ferromagnetic material was probed with a tungsten tip in a longitudinal configuration. (The applied magnetic field is parallel to both the surface plane and the plane of light detection [35].) The theory of radiative transfer has been used to investigate the interaction between linear or circular polarized light waves and a multiple scattering medium (spheres) according to the sizes of the objects and their relative index of refraction [36–38]. This theory shows that the circular depolarization length exhibits a strong dependence on the relative refractive index, whereas the linear one does not. Chiral and achiral molecules show optical activity which arises from the different interaction of chiral media with left- and right-hand circularly polarized light. This optical

activity and the circular difference effects can also occur in nonlinear optics for chiral or achiral structures and magnetic materials in the second-harmonic generation signals [39, 40]. In our case, using the same computation technique, it is interesting to see the impact of circular polarization on a dielectric structure in the nanoscopic regime. We took the same dielectric object used in the previous section and illuminated under the same conditions. The detection of the electromagnetic field is performed at a height of 60 nm above the dielectric object. In the case where the object is illuminated in normal incidence with a circular polarization (x- and y-components exist in this case), one can find that each component of the electric field gives information about the shape of the object in both directions. Therefore, an asymmetrical shape of the object can be detected with such method of illumination as the depolarization effects occur in both directions (x in Fig. 6b and y in Fig. 6c) using this particular incident polarization associated with the incident light (see Fig. 6a). This technique could give more information about the shape of the object and also of the optical confinement of the electric field around the different structures. The main problem occurs on the detection of scattering effects along the surface and of the optical patterns produced by the mesoscopic and nanoscopic structure.

5. CONCLUSION We present an accurate analysis of the optical effects produced by nanoscopic and mesoscopic structures in the near-field optics. The importance of the incident wavelength and of the particle size is one of the most important points to get a better optical resolution in the near-field optics. The depolarization effects associated with a nanoscopic object and the scattering properties of the structures were clearly shown. The analysis of polarization shows the possibility to extract optical effects relative to nanoscopic and mesoscopic objects in the near-field optics.

GLOSSARY (a)

(b)

(c) Figure 6. For  = 633 nm, variation of the intensity associated with the total electric field (a), the x-component (b), and the y-component (c) for a 100 × 100 × 40 nm3 glass pad. The incident polarization is circular and the object is illuminated in normal incidence by the substrate. The detection is performed at a height of 100 nm above the surface.

Depolarization of light On a smaller scale, when light waves pass near a barrier, they tend to bend around that barrier and spread at oblique angles. This phenomenon is known as diffraction of light, and occurs when the light wave passes very close to the edge of an object or through a tiny opening such as a slit or aperture. The light that passes through the opening is partially redirected due to an interaction with the edges. Mesoscopic regime The adjective mesoscopic is used to define the situations where the sizes of the structures are of the order of the incident wavelength. For visible light, it corresponds roughly to the length range between 0.1 and 1 micrometer. By nanoswpic, one usually means lowdimensional Structures smaller than 100 nm. Near-fields optics Near-field optics studies the behavior of light fields in the vicinity of matter and deals with phenomena involving propagating and evanescent electromagnetic wave which become critically significant when the typical

8 sizes of the object are of the order of the wavelength or smaller. Near-field optical microscopy is the straightforward application of near-field optics. Polarization A light wave is an electromagnetic wave which mvels through the vacuum of outer space. Light wave is produced by electric charges which vibrate in a multitude of directions. An electromagnetic wave is a transverse wave which has both an electric and a magnetic component. A light wave which is vibrating in more than one plane is referred to as unpolarized light. It is possible to transform unpolarized light into polarized light. Polarized light waves are light waves in which the vibrations occur in a single plane. The process of transforming unpolarized light into polarized light is known as polarization. Surface plasmon resonance Under the condition of total internal reflection, while incident light is totally reflected the electromagnetic filed component penetrates a short (tens of nanometers) distance into a medium of a lower refractive index creating an exponentially detenuating evanescent wave. If the interface between the media is coated with a thin layer of metal (gold), and light is monochromatic and ppolarized, the intensity of the reflected light is reduced at a specific incident angle producing a sharp shadow (called surface plasmon resonance) due to the resonance energy transfer between evanescent wave and surface plasmons, corresponding to a collective excitation of the electrons at the metal/lower refractive index medium interface. The resonance conditions are influenced by the material adsorbed onto the thin metal film. TE (s-mode) and TM (p-mode) In the case of a surface separating two dielectric media, two modes of polarization can be associated with the incoming light: TE and TM modes. The z direction being perpendicular to the glass-air interface, as the incident light is chosen to be linearly polarized, the TE mode (s polarization) corresponds to an incident electric field perpendicular to the plane of incidence (y-z plane). The TM mode (p polarization) corresponds to a field parallel to the plane of incidence. Tip detection In near-field optical microscopy, the local detection of the optical signal or the illumination of the sample relies on the use of nanometer-sized probes. In near-field optics, a tip is constituted by a pulled optical fiber which illuminates or collects the light from a sample surface. This tip can be coated with a thin metal film in order to achieve a narrow localization of the incident light on the sample or to improve the resolution in detection. Total internal reflection At an interface between two transparent media of different refractive index, light coming from the side of higher refractive index is partly reflected and partly refracted. Above a certain critical angle of incidence, no light is refracted across the interface, and total internal reflection is observed.

ACKNOWLEDGMENTS This paper is dedicated to Jacques and Antoinette Richard and to the memory of Marie Muggéo.

Near-Field Optical Properties of Nanostructures

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Encyclopedia of Nanoscience and Nanotechnology

www.aspbs.com/enn

Noble Metal Nanoparticles Yiwei Tan, Yongfang Li, Daoben Zhu Chinese Academy of Sciences, Beijing, People’s Republic of China

CONTENTS 1. Introduction 2. Synthesis 3. Spectroscopic Characterization 4. Properties 5. Self-Assembly 6. Applications 7. Summary Glossary References

1. INTRODUCTION During the final decade of the 20th century, nanomaterials were the focus of research in the field of materials science, which is driven by the expectations concerning the application of nanomaterials as a forthcoming generation of functional materials for the new century. A large amount of knowledge about the synthesis and properties of various nanoparticles and nanocomposites was accumulated within such a short period, with numerous new insights and techniques emerging with each passing day. The physical and chemical properties of substances can be significantly altered when they are exhibited on a nanometer-length scale, and this phenomenon opens up a completely new perspective for materials design that benefits from the introduction of not only particle size, but also particle morphology as new, powerful parameters. A brand new concept is arising in material science: to utilize nanoparticles as the building blocks to displace the conventional microdevices by nanodevices. This challenging innovation will give rise to a revolutionary development: a drastic reduction in the necessary amount of traditional materials, subsequently of the cost and pollution, and finally turning the modern manufacturing that is regarded as an industry of exhausted natural resources and environmental harm into “smart and green production.” The substances with one dimension shrinking down to 1–100 nm can be called nanoscale substances. The nanomaterials can display various geometrical morphologies, ISBN: 1-58883-064-0/$35.00 Copyright © 2004 by American Scientific Publishers All rights of reproduction in any form reserved.

which include zero-dimensional nanoparticles with an aspect ratio approximately equal to 1, one-dimensional nanorods (aspect ratio > 1), nanowires, nanofibers, nanotubes, and nanoribbons or nanobelts [1, 2], two-dimensional nanosheets [3–5] and nanoscale diskettes [6], and three-dimensional nanocages [7, 8]. Nanoparticles are the most thermodynamically stable form with respect to the other geometrically morphological nanoscale materials because they have the least surface energy. Having sizes located between those of small molecules ( 0 015 the connectivity increases at higher volume fractions, and the effect of field on hopping transport gradually decreases; hence the value of MR is less. This shows that MR is an ideal probe to investigate the role of nanoscopic level morphology in the charge transport properties in conducting polymer nanocomposites. The detailed analysis of MR results is described in [186]. Thermoelectric power [or thermopower S] is another phenomena to explore the charge transport mechanism in metallic and semiconducting systems. In the thermoelectric effect or Seebeck effect, a temperature gradient at the

Figure 6. Magnetoresistivity versus square of magnetic field for f = 0 015 •, 0.012 ∗, 0.01 (+), 0.008 (
), and 0.006 (△). The inset shows magnetoresistivity versus volume fraction at 4.2 K. Reprinted with permission from [186], R. Menon et al., Phys. Rev. B 50, 13931 (1994). © 1994, American Physical Society.

Polyaniline Fractal Nanocomposites

ends of a sample gives rise to an electric field opposite to the direction of the temperature gradient [192]. Usually the sign of thermopower is consistent with a positive or negative charge of the carrier. The diffusion thermopower (Sd  in metallic systems is a function of the first derivative of density of states at Fermi level. Although the temperature dependence of thermopower [S T ] is supposed to be linear in metals, it is usually complicated by scattering processes. However, in high quality metallic conducting polymers a quasilinear temperature dependence of thermopower has been observed down to 8 K, which is quite remarkable when the extent of disorder present in these systems is considered. In several conducting polymer composites a linear temperature dependence of thermopower has been observed, but only down to 100 K [13]. The S T  of PANI–PMMA nanocomposites is shown in Figure 7 [193]. The thermopower at room temperature is nearly 8 V/K for all volume fractions, and it is positive for T > 80 K. The data show the typical metallic linear temperature dependence over a wide range of volume fractions of PANI–CSA in PMMA; however, there is a clear deviation from linearity below 100 K, and this deviation increases as f is lowered. The characteristic U-shaped dependence of S T  below 100 K indicates the onset of the breakup of the conducting network into disconnected regions, and the thermally activated hopping transport [Shop T  ∝ T 1/2 for VRH] across these regions dominates over the metallic diffusion thermopower [Sd T  ∝ T ]. Because thermopower is a zero current transport coefficient, it is relatively less sensitive to the electrical conduction paths between the disconnected regions, and this is mainly due to the fact that nanoscopic level thermoelectric voltages sum up together as long as the thermal gradients take place across the conducting paths. Hence investigating the low temperature U-shape in thermopower can give some insight into how well the conducting network is connected at the nanoscopic level. Thus S T  is another useful probe to investigate the correlation between

725 morphology and charge transport mechanism in conducting polymer nanocomposites.

5. APPLICATIONS Conducting polymer nanocomposites are used for a wide range of applications as indicated in the following [194]: 1. PANI nanocomposites have a wide range of applications for antistatic coating, electromagnetic interference shielding, and anticorrosive coatings. In particular, the fibrillar fractal network of PANI nanocomposite has high conductivity at low volume fractions of PANI and hence is ideal for these types of electrical applications. 2. PEDOT–PSS is most widely used by photographic film and electronics packaging industries. An antistatic coating of PEDOT–PSS on films (photographic/ electronics packaging) having a surface resistance less than 109 '/m2 , eliminates the risk of static charge buildup, which may damage the films. Interestingly, more than 100 million square meters of photographic films are coated by PEDOT–PSS every year. Also, PEDOT–PSS is widely used for transparent conducting electrodes [157]. 3. Conducting polymer-coated fibers such as polyester or nylon have applications in electromagnetically camouflaged nets in stealth devices [183]. 4. Conducting polymer composites with various nanocrystals have had interesting applications in light-emitting diodes, solar cells, lasing medium, and electrochromic devices. For example, MEH–PPV/perylene bis(phenethylimide)-based photovoltaic cells show an open circuit voltage of 0.58 V and their performance is better than that of MEH–PPV/CN–PPV-based photovoltaic devices [195]; PPV/carbon nanotube-based photovoltaic devices show a quantum efficiency of 1.8%, which is twice that of standard ITO-based devices, with an open circuit voltage of 0.9 V [19]. Nanocomposites based on MEH–PPV and TiO2 nanocrystals show higher quantum efficiency of 12% [16]. TiO2 dispersed in an MEH–PPV/polystyrene blend acts as a lasing medium that shows excited emission at wavelengths of 532 and 435 nm [177]. Blends of PPy and epichlorohydrin and ethylene oxide (Hydrin C) show excellent electrochromicity and are used in electrochromic devices [183]. 5. Networks of PANI blends filled with semiconducting polymers can be used as grid electrodes in a polymer grid triode [196]. The open structures of fibrillar fractal networks of PANI nanocomposite have large active surface area for devices. 6. Conducting polymer nanocomposites have shown potential for use in molecular sensors, biosensors, and molecular electronics applications [197, 198].

6. CONCLUSIONS Figure 7. Thermopower versus temperature for various concentrations (y of PANI–CSA in PMMA: y = 100% (•), 66.6% (♦), 33.3% (
), 9.09% (∗), 4.76% (+), 2.43% (△), and 1.24% (). Reprinted with permission from [193], C. O. Yoon et al., Phys. Rev. B 48, 14080 (1993). © 1993, American Physical Society.

In conclusion, conducting polymer nanocomposites have broadened the horizon of conventional polymer composites. In usual polymer composites the physical and chemical properties of the composite are limited, and the volume fraction of guest material is above the percolation threshold

Polyaniline Fractal Nanocomposites

726 (16% volume fraction), which restricts the processibility and mechanical properties of the composite. Moreover, it is hard to attain uniform distribution of nano or meso particles in composites due to various problems with compatibility, and this usually leads to inhomogeneity in the physical properties. It is possible to overcome several of these shortcomings with the breakthrough in the self-assembled fibrillar fractal network of guest polymer chains in the host matrix. This is very well illustrated for the conducting PANI–CSA fibrillar fractal network in a PMMA matrix in which the nanoscale morphology and the associated physical properties can be controlled rather well. The connected network forms at a volume fraction of PANI–CSA as low as 0.3%, with conductivity values of ∼10−3 S/cm. The network is quite robust in that it remains well connected even after the removal of the host polymer. This large open area conducting fractal network is quite useful as an electrode in various applications, for example, in polymer grid triodes. It is possible to obtain excellent control of the electrical and optical properties of this network by subtle variations in the composition of the nanocomposite as demonstrated by the temperature dependence of conductivity, magnetoresistance, thermoelectric power, and optical transmission features. Further molecular scale engineering and functionalization of conjugated polymer chains, and fabrication of this type of self-assembled fractal networks can widen the scope of this category of nanostructured systems, which are rather unique compared with other types of nanosystems.

GLOSSARY Conducting polymer A long chain carbon polymer consisting of alternating single and double bonds, in which delocalized -electrons determine the physical and chemical properties. Fractal A system that looks self-similar at all length scales, in which the dimensionality has noninteger values [integer value means 1, 2 and 3 dimensions for Euclidean geometry]. Localization A phenomenon in which the wavefunctions associated with the electronic states get localized, to a few interatomic distances, by the random disorder potential fluctuations so that there is hardly any overlap with nearestneighbor wavefunctions. Lorentz force The force F experienced by a charge carrier q in electric E and magnetic field intensity B, and it is given by the following relation: F = q E + v × B where v is the velocity of charge. Magnetoresistance The variation of resistance as a function of magnetic field. It is mainly due to the bending of charge carrier trajectory by Lorentz force, which is usually proportional to the square of the field, with the proportionality constant expressed as a function of scattering time. Nanocomposite A nearly homogenous mixture of two or more components, in which the physical size of components is typically below 100 nm, and this imparts special sizedependent properties. Percolation threshold The minimum volume fraction of guest component in a composite, at which the physical properties increase by several orders of magnitude due to the connectivity of guest material. For example, for conducting

spherical particles, at around 16% volume fraction, the electrical conductivity increases by several orders of magnitude. Resistivity A basic property of a material that signifies the measure of resistance offered by it to the flow of charge carriers. Resistivity () is defined as  = R A/l, where R is the resistance, l is the length of the sample, and A is the cross-sectional area. The SI unit is ' · m. Thermopower In the Seebeck effect, a temperature gradient at the ends of a sample gives rise to an electric field in the opposite direction as the temperature gradient. It is a measure of the rate of change of potential difference across a material as a function of unit change in temperature gradient.

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Encyclopedia of Nanoscience and Nanotechnology

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Polymer Electrolyte Nanocomposites Mikrajuddin Abdullah1 , Wuled Lenggoro, Kikuo Okuyama Hiroshima University, Hiroshima, Japan

CONTENTS 1. Introduction 2. Conductivity Enhancement in Polymer Electrolytes 3. Development of Polymer Electrolyte Nanocomposites 4. Preparation Methods 5. Important Parameters 6. Charge Transport Characterizations 7. Spectroscopic Characterizations 8. Microscopic Analysis 9. Thermal Characterizations 10. Density Method 11. Electrical Properties 12. Mechanical Properties 13. Thermal Properties 14. Luminescent Composites 15. Conclusion Glossary References

1. INTRODUCTION Rechargeable cells are key components in mobile technologies, such as portable consumer electronics and electric vehicles [1]. A search for batteries that provide high energy density and multiple rechargeability has been a subject of considerable attentions. Even though battery technology developed one hundred years ago, progress and improvements in technology have been slow, particularly when compared to the growth of computer technology [2]. A Li-based battery provides a high density and flexibility of design. Today’s lithium battery has a high specific energy (>130 W h kg−1 ), a high energy density (>300 W h L−1 ), 1 Permanent address: Department of Physics, Bandung Institute of Technology, Jalan Ganeca 10 Bandung 40132, Indonesia.

ISBN: 1-58883-064-0/$35.00 Copyright © 2004 by American Scientific Publishers All rights of reproduction in any form reserved.

high cell voltage (3.5 V), as well as a long cycle life (500–1000) charge/discharge. Worldwide production of such devices exceeded 200 million in 1997 and it will be approximately three times that number during 2001 [1]. Since lithium produces an explosion reaction with water-based electrolytes, a search for nonaqueous electrolytes is critically important to the production of the next-generation lithium battery, using electrolytes in an solid phase in an effort to develop more environmentally friendly materials. Polymer electrolytes are potential candidates for replacing the conventional aqueous electrolytes in lithium batteries. Polymers containing esters, ethers, or mixtures thereof which have the ability to dissolve salts are the base materials for polymer electrolytes. Polymer electrolytes are generally prepared by mixing high molecular weight polymers (HMWPs) with a salt solution. The polymer serves as solid solvent, thus permitting the salt to dissociate into anions and cations. Since the mass of a cation is much smaller than that of an anion, the electrical conductivity is dominated by cation transfer. Lithium salts are usually used for this purpose since they are the most electropositive of materials (−304 V relative to the standard hydrogen electrodes) as well as the lightest metal (atomic mass 6.94 g/mol, and density 0.53 g/cm3 ) and thus facilitate the design of storage systems with high energy density (Watt hour/kg) [1]. Table 1 shows a comparison of the electrochemical properties of several metals. Until presently, however, no polymer electrolyte-based lithium batteries are commercially available in the market. Therefore, worldwide research is being focused on the development of high power and high energy density polymer electrolytes with a major attention to safety, performance, and reliability. A battery contains two electrodes: positive and negative (both sources of chemical reactions), separated by an electrolyte that contains dissociated salts through which ion carriers flow. Once these electrodes are connected to external circuits, chemical reaction appears at both electrodes to result in a deliverance of electrons to the external circuits. The properties of a battery thus strongly depend on the electrolyte, anode, and cathode. With the use of polymer electrolytes in lithium batteries, high specific energy and specific power, safe operation, flexibility in packaging, and low cost in fabrication as well as low internal voltage drop at relatively large current withdraw is expected [3].

Encyclopedia of Nanoscience and Nanotechnology Edited by H. S. Nalwa Volume 8: Pages (731–762)

Polymer Electrolyte Nanocomposites

732 Table 1. Electrochemical properties of several metals that have potential applications for use in batteries.

Metal Li Na Mg Zn Cd Pd

Atomic weight [g/mol]

Valence charge

Specific charge [A h kg−1 ]

Electrode potential [V]

694 2299 2431 6538 11241 20720

1 1 2 2 2 2

3862 1166 2205 820 477 250

305 271 238 076 040 013

Realization of commercial polymer electrolyte batteries is actively investigated in many companies worldwide. A major effort to develop advanced polymer batteries for electric vehicles began in the early 1990s by 3M and HydroQuebec [4]. The battery contains a lithium metal anode, a polyethylene oxide (PEO)-based polymer electrolyte, and a vanadium oxide (VOx ) cathode. The reversibility of lithium intercalation and deintercalation in the VOx is quite good but the average discharge of the cell is low. PolyPlus Battery company in the United States is developing polymer electrolyte-based lithium battery which would operate at room temperature with specific energy as high as 500 W h kg−1 [3]. In a prototype cell, using cathode made of lithium intercalated disulfide polymer, a specific energy as high as 100 W h kg−1 and charge and discharge cycles almost reproducible for over 350 cycles were observed at 90  C [5]. Moltec company reported a specific density of 180 W h kg−1 for an AA-sized battery based on organosulfur cathode [6]. Ultrafine Battery company reported a room-temperature solid polymer battery based on intercalation type electrode with a specific energy 125 W h kg−1 and charge/discharge cycling time of 500 [3]. This performance is still below the consumer expectation threshold. In 1995, Turrentine and Kurani in the United States did a survey on demand for alternative fuel cell for vehicles and found that consumers agreed to buy electric vehicles which would run for at least 200 km per battery [7].

2. CONDUCTIVITY ENHANCEMENT IN POLYMER ELECTROLYTES It is believed that in the polymer electrolytes, the cations are coiled by polymer segment leaving the anions to occupy separate positions [8]. Battery performance is limited by the speed of cation diffusion. The transport of cations takes place if there is a relaxation of the polymer segments so that cations are released from a segment and then occupy another segment. Segmental relaxation requires the presence of free volume in the polymer matrix, a condition that can be attained if the polymer is in an amorphous state. Unfortunately, most HMWPs crystallize at ambient temperatures. Ions are transported with difficulty in a crystalline matrix since no chain relaxation occurs and, as a result, the conductivity of polymer electrolytes in this phase (at ambient temperature) is depressed. The transport of ions in this state is dominated by the jumping of cations to the nearest location, which depends on the blocking potential (activation energy). This is similar to the jump of charge carriers in

crystalline solids. The characteristic time for jumping is proportional to the exponential of the blocking potential. This results in a conductivity of the order of 10−8 S/cm, a value that is far below the desired value of about 10−4 S/cm [9]. When it enters the amorphous state, that is, at temperatures above the melting point, a high conductivity appears. For a commonly used polymer, that is, polyethylene oxide, the melting temperature is 65  C. This is, of course, impractical since the operating temperature for most electronic devices is room temperature. In addition, at temperatures above the melting point, the polymer becomes soft, causing the solidstate properties to degrade. Initiated by the work of Wright and Armand [10–12], several kinds of polymer electrolytes have been intensively investigated around the world. Table 2 displays examples of polymer electrolytes and their measured conductivities at 20  C [13]. Improvements in the electrical conductivity of polymer electrolytes at ambient temperature is therefore of critical importance for technological applications. Several approaches have been explored to realize this aim. Some frequently used methods will be explained briefly here.

2.1. Preparing Low Degree of Crystallinity Polymers By considering that the presence of amorphous state is strictly important for improving the conductivity, the main strategy is to enhance the amorphous state at low temperatures. The first approach is to prepare low degree of crystallinity polymer from initial. It includes cross-linking of two polymers [13, 14], synthesis of new polymer, crosslinking high molecular weight polymer through -irradiation [15, 16], addition of plasticizers in polymer electrolytes, addition of fillers, and bending of two polymers [17, 18]. Another strategy is to prepare an amorphous polymer so as to obtain a polymer that is composed of four to five monomeric units. For this system, the chains must be sufficiently long to effectively complex cations but too short to crystallize at low temperatures. Thus the matrix would still be in the amorphous state even at low temperatures. The polymer host serves as a solvent and does not include any organic liquids.

2.2. Addition of Side Chains An alternative way to decrease the crystallinity of polymer matrix is to introduce side chain to the polymer main chain. Theoretically, chain ends and branch can be thought of as impurities, which depress the melting point of the polymer. Simple mathematical formulation can be used to explain the melting point lowering by the presence of chain ends and branch. If Xi is the mole fraction of impurities (chain ends, side chains, and branch), then the melting point of polymer, Tm , decreases according to [19] 1 R 1 − o = ln1 − Xi  Tm Tm Hu

(1)

where Tmo = melting point of polymer containing only polymer chain with infinite chain length, R = gas constant, and Hu = enthalpy of fusion per mole of repeat unit. Chung and Sohn showed that the XRD intensity of polymer

Polymer Electrolyte Nanocomposites

733

Table 2. Examples of polymer electrolytes with their corresponding electrical conductivities at 20  C.

Polymer host Poly(ethylene oxide), PEO

— CH2CH2O — n

Poly(oxymethylene), POM

— CH2O — n

Poly(propylene oxide), PPO

— (CH3)CH2CH2O — n

Poly(oxymethyleneoligo-ethylene), POO Poly(dimethyl siloxane), DMS

— (CH2O)(CH2CH2O) — n — (CH3)2SiO — n — HC=CH(CH2)4O(CH2CH2O)n(CH2)4 — x — CH2CHO — n

Conductivity (S/cm) at 20  C

(PEO)8 :LiClO4

10−8

POM:LiClO4

10−8

(PPO)8 LiClO4

10−8

(POO)25 :LiCF3 SO3

3×10−5

DMS:LiClO4

10−4

UP:LiClO4 (EO:Li+ = 32  1) (PMEGE)8 :LiClO4

10−5 10−5

—

Unsaturated ethylene Oxide segmented, UP Poly[(2-methoxy)ethyl glycidyl ether], PMEGE

Example polymer electrolyte

Repeat unit

CH2(OCH2CH2)2OCH3 PMG22 :LiCF3 SO3

CH3

—

3×10−5

— CH2C — n — — — —

Poly[(methoxy) poly(ethylene glycol)] methacrylate, PMGn (EO:Ll+ = 181)

C

O

O — (CH2CH2O)xCH3

(PEO-PPO-PEO)-SC SC = siloxane crosslinked

(PEO-PPO-PEO)-SC: LiClO4 (4:1 molar)

—

—

CH3 CH3

1–3×10−5

—

—

O

O

—

—

PEO–(CH2)3–Si–O–Si–(CH2)3–PEO

—

—

PEO–(CH2)3–Si–O–Si–(CH2)3–PEO CH3 CH3 PEO grafted polysiloxane, PGPS

PGPS:LiClO4

—

CH3

10−4

—

—SiO— n CH2CH2PEO OCH2CH2OCH2CH2OCH3 —

Poly[bis-2-(2-methoxyethoxy) ethoxy]phosphazene,MEEP

— P=N — n —

(MEEP)4 :LiBF4 (MEEP)4 :LiN(CF3 SO2 )4 (MEEP)4 :LiC(CF3 SO2 )4

2×10−5 5×10−5 10−4

OCH2CH2OCH2CH2OCH3

decreases with the increase in the length of chain of combshaped polymer [20]. Despite depressing the melting point of polymer, the presence of side chain also promotes the solvating of a salt as reported by Ikeda and co-workers [21, 22]. The side chain has shorter relaxation time compared to the main chain. The coupling of the side chain with the ion carrier, therefore, results in an increase in the conductivity. Watanabe et al. designed comb-shaped polyether host with short polyether side chain [23]. However, the mechanical properties decreased even as the conductivity increased. High conductivity with good mechanical properties was obtained by designing a polymer of high molecular weight with trioxyethylene side chain as reported also by Ikeda et al. [24]. With 18 mol.% of side chain, the conductivity was measured to be 1.5 × 10−4 S/cm at 40  C and raised to 1.4 × 10−3 S/cm at 80  C. Composite of polymer with room-temperature molten slat is also an interesting approach to improve the conductivity of polymer electrolytes. Watanabe et al. reported the composite

consisting of chloroaluminate molten salt that possesses a conductivity of 2 × 10−3 S/cm at 303 K [25, 26]. However, the disadvantage of chloroaluminate is its hygroscopic properties such that it is impractical in application. The use of non-chloroaluminate molten salt, therefore, is required to avoid the hygroscopic problem. Tsuda et al. reported a conductivity of 2.3 × 10−2 S/cm in composite of polymer and room-temperature molten fluorohydrogenates [27].

2.3. Addition of Plasticizers Another approach to improve the conductivity is by addition of additional material into the host polymer. This approach appears to be the simplest since a pre-produced polymer can be used to make the polymer electrolytes. Previously, low molecular weight polymers were usually used to reduce the operation temperature of polymer electrolytes. The low molecular weight polymers which were added to the matrix of HMWP to reduce the crystallinity at low temperatures are frequently known as liquid plasticizers.

Polymer Electrolyte Nanocomposites

734

1 W W = 1 + 2 Tg Tg1 Tg2

(2)

10–3

10–4

10–5 0

25

50

220

75

100

wt.% tetraglyme

Figure 2. Effect of plasticizer weight fraction on the conductivity at 25  C of a PEO-co-PPO (3:1):LiClO4 using plasticizer tetraglyme (tetraethylene glycol dimethyl ether). Data points were extracted from [29], D. R. MacFarlene et al., Electrochim. Acta 40, 2131 (1995).

particularly when the fraction of plasticizers is too high. For example, the modulus of elasticity and elastic strength significantly decreases by addition of plasticizers. This is because the plasticizers are usually low molecular weight polymer having low mechanical strength. Therefore, addition of plasticizers decreases the mechanical strength of the host polymer. Figure 3 shows the effect of plasticizer troglyme content on the elastic modulus and tensile strength of PEO-co-PPO (3:1):LiClO4 [29]. The use of moderate or large quantities of plasticizer results in the production of

2.0

Elastic modulus

Modulus [Mpa]

where W1 and W2 denote the weight fractions of component 1 and component 2, respectively, and Tg1 and Tg2 are their corresponding glass transitions. This equation tells that the glass temperature of the composite locates between the glass temperature of the components. This relation is also applicable for copolymer where Tg1 and Tg2 denote the glass temperature of polymers forming the copolymer. Reduction in the glass temperature means the enhancement in the amorphous state at low temperature, and therefore improves the conductivity at low temperatures. Figure 2 shows the enhancement of conductivity by the addition of plasticizer tetraglyme on the system of PEO-co-PPO (3:1):LiClO4 , measured at 25  C [29]. The decrease in the glass transition results in the improvement in the fraction of amorphous state at room temperature, therefore improving the conductivity. However, an improvement in conductivity is adversely accompanied by a degradation in solid-state configuration and a loss of compatibility with the lithium electrode [9],

10–2

σ [S/cm]

Feullade and Perche demonstrated the idea of plasticizing the polymer with an aprotic solution containing alkali metal salt in which the organic solution of the alkali metal salt remained trapped within the matrix of solid polymer matrix [28]. Such mixing results in formation of gels with ionic conductivity close to the liquid electrolytes. Less evaporating solvents such as ethylene carbonate (EC), propylene carbonate (PC), dimethyl formamide (DMF), diethyl phthalate (DEP), diethyl carbonate (DEC), methyl ethyl carbonate (MEC), dimethyl carbonate (DMC), -butyrolactone (BL), glycol sulfide (GS), and alkyl phthalates have been commonly investigated as plasticizers for the gel electrolytes. Figure 1 shows the effect of plasticizer content tetraglyme (tetraethylene glycol dimethyl ether) on the glass temperature of a system of PEO-co-PPO (3:1):LiClO4 [29]. The decrease in the glass temperature can be simply explained using a Fox equation:

Tg[K]

1.0

200

Tensile Strength 180

0

25

50

75

100

wt.% tetraglyme

Figure 1. Effect of plasticizer weight fraction on the glass temperature of a PEO-co-PPO (3:1):LiClO4 using plasticizer tetraglyme (tetraethylene glycol dimethyl ether). Data points were derived from [29], D. R. MacFarlene et al., Electrochim. Acta 40, 2131 (1995).

0.0

0

20

40

60

wt.% tetraglyme

Figure 3. Effect of plasticizer weight fraction on the modulus of a PEOco-PPO (3:1):LiClO4 using plasticizer tetraglyme (tetraethylene glycol dimethyl ether). Data points were extracted from [29], D. R. MacFarlene et al., Electrochim. Acta 40, 2131 (1995).

Polymer Electrolyte Nanocomposites

735

gel electrolyte. The presence of some plasticizer may also give rise to problems caused by its reaction with the lithium anode. The poor mechanical stability was accounted to be mainly due to the solubility of the polymer matrix in the plasticizer [30]. Cross-linking of the polymer with ultraviolet radiation [31], thermally [32], by photopolymerization [33], or electron beam radiation polymerization [34] was found to reduce the solubility of polymer in the solvent and also helped to trap liquid electrolytes within the polymer matrix.

3. DEVELOPMENT OF POLYMER ELECTROLYTE NANOCOMPOSITES Currently, one popular approach to improve the conductivity involves dispersing ceramic fillers (solid plasticizers) in the polymer matrix, producing what is currently known as composite polymer electrolytes. This approach was first introduced by Weston and Steele [35]. Ceramic filler was used to reduce the glass transition temperature and crystallinity of the polymer and thus allow the amorphous polymer to maintain the liquid-like characteristic at the microscopic level. Ceramic fillers that are frequently used have particle sizes in the range of about several ten nanometers up to several micrometers. Fortunately, such filler materials are commercially available in various sizes at low prices. Figure 4 shows the effect of filler content on the conductivity of polymer electrolytes PEO:LiClO4 [9]. Table 3 displays examples of polymer electrolyte nanocomposites and their conductivities at around room temperature. The inorganic filler also acts as a support matrix for the polymer, so that even at high temperature, the composite remains solid. However, at the microscopic level, it maintains a liquid-like structure, which is important for sufficient conductivity. The filler particles, due to high surface area, prevent the recrystallization of polymer when annealed above the melting point. The acid-base interaction between the filler surface group and the oxygen of the PEO leads to a Lewis acid characteristic of the inorganic filler and favors –2

Log σ [S/cm]

–4 VTF

–6

Arrhenius –8

2.4

2.6

2.8

3.0

3.2

3.4

3.6

1000/T [1/K]

Figure 4. Arrhenius plot of electrical conductivities of: (solid) ceramicfree PEO:LiClO4 , (triangle) PEO:LiClO4 containing 10 wt.% Al2 O3 (5.8 nm), and (square) PEO:LiClO4 containing 10 wt.% TiO2 (13 nm). Data points were extracted from [9], F. Croce et al., Nature 394, 456 (1998).

Table 3. Examples of polymer electrolyte nanocomposites with their corresponding electrical conductivities at around room temperature.

Polymer electrolytes PEO:LiBF4

Fillers

nano-sized-Al2 O3 micro-sized-Al2 O3 PEO:LiCIO4 SiC EO-co-PO:LiCF3 SO3 Li13 Al03 Ti17 (PO4)3 Brached-poly(ethylene silica (12 nm size) imine):H3 PO4 PEO:LiClO4 -Al2 O3 PEO:LiClO4 AlCl3 PEO:LiClO4 NNPAAM PEO-PEG:LiI Al2 O3 PEO-PMMA:EC:LiI Al2 O3 PEG:LiCF3 O4 SiO2 PEG:LiCF3 O4 C12 H25 OSO3 Li coated-SiO2 EC:PC:PAN:LiAsF6 porous zeolite PEO:LiClO4 AlN, BaTiO3 , Bi2 O3 B4 C, BN, CaSiO3 CeO2 , Fe2 O3 , MoS2 , PbTiO3 , Si3 N4 , PEO:LiClO4 carbon black PEO:Li[(SO2 CF3 )2 N] -LiAlO2 PEO:PMMA:EC:LiI MgO PEO:AgSCN Al2 O3 PEO:AgSCN Fe2 O3 PEO:AgSCN SO2 Na2 SiO3 PEO:NaClO4 PEO:LiCF3 SO3 mineral clay PEO:NH4 I PbS PEO:NH4 I CdS PEO:NH4 I Pbx Cd1−x S

Conductivity at around rt (S/cm)

Ref.

∼10−4 ∼10−5 ∼10−7 ∼2×10−4 (40  C) ∼10−7

[36] [37] [38] [39]

∼10−5 ∼10−5 >∼10−5 ∼10−6 ∼10−8 ∼10−5 ∼5 × 10−5

[40] [40] [40] [41] [41] [42] [43]

∼10−3 ∼10−7 –10−6

[44]

∼4 × 10−6 ∼10−7 ∼88 × 10−4 ∼11 × 10−5 ∼3 × 10−6 ∼2 × 10−6 ∼10−3 ∼099 × 10−6 ∼096 × 10−6 ∼063–084 × 10−6

[46] [47] [48] [49] [50] [51] [52] [53] [54] [54] [54]

the formation of complexes with PEO. The filler then acts as cross-linking center for the PEO, reducing the tension of the polymer for self-organization and promoting stiffness. On the other hand, the acid-base interaction between the polar surface group of the filler and electrolyte ions probably favors the dissolution of the salt. Another potential application of polymer electrolyte nanocomposites is for making solar cells [55]. Dye-sensitized solar cells have attracted great scientific and technological interest as potential alternatives to classical photovoltaic devices. The cell operation mechanism involves absorption of visible light by the chemisorbed dye, followed by the electron injection from the excited synthesizer into the semiconductor conduction band. The selection of liquid electrolytes, usually containing organic solvent such as acetonitrile and propylene carbonate, assures the perfect regeneration of the dye by direct interaction of the dye oxidized state and I− /I− 3 redox couple and leads to impressively high solar-to-electrical conversion efficiencies (7–11%) [56, 57]. However, the stability and long-term operation of the cell are affected by solvent evaporation or leakage. Thus commercial exploitation of these devices needs the replacement of the liquid electrolyte by a solid charge transport medium, which not only offers hermetic sealing and stability but also reduces design restriction and endows the cell

Polymer Electrolyte Nanocomposites

736 with shape choices and flexibility. Katsaros et al. investigated solid-state dye-sensitized solar cells using composite polymer electrolytes using PEO and TiO2 in the presence of I− /I− 3 redox couple [55]. Initially, dye:Ru(dcbpy)2 (NCS)2 (dcbpy is 4,4’-dicarboxylic acid-2-2′ -bipyridine) was attached on the surface of TiO2 nanoparticles by immersion of the TiO2 thin-film electrode overnight in ethanolic solution of the complex, followed by drying. The functionalized TiO2 nanoparticles, I− /I− 3 , and PEO were put in acetonitrile, followed by heating and drying to evaporate the solvent. Maximum incident photon to current efficiencies as high as 40% were obtained at 520 nm, only two times lower that than obtained using liquid electrolytes [58]. The overall conversion efficiency was 0.96%. For all-solid-state devices, such efficiency can be considered to be sufficiently high [59].

4. PREPARATION METHODS Now we will briefly explain several methods of preparation of polymer electrolyte nanocomposites that are commonly used. Which method should be used, of course, depends on the materials and the form of sample to be formed. One method can only produce sample in the form of thick film, and another one can produce a sample in the form of film of submicrometer thickness.

4.1. Casting Method This method is frequently used due to its simplicity. It can produce polymer film from several micrometers up to several millimeters thickness. Generally, this method includes the following steps: (a) dispersion of ceramic fillers in a salt solution, (b) addition of a specified amount of polymer to the mixture, (c) mixing by means of stirrer or ultrasonic equipment to disperse the particles homogeneously in the polymer matrix, (d) casting the mixture on a substrate, (e) finally drying in vacuum or in an atmosphere of argon. All these steps are usually performed in a glove box filled with argon gas and excluding oxygen and water to levels below 20 parts per million (ppm), to avoid the possible occurrence of a “dangerous reaction” between water and lithium. The solvent must be water-free and should be common solvent for both the salt and the polymer. Since the melting point of several polymers is as high as 65  C, the solvent must also easily evaporate so that drying can be performed at temperatures of around 65  C. Organic solvents such as acetonitrile, cyclopentanone, and propylene carbonate, plus inorganic solvents such as thionyl chloride (SOCl2 ), are typically used. Sometimes, the insertion of salt is performed after casting the film. For example, Ardel et al. prepared PVDF 2801 (Kynar)-based polymer electrolyte composites according to the following steps [60]. First, Kynar was dissolved into cyclopentanone. Nanoparticles of silica were added and the mixture was mixed for 24 h at room temperature to get homogeneous slurry. After complete dissolution, the slurry was cast on the Teflon support and spread with the use of

doctor blade technique. To prevent surface irregularities, the film was then covered with a box pierced with holes that allowed a slow evaporation of the cyclopentanone. After complete evaporation of the cyclopentanone, the polymer membrane was soaked in a lithium ion solution for 48 h. Several fresh lithium solutions for each soaking can be used to ensure a complete impregnation of lithium ion into the membrane.

4.2. Spin Coating The spin-coating method is very similar to the casting method. Instead of casting the film on a substrate, in this method, the mixture is dropped on a substrate and placed in a spin coater that can be rotated at adjustable rotation speed. The film thickness can be controlled easily by adjusting the viscosity (concentration) of the mixture and the speed of rotation. However, this method is only available if the viscosity of the mixture is not too high. For a gel mixture, the spin coater rotation is not enough to spread the mixture droplet to form thin film.

4.3. Hot Press Hot press technique equipment is illustrated in Figure 5. The equipment consists of: (A) weighing cylinder, (B) heating chamber, (C) basement, and (T) temperature controller. Proper amounts of polymer, salt, and filler are mixed in a mortar for about several minutes. The powder mixture is then sandwiched between two sheets of Mylar or other materials, and positioned inside the heating chamber that is controlled at temperatures lightly above the melting point of the polymer. If PEO is used as polymer matrix, temperature of 80  C is suitable [61]. The sample is then pressed overnight with a pressure that can be controlled by weighing cylinder. After heating and pressing, the sample is then slowly cooled to room temperature. The sample is then separated from the Mylar sheet and placed in a glove box.

A

B

C

T

Sample

Figure 5. Illustration of hot press equipment: (A) weighing cylinder, (B) heater, (C) base, and (T) temperature controller.

Polymer Electrolyte Nanocomposites

737

4.4. In-situ Preparation In-situ preparation explained here is the preparation of nanoparticles in the polymer matrix. Mikrajuddin et al. produced polymer electrolytes of polyethylene glycol with lithium ion by in-situ production of ZnO nanoparticles in the polymer matrix [62, 63]. The preparation methods will be briefly described as follows. Zinc acetate dihydrate, (CH3 COO)2 Zn · 2H2 O 0.1 M in 100 mL ethanol 99.5, was heated with stirring in distillation equipment at temperature of 80  C to produce about 60 mL condensate and 40 mL of hygroscopic solution. Lithium hydroxide monohydrate, LiOH · H2 O, of various concentrations was suspended in 40 mL ethanol and stirred until all the granular material dissolved. Polyethylene glycol (PEG) (Mn = 2,000,000) was suspended into each LiOH solution and then stirred with heating at around 60  C until homogeneous gel-type mixtures were obtained. The mixture temperatures were then left to go down several minutes, after which 10 mL of hygroscopic CH3 COO2 Zn · 2H2 O solution was added into each mixture. The new mixtures were then homogeneously mixed and then dried in an oven that was kept at temperature of 40  C during three days. The schematic of sample preparations is displayed in Figure 6. There are many differences between the present method and the commonly used ones. In the present approach: (a) Nanoparticles are grown in-situ in polymer matrix. (b) The size of dispersed particles is controllable. (c) Ion carriers are inserted in-situ in the polymer matrix during the growing process. (d) Finally, since the grown nanoparticles are luminescent, we obtain a new class of polymer electrolytes, namely luminescent polymer electrolytes with nanoparticles as luminescence centers. Based on the TEM picture, we found that the size of ZnO nanoparticles was 5 nm.

Ethanol

ZnAc2•2H2O

LiOH•H2O

Distilled at 80°C

Mixed around 10 min

Ethanol

Condensate (60%) Mixed at 60°C unused

PEG

Cooled at 0°C

Left cooling

Hygroscopic solution (40%) Mixed several minutes

ZnO nanoparticles are formed in the polymer matrix Dried at 40°C, 3 days

Characterizations

Figure 6. Diagram of in-situ preparation of PEG:Li containing nanoparticles of ZnO. Adapted with permission from [62], Mikrajuddin et al., J. Electrochem. Soc. 149, H107 (2002). © 2002, Elsevier.

Chandra et al. produced polymer electrolytes PEO:NH4 I containing nanometer-sized semiconductor particles PbS, CdS, Pbx Cd1−x S [54]. Methanolic solution of PEO and NH4 I was first stirred roughly at 40  C for 8–10 h, which resulted in viscous solution of the ion conducting complexes of PEO/NH4 I. To this solution, a solution Pb(CH3 COO)2 , Cd(CH3 COO)2 , or Pd(CH3 COO)2 + Cd(CH3 COO)2 in a desired fraction was added. The stirring was continued until the viscosity was back to the value it was before adding the acetate compounds. Subsequently, H2 S was bubbled through it giving PbS, CdS, or Pbx Cd1−x S. The final viscous solution was poured in a petri dish for obtaining solution-cast film. Then the film was dried in vacuum.

5. IMPORTANT PARAMETERS To bring polymer electrolytes as well as polymer electrolyte composites, these materials should provide enough values of several properties as follows.

5.1. Electrical Conductivity Conductivity defines the density of current that can be transported in the material by applying a certain electric field. If electric field E is applied in the material, the current density will be proportional to the applied electric field, where the proportional constant is the conductivity, or, J = E

(3)

with J the current density (A/m2 ) and  (S/m or S/cm) the electrical conductivity. It is clear that high conductivity material will produce high current density upon applying a certain electric field. The value of conductivity is determined by the density of mobile ions (ion carriers) in the material (n), the scattering time of the ion (), the ion charge (q), as well as the mass of ion carrier (m), according to a relation =

nq 2  m

(4)

This equation gives the reason why most polymer electrolytes use lithium ions as ion carriers. The mass of lithium is the smallest among all metals, so it produces the highest conductivity. For industrial application, the conductivity of polymer electrolytes must be as high as 10−2 S/cm. However, until presently, this conductivity can only be achieved at high temperatures in which the polymer is present in the soft phase, or even liquid phase. The conductivity at room temperature of most reported polymers is still below 10−4 S/cm.

5.2. Transference Number Since the electrochemical process in lithium batteries involves the intercalation and de-intercalation of lithium cations throughout host compound lattice, solid polymer electrolytes with cation transference number (t + ) approaching unity are desirable for avoiding a concentration gradient during repeated charge-discharge cycles. The reported t + value for dried polymer electrolytes range from 0.06 to 0.2 [64]. For a gel polymer system, t + value of 0.4–0.5 has

Polymer Electrolyte Nanocomposites

738 been found for poly(bis-methoxy ethoxy)phosphazene [65], and 0.56 in a system of UV-cured gel polymer electrolytes based on polyethylene glycol diacrylate/polyvinylidene fluoride [66]. Transference number of a particle is defined as the ratio of the conductivity due to it and the total conductivity. Assume the total conductivity  is due to ionic, ion , and to electronic, e , then  = ion + e

(5)

The ionic and electronic transference numbers are then ti =

ion 

(6)

te =

e 

(7)

and

For pure ionic, ti = 1, and for pure electronic, te = 1. For polymer electrolyte composites, a general condition satisfied is 0 < ti  te < 1.

5.3. Crystallinity Crystallinity plays an important role in determining the conductivity of polymer electrolytes. At crystalline phase, the transport of ion carriers is very difficult so that the conductivity is very low. At amorphous phase, there is a segmental motion of polymer chain that also assists the displacement of ions. As a result, the transport of ions is relatively easy. Thus, high conductivity will result. One major route to improve the conductivity of polymer electrolytes is by increasing the fraction of amorphous states. Addition of ceramic fillers, addition of plasticizer, and production of branch polymer are efforts to improve the amorphous state in the polymer.

5.4. Mechanical Strength One objective of the use of polymer electrolyte is to make a battery or fuel cell with a strength comparable to that of liquid electrolytes. Therefore, it is expected that the improvement of conductivity is not accompanied by a decrease in the mechanical strength. It is why the addition of ceramic filler has received more attention, since the conductivity and the mechanical strength can be improved simultaneously. In contrast, the use of liquid plasticizer, although it can enhance the conductivity much higher than the addition of ceramic filler, involves such a degradation in the mechanical strength as to make this approach less interesting.

6. CHARGE TRANSPORT CHARACTERIZATIONS Electrical conductivity is the critical parameter for polymer electrolyte composites. One target of the present research in this field is to produce polymer electrolyte nanocomposites that exhibit a high electrical conductivity, especially at room temperature. Conductivity at around 10−2 –10−3 S/cm is required to bring this material into industry. The electrical conductivity relates to the value of current that can be produced by the battery. The potential produced by the battery depends on the reaction of the battery with the electrode. Even though the electrode reaction can produce high electrical potential, the use of low conductive electrolytes can produce only small amount of electric current. And since the power can be calculated simply by the relation Power = Voltage × Current, the use of low conductive materials will produce a low specific energy battery.

6.1. d.c. Conductivity Ideally, the d.c. conductivity should be measured in order to be sure that the values pertain to long-range ion movement instead of dielectric losses such as would be associated with limited or localized rattling of ions within cages. However, the difficulty in making a d.c. measurement is in finding an electrode material that is compatible with the electrolyte composites. For example, if stainless steel electrodes are attached to an electrolyte composite, as displayed in Figure 7a, and small voltage is applied across the electrodes, Li+ ions migrate preferentially toward the cathode, but pile up without being discharged at the stainless/electrolyte interface. A Li+ ion deficient layer forms at the electrolyte/stainless steel interface. The cell therefore behaves like a capacitor. There is an accumulation of ions at interface region of electrode and composite. A large instantaneous current Io presents when the cell is switched on, whose magnitude is related to the applied voltage and the resistance of the electrolytes but then falls exponentially with time, as illustrated in Figure 7b. The characteristic time of current decreasing is relatively fast so that it is difficult to make an accurate measurement. Therefore, the a.c. method is commonly used in the present to make measurement over a wide range of frequencies. The d.c. value can be extracted from the a.c. data. Many a.c. measurements are performed with blocking I

(a) +

(b)

Io

CPE

5.5. Storage Time Battery or fuel cell made from polymer electrolytes should have to operate several weeks or several months. Thus, the properties of polymer electrolytes should not change too much during this time. For example, the conductivity should not depend so much on the storage time. Ideally, the properties should be time independent. However, in reality, the properties tend to degrade with storage time.

+

time Figure 7. (a) Polymer electrolyte composites sandwiched between two blocking electrodes. (b) The decay of current when a constant d.c. voltage is applied between two electrodes.

Polymer Electrolyte Nanocomposites

739

Z  = Z ′   − iZ ′′  

(8)

where is the frequency, Z ′   is the real part of impedance, contributed by resistive part, Z ′′   is the imaginary√part of impedance, contributed by capacitive part, and i = −1, the imaginary number. As an illustration, Figure 8 shows examples of simple RC circuits and the corresponding plot of impedance (Nyquist plot). For a serial arrangement of a resistor and a capacitor, as displayed in Figure 8b left, the impedance can be written as i Z =R− C

(9)

or Z′ = R Z ′′ =

1 C

(10a) (10b)

It is clear that the real part of impedance is constant, independent of the frequency, while the imaginary part depends on the frequency. For very small frequency, the imaginary part is very large and this value decreases inversely with frequency. For frequency approaches to infinity, the imaginary part of impedance closes to zero and the impedance

(a)

Z′′ [Ω]

R

R • Z′ [Ω]

R

C Z′′ [Ω]

(b)

R Z′ [Ω] R Z′′ [Ω]

(c) ωmCR = 1 •

R • C

(d)

Z′ [Ω]

R C2

Z′′ [Ω]

electrode such that no discharge or reaction occurs at the electrode/electrolyte interface. Because the current will flow back and forth, no ions pile up on electrode surface, especially when using a high a.c. frequency. This is why the a.c. resistance (impedance) tends to decrease with increase in the frequency. The electrodes that are commonly used are platinum, stainless steel, gold, and indium tin oxide (ITO) glass. The complex impedance method is widely used to determine the resistance of the sample. The principle of the method is based on measurements of cell impedance, which are taken over a wide range of frequency and then analyzed in the complex impedance plane which is useful for determining the appropriate equivalent circuits for a system and for estimating the values of the circuit parameters. Impedance is nothing but the a.c. resistance of the cell. The value in general contains the real and the imaginary part. An electrochemical cell, in general, exhibits resistive, capacitive, as well as inductive properties. The resistive property contributes to the real part of the impedance, while the capacitive and the inductive properties contribute to the imaginary part of the impedance. Therefore, an electrochemical cell can be considered as a network of resistor, capacitor, as well as conductor. Which arrangement for which cell is usually determined after performing a measurement, by analyzing the form of impedance curve. A capacitor that presents as an open circuit in a d.c. network and an inductor that appears as a straight conductor wire in a d.c. circuit, both appear as imaginary resistors in the a.c. circuit. Until presently, the inductive properties of the electrochemical cell are ignored so that the polymer electrolyte composite is considered only as a network of resistor and capacitor. The complex impedance can be written in a general form as

ωmC1R = 1 •

R C1

•

Z′ [Ω]

Figure 8. Examples of simple RC circuits and the corresponding impedance (Nyquist) plots.

value at this very high frequency equals to resistance. Thus the Nyquist plot for this arrangement appears as a vertical straight line, starting from a lower frequency value at the upper part downwards when the frequency increases, as shown in Figure 8b right. The intersection of this line with horizontal axis (the real value of impedance) corresponds to the resistance. For a parallel arrangement of resistor R and capacitance C, as appears in Figure 8c left, the real and imaginary parts of the impedance are given by Z′ =

R 1 +  RC2

(11a)

and Z ′′ = R

RC 1 +  RC2

(11b)

and the corresponding Nyquist plot appears in Figure 8c right. The Nyquist plot appears as an arc. The intersection of this arc with the vertical axis at a low frequency (right arc) corresponds to the resistance. The frequency at the peak of the arc, m , satisfies the relation m RC

=1

(12)

From the intersection point at the low frequency region and the position of the arc peak, the resistance and the capacitance of the system can be determined.

Polymer Electrolyte Nanocomposites

740 More complex arrangements, have a more complex expression for the impedance. For example, a combination of serial and parallel circuit as appears in Figure 8d left has the impedance as −1
1 1 + i C1 (13) + Z= R i C2 with the corresponding Nyquist plot appearing in Figure 8d right. It contains a vertical line that intersects the horizontal axis at Z ′ = R, and an arc with the peak satisfies m RC1 = 1. Again, from these two values, one can determine R and C1 . The value of C2 is determined by measuring the vertical component of impedance at a certain frequency, say ∗ . If ′′ the vertical component of impedance at this point is Z ∗ , the value of C2 satisfies Z

′′ ∗

=

1 ∗C 2

(14)

Sometimes, the form of curve is not as simple as that described here. However, in principle, we can find some circuit arrangement such that the theoretical Nyquist plot is in agreement with the measured data. Some computer software is commercially available for extracting the equivalent circuit for measured data. As an example, the impedance measurement of a system of PEO:LiCF3 SO3 containing Li14 Al04 Ge16 (PO4 3 fillers is displayed in Figure 9a [67]. The corresponding a.c. circuit that can produce this impedance data appears in Figure 9b, with Rb = bulk resistance, Rpb = phase boundary resistance, Rint = interfacial resistance, Cpb = phase boundary capacity, Cint = interfacial capacity, Zd = diffusive impedance. The corresponding parameter values that can properly fit the measured data are

=

1 ℓ Re A

(15)

where Re = resistance of polymer electrolyte, ℓ = material thickness (electrode spacing), and A = material cross section. The common procedure for measuring the temperature dependence of conductivity is as follows. (a) Heat the sample at a required temperature. Sometimes, it needs a half hour or more to equilibrate the sample temperature. (b) Measure the impedance at all range of frequency. Sometimes, it can take from tens of mHz up to several MHz. The computerized measurement is usually performed since a great number of data should be collected for each setting temperature. (c) Change the setting temperature, and again collect the impedance data in all frequency regions. (d) Analyze the collected data and find the equivalent circuit. (e) Determine the resistance of the electrolytes based on the impedance plot and the equivalent circuit at each setting temperature. (f) Calculate the conductivity at each setting temperature.

6.2. a.c. Conductivity

0.6

Despite the d.c. conductivity, the a.c. conductivity sometimes gives important information such as the dielectric properties of the composites. The frequency dependence of a.c. conductivity in polymer electrolytes can be written as [38]

Z′′ [kΩ]

0.4

ac   = dc + A

0.2

0

Rb = 593 ", Rpb = 1637 ", Cpb = 31 nF, and Cint = 19 #F [67]. From the measured resistance of polymer electrolytes, the electrical conductivity can be calculated using a simple equation

0

0.5

1.0

1.5

2.0

2.5

3.0

Z′ [kΩ] Rpb

Rint

Rb

Zd

Cpb

(16)

where dc = d.c. conductivity, A and n are the material parameters, 0 < n < 1, and is an angular frequency. The curve might consist of three regions, a spike at low frequency, followed by a plateau at medium frequency, and another spike at high frequency. The high frequency part corresponds to bulk relaxation phenomena, while the plateau region is connected to d.c. part of conductivity. The lower spike is connected to electrode/electrolyte phenomena. Fitting the curve with Eq. (16), one can determine the parameters A and n, and from those parameters, the hopping frequency [68],

Cint

Figure 9. (Top) Impedance plot PEO:LiCF3 SO3 containing Li14 Al04 Ge16 (PO4 3 obtained from experiment. Data points were extracted from [67], C. J. Leo et al., Solid State Ionics 148, 159 (2002). (Bottom) The suggested RC circuit for data in (a). See text for the explanation of symbols.

n

p

=

  1/n dc

A

(17)

By fitting the experimental data of ac − , one can determine the dc and p at each temperature. Using this approach, Siekierski et al. [69] found in a system of

Polymer Electrolyte Nanocomposites

p

satisfy the

–7.2

(18)

where C is either dc or p , and Co is the corresponding prefactor. Furthermore, the temperature-dependent dielectric constant can also be obtained from the ac data. The real part of the dielectric constant, ,′ , can be expressed as  ′′ ,′ = ac ,o

  ,′ s 2 ds P 2 2 0 s −

(20)

2   s,′′ s ds P 2 2 0 s −

(21)

6.3. Diffusion Coefficient Electrical conductivity can also be determined by measuring the diffusion coefficient. From the temperature-dependent diffusion coefficient, the temperature dependence of electrical conductivity can be determined using Nerst–Einstein equation =

ne2 D kT

- 2 Ds t + A1 L2

–7.8

0.0

0.5

1.0

(23)

where 1 = measured cell potential, Ds = salt diffusion coefficient, L = electrolyte thickness, t = time, and A1 = a constant. It appears that Ds is proportional to the slope of curve ln 1 with respect to t. The dependence of salt diffusion constant on the salt concentration is displayed in Figure 10 [71] for system of PEO:NaCF3 SO3 at 83  C. The Ds decreases

1.5

2.0

2.5

Salt concentration [mol/L]

Figure 10. Effect of salt concentration on the diffusion coefficient for PEO:NaCF3 SO3 system at 83  C. Data points were extracted from [71], Y. Ma et al., J. Electrochem. Soc. 142, 1859 (1995).

as the salt concentration increases from about 8 ×10−8 cm s for dilute solution. Diffusion coefficient can also be determined from the Nyquist plot as discussed by Strauss et al. [72]. The medium frequency arc is attributed to the solid/electrolyte interface. At lower frequencies, the impedance is affected by concentration gradient (diffusion) and ionic aggregates. The diffusion impedance of symmetric electrolyte with no-blocking electrode, such as Li/CPE/Li, can be written as D=

RT L n2 F 2 Cb ZDC

(24)

where R = the gas constant, n = ratio of EO/cations, F = Faraday number, Cb = bulk concentration of cation, T = temperature, and L = electrolyte thickness. Lorimer also introduced another formula for calculating the diffusion constant, that is [73],

(22)

where n = charge carrier concentration e = electron charge, and D = diffusion coefficient. Salt diffusion coefficient can be obtained by galvanostatically polarizing a symmetric cell containing no-blocking electrode for a short period of time. For example, assume a cell containing Li-based polymer electrolytes and lithium electrodes at both sides. When the current is turned off, the induced concentration profile is allowed to relax. At long time after the current interrupt, the following equation is applicable [71]: ln 1 =

–7.6

–8.0

where P denotes the principal part of the integral [70]. On the other hand, if the imaginary part has been known, the real part can be determined using a relation ,′   =

–7.4

(19)

′′ where ac is the imaginary part of the a.c. conducttivity, and ,o is the permitivity of vacuum. The complex dielectric constant can be written as ,  = ,′   + i,′′  , and the imaginary part can be obtained from the real part using a Kramer–Kronig relation

,′′   = −

–7.0

Log Ds [cm2/s]

PEO3 :LiClO4 + -Al2 O3 , that both dc and Arrhenius expression   E C = Co exp − kT

741

D=

mL

2

254

(25)

where m = the frequency at the maxima of low frequency arc, and L = electrolyte thickness. The values predicted by Eq. (25), however, are around 6–10 times as large as that predicted by Eq. (14). The error can be contributed by the shift of m due to the formation of ion pairs [72].

6.4. Transference Number Transference number can be calculated by analyzing the arc impedance spectrum of symmetrical cell with no blocking electrode. The transference number can be calculated by comparing the width of the skew low frequency semicircle, Zd , with the value of the bulk resistance, that is [74], t+ =

1 1 + Zd /Rb

(26)

Transference number can also be determined by measurement of the electrochemical potential of the cell as illustrated in Figure 11 [75]. Suppose the polymer composite is

Polymer Electrolyte Nanocomposites

742 Electrode 1

Table 4. Transference number of several composites.

Electrode 2

Transference number Temperature Ref.

Composites

µ1

CPE

µ2

Figure 11. A simple experiment for determining the transference number to electrodes with differential chemical potentials.

sandwiched between two electrodes with different chemical potential #1 and #2 . The electrochemical potential across this cell is given by 1 1  #2 t d# = t # − #1  (27) E= z F #1 i z F i 2

where z = absolute value of the valence of the mobile ion in the electrolyte; and F = Faraday number. For pure ionic composite, ti = 1 so that Thus

Epure = #2 − #1  z −1 F −1

(28)

E = ti Epure

(29)

By measuring E and calculating Epure , we can obtain ti . Another method based on a combination of d.c. polarization and a.c. impedance has been introduced by Evans et al. This method involves measuring the resistance and current across a symmetrical Li/electrolyte/Li cell polarized by a d.c. voltage [76]. The t + is given by t+ =

IS V − Io Ro  Io V − IS RS 

(30)

where V = d.c. voltage applied to the cell, Ro = initial resistance of the passivating layer, RS = steady-state resistance of the passivating layer, Io = initial current, and IS = steadystate current. The d.c. polarization potential usually used is several tens of millivolts. This equation is applicable for ideal, dilute solutions. However, Doyle and Newman state that although this equation is not strictly applicable in concentrated electrolytes, the ratio of steady-state to initial current provides useful information on the contribution by organic additives to the ionic conductivity of polymer electrolytes [77]. The simplification of Eq. (30) was also used, that is, t + = ISS /IO . However, significant errors resulted from neglect of kinetic resistances at the electrode/electrolyte interface [78]. Transference numbers of some composites appear in Table 4.

7. SPECTROSCOPIC CHARACTERIZATIONS 7.1. NMR Spectroscopy A moving ion would substantially modify the interaction of electromagnetic waves with matter. Investigating this interaction gives a better understanding of ion dynamics on

PEO:LiCF3 SO3 + -LiAlO2 (4 #m) PEO:LiBF4 + -LiAlO2 (4 #m) PEO:LiClO4 + TiO2 (13 nm) PEO:LiClO4 + Al2 O3 (6 nm) (PEO)30 LiClO4 (PEO)8 LiClO4 (PEO)8 LiClO4 + SiO2

0.29 0.26 0.5–0.6 0.31–0.33 0.18–0.19 0.19–0.20 0.22–0.23

90 90 90 90 100 90 100

C C  C  C  C  C  C 



[79] [79] [79] [80] [80] [80] [80]

a microscopic scale. An example of method for studying the ion dynamics is nuclear magnetic resonance (NMR) spectroscopy. This method probes the spin of ion using an electromagnetic wave in radio frequency. In amorphous single-phase polymer electrolytes, there is usually found a straight relationship between polymer segmental motion and ionic mobility by observing a strong correlation between the onset of NMR line-narrowing and the glass transition [81]. NMR has contributed significantly to the understanding of the physical properties of the composite polymer electrolytes mainly because it offers the possibility to selectively study the ionic and polymer chain dynamics. For example, measurement of the temperature dependence of 7 Li lineshapes and spin-lattice relaxation allows the determination of the activation energy and the correlation time of the cation motion. Gang et al. described the 7 Li line-narrowing in the composite of PEO:LiBF4 + -LiAlO2 (10–30 wt%) in the temperature range of 270–270 K [82]. Dai et al. reported wide line and high resolution solid-state 7 Li NMR [83]. In material, each spin interacts with other spins, giving rise to spin-spin interaction or relaxation time T2 . Furthermore, a new thermal equilibrium distribution of the spin, which has to be mediated through lattice, is forced by the magnetic field. The characterization time required for the excess energy to be given to the lattice or for attainment of new thermal equilibrium is expressed in terms of spinlattice or thermal relaxation time T1 . Under simultaneous application of static and radio frequency magnetic field in perpendicular direction, (31a)

Hz = Ho

Hx = 2H1 cos t

(31b)

The interaction of this magnetic field with the nuclear spin results in the Bloch susceptibility [84] 9′ =

1 9 2 o

o T2

9 ′′ =

1 9 2 o

o T2

1 + T23  1 + T22 

T2  o −  2 2 2 o −  +  H1 T1 T2

1 − 2 +  2 H12 T1 T2 o

(32a) (32b)

where o = Ho , and  is the gyromagnetic ratio of the spin. For low RF field H1 ,  2 H12 T1 T2 ≪ 1, then Eqs. (32a) and (32b) give the familiar absorption curve with half-width  =

o

−

 1/T2

(33)

However, the exact lineshape and linewidth can be determined using Van Vleck method of moment. This method

Polymer Electrolyte Nanocomposites

743

allows the connection of the absorption line with the motional behavior of the nuclei. The second moment, M2 is given by   − o 2 f   d M2 = −

=

2

 1 − 3 cos