Carbon Nanotubes: New Research [1 ed.] 9781608767007, 9781606922361

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Copyright © 2009. Nova Science Publishers, Incorporated. All rights reserved.

Copyright © 2009. Nova Science Publishers, Incorporated. All rights reserved.

CARBON NANOTUBES: NEW RESEARCH

Copyright © 2009. Nova Science Publishers, Incorporated. All rights reserved.

No part of this digital document may be reproduced, stored in a retrieval system or transmitted in any form or by any means. The publisher has taken reasonable care in the preparation of this digital document, but makes no expressed or implied warranty of any kind and assumes no responsibility for any errors or omissions. No liability is assumed for incidental or consequential damages in connection with or arising out of information contained herein. This digital document is sold with the clear understanding that the publisher is not engaged in rendering legal, medical or any other professional services.

Copyright © 2009. Nova Science Publishers, Incorporated. All rights reserved.

CARBON NANOTUBES: NEW RESEARCH

AVERY P. OTTENHOUSE

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EDITOR

Nova Science Publishers, Inc. New York

Copyright © 2009 by Nova Science Publishers, Inc. All rights reserved. No part of this book may be reproduced, stored in a retrieval system or transmitted in any form or by any means: electronic, electrostatic, magnetic, tape, mechanical photocopying, recording or otherwise without the written permission of the Publisher. For permission to use material from this book please contact us: Telephone 631-231-7269; Fax 631-231-8175 Web Site: http://www.novapublishers.com NOTICE TO THE READER The Publisher has taken reasonable care in the preparation of this book, but makes no expressed or implied warranty of any kind and assumes no responsibility for any errors or omissions. No liability is assumed for incidental or consequential damages in connection with or arising out of information contained in this book. The Publisher shall not be liable for any special, consequential, or exemplary damages resulting, in whole or in part, from the readers’ use of, or reliance upon, this material. Any parts of this book based on government reports are so indicated and copyright is claimed for those parts to the extent applicable to compilations of such works. Independent verification should be sought for any data, advice or recommendations contained in this book. In addition, no responsibility is assumed by the publisher for any injury and/or damage to persons or property arising from any methods, products, instructions, ideas or otherwise contained in this publication.

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This publication is designed to provide accurate and authoritative information with regard to the subject matter covered herein. It is sold with the clear understanding that the Publisher is not engaged in rendering legal or any other professional services. If legal or any other expert assistance is required, the services of a competent person should be sought. FROM A DECLARATION OF PARTICIPANTS JOINTLY ADOPTED BY A COMMITTEE OF THE AMERICAN BAR ASSOCIATION AND A COMMITTEE OF PUBLISHERS. LIBRARY OF CONGRESS CATALOGING-IN-PUBLICATION DATA Ottenhouse, Avery P. Carbon nanotubes : new research / Avery P. Ottenhouse. p. cm. Includes bibliographical references and index. ISBN 978-1-60876-700-7 (E-Book) 1. Carbon. 2. Nanostructured materials. 3. Nanotubes. I. Title. TA455.C3O88 2009 620.1'93--dc22 2008037516

Published by Nova Science Publishers, Inc.    New York

CONTENTS

Preface Short Communications: On the Drude Model to Explain Quantum Transport in Carbon Nanotubes M. A. Grado-Caffaro and M. Grado-Caffaro

1

Short Communications: Asymptotic Analysis of Coagulation–Fragmentation Equations Francisco Torrens, and Gloria Castellano

7

Chapter 1

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Gas-Carbon Nanotubes Interactions: A Review of ultra-high vacuum Surface Science Studies on CNTs U. Burghaus

Chapter 2

On Residual Metallic Catalyst Impurities in Carbon Nanotubes Martin Pumera

Chapter 3

Insight of the Kinetics Carbon Nanotubes Growth and Funcionalization with Freestanding Silicon Nanocrystals Vladimir Švrček

Chapter 4

Carbon Nanotube Array Thermal Interfaces Baratunde A. Cola, Timothy S. Fisher, and Xianfan Xu

Chapter 5

Computational Analysis of the Interfacial Bonding Characteristics of Carbon Nanotube/Polymer Composites Qingzhong Xue and Qingbin Zheng

Chapter 6

Mechanical Properties of Carbon Nanotubes Q. Wang and K. M. Liew

Chapter 7

Electrical Properties of a Carbon Nanotube/Polymer Nanocomposite and its Application as Highly Sensitive Strain Sensors Ning Hu, Zen Masuda and Hisao Fukunaga

17 75

81 101

119 157

175

vi Chapter 8

Chapter 9

Chapter 10

Chapter 11

Chapter 12

Chapter 13

The Ferrochemistry of Carbon Nanotubes, Diamond, Nucleic Acids and Proteins: The Magnetic Synergism of Macromolecules And Life’s Chemical Patterns Reginald B. Little Biocompatibility Differences between Dispersed and VerticallyAligned Carbon Nanotubes: An In Vitro Assays Review A.O. Lobo, E.F. Antunes; M.B.S. Palma; C. Pacheco-Soares, M.A.F. Corat, V.J. Trava-Airoldi and E.J. Corat Engineered Electrical and Mechanical Properties of Carbon Nanotube Added Si3N4 Nanocomposites Csaba Balázsi, Orsolya Koszor, Balázs Fényi and Katalin Balázsi Fluorinated Carbon Nanotubes: State of the Art, Trends and Advanced Concepts Daniel Claves Carbon Nanotubes: Applications of this Nanostructured Material for the Development of Analytical Methods César Ricardo Teixeira Tarley, Gustavo Silveira, Bruno Eduardo Lobo Baêta, Vivian Silva Santos, Lucas Rossi Sartori, Alexandre Kisner, Arnaldo César Pereira and Lauro Tatsuo Kubota Physical Characteristics of Carbon Nanotubes: Experiments and Analysis Te-Hua Fang, Ruo-Ping Chang and Win-Jin Chang

223

281

317

341

371

407

Chapter 14

Dispersion and Field Emission Properties of Carbon Nanotubes Hyun-Tae Kim and Dang-Hyok Yoon

433

Chapter 15

Application of C-Nanotubes in Ceramics Guenter Motz and Sylvia Kokott-Wenderoth

463

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Contents

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PREFACE This new and important book presents significant research on carbon nanotubes (CNTs) which are allotropes of carbon with a nanostructure that can have a length-to-diameter ratio greater than 1,000,000. These cylindrical carbon molecules have novel properties that make them potentially useful in many applications in nanotechnology, electronics, optics and other fields of materials science, as well as extensive use in arcology and other architectural fields. They exhibit extraordinary strength and unique electrical properties, and are efficient conductors of heat. Inorganic nanotubes have also been synthesized. Nanotubes are members of the fullerene structural family, which also includes the spherical buckyballs. The cylindrical nanotube usually has at least one end capped with a hemisphere of the buckyball structure. Their name is derived from their size, since the diameter of a nanotube is in the order of a few nanometers (approximately 1/50,000th of the width of a human hair), while they can be up to several millimeters in length (as of 2008). Nanotubes are categorized as single-walled nanotubes (SWNTs) and multi-walled nanotubes (MWNTs). Short Communications - The Drude model relative to carrier drift mobility and conductivity is discussed in relation to its applicability to explain quantum transport through both single-walled and multiwalled carbon nanotubes. The authors show that the Drude model, suitable to describe electrical conductivity in solids as, for instance, semiconductors, is certainly adequate to discuss key aspects of quantum transport in multiwalled carbon nanotubes. In this respect, conductance quantization is treated in relation to the model in question by calculating carrier mobility and conductivity under ballistic regime. As a consequence, an expression for the quantized conductance of a multiwalled carbon nanotube is derived. The existence of single-wall carbon nanotubes (SWNTs) in organic solvents in the form of clusters is discussed. A theory is developed based on a bundlet model for clusters describing the distribution function of clusters by size. The phenomena have a unified explanation in the bundlet model of a cluster, in accordance with which the free energy of an SWNT involved in a cluster is combined from two components: a volume one proportional to the number of molecules n in a cluster, and a surface one proportional to n1/2. A comparative study of the droplet and bundlet models is carried out. The model yields an activation barrier and predicts that pores with a radius below a certain critical value are unstable, while those above this radius will grow indefinitely until the membrane ruptures. During the latter stage of the fusion process, the dynamics were governed by the displacement of the volume of liquid around the fusion site. Based on a simple kinetic model, micellization of rod-like

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aggregates occurs in three separated stages. A convenient relation is obtained for at transient stage; at equilibrium another relation determines binding energy. A relation with surface dilatational viscosity is obtained. The model predicts that pores with a radius below a certain critical value are unstable. Chapter 1 - While numerous studies concerning the synthesis and materials science applications of carbon nanotubes have been conducted, the data obtained at well-defined ultra-high vacuum conditions by means of surface science techniques is still scarce. The author presents specific examples of recent ultra-high vacuum surface science projects from the authors laboratory conducted on clean carbon nanotubes with an emphasis on applications in heterogeneous catalysis. In addition the related surface science literature is summarized and future directions are outlined. In particular, kinetics and molecular beam scattering (dynamics) results for alkanes, alcohols, and thiophene are described. Alkanes perfectly allow for characterization of different adsorption sites on carbon nanotube bundles, while alcohols are related to fuel cell applications, i.e., to renewable energy production and a green (environmentally friendly) chemistry approach. Thiophene is the probe molecule of choice to characterize desulfurization catalysts which are important for the petroleum industry. Kinetics experiments quantify the binding strength of these probe molecules on carbon nanotubes and provide evidence for capture effects, which are one of the main advantages of nanotubes in catalysis. Molecular beam scattering has characterized gas-surface energy transfer processes and, again capture effects, i.e., the adsorption of the probe molecules in carbon nanotubes. In addition, a brief review of the related literature is included. The literature survey (conducted early in 2008) focuses on experimental research conducted at high vacuum (< 106 torr) where common surface science techniques have been applied. A number of theoretical studies addressing a structure activity relationship (SAR) are included too. However, electrochemistry or pure catalysis studies (conducted at high pressure and high temperatures) are mostly omitted. Finally, an outline of future directions in surface science on CNTs is kindly proposed. Chapter 2 - The aim of this chapter is to discuss the problematic of residual metallic catalyst impurities in carbon nanotubes. Chapter 3 - In this chapter the growth kinetics of most common carbon nanotubes (CNTs) synthesis at industrial scale by catalyst assisted chemical vapor deposition (CVD) is discussed. It is shown that the monitoring of CNTs growth at initial stages by using a Tapered Element Oscillating Microbalance (TEOM) brings new insights into synthesis and controllability of the CNTs properties. The high sensitivity of the TEOM technique allows precisely determinates the crucial synthesis parameters. We argue that precise TEOM control of the reaction temperature and the partial pressure allows evaluate the order of the reaction kinetics and absolute reaction rate. Furthermore, CNTs solve some challenges linked with connection and manipulation of silicon nanocrystals (Si-ncs) at nanoscale level. Particularly, direct growth of CNTs on Si-ncs in the TEOM is performed in order to connect single Si-nc. Compared to porous catalyst supports substantial differences in CNTs growth kinetics are observed when the synthesis is performed on flat Si-ncs surface. A model taking into accounts an associative and competitive adsorption of ethane is used to interpret obtained results. The diameter of the CNTs depends on the size of the Si-ncs, which remains connected on the tip of the CNTs. The wired Si-ncs keep room temperature photoluminescence properties. It is shown that the CNT cavity, in additionally, can serve as nano-reservoir for

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freestanding Si-ncs. Colloidal dispersion of freestanding Si-ncs allows entering into CNT cavity by induced capillary force. Alternatively, the shock waves generated during Si-ncs formation in transparent polymer by nanosecond laser processing assure the filling as well. The authors believe that the present findings might open new opportunities and situations in a development of new class of nanodevices for the environmental friendly applications. Chapter 4 - Because of their excellent thermal and mechanical properties, the efficacy of carbon nanotubes (CNTs) as a thermal interface material has recently been studied. Vertically oriented arrays of CNTs directly synthesized on substrates form dry and separable interfaces that have been demonstrated to achieve thermal resistances that compare favorably to stateof-the-art thermal interface materials. A transient photoacoustic (PA) technique is used to measure the total thermal resistances of different interface structures that comprise CNT arrays directly synthesized on various substrates, and on one and both sides of the interface and on thin metal foils inserted into the interface. The PA technique is also employed to measure the CNT-substrate (growth substrate and opposing substrate) resistances and the intrinsic resistance of the CNT arrays that sum to produce the total thermal resistance of the CNT array interface structures. The measurements reveal that CNT-substrate resistances are the largest local resistances in CNT array interfaces, and that the resistances at the CNT free ends are significantly larger than the resistances at the CNT-growth substrate interfaces. Chapter 5 - Since the discovery of carbon nanotubes (CNTs) by Iijima in 1991, CNTs have attracted great research interest due to their unique properties such as high electrical and thermal conductivity, excellent stiffness against bending, and high tensile strength. Using carbon nanotubes (CNTs) as nanofibers to enhance the mechanical, electrical, thermal, and optical properties of composite materials has been pursued extensively. Molecular mechanics (MM) and molecular dynamics (MD) simulations have become increasingly popular in the theoretical investigations of reinforcement mechanisms in CNT-polymer composite systems. This paper is dedicated to conduct theoretical study on the interfacial characteristics of CNT reinforced polymer composites. Firstly, force-field-based MD simulations are performed to study the interaction between polymers and SWNTs. The “wrapping” of nanotubes by polymer chains was computed. The influence of temperature, nanotube radius and chirality on polymer adhesion was investigated. Furthermore, the “filling” of nanotubes by polymer chains was examined. The results show that the interaction between the SWNT and the polymer is strongly influenced by the specific monomer structure such as aromatic rings, which affect polymers’ affinities for SWNTs significantly. The attractive interaction between the simulated polymers and the SWNTs monotonically increases when the SWNT radius is increased. The temperature influence is neglectable for PE and PP but strong for PS and PANI. Secondly, the authors simulations indicate that the adhesion energy between the SWNT and the polymer strongly depends on the chirality. For SWNTs with similar molecular weights, diameters and lengths, the armchair nanotube may be the best nanotube type for reinforcement. The simulations of filling reveal that molecules of PE, PP and PS can fill into a (10, 10) SWNT cavity due to the attractive van der Waals interactions. The possible extension of polymers into SWNT cavities can be used to structurally bridge the SWNTs and polymers to significantly improve the load transfer between them when SWNTs are used to produce nanocomposites. Finally, the influence of chemical functionalization on the interfacial bonding characteristics of SWNTs reinforced polymer composites was investigated using MM and

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MD simulations. The simulations show that functionalization of nanotubes at low densities of functionalized carbon atoms drastically increase their interfacial bonding and shear stress between the nanotubes and the polymer matrix. This indicates that increasing the load transfer between SWNTs and a polymer matrix in a composite via chemisorption may be an effective way and chemical attachment of nanotubes during processing may be in part responsible for the enhanced stress transfer observed in some systems of the nanotube-polymer composites. Furthermore, this suggests the possibility to use functionalized nanotubes to effectively reinforce other kinds of polymer-based materials as well. The simulation results would be of important in the production of CNTs reinforced polymer composites. Chapter 6 - Molecular mechanics calculations for the in-place stiffness, shear modulus, and bending rigidity of both single- and double-walled carbon nanotubes are reported by calculating the strain energy of carbon nanotubes and graphite sheets subject to various types of loading. Elastic rod and plate theories are employed to link the material properties of carbon nanotubes directly to the molecular mechanics calculations. The length dependence of these material properties is reported and investigated via nonlocal elasticity theory. In addition, the van der Waals effect on the differences between the material properties of double- and single-walled carbon nanotubes is also examined. The diminishment of such differences in large sizes of carbon nanotubes is revealed from the simulations. Molecular mechanics calculations for the in-place stiffness, shear modulus, and bending rigidity of both single- and double-walled carbon nanotubes are reported by calculating the strain energy of carbon nanotubes and graphite sheets subject to various types of loading. Elastic rod and plate theories are employed to link the material properties of carbon nanotubes directly to the molecular mechanics calculations. The length dependence of these material properties is reported and investigated via nonlocal elasticity theory. In addition, the van der Waals effect on the differences between the material properties of double- and single-walled carbon nanotubes is also examined. The diminishment of such differences in large sizes of carbon nanotubes is revealed from the simulations. Chapter 7 - Carbon nanotubes (CNTs) of high aspect ratio possess excellent electrical conductivity. Therefore, with a little amount of CNTs, which are dispersed into insulating polymers, it is possible to manufacture CNT/polymer nanocomposites with very high electrical conductivity. This kind of conductive nanocomposites can be employed in various applications, such as highly sensitive strain sensors and electromagnetic interference materials. In this Chapter, the authors will mainly describe the research outcomes about the electrical properties of CNT/polymer nanocomposites from experimental and theoretical studies. First, in this work, based on the statistical percolation theory, the authors proposed a three dimensional (3D) numerical model to predict the electrical properties of a nanocomposite made from an insulating polymer with filled CNTs. In this model, with the assumption of randomly distributed CNTs in the polymer, the percolation threshold was estimated at the volume fraction of CNTs when the first complete electrically- conductive path connected by some CNTs is formed. Furthermore, to predict the electrical conductivity of the nanocomposite after the percolation threshold, a 3D resistor network model was constructed, in which Kirchhoff’s current law was adopted to set up the system algebraic equations at different nodes in the network formed by CNTs. The macroscopic current of the nanocomposite under the applied external voltage was calculated by solving these equations,

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and then Ohm’s law was employed to predict the macroscopic electrical conductivity of the nanocomposite. The influences of curved shapes of CNTs, aggregates of CNTs and tunnel effect among CNTs on the percolation threshold and the electrical conductivity have been investigated in detail. To verify the above numerical model, a lot of experiments have also been performed by the authors. The effects of various factors in the in situ polymerization fabrication process on the electrical performances of the nanocomposite were explored. The present experimental results plus some previous experimental results by other researchers were found to agree with the present numerical results very well. Moreover, a simple yet reliable empirical percolation theory has been obtained based on the detailed numerical investigations. For the application of this nanocomposite as highly sensitive strain sensors, by considering the tunnel effect among CNTs and the rigid-body movement of CNTs in the polymer caused by the prescribed strain, the above numerical model was further extended for modeling the electrical resistance change of the nanocomposite due to the strain. The relation between the applied strain and the electrical resistance change was estimated numerically and measured experimentally. Both numerical and experimental results, which are in very good agreement, demonstrate that the CNT/polymer sensors possess much higher sensitivity or gauge ratio compared with the traditional strain gauge. The tunnel effect was found to be a key factor to control the performance of this new-type strain sensor. Chapter 8 - Magnetic and electric phenomena have been known in matter for over 2 millennia. The existence of magnetism and electricity in both living and nonliving materials and the intrinsic relationship between electricity and magnetism suggest intrinsic magnetic effects on the chemistry and chemical dynamics of both inorganic and organic substances. Such a magnetic role in matter is supported by the different types of bonds: ionic, covalent, metallic and hydrogen bonding. The internal charges and charge motions for atomic structure further support the magnetic role in the structure and dynamics of matter. In this perspective, an electromagnetic interpretation by cooperative self-interactions is given for the quantum and wave descriptions of internal charges of the atoms of matter. By considering such magnetic effects, the nature of valence, covalent bond, and catalysis is explained. The photophysics of organic molecules and transition metal complexes are given more meaning by this magnetic perspective. Such a magnetic consideration allows the chemical reaction dynamics to be explained in a more general manner for organic, organometallic, nonmetal, ionic, transition metal and complexes substances thereof. New chemistry by the nonpreservation of orbital symmetry becomes meaningful. The ferrochemistry (the Little Effect) is discovered wherein the bond rearrangements and bonds of many atoms between reacting substances are transformed by many polarized spins during the interactions. Such ferrochemistry was discovered while determining the mechanism of carbon nanotube formation. Ferrochemistry has resolved the two hundred year old diamond synthesis problem. Unconventional nuclear phenomena have been understood by ferrochemical effects. In this perspective, ferrochemistry is further developed among the branches of chemistry. By correlated and exchanged fermions during macromolecular reactions, a quantum/wave consideration of ferrochemical reactions in plasma, liquids and solids is presented. Such a quantum/wave nature of ferrochemical dynamics determines the basis of resonance and tautomerism. On the basis of the uniqueness of compositions of biomacromolecules and their aqueous environments, the quantum/wave natures of many, varied, nano-arrayed, ferrochemically reacting functional groups of proteins and nucleic acids and complexes

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thereof are considered to determine emerging structures, dynamics and properties of proteins and nucleic acids. The magnetism, magnetic order and ferrochemistry arise within and between the biomacromolecules due to the many coupled varied weak acid - weak base reactions by p+ transfers among the many functional groups and the continual shift and magnetic p+ currents for their dis-equilibriums by the quantum/wave internal motions and interactions. Chapter 9 - An overview about carbon nanotube (CNT) production and quality parameters will be presented, as well a review of current literature about “in vitro” assays commonly used to evaluate the biocompatibility of CNT. The limits of colorimetric assays for CNTs evaluation will be discussed, using comparisons between dispersed CNT and CNT arrays. The influence of nanotopography and wettability of CNT scaffolds for cell adhesion will be shown. Studies carried out in the authors laboratories with vertically-aligned carbon nanotubes (VACNT) will also be presented. The authors have shown the interaction among CNT (VACNT) and four cell lines: mouse fibroblasts (L-929), mouse embryo fibroblast (C57/BL6) with or without green fluorescent protein (GFP) and human osteoblast (SaOS-2). The biocompatibility tests were performed with in vitro tests on raw-VACNT and after superficial modification by O2 plasma, which changes its hydrophobic character. The nontoxicity, cell viability, proliferation and cell adhesion were evaluated by: (i) 2-(4,5-dimethyl2-thioazoly)-3,5-diphenyl-2H-tetrazolium bromide (MTT) assay; (ii) Lactate dehydrogenase (LDH) assay; (iii) neutral red (NR) assay; (iv) Scanning electron microscopy (SEM); and fluorescence microscopy. The influence of catalyst type, VACNT density and superficial modification were evaluated by morphological, structural and superficial techniques: SEM, Transmission electron microscopy (TEM), Raman spectroscopy, contact angle (CA) and XRay Photoelectron Spectroscopy (XPS). High cell viability, exceptional cell adhesion and preference were achieved. Chapter 10 - This research explores the use of a variety of nanoparticles to impart conductivity to ceramic matrices. The authors have chosen some highly promising families of carbon materials: multiwall carbon nanotubes (MWCNTs), singlewall carbon nanotubes (SWCNTs), carbon black nanograins and graphite micrograins for use as fillers. In this book chapter, the authors report the results about two types of carbon nanotubes. The MWCNTs and SWCNTs were dispersed in silicon nitride matrix in different percentages high as 15wt%. A high efficient attritor mill has also been applied for proper dispersion of MWCNTs in the matrix. In order to get the full use of the benefits provided by carbon nanotubes (CNT) it is crucial to retain CNT un-attacked in the composites and to optimize the interfacial bonding between CNT and matrix. By conventional sintering techniques, which are characterized by the requirement of extended holding at very high temperatures, the destruction of CNT has been reported. In the present work the development of sintering processes have been performed to consolidate and tailor the microstructure of MWCNTs reinforced silicon nitride-based ceramic composites. The silicon nitride nanocomposites systems retained the mechanical robustness of the original systems. Bending strength high as 700 MPa was maintained and an electrical conductivity of 10 S/m was achieved in the case of 3 wt% MWCNT addition. Electrically conductive silicon nitride ceramics have also been realized by carbon black (in order of 1000 S/m) and graphite additions in comparison. Examples of these systems, methods of fabrications, electrical percolation, mechanical properties and potential uses will be discussed.

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This research explores the use of a variety of nanoparticles to impart conductivity to ceramic matrices. The authors have chosen some highly promising families of carbon materials: multiwall carbon nanotubes (MWCNTs), singlewall carbon nanotubes (SWCNTs), carbon black nanograins and graphite micrograins for use as fillers. In this book chapter, the authors report the results about two types of carbon nanotubes. The MWCNTs and SWCNTs were dispersed in silicon nitride matrix in different percentages high as 1-5wt%. A high efficient attritor mill has also been applied for proper dispersion of MWCNTs in the matrix. In order to get the full use of the benefits provided by carbon nanotubes (CNT) it is crucial to retain CNT un-attacked in the composites and to optimize the interfacial bonding between CNT and matrix. By conventional sintering techniques, which are characterized by the requirement of extended holding at very high temperatures, the destruction of CNT has been reported. In the present work the development of sintering processes have been performed to consolidate and tailor the microstructure of MWCNTs reinforced silicon nitride-based ceramic composites. The silicon nitride nanocomposites systems retained the mechanical robustness of the original systems. Bending strength high as 700 MPa was maintained and an electrical conductivity of 10 S/m was achieved in the case of 3 wt% MWCNT addition. Electrically conductive silicon nitride ceramics have also been realized by carbon black (in order of 1000 S/m) and graphite additions in comparison. Examples of these systems, methods of fabrications, electrical percolation, mechanical properties and potential uses will be discussed. Chapter 11 - The present contribution details, in an as exhaustive as possible way, the fundamental knowledge acquired on fluorinated carbon nanotubes (CNT), also termed fluorotubes. Since the discrete pioneering articles published in the field a bit more than 10 years ago, around 70 additional references have now appeared which bear witness to the dynamism of this emergent part of the chemistry of nanotubes. As a matter of fact, fluorination stands as the starting point for a great part of the modifications performed on CNT, rendering fluorotubes fundamental intermediates for the integration of CNT in the nanotechnology processes. Many synthesis routes use fluorotubes as precursors in view of the subsequent chemical derivatization of CNT, for instance. In parallel, several attempts of practical developments based on fluorotubes have also lately appeared throughout the literature, covering the tribology, nanocomposites, or electrochemistry sectors, which outline the potential interest of such fluorinated nanostructures. The first part of this chapter compiles the main knowledge reported to date on the subject throughout a still reasonable but increasingly abundant body of literature. The physicochemical properties and special characteristics of the C-F chemical bond in fluorotubes are critically analyzed in a second part, and the last section is devoted to some recent tentative applications and future concepts relating to the fluorination of carbon nanotubes. The present review is essentially depicted from the chemistry of materials standpoint. Some of the concepts illustrated throughout the text are enriched by a few works of unpublished data from the authors group. Chapter 12 - The use of carbon nanotubes as an analytical tool in filters and membranes, as solid sorbent material, in electrochemical systems involving the building of sensors, biosensors or carbon nanotube paste electrodes for stripping techniques and in separation methods including chromatography and electrophoresis can be found in the literature. In this chapter the authors will present a brief review of the application of CNTs in the analytical sciences. Finally, the authors will demonstrate new analytical data (a case study) obtained in the authors research groups involving the development of a solid phase extraction system for

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cobalt determination using CNT as well as a new potentiommetry stripping method for antimony determination using CNT as the electrode. Chapter 13 - This chapter studies the physical characteristics of carbon nanotubes (CNTs) films and Co-filled CNTs by using an electron cyclotron resonance chemical vapor deposition (ECR-CVD) method. The results show that the optimum relative intensity ratio of the D band to G band (i.e., I D / I G ) is 2 for the cases considered in this study. The effects of different plasma powers of 200W, 300W, 400W and 500W, on the morphology, structure and electrical properties of the CNTs film, are also studied. The surface density of the vertical nanotubes decreases when the plasma power is higher than 200W. The Co-filled CNTs grown at 300W and 400W have a current discharge at the applied voltages of 30 V and 40 V, respectively. In addition, this chapter also develops a model that analyzes the resonant frequency of the chiral single-walled carbon nanotubes (SWCNTs) subjected to a thermal vibration by using Timoshenko beam model, including the effect of rotary inertia and shear deformation. The frequency obtained by Timoshenko beam model is lower than that calculated by Euler beam model. As the nanotube aspect ratio of length to diameter decreases, the discrepancy is more obvious. As the effect of thermal vibration increases, the frequency for chiral SWCNTs decreases. Furthermore, the oxidation characteristics of TiN thin films by atomic force microscopy (AFM) electrochemical nanolithography with carbon nanotube tip are investigated. Chapter 14 - Since carbon nanotubes (CNTs) show strong tendency to form aggregates due to their high van der Waals interactions, their dispersion is a prerequisite for practical applications. In order to enhance the dispersion of multi-walled carbon nanotubes (MWNTs) in texanol, optimum type of dispersant and its concentration for six commercial dispersants were evaluated based on the rheological results. Moreover, the cutting and dispersion efficiencies of MWNTs were compared using conventional ball milling and high energy milling, whereby the latter was found to be more effective. High energy milling for two hours produced a large portion of MWNT agglomerates smaller than 150 nm, showing a drastic increase in slurry viscosity due to the dispersion into individual CNTs. On the other hand, 120-hour ball milling was required to achieve the agglomerate size of 300 nm with less viscosity increase upon milling. Decrease in the degree of MWNT crystallinity was observed by both milling, even though 2-hour high energy milling showed slightly less damage than 120-hour ball milling based on XRD and Raman spectroscopy results. The field emission properties of MWNTs were examined using a screen-printed thick film prepared by 3-roll milling of MWNTs and UV-sensitive binder solution, with a diode-type configuration in a vacuum for field emission display (FED) application. The effects of MWNT milling, and various types of ceramic and metal fillers on the emission current density and turn-on field were evaluated by design of experiment (DOE), whereby the emission properties were shown to be dependent significantly on both factors. Considerably enhanced emission properties were obtained with the paste containing 5 – 10 wt. % of either ITO or the glass frit compared with those without a filler. The paste containing 10 wt. % ITO represented an emission current density of 176.4 μA/cm2 at 5V/μA, a turn-on field of 1.87 V/μA for an emission current density of 1 μA/cm2 and a field enhancement factor of 7,580. The paste formulation was also found to be suitable for fine patterning using UV-lithography techniques. A longterm stability test for 110 hours of a paste containing 10 wt. % ITO revealed a half-life of approximately 30,000 hours, which is appropriate for commercial applications.

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Chapter 15 - Due to their molecular configuration, carbon nanotubes (CNT´s) have the greatest tensile strength and stiffness of all known fiber-like materials combined with an unusual flexibility and stretchability. Additionally, CNT´s exhibit an excellent electrical as well as thermal conductivity depending on the modification. On the basis of these properties and owing to the high aspect ratio, carbon nanotubes offer interesting possibilities for improving the mechanical stability of plastics provided that the load can be transferred from the polymer matrix on the CNT´s. But it is also possible to incorporate some functional properties to use the CNT/polymer-composites as antistatic, electrostatic dissipative materials as well as for electromagnetic shielding and absorbing. Beside the polymer applications, research activities have also focused on the incorporation of CNT´s into a crystalline ceramic matrix. In the case of non-conductive ceramics, the modification with carbon nanotubes leads to an adjustable electrical conductivity. The results from experiments to reinforce ceramics with CNT´s and to reduce the brittleness vary according to the processing method used and the kind of nanotubes. Especially powder ceramic/CNT-composites produced via the Spark-Plasma-Sintering (SPS) process exhibit higher tensile strength and strain to failure values. In contrast, the traditional hot pressing techniques do not lead to an improvement of the mechanical properties because of the necessary higher processing temperatures and the longer manufacturing time. A new approach to improve ceramic materials by the incorporation of C-nanotubes is seen in polymer derived ceramic (PDC) technology, which combines both classes of materials, polymers and ceramics. Main applications for preceramic polymers (precursors) are in ceramic fibers, ceramic matrices and polymers as well as ceramic-like coatings. During the last years a special polycarbosilazane (ABSE) was developed at the University of Bayreuth for the processing of ceramic SiCN-fibers. The optimized, sequenced manufacturing consists of four steps: polymer tailoring, fiber spinning, fiber curing and subsequent transformation of the cured polymer fibers into ceramic fibers by pyrolysis at elevated temperatures. Because of the low molecular weight of the crude ABSE-polymer, which results in a Newtonian melt behavior, it was not possible to establish a stable melt-spinning process. Therefore, multi-wall carbon nanotubes (MWCNT´s) were added to use the strong interaction between the surface of the nanotubes with the ABSE-polymer to influence the rheology of the polymer melt with regard to viscoelasticity. The MWCNT content also led to a remarkable increase in tensile strength of 50 % of the polymer as well as of the resulting ceramic C/SiCN fibers.

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In: Carbon Nanotubes: New Research Editor: Avery P. Ottenhouse

ISBN 978-1-60692-236-1 © 2009 Nova Science Publishers, Inc.

Short Communications

ON THE DRUDE MODEL TO EXPLAIN QUANTUM TRANSPORT IN CARBON NANOTUBES M. A. Grado-Caffaro and M. Grado-Caffaro Permanent address: SAPIENZA-Scientific Consultants, C / Julio Palacios 11, 9-B, 28029-Madrid (Spain)

ABSTRACT The Drude model relative to carrier drift mobility and conductivity is discussed in relation to its applicability to explain quantum transport through both single-walled and multiwalled carbon nanotubes. We show that the Drude model, suitable to describe electrical conductivity in solids as, for instance, semiconductors, is certainly adequate to discuss key aspects of quantum transport in multiwalled carbon nanotubes. In this respect, conductance quantization is treated in relation to the model in question by calculating carrier mobility and conductivity under ballistic regime. As a consequence, an expression for the quantized conductance of a multiwalled carbon nanotube is derived.

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Keywords: Drude model; carbon nanotubes; electrical conductivity; drift mobility; ballistic regime.

1. INTRODUCTION The well-known Drude model relative to electron transport in macroscopic systems is extrapolable, under certain conditions, to nanoscopic structures [1-6]. In fact, by means of this model, analytical approaches have been made to determine electron conductance through both single-walled and multiwalled carbon nanotubes [3-5]. In this respect, we wish to remark the significant importance of the theoretical determination of the electrical conductance in carbon nanotubes. This conductance was found to be quantized [3-5, 7, 8] which constitutes a relevant fact. Conductance quantization will be treated in the following in relation to ballistic transport; at this point, let us remember that ballistic transport is a necessary condition (but

2

M. A. Grado-Caffaro and M. Grado-Caffaro

not sufficient) for conductance quantization (see, for example, ref.[7]). In other words, conductance quantization implies ballistic regime but the reciprocal assertion is not true in general. Therefore, if the carrier transport is diffusive, conductance is not quantized. Ballistic transport through a nanotube, that is, when the electronic mean free path is much longer than the tube length, is the regime under which, in fact, carbon nanotubes behave (see previous references) so that scattering in these tubes should consist of elastic collisions (see, for instance, ref.[7]). This communication is devoted to examine the Drude model within the context of carbon nanotubes by emphasizing the main aspects related to ballistic regime and conductance quantization.

2. THEORY Let us consider the Drude model by which one has that the electrical conductivity is given by σ = eNμ where e is the absolute value of the electron charge, N is the spatial carrier density, and

μ denotes carrier drift mobility which, in turn, reads μ = eτ m ∗ where

τ designates relaxation time (or momentum-scattering rate) and m ∗ stands for carrier effective mass. Then, by replacing the second formula into the first one, it follows:

σ=

e 2 Nτ m∗

(1)

Eq.(1) is standard in physics of semiconductors and constitutes a relevant element of reference within the context of macroscopic condensed-matter systems. Under certain conditions, this formula can be extrapolated to nanoscale systems (see, for instance, refs.[16]). In particular, let us consider a multiwalled carbon nanotube (MWCNT) conceived as a longitudinal quantum box [2, 3]; in such a tube, conductance is quantized according to the fact that the involved quantum number coincides with the numbering of the layers of the tube (conductance scales with the number of layers) [2-5, 7, 8]. Therefore, quantizing formula (1)

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for a metallic MWCNT, one has for the conductivity due to the n refs.[3, 5, 6]):

σn =

th

layer (see, for instance,

e 2 N nτ n m

(2) ∗

where n designates quantum number ( n = 1,2,... ) and m has been replaced by the freeelectron mass denoted by m . In addition, now transport is ballistic) so that

τ n is transit time or motion time (note that

τ n = l v n where l is the length of the tube and v n stands for

the magnitude of the quantized Fermi velocity which, for n >> 1 , approaches the electron velocity deduced from equating the quantized electron energy E n = h n 2

2

(8ml ) 2

On the Drude Model to Explain Quantum Transport in Carbon Nanotubes

3

(corresponding to the electron confinement in the tube as a longitudinal ideal quantum box) to

(1 2)mvn2

vn ≈

[6]. Hence, it follows:

hn 2ml

(3)

where h is the Planck constant. We regard our MWCNT as a quasi-one-dimensional structure [2-5] so that A > 1 (quasi-classical case). Repeating the calculation process in the light of the Drude model developed previously by employing now formula (5) for the electron velocity, the quantized conductance can be expressed as:

4kG0 n 2 Gn = 2n + 1

(6)

4

M. A. Grado-Caffaro and M. Grado-Caffaro

where k is a phenomenological parameter such that 0 < k < 1 which is a measure of the interwall (interlayer) coupling in the tube. We assume that k is a uniform continuous random variable so its average or expected value is k = 1 2 . In the quasi-classical case, that is, when n >> 1, from relationship (6) it follows that G n ≈ 2kG0 n which gives an expected value G n ≈ 2 k G0 n = G0 n . This result agrees with experimental data [7]. For a single-walled carbon nanotube (SWCNT), we use formula (6) when n = 1 (ground state of our quantized system) [4] so that the corresponding conductance reads G1 = 4kG0 3 . In this case, k belonging to the above range is invalid since now it is obvious that speaking of interlayer coupling does not make sense. Consequently, extrapolation of k to values outside the range in question is necessary. Given that, as it is well-known, the conductance through an SWCNT is 2G0 , by equating this value to the previous expression for G1 , one gets that k = 3 2 which evidently is outside the open interval 0 < k < 1 . However, this extrapolation cannot be derived from our formulation.

CONCLUSION

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In essence, a mathematical relationship for the quantized conductance through an MWCNT has been obtained in the light of the Drude model within a quantum-box approach. The applicability of the Drude model to metallic tubes is acceptable in the quasi-classical case. In this case, the conductance is approximately proportional to the number of quantized modes (conducting channels). At any rate, eq.(6) is valid for all the values of n . The interaction between consecutive layers has been specified by using the statistical parameter k whose possible values have been discussed. In addition, considerations relative to SWCNTs have been made. We emphasize the fact that our results agree well with experimental observations [7]. Finally, we wish to remark the usefulness of certain approaches [9, 10] to elucidate problems related to quantum transport in carbon nanotubes. We can also mention potential-well based formulations [2, 3, 4, 6].

REFERENCES [1] [2] [3] [4]

T. Dürkop, B.M. Kim, M.S. Fuhrer: Properties and applications of high-mobility semiconducting nanotubes, J. Phys. Condensed Matter 16 (2004) R553-R580. M.A. Grado-Caffaro, M. Grado-Caffaro: A theoretical analysis on the Fermi level in multiwalled carbon nanotubes, Mod. Phys. Lett. B 18 (2004) 501-503. M.A. Grado-Caffaro, M. Grado-Caffaro: Fractional conductance in multiwalled carbon nanotubes: a semi-classical theory, Mod. Phys. Lett. B 18 (2004) 761-767. M.A. Grado-Caffaro, M. Grado-Caffaro: On the size of small single-walled carbon nanotubes, Optik 116 (2005) 459-460.

On the Drude Model to Explain Quantum Transport in Carbon Nanotubes

M.A. Grado-Caffaro, M. Grado-Caffaro: Theoretical characterization of quantum ballistic conduction through multiwalled carbon nanotubes, Mod. Phys. Lett. B 19 (2005) 967-969. [6] M.A. Grado-Caffaro, M. Grado-Caffaro: A potential-well based formulation to calculate the quantized conductance of a one-atom constriction, Phys. Lett. A 372 (2008) 3573-3576. [7] S. Frank, P. Poncharal, Z.L. Wang, W.A. de Heer: Carbon nanotube quantum resistors, Science 280 (1998) 1744-1746. [8] M.F. Lin, K.W.-K. Shung: Magnetoconductance of carbon nanotubes, Phys. Rev. B 51 (1995) 7592. [9] N.B. Brandt, S.M. Chudinov, Ya.G. Ponomarev: Semimetals 1, Graphite and its Compounds, vol.20.1 of Modern Problems in Condensed Matter Science (NorthHolland, Amsterdam, 1988) pp. 74-77. [10] J. Chen, Z. Yang, J. Gu: Energy gap of the “metallic” single-walled carbon nanotubes, Mod. Phys. Lett. B 18 (2004) 769-774.

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[5]

5

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In: Carbon Nanotubes: New Research Editor: Avery P. Ottenhouse

ISBN 978-1-60692-236-1 © 2009 Nova Science Publishers, Inc.

Short Communications

ASYMPTOTIC ANALYSIS OF COAGULATION– FRAGMENTATION EQUATIONS Francisco Torrens∗,a and Gloria Castellanob a

Institut Universitari de Ciència Molecular, Universitat de València, Edifici d'Instituts de Paterna, P. O. Box 22085, E-46071 València, Spain b Instituto Universitario de Medio Ambiente y Ciencias Marinas, Universidad Católica de Valencia San Vicente Mártir, Guillem de Castro-94, E-46003 València, Spain

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ABSTRACT The existence of single-wall carbon nanotubes (SWNTs) in organic solvents in the form of clusters is discussed. A theory is developed based on a bundlet model for clusters describing the distribution function of clusters by size. The phenomena have a unified explanation in the bundlet model of a cluster, in accordance with which the free energy of an SWNT involved in a cluster is combined from two components: a volume one proportional to the number of molecules n in a cluster, and a surface one proportional to n1/2. A comparative study of the droplet and bundlet models is carried out. The model yields an activation barrier and predicts that pores with a radius below a certain critical value are unstable, while those above this radius will grow indefinitely until the membrane ruptures. During the latter stage of the fusion process, the dynamics were governed by the displacement of the volume of liquid around the fusion site. Based on a simple kinetic model, micellization of rod-like aggregates occurs in three separated stages. A convenient relation is obtained for at transient stage; at equilibrium another relation determines binding energy α. A relation with surface dilatational viscosity is obtained. The model predicts that pores with a radius below a certain critical value are unstable.

Keywords: nanostructure, diffusion, phase equilibrium, thermodynamic property, transport property. ∗

Tel : +34-963-544-431, Fax : +34-963-543-274, E-mail : [email protected]

8

Francisco Torrens and Gloria Castellano

INTRODUCTION Among the unusual properties of fullerene solutions, it should be mentioned the nonmonotonic temperature dependence of solubility [1] and the nonlinear concentration dependence of the third-order nonlinear optical susceptibility [2]. The solvatochromic effect is exhibited in a sharp alteration in the spectrum of the optical absorption of C70, dissolved in a mixture of organic solvents, of a result of a slight change in the solvent content [3, 4]. The behaviour of fullerene solutions is attributable to cluster formation [5, 6]. It was examined the decrease in pyridine-soluble material observed after soaking coals in solvents, because of an increase in cross-linking associated with the formation of ionic domains [7]. It is not possible to extract C60–70 from a solution in toluene to water and from a dispersion in water to toluene [8]. In water C60 spontaneously forms a stable aggregate (C60)n with nanoscale dimensions [9]. Water might form a donor–acceptor complex with C60 leading to a weakly charged colloid [10–12]. C60, dissolved in water via complexation with cyclodextrin8, was extracted to toluene [13, 14]. In C60 incorporated into artificial lipid membranes, it was not extracted to toluene, but extraction became possible once the vesicle was destructed by adding KCl [15]. Addition of KCl was required to extract poly(vinylpyrrolidone)-solubilized C60–70 to toluene [16–20]. In earlier publications, periodic tables of single-wall carbon nanotubes (SWNTs) were discussed [21, 22]. A molecular modelling comparative study of SWNT solvents and cosolvents provided a classification in best, good and bad solvents [23–26]. A program based on the AQUAFAC model was applied to calculate the aqueous coefficients of SWNTs [27]. The bundlet model for clusters of SWNTs was presented [28–32]. The aim of the present report is to perform a comparative study of the properties of fullerenes (droplet model) and SWNTs (bundlet). A wide class of phenomena accompanying the behaviour of SWNT solutions is analyzed from a unique point of view, taking into account the tendency of SWNTs to cluster formation. Based on the droplet model of C60–70 the bundlet model of SWNTs is proposed. The next section presents the computational method. Following that the asymptotic coagulation–fragmentation equations are described. Next the calculation results are discussed. The last section summarizes the perspectives.

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COMPUTATIONAL METHOD A solubility mechanism is based on SWNT cluster formation in solution. Aggregation changes SWNT thermodynamic parameters, which displays phase equilibrium and changes solubility. The bundlet model is valid when the characteristic number of SWNTs in the cluster n >> 1. In saturated SWNT solution, the chemical potentials per SWNT for dissolved substance and for a crystal are equal. The equality is valid for SWNT clusters. The free energy of a cluster is made up of two parts: the volume part proportional to the number of SWNTs n in the cluster, and the surface one proportional to n1/2 [33–43]. The model assumes that clusters consisting of n >> 1 particles have a cylindrical bundlet shape and permits the Gibbs energy Gn for a cluster of size n to be

Asymptotic Analysis of Coagulation–Fragmentation Equations

Gn = G1 n − G2 n

9

12

(1)

where G1–2 are responsible for contribution to Gibbs energy of molecules placed inside the volume and on surface of a cluster. Chemical potential μn of a cluster of size n is

μn = Gn + T ln Cn

(2)

where T is temperature. With (1) this results

μn = G1n − G2 n1 2 + T ln Cn

(3)

where G1–2 are in temperature units. In a saturated SWNT solution, cluster-size distribution function is determined via equilibrium condition linking the clusters of a specified size with a solid phase, which corresponds to the equality between the chemical potentials for molecules incorporated into clusters and into crystal, resulting in the cluster-size distribution function in saturated solution

⎛ − An + Bn1 2 ⎞ f (n) = gn exp ⎜ ⎝ ⎠ T

(4)

where A is the equilibrium difference between interaction energies of an SWNT with its surroundings in solid phase and in cluster volume, B, the similar difference for SWNTs located on the cluster surface, gn, the statistical weight of a cluster of size n. We shall neglect gn(n,T) dependences in comparison with exponential (4). Normalization for distribution function (4) ∞

∑ f (n)n = C n=1

(5)

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requires A > 0. Here C is solubility in relative units. As n >> 1 normalization (5) results ∞ ⎛ − An + Bn 1 2 ⎞ C = gn ∫n =1 n exp⎜ dn ⎝ ⎠ T

(6)

where gn is the statistical weight of a cluster averaged over the range of n that makes the major contribution to integral (6), and C0, SWNT molar fraction. The A, B and C0 have been taken equal to those for C60 in hexane, toluene and CS2: A = 320K, B = 970K, C0 = 5·10–8 (molar fraction) for T > 260K. A correction takes into account the different packing efficiencies between C60 and SWNTs

10

A′ =

Francisco Torrens and Gloria Castellano

ηcyl A ηsph

B′ = and

ηcyl B ηsph

(7)

where ηcyl = π/2(3)1/2 is the packing efficiency of cylinders, and ηsph = π/3(2)1/2 the one of spheres (face-centred cubic, FCC). Software is available from the authors.

DESCRIPTION OF THE ASYMPTOTIC COAGULATION– FRAGMENTATION EQUATIONS Finding a manageable approximation to the behaviour of the coagulation–fragmentation equations is challenging. The approximation is presented by asymptotic analysis. Results have been checked against numerical solutions to the equations dealing with the Becker– Döring equations. Typical models for the binding energy of a n cluster follow. For rod-like aggregates

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ε n = (n − 1)α k BT

(8)

where αkBT is the monomer–monomer binding energy [44–46]. In the Becker–Döring model, reactions only between monomers and other clusters are taken into account. Expression (8) is suitable for aggregates of certain kinds of lipids, when these form rod-like clusters. The lipid molecules typically have a hydrophilic head and a hydrophobic tail so, in aqueous solution, they spontaneously arrange themselves so that tails are away from the surrounding water, and heads in contact with it. Depending on the shape of the particular molecule, they can form spherical aggregates with tails pointing inwards and heads pointing outwards, or form lipid bilayers, where lipid molecules form a double layer with heads on the external surface and tails on the inside. Clusters formed by lipids in aqueous solution are called micelles, and the process by which they form is called micellization. To determine the time scale, one needs a measure of the kinetic coefficient of the d decay reaction, which was set equal to one. A convenient relation could be an equation, which in dimensional units is ≈ (dπt)1/2. In case the self-similar size distribution is not reached during the intermediate phase, another way to determine d is to study the equilibration era and compare the experimental size distribution with the numerical solution of the model. By combining τearly ~ ηs/σ with ≈ (dπt)1/2 it is obtained ≈ (dπηs/σ)1/2. The original software used in the investigation is available from the authors.

CALCULATION RESULTS AND DISCUSSION The line graphs in Figure 1 depict 2rk as a function of x = k/ for the times τ = 0.5×105, 105 and 1.5×105. They are nearly superimposed on top of each other. The heavy dots correspond to the plateau time τ = 20, so the change in the distribution shape over the whole time span 20 < τ < 1.5×105 is not rather great.

Asymptotic Analysis of Coagulation–Fragmentation Equations

11

Figure 1. Approximate self-similar behaviour of the size distribution at times τ = 50 000, 100 000 and 150 000 (solid lines). Notice that 2rk is approximately the same function of k/ at different times. The dots correspond to τ = 20.

Figure 2 illustrates the evolution of the size distribution for the rescaled binding energy

ε = e–α/ρ = 4.54×10–4 (corresponding to α = 10 and ρ = 0.1), where the binding energy of the k cluster εk = (k–1)αkBT, and ρ is the ratio number of particles/number of spaces. It records

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the time-dependent behaviour of the average cluster size . It is a log-log plot of /e vs. τ. It reveals an initial rapid growth of to a plateau value close to e, roughly located in the interval 10 < τ < 100. In the subsequent growth after the plateau large clusters with k >> 1 eventually appear. Figure 2 indicates that by time τ = 5×104, k clusters having ≈ 10 are prevalent. In the time interval 2×104 < τ < 5×105, the log-log plot of /e vs. τ is close to a straight line of slope 1/2. This strongly supports the existence of a self-similar stage of the kinetics. Notice that the average cluster size corresponding to the intermediate transient (Figure 2, dotted line) approaches the asymptotic value (straight line of slope 1/2).

Figure 2. Evolution of the average cluster size /e vs. the scaled time τ (thick solid line). The dotted line corresponds to the intermediate transient with an initial condition corresponding to the dot. The straight line of slope 1/2 corresponds to the asymptotic self-similar continuum size distribution.

12

Francisco Torrens and Gloria Castellano

1000

Energy (K)

C60 SWNT 0

SWNT η-correction SWNT n→∞ SWNT η-correction n →∞

-1000

0

20

40

Number of molecules in cluster

Figure 3. SWNT interaction energy with its surroundings in cluster volume or surface.

Solubility, molar fraction

0.0008 C60 0.0006

SWNT SWNT η-correction

0.0004

SWNT n→∞ 0.0002

SWNT η-correction n →∞

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0 200

300

400

Temperature (K)

Figure 4. Temperature dependence of solubility of C60 (droplet) and SWNT (bundlet).

Figure 3 illustrates the equilibrium difference between the Gibbs free energies of interaction of an SWNT with its surroundings, in the solid phase and in the cluster volume, or on the cluster surface. On going from C60 (droplet model) to SWNT (bundlet) the minimum is less marked (55% of droplet), which causes a lesser number of units in SWNT (nminimum ≈ 2) than in C60 clusters (≈8). Moreover the abscissa is also shorter in SWNT (≈9) than in C60

Asymptotic Analysis of Coagulation–Fragmentation Equations

13

clusters (≈28). In turn when the packing-efficiency correction (7) is included, the C60–SWNT shortening decreases (68% of droplet) while keeping nminimum ≈ 2 and nabscissa ≈ 9. The temperature dependence of SWNT solubility S (cf. Figure 4) shows that S decreases with temperature, because of cluster formation. At T ≈ 260K, the C60 crystal presents an orientation disorder phase transition from FCC to simple cubic. The reduction is less marked for SWNT, in agreement with the lesser number of units in SWNT clusters. In particular at T = 260K on going from C60 (droplet) to SWNT (bundlet), S drops to 1.6% of droplet. In turn when the packing-efficiency correction is included (7), the shortening decreases (2.6% of droplet). The concentration C dependence of the heat of solution H in toluene, benzene and CS2, calculated at solvent temperature T = 298.15K (cf. Figure 5), shows that for C60 (droplet), on going from C < 0.1% of saturated ( ≈ 1) to C = 15% ( ≈ 7), H decreases by 73%. In turn for SWNT (bundlet) H increases by 98% in the same interval. However, when the packing-efficiency correction (7) is included, the increment in H is reduced to 54%. The discrepancy between various experimental H data of fullerenes and SWNTs may be ascribed to the sharp C dependence of H. The results for the dependence of diffusion coefficient D on C in toluene, at T = 298.15K (cf. Figure 6), show that the cluster formation in a solution close to saturation decreases D by 58%, 73% and 69% for C60, SWNT and SWNT with packing-efficiency correction, respectively, as compared with D0 for an SWNT. For SWNT (bundlet) D decreases by 35% with regard to droplet. In turn when the packing-efficiency correction (7) is included, the decrease is reduced to 27%. The discrepancy between experimental data, on fullerene–SWNT Ds, may be because of the sharp concentration dependence of D for the systems. The results for SWNT (bundlet) with packing-efficiency correction and extrapolation n → ∞ are superposed to SWNT (bundlet, n → ∞).

Heat of solution (kJ/mol)

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5

C60 0

SWNT SWNT η-correction SWNT n→∞

-5

SWNT η-correction n →∞

-10 0

0.5

1

C/C sat

Figure 5. Heat of solution vs. concentration in toluene, benzene and CS2 at 298.15K.

Francisco Torrens and Gloria Castellano

Diffusion coefficient (m 2 /s)

14

8E-10

C60 SWNT

6E-10

SWNT η-correction SWNT n→∞

4E-10

SWNT η-correction n →∞

0

0.5

1

C/C sat

Figure 6. Diffusion coefficient vs. concentration of C60/SWNT in toluene at 298.15K.

PERPECTIVES

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From the discussion of the present results the following perspectives can be drawn. 1. Based on a simple kinetic model, micellization of rod-like aggregates occurs in three separated stages: (a) many clusters of small size are produced while the number of monomers decreases sharply; (b) aggregates are increasing steadily in size, and their distribution approaches a self-similar solution of the diffusion equation; (c) a simple mean-field Fokker–Planck equation describes the third era until the equilibrium distribution is reached. In order to validate the theory by an experiment, it would be important to measure the average cluster size as a function of time. To determine the time scale, one needs a measure of the cluster diffusion coefficient d that was set equal to 1. A convenient relation in dimensional units is ≈ (dπt)1/2. In case the self-size similar distribution is not reached during the intermediate phase, another way to determine d is to study the equilibration era and compare the experimentally obtained size distribution with the numerical solution of the model. At equilibrium 2 ≈ ρeα, and this relation determines the dimensionless binding energy α. 2. Fullerene–SWNT cluster formation suggests that the cluster sheath is filled with pores. The membranous character of growth process in clusters explains experimental data dispersion. The model yields an activation barrier and predicts that pores with a radius below a certain critical value are unstable, while those above this radius will grow indefinitely until the membrane ruptures. During the latter stage of fusion the site expansion velocity slowed down by two orders of magnitude. Dynamics were governed by the displacement of the volume of liquid around the fusion site.

Asymptotic Analysis of Coagulation–Fragmentation Equations

15

REFERENCES [1] [2] [3] [4] [5] [6] [7] [8] [9]

[10] [11] [12] [13] [14] [15] [16]

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[17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31]

Ruoff, R. S.; Malhotra, R.; Huestis, D. L.; Tse, D. S.; Lorents, D. C. Nature (London) 1993, 362, 140-141. Blau, W. J.; Byrne, H. J.; Cardin, D. J.; Dennis, T. J.; Hare, J. P.; Kroto, H. W.; Taylor, R.; Walton, D. R. M. Phys. Rev. Lett. 1991, 67, 1423-1425. Sun, Y.-P.; Bunker, C. E. Nature (London) 1993, 365, 398-398. Ghosh, H. N.; Sapre, A. V.; Mittal, J. P. J. Phys. Chem. 1996, 100, 9439-9443. Ying, Q.; Marecek, J.; Chu, B. Chem. Phys. Lett. 1994, 219, 214-218. Ying, Q.; Marecek, J.; Chu, B. J. Chem. Phys. 1994, 101, 2665-2672. Painter, P. C.; Opaprakasit, P.; Scaroni, A. Energy Fuels 2000, 14, 1115-1118. Scrivens, W. A.; Tour, J. M.; Creek, K. E.; Pirisi, L. J. Am. Chem. Soc. 1994, 116, 4517-4518. Fortner, J. D.; Lyon, D. Y.; Sayes, C. M.; Boyd, A. M.; Falkner, J. C.; Hotze, E. M.; Alemany, L. B.; Tao, Y. J.; Guo, W.; Ausman, K. D.; Colvin, V. L.; Hughes, J. B. Environ. Sci. Technol. 2005, 39, 4307-4316. Andrievsky, G. V.; Kosevich, M. V.; Vovk, O. M.; Shelkovsky, V. S.; Vashchenko, L. A. J. Chem Soc., Chem. Commun. 1995, 1281-1282. Deguchi, S.; Alargova, R. G.; Tsujii, K. Langmuir 2001, 17, 6013-6017. Andrievsky, G. V.; Klochkov, V. K.; Bordyuh, A. B.; Dovbeshko, G. I. Chem Phys. Lett. 2002, 364, 8-17. Andersson, T.; Nilsson, K.; Sundahl, M.; Westman, G.; Wennerström, O. J. Chem. Soc., Chem. Commun. 1992, 604-606. Sundahl, M.; Andersson, T.; Nilsson, K.; Wennerström, O.; Westman, G. Synth. Met. 1993, 56, 3252-3257. Hungerbühler, H.; Guldi, D. M.; Asmus, K.-D. J. Am. Chem. Soc. 1993, 115, 33863387. Yamakoshi, Y. N., Yagami, T.; Fukuhara, K.; Sueyoshi, S.; Miyata, N. J. Chem Soc., Chem. Commun. 1994, 517-518. Scott, G. D.; Charlesworth, A. M.; Mak, M. K. J. Chem. Phys. 1964, 40, 611-612. Scott, G. D.; Kilgour, D. M. Br. J. Appl. Phys. 1969, 2, 863-866. Baram, A.; Luban, M. J. Phys. C, Solid Satate Phys. 1979, 12, L659-L664. Alievsky, D. M.; Kamenin, I. G.; Kadushnikov, R. M.; Alievsky, V. M. Modelling 2001, 1, 1-3. Torrens, F. Internet Electron. J. Mol. Des. 2004, 3, 514-527. Torrens, F. Internet Electron. J. Mol. Des. 2005, 4, 59-81. Torrens, F. Mol. Simul. 2005, 31, 107-114. Torrens, F. J. Mol. Struct. (Theochem) 2005, 757, 183-191. Torrens, F. Nanotechnology 2005, 16, S181-S189. Torrens, F. Probl. Nonlin. Anal. Eng. Syst. 2005, 11(2), 1-16. Torrens, F. Int. J. Quantum Chem. 2006, 106, 712-718. Torrens, F.; Castellano, G. Comput. Lett. 2005, 1, 331-336. Torrens, F.; Castellano, G. Curr. Res. Nanotechn. 2007, 1, 1-29. Torrens, F; Castellano, G. Microelectron. J. 2007, 38, 1109-1122. Torrens, F.; Castellano, G. J. Comput. Theor. Nanosci. 2007, 4, 588-603.

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[32] Torrens, F.; Castellano, G. Nanoscale Res. Lett. 2007, 2, 337-349. [33] Bezmel’nitsyn, V. N.; Eletskii, A. V.; Stepanov, E. V. J. Phys. Chem. 1994, 98, 66656667. [34] Bezmel’nitsyn, V. N.; Eletskii, A. V.; Stepanov, E. V. Zh. Fiz. Khim. 1995, 69, 735735. [35] Bezmel’nitsyn, V. N.; Eletskii, A. V.; Okun’, M. V. Physics–Uspekhi 1998, 41, 10911114. [36] Bezmel’nitsyn, V. N. Khim. Fiz. 1994, 13(12), 156-156. [37] Bezmel’nitsyn, V. N. Phys. Scr. 1996, 53, 364-367. [38] Bezmel’nitsyn, V. N. Tech. Phys. 1996, 41, 986-986. [39] Bezmel’nitsyn, V. N. Phys. Scr. 1996, 53, 368-370. [40] Eletskii, A. V.; Okun’, M. V.; Smirnov, B. M. Phys. Scr. 1997, 55, 363-366. [41] Gasser, U.; Weeks, E. R.; Schofield, A.; Pusey, P. N.; Weitz, D. A. Science 2001, 292, 258-262. [42] Notman, R.; Noro, M.; O’Malley, B.; Anwar, J. J. Am. Chem. Soc. 2006, 128, 1398213983. [43] Haluska, C. K.; Riske, K. A.; Marchi-Artzner, V.; Lehn, J.-M.; Lipowsky, R.; Dimova, R. Proc. Natl. Acad. Sci. USA 2006, 103, 15841-15846. [44] Neu, J. C.; Cañizo, J. A.; Bonilla, L. L. Phys. Rev. E 2002, 66, 61406–1-9. [45] Cañizo, J. A.; López, J. L., Nieto, J. J. J. Differential Equations 2004, 198, 356-373. [46] Cañizo Rincón, J. A. Proc. R. Soc. London, Ser. A 2004, 461, 3731-3745.

In: Carbon Nanotubes: New Research Editor: Avery P. Ottenhouse

ISBN 978-1-60692-236-1 © 2009 Nova Science Publishers, Inc.

Chapter 1

GAS-CARBON NANOTUBES INTERACTIONS: A REVIEW OF ULTRA-HIGH VACUUM SURFACE SCIENCE STUDIES ON CNTS U. Burghaus∗ Department of Chemistry and Molecular Biology, North Dakota State University, Fargo, North Dakota 58105, USA

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ABSTRACT While numerous studies concerning the synthesis and materials science applications of carbon nanotubes have been conducted, the data obtained at well-defined ultra-high vacuum conditions by means of surface science techniques is still scarce. We present specific examples of recent ultra-high vacuum surface science projects from our laboratory conducted on clean carbon nanotubes with an emphasis on applications in heterogeneous catalysis. In addition the related surface science literature is summarized and future directions are outlined. In particular, kinetics and molecular beam scattering (dynamics) results for alkanes, alcohols, and thiophene are described. Alkanes perfectly allow for characterization of different adsorption sites on carbon nanotube bundles, while alcohols are related to fuel cell applications, i.e., to renewable energy production and a green (environmentally friendly) chemistry approach. Thiophene is the probe molecule of choice to characterize desulfurization catalysts which are important for the petroleum industry. Kinetics experiments quantify the binding strength of these probe molecules on carbon nanotubes and provide evidence for capture effects, which are one of the main advantages of nanotubes in catalysis. Molecular beam scattering has characterized gas-surface energy transfer processes and, again capture effects, i.e., the adsorption of the probe molecules in carbon nanotubes. In addition, a brief review of the related literature is included. The literature survey (conducted early in 2008) focuses on experimental research conducted at high vacuum (< 10-6 torr) where common surface science techniques have been applied. A number of theoretical studies addressing a structure activity relationship (SAR) are included too. ∗

E-mail [email protected] URL www.uweburghaus.de

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U. Burghaus However, electrochemistry or pure catalysis studies (conducted at high pressure and high temperatures) are mostly omitted. Finally, an outline of future directions in surface science on CNTs is kindly proposed.

ABBREVIATIONS Materials AC BNNT BCNTs Bucky paper t C60 C70 C76 C84… AP-CNTs CNTs DWNT SWCNTs SWNTB MWCNTs cut-CNTs

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o-CNTs c-CNTs f-CNTs SC-CNTs s-CNTs CNFs x@CNTs SWNHs SDS EG EG HOPG IF INT MeOH MCG Nanobud NT Peapods TiNTs

activated carbon boron nitride nanotubes bamboo-like carbon nanotubes thick multi-wall CNTs layers Buckminsterfullerene Fullerenes as-prepared CNTs (raw soot) carbon nanotubes double-wall CNTs single-wall carbon nanotubes (less common is C-SWNTs) single-wall carbon nanotube bundles multi-wall carbon nanotubes (less common is C-MWNTs) CNTs cut by means of acidic treatments (but not a very common term); see o-CNTs open-end CNTs closed-end CNTs functionalized CNTs semiconducting CNTs semiconducting CNTs cup-stacked carbon nanofibers With x for a metal, e.g. Au@CNTs. Metal nanoparticles (Au) functionalized CNTs single-wall carbon nanohorns sodium dodecyl sulfate ethylene glycol epitaxial graphene highly oriented pyrolytic graphite inorganic fullerene-like nanoparticles (non-carbon nanomaterials) inorganic nanotubes methanol micromechanical cleavaged graphene C60-CNT hybrid material nanotubes C60 inside NTs TiO2 nanotubes

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Techniques BSSE CVD CCVD DFT EDX FTIR GCMS HF HREELS IR LEED LDA-DFT GGA-DFT MAS NMR MP2 MBS MM MD NEXAFS NMR RR RAIRS STM TDS / TPR UVvis-NIR XPS

basis set superposition error chemical vapor deposition catalytic CVD density functional theory energy-dispersive X-ray spectroscopy Fourier transform infrared spectroscopy Grand canonical Monte Carlo simulations Hartree-Fock high resolution electron energy loss spectroscopy infrared spectroscopy low energy electron diffraction local density approximation DFT generalized-gradient approximation DFT magic angle spinning NMR Moller-Plesset perturbation theory molecular beam scattering molecular mechanics simulations molecular dynamics near edge X-ray absorption fine structure nuclear magnetic resonance retarded reflector (King and Wells) technique – adsorption transients reflection absorption infrared spectroscopy scanning tunneling microscopy thermal desorption spectroscopy/temperature programmed reactions ultra violet-visible-near infrared spectrophotometer x-ray photoelectron spectroscopy

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Further Symbols and Acronyms d n, m S0 S(Θ) Θ L SAR NSF ASW CW CW CoMoCAT

diameter of CNTs chiral indices of CNTs, i.e. (n,m)-CNT initial (zero coverage) adsorption probability coverage dependent adsorption probability coverage, surface particle density Langmuir (one sec gas exposure at 1x10-6 torr) structure activity relationship National Science Foundation amorphous solid water clustered water crystalline water s-CNTs (South West Nanotechnologies)

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U. Burghaus HV HiPco HDS POAV

Θσπ φ UHV

high-vacuum high pressure CO disproportionation synthesis of CNTs hydrodesulfurization π-orbital axis vector (vector pointing in the direction of a π-orbital) Pyramidalization angle Θp = Θπσ-0º (90º for a sp2 hybridized C atom, 19.5º for sp3-hybrid orbital) Angle between π and σ orbitals (90º for sp2, 109.47º for sp3 orbitals) Misalignment angle of POAV of different carbon atoms ultra-high vacuum (typically pressure 50 nm) porous materials [15].

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2. SAMPLE PREPARATION FOR SURFACE SCIENCE STUDIES The following section may seem somewhat technical. However, first, the sample preparation is pertinent for any subsequent experimental study; second, information provided in the following is typically not included in very great detail in journal publications.

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2.1. Monolayer CNT Samples: Drop-and-Dry Technique Samples for surface science studies can be obtained based on CNT solutions using the socalled drop-and-dry technique. The “cooking recipe” outlined in the following is well tested [17]. Hydrophobic CNTs are insoluble in water, but amphiphilic surfactants such as SDS can be used to obtain colloidal suspensions. In this procedure, one micro spatula of CNTs powder ( metallic CNTs > s-CNTs > graphene

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i.e., fullerenes are most reactive, graphene mostly inert, simply due to the decrease of the curvature-induced strain (pyramidization) of the graphene sheet going from “spherical” fullerenes to planar graphene. The larger the curvature (pyramidalization angle; see Fig. 11, 12), the larger the reactivity. Therefore, the reactivity of (the outer surface of) CNTs should increase with decreasing diameter. Similarly, interior sites of CNTs provide more nearestneighbor sites for adsorbates and should be more reactive than exterior sites of CNTs. Furthermore, metallic CNTs with comparable diameters/curvatures may be catalytically more active than semiconducting CNTs. Detailed theoretical studies, however, predict different trends and more subtle effects in some cases, which will briefly be discussed below. The theoretical data base is quite extensive. Unfortunately, a large number of theoretical studies have been conducted on rather exotic systems with very small diameters. However, interesting trends have been seen and some concepts, including SAR rules, have been proposed. Unfortunately, no detailed experimental surface science data are available yet.

6.3.1. Donor-Acceptor Models According to DFT calculations [171], a most distinct SAR is expected for charge acceptor molecules (such as O2, NO2) which significantly modify the density of states of the CNTs, whereas charge donors (such as N2, H2O, CO2) would interact only weakly and nonspecifically with CNTs [171]. Variations in binding energies as large as 36 kJ/mol (for NO2) and 20 kJ/mol (for O2), depending on the diameter of the CNTs, have been proposed theoretically. A clear trend for the binding energy on tube diameter –smaller diameter tubes are more reactive – has been seen for NO2, O2, NH3, and CO2 but not for H2O, CH4, H2, N2, and Ar. Although trends in binding energies are typically correctly predicted by DFT, some of the theoretical binding energies appear not to be consistent with available experimental data.

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6.3.2. POAV Misalignment – Noncovalent Interactions Astonishingly for CO2, binding energies which increase with increasing CNT diameter have been predicted theoretically [93, 179]; similar trends have been proposed for benzene physisorption [107]. Benzene adsorbed more strongly on HOPG than on CNTs, according to theoretical predictions. Experimental data are not available.

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Figure 10. Expected structure activity relationship based on the curvature of the nanostructures which appears to be obeyed in the case of covalently bonded probe molecules.

Figure 11. The carbon atoms in planar graphite (HOPG) are well described by a sp2-hydridization, which is not necessarily the case for a bent graphene sheet (i.e. CNTs). The pydamidalization angle allows quantifying the effect of CNT curvature on binding energies of probe molecules using molecular orbital theory.

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The calculations predict a non-trivial dependence of binding energies on curvature and chiral angle of CNTs. However, a simple SAR rule has been stated: “the smaller the π orbital axis vector (POAV) misalignment angle is, the larger the binding energy.” [107] (See Fig. 12.) Although, all C atoms in a CNT are equivalent, the C-C bonds are not. These bonds differ by the direction of the π orbitals (POAV) with respect to the σ-orbitals (the bond directions) of the C atoms in the CNTs. Due to the CNT curvature, the POAV of neighbor C atoms is misaligned. This misalignment depends on the tube diameter. In turn, a perhaps unexpected dependence of the CNT reactivity (e.g. binding energy) on the diameter (and curvature) of the NT is predicted theoretically [107] for noncovalent interactions of CNTs (such as benzene adsorption on CNTs). However, experimental data confirming the theoretical predictions are missing so far. The POAV misalignment leads to kinetically distinct adsorption sites on the CNT surface. In addition, the curvature-induced pyramidization (Θσπ > 90º, for C60: Θp = 11.6º, for (5,5)-CNT: Θp(side wall) = 6.0º, see Fig. 12 and ref. [72]) of the C atoms leads to deviations from the carbon sp2-hydridization seen for planar HOPG; the amount of s-p mixing has been calculated in ref. [107]. Both effects (POAV misalignment and pyramidalization) induce a local strain in the CNTs. For the same reasons, the fullerene caps of c-CNTs should be more reactive than the CNT walls [72]. The larger Θp, the larger the reactivity of the system. CNTs may be considered “cylindrical aromatic macromolecules” when applying MO-type theory to understanding the adsorbate-CNT interactions, as discussed in ref. [72], when comparing the electronic structure of fullerenes with CNTs. In summary, for weakly interacting adsorbates (with dominating π-orbitals) a trend of increasing reactivity with increasing CNT tube diameter is predicted. Unexpectedly, large diameter tubes are catalytically more active than small diameter CNTs.

6.3.3. Covalent Interactions Probe molecules which result in a more covalent binding to CNTs show the opposite trend: smaller diameter CNTs are more reactive; i.e., the binding energies increase with decreasing diameter. Artificially bent CNTs have been considered in a number of theoretical studies; in all cases a large curvature was related with high chemical activity [94, 229]. For example, CO only physisorbs on unperturbed (8,0)-CNTs with basically repulsive interaction (extremely small binding energy), but chemisorbs (with larger binding energies) on bent CNTs [94]. Thus, regions of larger curvature of the CNTs are catalytically more active — at least theoretically; experimental data is missing. Similar conclusions have been drawn for other strongly bonded adsorbates: the smaller the diameter, the larger the binding energies for hydrogen [230, 231], fluorine [353], and aluminum [230] adsorption on the other CNT surfaces. Thus, it appears that the interactions of molecules with CNTs can be classified according to the covalent character of the binding to the CNTs. For covalent binding, small diameter CNTs are best; for non-covalent binding, large diameter CNTs are catalytically more active.

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Figure 12. I) On a planar surface such as HOPG, the C atoms are sp2-hybridized and the π-orbitals of different C-atoms point in the same direction, called the POAV- π orbit axis vector. On a planar surface, equivalent sets (on top sites, bridge sites, etc.) of adsorption sites exist, independent of the given patch on the planar surface considered, i.e., all C-C bonds are equivalent. II) However, on a curved surface, such as the CNT surface, the POAVs of different C-atoms are misaligned, as can be quantified by the angle φ (POAV misalignment angle). III) Thus, although all C-atoms on the CNT surface are equivalent, having the same chemical environment, their bonds differ, which can result in different binding energies of adsorbates depending on the CNT diameter, since φ certainly depends on the diameter (curvature) of the CNTs. In addition, φ differs for different bonds on the CNT surface, which can result in different binding energies for adsorbates along the surface of the CNTs.

6.3.4. Reactivity of the Inner and Outer Surface of CNTs In ref.[353] the possible differences in the reactivity of the outer convex (excahedral) surface and the inner concave (endohedral) surface of CNTs have been considered by quantum chemical techniques in analogy to fullerene chemistry. The binding energies of H and F atoms on (n,n)-CNTs have been calculated [353]. For these covalent interactions, the binding energies for adsorption on the inner CNT surface decreases with increasing CNT diameter. (Small diameter CNTs are “best.”) In contrast, the binding energies on the outer surface are much smaller and rather independent of the CNT diameter, except for very narrow CNTs, according to ref. [353]. In other words, most reactive for covalent bond formation is the inner surface of small diameter CNTs. The trends observed in the binding energies for small diameter (n,n)-CNTs (2 < n < 7) are related to the pyramidalization angle (angle between π and σ orbitals of the C atoms in the tube wall, Fig. 12). The larger the pyramidalization angle, the larger the binding energies on the interior surface of the CNTs, similarly to the discussion in ref. [107] mentioned above. Unfortunately, it is doubtful that related experiments with exotic (2,2)-CNT tubes and atomic hydrogen (sect. 3.1.1) will ever be doable. 6.3.5. Kinetically Distinct Adsorption Sites in CNT Bundles and Isolated CNTs Kinetically distinct adsorption sites have been seen for CNT robes/bundles in a number of experimental projects (see Tab. 8, sect. 5.1); theoretical studies are rather rare [181, 361].

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Accordingly, for most molecules interstitial sites have the largest reactivity, followed by groove sites and internal sites[181]. Slightly different trends have been proposed in experimental work, where the binding energies on internal sites were always larger than on groove sites. However, these results certainly depend critically on the CNT diameter and the geometrical arrangement of the CNT bundles. Binding energies of small molecules on isolated CNTs have been calculated for a number of different adsorbates including hydrogen [362] and benzene [107]. For hydrogen, hollow sites are energetically favored; benzene adopts bridge sites.

6.3.6. Metal-to-Semiconductor Transitions (vice versa) A metal to semiconductor transition of metallic CNTs upon O2 adsorption has been predicted theoretically, whereas semiconducting CNTs are less affected [232]. Related effects have been discussed for the adsorption of hydrogen [233]. In this case, a massive reconstruction of the CNTs was proposed theoretically; related effects have apparently been seen experimentally [23] (see sect. 3.1.1). 6.3.7. IR and NMR Characterization of CNT SAR Just as a brief note, since these techniques typically do not operate under UHV conditions, we would like to mention that IR peaks shifts (see e.g. ref. [30]) as well as chemical shifts in NMR, may be used to evaluate a SAR. For example, chemical shifts in NMR increase systematically with CNT tube diameter, as theoretically determined for a variety of probe molecules [363].

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6.3.8. SAR of Diffusion Properties of CNT The diffusion of molecules through CNTs is certainly dominated by surface effects. Interestingly, it has theoretically predicted that, in addition to the tube diameter, the crystallography of the CNTs affects the diffusion of, for example, water through CNTs (see e.g. ref. [364]). Molecular dynamics calculations combined with calculated potential energy surfaces predict that the diffusion of water is more efficient for zigzag CNTs as compared with armchair CNTs. The CNT crystal structure affects the trajectories of water diffusion inside the CNTs. It appears the SAR of CNTs is more subtle than considering only the curvature of the CNTs. However, most likely different classes of probe molecules (covalent vs. noncovalent interactions) can be distinguished and SAR rules will be developed. As for now, basically no UHV surface chemistry data are available which would characterize in detail the dependence of binding energies on, for example, the CNT tube diameter.

SUMMARY The surface science of CNTs studied at ultra-high vacuum conditions by traditional surface chemistry techniques is still in its infancy (see Tab. 1). So far mostly mixed CNT samples have been studied, which consist of a rather large distribution of diameters and tube lengths. In addition, metal supported or otherwise functionalized CNT samples have, to the best of our knowledge, not been studied yet in detail under UHV conditions with surface

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chemistry techniques. The data base is even scarcer concerning inorganic nanotubes. A lessthan-optimal selectivity of catalysts which makes sophisticated separation and cleaning procedures of the products pertinent is a major hassle in many industrial catalytic processes. However, it appears to be just a matter of a few years before more efficient procedures will be developed to synthesize CNTs of specific crystal structure. Most “wet-chemistry” strategies for the separation of CNTs (according to their crystal structure) take advantage of a structureactivity relationship. Therefore, a better understanding of the SAR of CNTs is critical in this endeavor. A number of theoretical studies (see Tab. 8) have already been conducted and predict a SAR for CNTs, i.e., the adsorbate-CNT interactions depend on the CNT crystal structure (curvature and/or chirality).

ACKNOWLEDGMENTS

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The first project on alkane adsorption on CNTs by my group has been conducted in collaboration with B. White, S. O’Brien, and N.J. Turro (Columbia University, New York), and the first alcohol/CNT kinetics experiments were part of a physical chemistry laboratory class experiment at NDSU, which was a joint nanoscience teaching project, together with students and their teacher, D. Ulness, from Concordia College (MN). Most of our projects summarized here were part of the thesis work of S. Funk [267] and J. Goering [20] at North Dakota State University (NDSU). Projects together with Ya-Ping Sun’s group (Clemson University, South Carolina) concerning the effect of CNT crystal structure on their chemical activity are on the way at NDSU. This short review also includes some work done with P. Schmuki’s group at Erlangen-Nuerberg University on TiO2 nanotubes, as well as a project with R. Tenne’s group (Weizmann Institute of Science, Israel) on WS2/MoS2 nanoparticles/nanotubes. The support, fruitful teamwork, and discussions with all colleagues are gratefully acknowledged. Financial support from the Chemical Sciences, Geosciences, and Biosciences Division, Office of Basic Energy Sciences, Office of Science, U.S. Department of Energy is acknowledged (DE-FG02-08ER15987) as well as support through NSF CAREER (CHE0743932) is acknowledged.

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In: Carbon Nanotubes: New Research Editor: Avery P. Ottenhouse

ISBN 978-1-60692-236-1 © 2009 Nova Science Publishers, Inc.

Chapter 2

ON RESIDUAL METALLIC CATALYST IMPURITIES IN CARBON NANOTUBES Martin Pumera Biomaterials Center, National Institute for Materials Science, Nanomaterials & Biomaterials Research Building, 1-1 Namiki, Tsukuba, Ibaraki, Japan. Fax: +81-29-860-4714 Email: [email protected]

ABSTRACT The aim of this chapter is to discuss the problematic of residual metallic catalyst impurities in carbon nanotubes.

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MAIN TEXT Carbon nanotubes are one of the most promising nanomaterials with wide variety of applications, such as electronic [1], field emission [2], optic [3], biosensing [4]and biomedical [5] devices. However, there are numerous challenges to be resolved before their realistic utilization. A several problems that obstruct the useful applications of carbon nanotubes are related to their phase purity, chirality, large uncertainty in conductivity, spread diameter and length, industrial scalability and financial viability. The quality and purity of the carbon nanotubes (CNTs) depend significantly on supplier and often the purity of commercially available CNTs is overstated. The product offered commercially as CNTs contains secondary phases such as graphite, graphene sheets and metal catalyst nanoparticles usually embedded into CNTs. We examined [6] carbon nanotubes (single walled (SWCNT) and multi walled (MWCNT)) from five different commercial sources on presence of metallic impurities using thermogravimetric analysis (TGA) and we found the that provider purity information relevant to metallic impurities for as-received CNTs was in several cases more optimistic than the real value (see Table 1), and therefore, at least TGA characterization of a particular CNT material is always needed in order to obtain the real information on purity of the CNT material. Itkis et

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al [7] demonstrated that this is also true for amount of secondary carbon phases (amorphous carbon, graphitic carbon) in commercial CNTs and one should always characterize their CNT samples even though the certificate of analysis from producer is enclosed. Table 1. Amount of Metal Catalyst Nanoparticles in Carbon Nanotube Materials before and after Nitric Acid “Washing” (36 h, 80 °C) by TGA

Carbon Nanotube Material

TGA of asreceived CNT (w/w)

TGA of CNT "washed" at Elevated Temperature (w/w)

Minimum Guaranteed Purity of as-received CNT by Supplier (in Terms of Amount of Metal Residues) (w/w)*

MWCNT-A MWCNT-B MWCNT-C MWCNT-D SWCNT

6.80% 11.70% 1.45% 5.26% 10.82%

4.84% 1.40% 0.77% 2.75% 6.80%

5.00% 10.00% 3.00% 3.00% 7.00%

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*Based on provider information on specific lot of CNT. Reprinted from [6] with permission.

One of the problems with residual metallic impurities in carbon nanotube samples is their synthesis. CNTs are usually synthesized using metallic precursor (typically Fe, Ni, Co, Mo; however, in principle any metallic nanoparticle can behave as precursor) [8]. The actual mechanism of CVD growth and arch-evaporation is still under discussion, but it is suggested that the metal catalyst dissolves carbon from the carbon containing gas and the carbon is later transported to the edges of catalyst nanoparticles where it forms nanotubes (See Figure 1). The metal catalyst particle remains at the base of the nanotube, on its tip, or it is incorporated within the nanotube [9]. The most used purification procedure uses ‘washing’ carbon nanotubes with nitric acid which is expected to remove residual metallic impurities and partly also amorphous carbon – however, this is far from truth as we demonstrated in [6]. In this context it is important to bear in mind that after CNT synthesis, the metal nanoparticles are in form of oxides and/or carbides. It is known that kinetics of dissolution of many metal oxides and carbides even in concentrated mineral acids can be very slow [10] (for typical washing procedure, see Figure 2). We showed that MWCNTs and SWCNTs contain residual metal catalyst impurities even after prolonged period of ‘washing’ with concentrated nitric acid at temperature of 80°C. Transmission electron microscopy (TEM) and high resolution TEM revealed that this is due to the fact that such metal impurities are intercalated in the nanotube channel (in the case of MWCNT), in ‘bamboo’ segment of nanotube (in the case of ‘bamboo’-like MWCNT) or they create graphene sheet protected metal core/shell nanoparticles (in the case of SWCNT) [6].

On Residual Metallic Catalyst Impurities in Carbon Nanotubes

77

growth of CNT catalyst nanoparticle

carbon containing gas

Substrate Figure 1. Schematic of growth of carbon nanotubes.

Purification of CNT

MWCNT 6M HNO3 24 h COOH

O

COOH

f-MWCNT

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COOH OH

COOH

Metal, but also MxOy and MC Figure 2. Scheme of purification of carbon nanotubes using nitric acid.

It has been recently demonstrated that metal impurities in carbon nanotubes are in some cases responsible for the outstanding electrocatalytic properties of CNT-based electrodes and that different metal impurities can electrocatalyse oxidation/reduction of biomarkers at different electrochemical potentials [21, 22, 23]. It was also demonstrated that metallic nanoparticles intercalated within the CNT graphene lattice may still be chemically accessible; they can participate in the redox chemistry of biomarkers via intercalation of molecules within the CNT lattice [24]. Since CNT-based devices are expected to be used in a large amount of commercial products, many toxicological studies of CNTs were carried out with

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surprisingly contradictory results [25, 26, 27, 28, 29]. It might be possible that the uncertainty in the level of toxicity of the CNTs comes from the large scatter in concentration and type of the residual metal impurities (Fe, Ni, Co, Mo, etc.) in different CNTs studied [18, 19, 20, 21, 22]. These metal nanoparticles are strongly toxic for living organisms (with exception of iron) and as it was noted above, such nanoparticles can still interact with molecules even though they are intercalated within the CNT [17]. In order to address these problems and to simplify the purification procedures [20, 21, 22], several groups started to aim at production of catalyst-free CNTs [23, 24, 25, 26, 27]. However, the main question remains: Are the resulting CNTs truly pure? Are we using the correct and enough sensitive technique to ensure their purity to trace levels and to avoid falsenegative information? A number of studies use surface sensitive methods, such as X-ray photoelectron spectroscopy [30] or energy-dispersive X-ray spectroscopy [14, 28] for metal impurities determination. These methods might not be sensitive enough to detect the trace levels of metal nanoparticles especially when these are intercalated in the CNT. We can say the same for thermogravimetric analysis (TGA) which in addition does not offer any elemental analysis information [27]. While one might suppose that the purity control of carbon nanotubes is no longer an issue because it has been almost two decades since their discovery [29, 30, 31] and billions of dollars pumped into their research, the opposite is true. There is a growing crisis in the field due to the lack of standard, sensitive and selective analytical method for CNT purity evaluation. Critical comparison and evaluation of the methods for determination of metallic impurities in carbon nanotubes was still lacking until recently [32]. We recently presented [32] comparative study of several techniques for quality control of carbon nanotubes in terms of metallic impurities, namely magnetic susceptibility, electron paramagnetic resonance, energy-dispersive X-ray spectroscopy, X-ray photoelectron spectroscopy and thermogravimetry. We found that the dc magnetic susceptibility is the most sensitive method in a way that we could detect the difference between the two CNT samples that underwent slightly different treatment whereas for other techniques these two samples were indistinguishable. Therefore we suggested that the most accurate statistical method for quality control of carbon nanotubes is dc magnetic susceptibility which is able to detect traces of magnetic metal impurities embedded in purified carbon nanotubes while other methods may provide false “impurity-free” information [32]. In conclusion, I would like to alarm scientific community about the problem of residual metallic impurities in CNTs and urge the researchers working in this field to always carefully characterize their CNT materials in respect to metallic impurities.

REFERENCES [1] [2] [3] [4]

S. J. Tans, M. H. Devoret, H. J. Dai, A. Thess, R. E. Smalley, L. J. Geerligs, and C. Dekker, Nature, 1997, 386, 474. N. de Jonge N, Y. Lamy, K. and Schoots, T. H. Oosterkamp, Nature 2002, 420, 393. J. A. Misewich, R. Martel, Ph. Avouris, J. C. Tsang, S. Heinze, and J. Tersoff, Science, 2003, 300, 783. M. Pumera, S. Sánchez, I. Ichinose, and J. Tang, Sensors Actuators B. 2007, 123, 1195.

On Residual Metallic Catalyst Impurities in Carbon Nanotubes [5] [6] [7] [8] [9]

[10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26]

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[27] [28] [29] [30] [31] [32]

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D. W. Grainger, and D. G. Castner, Adv. Mater. 2008, 20, 867. M. Pumera, Langmuir. 2007, 23, 6453. M. E. Itkis, D. E. Perea, R. Jung, S. Niyogi, and R. C. Haddon, J. Am. Chem. Soc. 2005, 127, 3439. D. Takagi, Y. Homma, H. Hibino, S. Suzuki, Y. and Kobayashi Y. Nano Lett. 2006, 6, 2642. S. Hofmann, R. Sharma, C. Ducati, G. Du, C. Mattevi, C. Cepek, M. Cantoro, S. Pisana, A. Parvez, F. Cervantes-Sodi, A. C. Ferrari, R. Dunin-Borkowski, S. Lizzit, L. Petaccia, A. Goldoni, and J. Robertson, Nano Lett. 2007, 7, 602. Ed., McGraw-Hill P. Patnaik, Dean's Analytical Chemistry Handbook, 2nd Professional, New York, 2004; Chapter 1. C. E. Banks, A.Crossley, C.Salter, S.J. and Wilkins, R.G. Compton, Angew. Chem. Int. Ed. 2006, 45, 2533. B. Šljukić, C. E. Banks, and R. G. Compton, Nano Lett. 2006, 6, 1556. X. Dai, G. G. Wildgoose, and R. G. Compton, Analyst, 2006, 131, 901. J.L. Lyon, and K.J. Stevenson, Langmuir 2007, 23, 11311. A. Nel, T. Xia, L. Madler, and N. Li, Science 2006, 311, 622. S. K. Smart, A. I. Cassady, G. Q. and Lu, D. J. Martin, Carbon 2006, 44, 1034. J. M. Wörle-Knirsch, K. Pulskamp, and H. F. Krug, Nano Lett. 2006, 6, 1261. L. Zhu, D. W. Chang, L. Dai, and Y. Hong, Nano Lett. 2007, 7, 3592. J. Muller, F. Huaux, and D. Lison, Carbon, 2006, 44, 1048. S. Arepalli, P. Nikolaev, O. Gorelik, V. G. Hadjiev, W. Holmes, B. Files, and L. Yowell, Carbon, 2004, 42, 1783. D. Chattopadhyay, I. Galeska, and F. Papadimitrakopoulos, Carbon, 2002, 40, 985. J. Chen, A. Kuno, M. Matsuo, T. Tsukada, T. Tamura, K. Osato, J.Y. Shan, F. Munekane, Y.A. Kim, T. Hayashi, and M. Endo, Carbon 2008, 46, 391. S. Irle, Z. Wang, G. Zheng, K. Morokuma, and M. Kusunoki, J. Chem. Phys. 2006, 125, 044702. J. Hahn, S. B. Heo, J. and S. Suh, Carbon, 2005, 43, 2638. S. Botti, L.S. Asilyan, R. Ciardi, F. Fabbri, S. Loreti, A. Santoni, and S. Orlanducci, Chem. Phys. Lett. 2004, 396, 1. B. Corzilius, A. Gembus, N. Weiden, K.-P. Dinse, and K. Hata, Phys. Stat. Sol. 2006, 243, 3273. C. P. Jones, K. Jurkschat, A. Crossley, R. G. Compton, B. L. Riehl, and C. E. Banks, Langmuir, 2007, 23, 9501. N. S. Lawrence, R. P. and Deo, J. Wang, Electroanalysis 2005, 17, 65. S. Iijima, Nature 1991, 354, 56. D. S. Bethune, C. H. Kiang, M. S. De Vries, G. Gorman, R. Savoy, J. Vazquez, and R. Beyers, Nature 1993, 363, 605. S. Iijima, and T. Ichihashi, Nature 1993, 363, 603. T. Kolodiazhnyi, and M. Pumera, Small, 2008, in press. DOI: 10.1002/smll.200800125.

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In: Carbon Nanotubes: New Research Editor: Avery P. Ottenhouse

ISBN 978-1-60692-236-1 © 2009 Nova Science Publishers, Inc.

Chapter 3

INSIGHT OF THE KINETICS CARBON NANOTUBES GROWTH AND FUNCIONALIZATION WITH FREESTANDING SILICON NANOCRYSTALS Vladimir Švrček∗ Novel Si Material Team, Research Center for Photovoltaics, National Institute of Advanced Industrial Science and Technology (AIST), Central 2, Umezono 1-1-1, Tsukuba, 305-8568, JAPAN

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ABSTRACT In this chapter the growth kinetics of most common carbon nanotubes (CNTs) synthesis at industrial scale by catalyst assisted chemical vapor deposition (CVD) is discussed. It is shown that the monitoring of CNTs growth at initial stages by using a Tapered Element Oscillating Microbalance (TEOM) brings new insights into synthesis and controllability of the CNTs properties. The high sensitivity of the TEOM technique allows precisely determinates the crucial synthesis parameters. We argue that precise TEOM control of the reaction temperature and the partial pressure allows evaluate the order of the reaction kinetics and absolute reaction rate. Furthermore, CNTs solve some challenges linked with connection and manipulation of silicon nanocrystals (Si-ncs) at nanoscale level. Particularly, direct growth of CNTs on Si-ncs in the TEOM is performed in order to connect single Si-nc. Compared to porous catalyst supports substantial differences in CNTs growth kinetics are observed when the synthesis is performed on flat Si-ncs surface. A model taking into accounts an associative and competitive adsorption of ethane is used to interpret obtained results. The diameter of the CNTs depends on the size of the Si-ncs, which remains connected on the tip of the CNTs. The wired Si-ncs keep room temperature photoluminescence properties. It is shown that the CNT cavity, in additionally, can serve as nano-reservoir for freestanding Si-ncs. Colloidal dispersion of freestanding Si-ncs allows entering into CNT cavity by induced capillary force. Alternatively, the shock waves generated during Si-ncs formation in transparent polymer by nanosecond laser processing assure the filling as well. We believe that the present

∗

Tel: +81-29-861-5429; Fax: +81-29-861-3367; e-mail: [email protected]

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Vladimir Švrček findings might open new opportunities and situations in a development of new class of nanodevices for the environmental friendly applications.

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1. INTRODUCTION There has been much interest in carbon nanotubes (CNTs) [1-4] last decade, especially for potential use in microelectronic, photovoltaics and other terrestrial useful devices [5, 6]. The synthesis of CNTs can be performed by different kind of techniques. There are three commonly used means by which to prepare CNTs. The first of these methods is laser ablation [7]. A high power laser is applied across a carbon target and in the plasma plum the generation of CNTs is achieved. The second is the Arc-discharge method synthesizes by using a fairly low voltage power supply to strike an electrical arc between two carbon electrodes. The CNTs form in the arc and collect on the anode electrode [8]. Chemical vapor deposition (CVD) is the third most common way of CNTs synthesis [9, 10]. This means is the most common synthesis at industrial scale and is achieved by taking a carbon species in the gas phase. An energy source, such as plasma or a resistively heated coil, to impart energy to a gaseous carbon molecule is used. Most often use gaseous carbon sources include methane, ethane, carbon monoxide, and acetylene. CVD growth of CNTs by decomposition of ethane is the means of synthesis that is of interest for this chapter. CVD carbon nanotube synthesis is essentially a two-step process; (i) a catalyst and (ii) actual synthesis of the CNTs [4]. Up to date, however, the mechanisms of CVD kinetics of CNTs synthesis at early stage are under debate and not well understood yet. The close relationship between nanotube properties and geometrical structure forcedly need this understanding. In our knowledge, there are only few reports that investigate the kinetics of CNTs growth in a methodical manner [11, 12]. In ccontrast to that the growths of carbon nanofibers is better described and comprehend [13, 14]. Two methods are mainly used to insitu investigate the kinetic of the carbon nanofibers synthesis; (i) controlled atmosphere electron microscopy [15], and (ii) thermogravimetric measurements [16-20]. One solution to complete in-situ CNTs growth monitoring at early stages is accessible by using a tapered element oscillating microbalance (TEOM) technique [21, 22]. This experimental set up allows achieving homogeneity in contact with the catalyst and determining of absolute reaction rate [23]. The growths of CNTs, either free standing (powder like) or solidly attached on substrate, is achieved. At the same time an accurate reaction kinetic can be acquired [22]. The CNTs apart from being the best within the most of available one-dimensional (1D) model systems show strong application potential as well. While some of the proposed applications remain still a dream, others are close to technical realization. State-of-the-art such dream is using CNTs in purpose to wire the single nanocrystals or quantum dots [24]. We like to emphasize that the excellent CNTs transport properties, with conductivity 1000 times the one of copper nowadays mostly technologically used, suggest them reach this goal. The achievement allows solve some challenges linked with the manipulation and the device fabrication at nanoscale level [24]. A silicon nanocrytal few nanometers in diameter (< 10 nm) is particularly attractive candidate for nanoscale device fabrication. Discovery of bright photoluminescence (PL) in silicon nanocrystals (Si-nc) at room temperature increased hopes in Si-ncs for many terrestrial applications [25-31]. The usefulness is amplified in a form soluble freestanding and surfactant free Si-ncs [28, 30]. The development of reliable methods

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for the connection of the CNTs with Si-ncs might provide an additional impetus towards extending the scope of nanotubes application. The precise control of the CNTs synthesis by TEOM on Si-ncs provides a route to connect Si-ncs with the characteristics as a will. All at once offers the possibility to get better in manipulation and effective elaboration of Schottky nanojunctions [24]. It is distinguished that the cavity of CNTs can serve as nano-reservoir for stabilization of the nanoparticles and molecules [32-36]. The freestanding Si-ncs are soluble in almost any liquid resulting to surface tension variation [37]. This allows an encapsulation of Si-ncs inside CNTs cavity [38]. Contrary to the high surface tension of silicon that makes filling of CNT cavity impossible [39], a dispersion of freestanding Si-ncs in organic solution can overcome some related problems [38, 40]. Other technique that effectively varies Si-ncs surface tension is laser processing in liquid [41, 42]. Direct laser processing of Si-ncs in liquid media (e.g. transparent commercially available ethylpolysillicate polymer, water) [37, 42] decreases surface tension and permits an introduction of Si-ncs within CNT cavity. In-situ CNT cavity Si-ncs stabilization throughout laser processing prevents pollution, agglomeration of Si-ncs andmight leads to original class 1D nano-composite fabrication at low cost [43]. In this chapter investigations the kinetics of CNTs growth in TEOM micro-reactor by catalyst assisted CVD are described. We focus on influence of the reaction temperatures, gas content and structure of catalyst support on the growing CNTs processes. The synthesis of CNTs is studied on iron and on nickel catalyst. Catalyst is sited either on porous alumina or flat Si-ncs support. The CNTs synthesis is assured by decomposition of ethane. The obtained results clearly show that TEOM has unique capability precisely determinates reaction kinetic order. Furthermore, connecting of single Si-nc in TEOM with conducting CNTs is regarded to establish electrical contact and improved the localization of single Si-nc. After all, the functionalization by assemblies of luminescent Si-ncs in carbon nanotube cavity is overviewed. We briefly provide some highlight of the assemblies freestanding Si-ncs within CNTs cavities.

2. EXPERIMENTAL

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2.1. Experimental Set Up The investigations of catalyst assisted CVD kinetics growth of CNTs are performed in a commercially available TEOM from Rupprecht and Patashnick Co., Inc. Figure 1 (a) shows the scheme of experimental set up used in this study. TEOM design permits a defined control of the variety CNTs growth parameters. The TEOM is provided with two automatic heating zones and gases flow control. The pre-heating zone 1 (Fig. 1(a)) controls the temperature of the gas stream in the upper part of the sensor. The heat zone 2 controls temperature of the tapered element and the micro-reactor where the CNTs synthesis takes place. An automatic run of purge helium gas flows through the tapered element micro-reactor is managed. Catalyst support in the microreactor between quartz cotton is positioned. In all presented experiments the synthesis of CNTs is achieved with a gas mixture of ethane and hydrogen (C2H6:H2). The vibration frequency of the tapered micro-reactor is monitored by an optical way. A transmitter and a receiver are located on the opposite sides of the micro-reactor.

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Figure 1. (a) Sketch of experimental set up of the Tapered Element Oscillating Microbalance (TEOM) used for kinetics of CNTs growth studies. (b) One typical plot of the temperature variation in the microreactor during the growth of CNTs by catalyst assisted CVD process.

The system resolute the mass uptake Δm = m(t) – m0 of the microreactor during the synthesis times t and t = 0 using the following equation:

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(1) where f0 and f1 are the natural oscillating frequency at times t0 and t1, respectively, and K is a constant that depends on the geometry of the experiment. At the beginning of the each novel experiment a new frequency f0 is automatically settled after the catalyst with wool is placed into the micro-reactor. Then the change in the frequency between f1 and f0, permits to calculate the absolute values of the mass uptakes (Eq. 1.). Figure 1 (b) displays typical variation of the temperature in the micro-reactor during the synthesis and monitoring of CVD synthesis process. CNTs growth by introduction of the catalyst on support and decomposition of ethane is assured. The temperature increases about 40 min under hydrogen flow from room temperature to 400 °C (673 K), and then this temperature is maintained one hour to reduce the oxide form the catalyst precursor. The temperature is then continuously increased up to reaction temperature. Figure 1 (b) represents typical process of the CNTs growth at reaction temperature 750 °C (1023 K) that takes 5 min. At this temperature, a mixture of ethane and hydrogen replaces the hydrogen flow. Helium is used as a vector gas with a flow rate similar to the total flow rate of C2H6 and H2 (60 sccm). In this chapter the similar process is applied. Whenever just one parameter for each experiment i.e. reaction temperature, ratio of ethane and hydrogen, catalyst and catalyst support is varied. When the influence of reaction temperature is investigated the temperature varied from 873 to 1113 K and mixture of ethane and hydrogen (C2H6:H2 at 1:2 ratio) is kept constant at 60 sccm for all series. For following experiments (e. g. variation of ethane and

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hydrogen ratio, influence of the catalyst nature (Fe, Ni) and catalyst support (porous alumina, Si-ncs)} the reaction temperature was 1023 K. Since the volume of the CNTs increases markedly in the course of the synthesis, the growth time is consequently limited. Therefore the synthesis for all cases not exceeds 5 min. After the synthesis the samples are cooled in hydrogen atmosphere to room temperature for several hours.

2.2. Catalyst Supports

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The CNTs growth by introduction of the catalyst on porous alumina and Si-ncs, supports is promoted. Porous alumina support is a high surface area γ-Al2O3 (CK 300B Ketjen with a surface area of 220 m2. g-1), which is mainly made up of a mesoporous network. Iron deposited on alumina (Fe/Al2O3) is used as catalyst to insure the CNTs synthesis. The alumina support is crushed and sieved. A fraction of 40 - 80 μm is retained for catalyst preparation. The catalyst is prepared by using an aqueous solution of (Fe(NO3)3⋅9 H2O), with a Fe concentration fixed at 20 wt. % (20% Fe/Al2O3 catalyst). The wet solid is dried at 100 °C and further calcined in air at 350 °C for 2 h in order to obtain an oxide form of the catalyst precursor. Then 10 mg of the impregnated alumina support is placed in the micro-reactor of TEOM between quartz wool (Figure 1 (a)). For the purpose of the Si-ncs connection by CNTs the catalytic particles are deposited on the freestanding Si-ncs prepared by electrochemical etching. The preparation of freestanding and surfactant free Si-nc is described elsewhere [30]. Briefly, the Cz silicon, p-type boron doped, , 1 Ohm.cm is used as starting material to fabricate room temperature photoluminescent Si-ncs. We compare CNTs growing process on Si-ncs coated either by iron (Fe/Si-nc) or nickel (Ni/Si-nc). Those catalysts are prepared by following way. The Si-nc are introduced into an aqueous solution of Fe (Fe(NO3)3⋅9 H2O) or nickel nitrade hexahydrate (N2NiO6⋅6 H2O with the Fe (Ni) concentration fixed at 20 wt. %. This solution is then kept in an ultrasonic bath for 30 min. The operation is repeated five times in order to ensure the deposition of iron particles on the Si-nc surface. Then the solution is dried at 100 °C and then calcined in air at 350 °C for 2 h. Similar to porous alumina, the catalyst reduction is guaranteed in-situ in TEOM micro-reactor, before the CVD synthesis takes place, under a hydrogen atmosphere at 450 °C.

2.3. CNTs Cavity Filling with Silicon Annotates As reported elsewhere, basically, two means for opening of the CNTs ends are used. The first one is thermal annealing [44–46] and the second one is chemical treatments [45-48]. In order to open ends by thermal approach, the CNTs are thermally annealed in oxygen or air atmosphere. The reactivity of graphite at the ends of the tube is higher than on the walls, due to the stress-induced by the curvature [49]. In our case the opening temperature of CNTs has been preliminary determined by thermogravimetric (TGA) analysis. The CNTs are annealed at a rate of 5°C/min up to the temperature of the inflexion point deduced from TGA analyses (T = 580°C). After use of this approach more than 80 % of observed carbon nanotubes were

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opened [49]. Opened nanotubes are filled with together Si-ncs dispersed (0.01 wt.%) in commercially available silicate based polymer [30]. For the CNTs cavity filling experiment by laser fragmentation same opened nanotubes were used. The Si micrograins prepared by electrochemical etching serve as the source for Sincs fabrication by pulsed laser fragmentation in transparent polymer [42]. In 30 ml of polymer 0.01 mg of CNTs is homogenously dispersed. Then added 0.01 wt% of micrograins and a 5 ml of such solution (micrograins/CNTs/polymer) is irradiated by a pulsed laser (Nd:YAG, 355 nm, 30 Hz, 8 ns) at fluence 6 mJ/pulse for 2 hours at room temperature. The laser beam on the liquid surface is focused and the glass container is rotated during laser processing.

3. KINETCIS OF THE CARBON NANOTUBES GROWTH 3.1. Kinetics on Porous-Alumina Catalyst Support

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Synthesis parameters, such as reaction temperature and partial pressure, heavily affect the CNTs kinetics of growth. Therefore, in order to evaluate the reaction kinetics those parameters are investigated and discussed in details in this section. In our TEOM experimental configuration and used catalyst (iron on alumina support) the CNTs formation starts at reaction temperature around ~ 963 K. In figure 2 (a-c) typical mass-uptakes in TEOM micro-rector for three different temperatures are shown. It has to be noted that below < 933 K an amorphous carbon is mainly formed. The mass uptake is associated to the initial mass m0 of catalyst (10 mg) at t = 0 min. It is observed that the mass uptake strongly increases with temperature from 933 K up to 1083 K and then abruptly drops at 1113 K [50]. This is the region of the temperatures where a significant weight changes in micro-reactor occur induced by the growth of CNTs. Figure 2(b) shows mass uptake and growth rate when the formation of CNTs takes place at temperature 1023 K. Two region indicated by red lines corresponding two growth rates v1 and v2. What is the origin of the difference in growth rates? In general it is accepted that the growing rate vi (i = 1, 2) is defined as the initial rate of mass increase (t = 0) and the subsequent linear mass increase described as follow [6]

⎧ E ⎫ v = A exp⎨− a ⎬ , ⎩ R0T ⎭

(2)

where R0 is the perfect gas constant (R0 = 8.31 J/K) and T (K) is reaction temperature. The initial growth rate v1, is associated with the initial carbon uptake. This mass increase displays the largest variations of the activation energy. At low reaction temperatures from 873 K to 993 K low activation energy of 12 kJ/mole is evaluated. Within 993K and 1023K fast increase in activation energy is observed (146 kJ/mole). Above 1023K up to 1083K, however, the grow rate is constant or slightly decreasing (– 12 kJ/mole). Finally, over the temperature > 1083 K the initial rate drops abruptly. Detailed kinetics analysis show that v1 can be assigned to the formation of a dynamic equilibrium between carbon adsorption-bulk diffusion-

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segregation on the iron catalytic nanoparticle, whatever the nature of this carbon is made up, and the growth rate v2 to the specific formation of the CNTs. In addition, also Arhenius plot show two growth rates; (i) v1 initial due to the adsorption /disorption C2H6:H2 on the catalyst, and (ii) v2 rate attributed to the growing of the CNTs. Activation energies suggest the reaction order toward a common kinetics [49]. Right panel in figure 2 shows corresponding SEM images of the samples after synthesis at reaction temperatures 873, 1023 and 1113 K, respectively. With increased temperature the CNTs are prolonged and diameter of the CNTs varies. Up to 993 K the outer diameter increases and reaches of about 47 nm in average, then decreases to 20 nm. However to evaluate the longer of CNTs is quite difficult because of forming bunches specially for higher temperatures (> 850 K). The structural characterization by transmission electron microscopy (TEM) clearly displays graphitic multiwalls around the tubule.

Figure 2. Left panel (a-c) shows time dependence of the weight mass uptake in the micro-reactor of TEOM for CNTs grown 5 min at three different temperatures. Synthesis is ensured by decomposition of a gas mixture of ethane and hydrogen C2H6:H2 at molar ratio 1:2 and 60 sccm. The growth rates v1 and v2 are indicated for temperature 1023 K. Right panel shows corresponding SEM images.

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In addition, the Raman spectra of the carbon deposit exhibit the two narrow bands D and G at 1340 and 1570 cm-1 with a clear tailing around 1610 cm-1 [22, 49] These contributions are quite characteristic of the presence of CNTs with some extent of defects as also evidenced by the TEM image. Similar spectra are recorded on each sample when considerable uptake of mass in TEOM was observed. When we investigated an influence of the partial pressure on growing process we kept constant the total flow D = DC 2 H 6 + DH 2 = 60 sccm and reaction temperature at 1023 K. In this case the variable parameter of the synthesis is the ratio RM = (DC2H6 / DH2) = (PC2H6 / PH2.). It is observed that besides of the reaction temperature also an increased content of ethane substantially influence the initial growth rate. For instance, by decreasing of dilution ratio of gas mixture from a 1:5 C2H6:H2 to a 1:1 C2H6:H2 the growth rate increased from 0.050 mg/mg(cat).min to 0.115 mg/mg(cat).min, respectively. With the ethane concentration increases in the gas flow, sooner saturation of the mass uptake occurs [22]. In our particular case, with a (1:5) C2H6:H2 gas mixture, saturation is not observed whereas with a 1:1 mixture saturation starts after three minutes of the synthesis. This is in agreement with a promoted coking process at higher hydrocarbon pressure, which is widely reported elsewhere [22, 50, 52]. In figure 3 the initial growth rate is plotted as a function of gas ratio. The linear behaviour in a semi-logarithmic scale allows determining the power law of rate CNTs growth v2 versus gaseous carbon sources mixture that can be expressed as follow

⎛ − Ea ⎞ ⎟⎟ v = kR x exp⎜⎜ ⎝ R0T ⎠

(3)

where k is a kinetic constant and Ea is the activation energy of the mass increase process. From the linear extrapolation of the plot in figure 3

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ln(v) = x. ln( RM ) + C

(4)

an exponent x = 0.50 ± 0.03 can be evaluated. It is shown that the growth rate increases linearly with the square root of the ethane-to-hydrogen ratio of partial pressures. Thus a first order kinetics with regard to carbon concentration can be deduced from these results, whereas hydrogen competes with hydrocarbon for the adsorption on the catalytic sites of the catalyst. These results are coherent with a simple model where the dissociative adsorption of the hydrocarbon is the rate-determining step of the overall process within the assumed limitations that the carbon partial pressure is low compare to the hydrogen partial pressure. Thus the corrected expression is

⎛ − Ea ⎞ ⎟⎟ . v = k ( P C 2 H 6 / PH 2 ) 0.5 exp⎜⎜ R T ⎝ 0 ⎠

(5)

It means that the kinetics of carbon mass increase is first order with regard to carbon partial pressure and is prevented to the first order by hydrogen partial pressure. The fact that

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hydrogen is competing with hydrocarbon source strongly supports a rate-limiting step due to the adsorption on iron active catalytic sites. The carbon molar rate yield RM (%) calculated according to expression (3) and (5) can be written as follows RM = [R0 . T . k / 2 . D Mc . (PC2H6 / PH2)0.5] . exp(-EA / R0 .T),

(6)

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with D = 20 10-6 m3/min; Mc = 12 g/mole. The growing rates linear increases of allows estimate the net molar rate of carbon deposition. In our case hydrocarbon flow fully contacts the catalyst and therefore the initial mass increase is due to the pure carbon. We observe that molar ratio increases linearly and for growth rates being rather similar slope for all series of samples. This means that carbon is much easier to deposit on catalyst at higher temperature. Carbon yields fall between 20% and 25% that means that one fourth to one fifth of the input carbon is decomposed and used for the CNT growth. The beneficial effect of hydrogen is explained by a probable hydrogenation of the coke deposited at the iron catalyst, leaving some surface sites free for the reaction. These results together with reaction temperature dependence growth corroborate and confirm that we deal with the reaction order toward a common kinetics. From structural viewpoint, as the concentration of ethane increases the quantity and structural properties of synthesized CNTs altered as well. Ethane concentration results to the synthesis with larger amount of CNTs and smaller diameter. For example, when the ethane:hydrogen ratio is increased from 1:3 to 1:1, the average outer diameter of the CNTs decreases from about 45 nm to 21 nm. It should be emphasized that this behaviour can qualitatively be correlated with an increasing density of CNTs. New catalytic sites for CNTs nucleation and growth are active with higher carbon content. As the density of tubes significantly increase then less carbon is available for each catalytic particle and thinner CNTs are grown.

Figure 3. Initial rate CNTs growth (G) as a function of the carbon molar rate yield (RM).

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3.2. Flat Catalyst Support and Single Silicon Nanocrystal Connection

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Subsequently direct functionalization of single Si-ncs by connecting with conducting multiwalled CNTs is discussed. Figure 4 represents the average mass uptake in the microreactor of TEOM at reaction temperature 1023 K. Iron and nickel catalysts sited onto Si-ncs surface promote the CNTs synthesis. Open circles represent the iron (Fe/Si-nc) and full squares the nickel (Ni/Si-nc) catalyst. The catalyst amount is the same (20 wt.%) for both cases. The total mass uptakes increase linearly without saturation. Contrary to the porous alumina, flat nanocrystal surface reduces inter porous diffusion and inhibit the mass uptake saturation [22]. Then catalyst is assumed to be quite accessible to the ethane, whereas on high surface area catalytic nanoparticles supported on alumina the accessibility perturbed. In addition, on the flat surfaces, the growth rate is linear over the whole time range as it is neither disturb by long-term poisoning of the catalyst, nor by the rapid initial transient steps due to carbon saturation of the metal particle and nanotube nucleation. This infers that nonsteady state kinetics occur when encompassing a large time period of mass uptake over high surface area catalysts. This non-stationary state has been explained by a selective coking of the catalytic particles either located outside or inside the pores of the support [22]. Over a long period of mass increase, the measured kinetics tends rapidly to saturation and the determination of the kinetic order may be strongly changed. Indeed it is tempting to consider that the initial rate at t = 0 would be the true rate corresponding to carbon incorporation. However it was shown independently that the initial carbon uptake also involves the irreversible carbon bulk saturation of the catalyst particle [32].

Figure 4. Time dependence of average mass increase in the micro-reactor of TEOM at temperature 1023 K. Two catalysts are supported into silicon nanocrystals surface. Red circles represent 20 wt.% of iron and black squares represent 20 wt.% of nickel catalyst.

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For both catalysts, after initial carbon absorption and nucleation at the interface between the Si-ncs and the carbon nanotube the growth take place. It is observed that the growing on the iron catalyst is more efficient compared to nickel. In iron case the growing rate reaching the value of 1.21 + 0.02 mg/min with RM = 21.43 %. This value is very similar as iron catalyst deposited on porous support. However, the growing rate on nickel is lower and reaches 0.2096 + 0.046 mg/min with corresponding carbon yield RM = 3.71 %. This rather low rate is assumed be assigned to low portion of the input carbon decomposition. A fast carbon covering of the Ni particles cannot explain the deactivation of the nickel. If so then a rapid initial mass increase followed by saturation would be observed. The low growth rate can be explained by etching of the Si-ncs by hydrogen and formation of nickel silicide [22] resulting lower mass uptake. Figure 5 shows corresponding SEM images of CNTs obtained by CVD in TEOM when nickel and iron catalyst is sited onto Si-ncs surface. From the SEM micrographs, it appears that CNTs are grown with a random growth direction with lengths that exceed several micrometers. It is observed that the diameters of CNTs grown on nickel catalyst are smaller compared to iron. In the case of iron catalyst the average diameter is around 58 nm while for nickel reaching of 29 nm.

Figure 5. Corresponding scanning electron microscopy (SEM) images of CNTs obtained by CVD in TEOM when the catalyst is introduced into silicon nanocrystals; a) nickel b) iron.

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As mentioned earlier this might be related the etching process of Si-ncs surface by hydrogen that promotes nickel silicide formation leading to lower mass uptake (Fig. 4, squares). Similar to the porous alumina support, no significant difference is observed in the distribution in lengths and the purity. The length of the carbon nanotubes is several micrometers and is rather similar for both catalysts and supports. In all cases the purity is estimated to be larger than > 90%. Detailed structural analysis reveals that the Si-nc stays stuck on tip of the CNT end. This consequences direct nanotube connection to the Si-nc surface with a strong adhesion force. In Figures 6 (a) a TEM image of a single Si-nc on top of a CNT is shown. In this case the iron catalyst is coated on Si-ncs surface. It exhibits a size of about 50 nm fully capping the asgrown carbon nanotube with a slightly smaller diameter. Apparently, the adhesion force is strong enough to avoid the loss of the Si-nc from the tube tip. The CNTs direct growth on Sinc and a disappearance of the catalyst from the Si-nc surface is observed [24].

Figure 6. a) Typical TEM image of a single silicon nanocrystal (size around 50 nm) connected to a carbon nanotube (CNT). b) Room temperature photoluminescence (PL) spectra of Si-ncs connected with CNTs (full triangle) and CNTs (open circle) synthesized at the same conditions on porous alumina support.

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The carbon segregation from the catalyst phase localized on the surface of the Si-nc allows the wetting of the rear face of the Si-nc and thus induces the formation of the CNT with a diameter similar to that of the support i. e. Si-nc. It has to be emphasized that we check that CNTs cannot be grown on Si-nc alone. This stresses that the catalyst plays a crucial role in the growth of carbon nanotubes and connection of Si-ncs. The catalyst is a necessary condition to allow the decomposition of the hydrocarbon ethane based precursor. From the walls of the starting nanotubes, the interplanar distance characteristic of graphite can be estimated to 0.338 nm. Detailed HR-TEM analysis revealed parallel stripes of Si-nc with a diamond lattice same as the initial orientation of the starting material [24]. Next question that one can ask is whether the Si-ncs keep the luminescence properties after CNTs synthesis and connection. We have investigated room temperature PL properties of such Si-ncs wired with CNTs. The connected Si-ncs to CNTs showed visible room temperature PL under YAG blue light illumination at wavelength 355 nm. Triangles in Figure 6 (b) represents PL spectrum of connected Si-ncs by CNTs where the iron catalyst promoted the synthesis. The CNTs (open circles) grown on alumina support at same conditions showed no visible PL in this spectral region at room temperature. In fact the PL peak maximum is located at the same wavelength as for freestanding Si-ncs only [24, 30]. It has to be noticed that the intensity is weaker more than 50 times compared to the intensity before CVD process. Several causes are responsible for this decrease. When the Si-ncs are exposed to high temperature treatment (> 600 °C) the changes of the surface states and the defect diffusion induces a quenching of the PL intensity.

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4. FILLING CARBON NANOTUBE CAVITY BY SILICON NANOCRYSTALS As it is well known, the high surface tension of molten silicon disallow direct filling of CNT cavity [39]. An immersion of CNTs into organic solutions containing of Si-ncs enables to obtaining surface threshold values for nanotube wetting and introducing luminescent Si-ncs into CNTs cavity [38, 40]. Here, we discuss the results of filling CNTs by two diverse approaches based on different physical phenomena that promote the filling. Firstly, by capillary forces induced by CNTs cavity, and secondly, by shock waves generated during pulsed nanosecond laser irradiation of colloidal solution. In our explorations we have investigated Si-ncs surface tension variation and cavity filling in environmental (e.g. water) and technological (spin on glass) friendly solutions. A figure 7 (a) shows the TEM image of CNTs cavity filling promoted by capillarity force after immersion of CNTs in the Si-ncs/polymer solution. The solution is silicate-based polymer containing homogenously dispersed Si-ncs. The image shows of a CNT with a diameter of 50 nm, where a Si-ncs are observed in the core of the nanotube. The circles indicate spots a size of around 3 nm and might correspond to a Si-nc. It has to stress that such Si-ncs are found quite far, around 500 nm, from any end of the CNT [38]. This is in agreement with the findings that most of the CNTs used here are not bamboo-like, without internal carbon membranes that would stop the Si-nc incorporation [32, 40]. The high amount of embedding amorphous polymer surrounding the Si-ncs does not allow resolving the Si interplanar distances. In order to confirm Si-ncs presence, a selective diffraction analysis is conducted on this area. A diffraction pattern taken in the tube is displayed in figure 7(b). Due

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to the random Si-ncs orientation the rings were recorded and could be assigned to the silicon lattice planes with diamond like structure.

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Figure 7. (a) A plan-view HRTEM image of an open CNT and filled with a Si-nc/polymer solution. The Si-ncs were prepared by electrochemical etching and homogeneously dispersed in organic based polymer solution. (b) Corresponding diffraction pattern taken in the tube confirms the presence of silicon nanocrystals with diamond like structure.

Recent development of fabrication of Si-ncs in liquid media by pulsed laser processing allows preparation of Si-ncs with surface tension different to bulk silicon and unusual wetting phenomena [41]. We have focused on introducing of freshly prepared Si-ncs by laser processing in liquid transparent polymer. At the same times, as the Si-ncs are prepared the shock waves are generated through the solution (polymer/CNTs/micrograins) [42, 43]. We exploit shock waves as a principal force to fill CNTs cavities by Si-ncs freshly prepared in polymer solution. To suppress the effect of the capillary forces the CNTs were prior to introduce into solution. Detailed HR-TEM analysis is performed to confirm the presence of Si-ncs within the CNTs cavity after laser processing. Figure 8 displays image of filled CNT with inner diameter of 50 nm when the solution is irradiated at laser fluence of 6 mJ/pulse. It is observed that nanotubes cavities are fully filled with Si-ncs/polymer composite. Corresponding electron diffraction pattern (inset), reveals silicon diffraction rings that could be assigned to the lattice planes , , with cubic phase. It is assumed that the filling occurred by following way. The shock waves propagating through the solution generate reflux, which is the principal driving force to introduce the freshly formed Si-ncs into CNT cavity. For generation of shock waves are responsible two major effects. Firstly, the strong electric field generated by the laser causes the electron avalanche near the silicon micrograin, and secondly, the breakdown of the polymer in liquid phase. In our experiments, a bright spot near the surface level is observed and one could hear explosion sounds due to the optical breakdown of the polymer. Either the collapse of vaporized cavitations bubbles or the grains that can be accidentally diffused under the beam cause these explosions. Even more, the shock waves are accelerated at large distances with the explosion [43]. As a sign of a micrograins fragmentation and nanocrystals formation is change of the solution color [42].

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Figure 8. HR-TEM image of Si-ncs fragmented in silcate polymer and filled in CNTs cavity at laser fluence of 6 mJ/pulse. Inset shows selected area electron diffraction pattern in the tube.

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Also in our case the solution (polymer/CNTs/micrograins) when is irradiated with enough high intensities (>4 mJ/pulse), loses its characteristic yellowish color and becomes transparent. As the fragmentation occurs freshly-produced Si-ncs embedded in hydrophilic polymer solution are introduced in the CNT cavity. The question arises what happens with the CNTs during the pulsed laser irradiation. The CNTs itself at this dispersed concentrations and used irradiation intensities have weak absorption at the wavelength at 355 nm [43]. Therefore, mostly the micrograins fragmentation occur. However, at higher fluencies also broken CNTs are found.

Figure 9. Normalized photoluminescence intensity as a function of wavelength of Si-nc/polymer/CNTs composites. Full red squares represent CNTs filled with Si-ncs/polymer by capillary force. Open blue circles correspond to filled CNTs by Si-ncs fabricated by laser fragmentation of the micrograins in polymer solution at laser fluence 6 mJ/pulse.

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It has to be stressed that both filling processes are achieved at room temperature (300 K). This has several advantageous: (i) the inhibition of the emptying of the tubes [52], (ii) the absence of defects formation in Si-ncs, and (iii) the limitation of the degradation of Si-ncs based nanocomposite luminescence properties. Figure 9 compares the PL spectra of filled CNTs by capillary force and shock waves generated during the laser processing. We found that encapsulated Si-ncs keep their PL properties. Open circles represent filled CNTs with Sincs fabricated by nanosecond pulsed laser fragmentation directly in the polymer solution. The laser processing at laser irradiation at 6 mJ/pulse is performed. The composite shows rather same characteristic as for Si-ncs formation in polymer only [42], leading to fabrication of blue room temperature photoluminescent nanocomposite. The Si-ncs emit light with PL maxima located at 450 nm. The filling CNTs by immersion leads to formation of nanocomposites with typical red PL with maximum located at 680 nm. Laser fragmentation process prepares nanocomposites that show significantly blue shift of the PL maximum (more than 300 nm). Full squares represent the CNTs filled with Si-ncs/polyner by capillary force. An encapsulated Si-ncs do not disturb PL properties and the intensity of PL is proportional to the inner diameter of CNTs. However, neither a shift of the light nor a narrowing of the emission band is observed [40]. This is explained because the inner diameter is generally larger than the size of Si-ncs. In principle decreasing inner diameter of nanotubes would play the role of a filter for promoting the insertion of smaller Si-nc. Then one can expect a narrowing full width at half maximum of the PL signal. Moreover, after such a confinement in CNTs, the Si-ncs with the lower mean sizes would emit light with a shift of the maximum frequency due to quantum confinement size effect [31]. Both the PL intensity and diffraction analysis indicate that the lower concentration of encapsulated Si-ncs in CNT cavity compared to simple immersion is achieved by laser processing. For further improvement of the processes to obtain the cavities with higher concentrations, it is necessary to find the optimized conditions to get an efficient yield of filling Si-ncs/polymer. For instance, this might be accomplished by laser elaboration of Si-ncs surface in different liquids that offers fabrication of smaller and non-aggregated Si-ncs [43]. Those avoids capping of CNTs ends by larger particles aggregates and set aside the higher concentration of Si-ncs inside of CNT cavities. An assembly of luminescent Si-ncs inside CNTs cavity might lead to 1D nanocomposite where the single Si-ncs are either randomly placed or display a chain-like character which can be controlled by the diameter of the CNTs. In the case of blue luminescent Si-ncs a superior operation and a possibility of higher integration could be expected.

CONCLUSION In this chapter, we discussed growth and functionalization of carbon nanotubes (CNTs) prepared by catalyst assisted chemical vapor deposition (CVD) most commonly used at industrial scale. An employment of Tapered Element Oscillating Microbalance (TEOM) for CNTs reaction kinetics is explored. Hydrodynamic characteristics of the CVD process in TEOM reactor, like a homogeneous and high degree of contact with catalyst allow accurate monitoring of the growing process. The unique capacity of TEOM provides new physical insight in CNTs reaction kinetics. By recording of small weight uptakes at initial stages of the

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CNTs growth at different reaction temperatures, partial pressures on different catalyst supports the reaction kinetics has been determined. We demonstrated that it is beneficial to work in TEOM apparatus to describe more accurately the fundamental kinetics of the CNT growth. Then morphology of the CNTs at the large-scale synthesis can be controlled via wellestablished parameters determined from TEOM. The harvested knowledge might forcedly lead to considerable improvement of CNTs production at industrial scale. Moreover, better understanding of the kinetic processes on flat silicon nanocrystals (Sincs) catalyst supports has been explored as well. Contrary to the porous alumina flat Si-ncs surface reduce inter porous diffusion and do not allows to mass uptake saturation. It has been showed that the catalyst coated on Si-ncs surface promote direct connection with CNTs. Fully capped the as-grown carbon nanotube on Si-ncs are found with the adhesion force strong enough to avoid the loss of the Si-nc from the tube tip. What's more ethylpolysillicate based polymer naturally wets Si-nc surface and simply allows encapsulation of luminescent Si-ncs in the CNT cavity by induced capillary force. In addition, a CNTs cavity filling by the blue luminescent Si-ncs by nanosecond laser fragmentation was achieved. The shock waves generated during the laser processing induce an entering of the fresh formed Si-ncs into the CNTs cavities. Development of the concept of functionalization Si-ncs with CNTs by connecting or by filling could opens up a wide range of new situations and potential applications.

ACKNOWLEDGMENTS We are deeply indebted to all colleagues who contributed to this work over the past 5 years. Especially we wish to mention the members of groups in Strasbourg (Laboratoire des Matériaux, Surfaces et Procédés pour la Catalyse (LMSPC), Ecole Supérieure de ChimiePhysique-Matériaux (ECPM), Institut de Physique et Chimie des Matériaux (IPCMS)) and Japan (Nanoarchitectonics Research Center, National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba). This work was also partially supported by a JSPS fellowship.

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REFERENCES [1] [2] [3] [4] [5] [6] [7] [8]

Ijima, S. Nature 1991, 354, 56. Iijima, S.; Ichihashi, T. Nature 1993, 363, 603. Ajayan, P. M. Nature, 2004, 427, 402. Ebbesen, T.W. Carbon Nanotubes – Preparation and Properties, CRC Press, Boca Raton, FL (1997). Harris, P. J. Carbon Nanotubes and Related Structures, Cambridge Press, (Cambridge, London, 1999). Dresselhaus, M. S.; Dresselhaus, G.; Ecklund, P. C. Science of Fullerenes and Carbon Nanotubes, AP, (New York, 1996). Guo, T.; Nikolaev, P.; Thess, A.; Colbert, D. T.; Smalley, R. E. Chem. Phys. Lett. 1995, 243, 49. Ebbesen, T. W.; Ajayan, P. M. Nature 1992, 358, 220.

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[39] Loiseau, A.; Pascard, H. Chem Phys. Lett. 1996, 56, 246. [40] Švrček,V.; Le Normand, F.; Pham-Huu, C.; Ersen, O.; Ledoux, M.-J. Appl. Phys. Lett. 2006, 88, 033112. [41] Švrček,V.; Sasaki, T.; Shimizu, T.; Koshizaki, Appl. Phys. Lett. 2006, 89, 213113. [42] Švrček,V.; Sasaki, T.; Shimizu, T.; Koshizaki, N. Chem. Phys. Lett. 2006, 429, 483. [43] Švrcek, V. Mat. Lett. 2008, Doi:10.1016/j.matlet.2007.12.058. [44] Ajayan, P. M.; Ebbesen, T. W. ; Ichihashi, T.; Iijima, S.; Tanigaki, K.; Huira, T. Nature 1993, 362, 522. [45] Morishita, K.; Takarada, T. Carbon 1997, 35, 977. [46] Esumi, K.; Ishigami, M.; Nakajima, A.; Sawada, K.; Honda, H. Carbon 1995, 34, 279. [47] Tohji, K. et al. Nature 1996, 383, 679. [48] Colomer, J. F.; Piedigrosso, P.; Willens, I.; Journet, A. J. Chem. Soc.,Faraday Trans. 1998, 94, 3753. [49] Le Normand, F.; Senger, A.; Švrček, V.; Pham-Huu, C.; Ersen, O.; Ledoux, M.J. to be published in Journal of Physical Chemistry B. [50] Hofmann, S.; Ducati, C.; Kleinsorge, B.; Robertson, J. New J. Phys. 2003, 153, 1. [51] Hofmann, S.; Csanyi, G.; Ferrari, A. C.; Payne, M. C.; Robertson, J. [52] Phys. Rev. Lett. 2005, 95, 03610. [53] Kim, B. M.; Sinha, S.; Bau, H. H. Nano Lett. 2004, 4(11), 2203.

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In: Carbon Nanotubes: New Research Editor: Avery P. Ottenhouse

ISBN 978-1-60692-236-1 © 2009 Nova Science Publishers, Inc.

Chapter 4

CARBON NANOTUBE ARRAY THERMAL INTERFACES Baratunde A. Cola, Timothy S. Fisher1, and Xianfan Xu Purdue University Birck Nanotechnology Center, and School of Mechanical Engineering 1205 W. State St.West Lafayette, IN 47907-2057 USA

ABSTRACT

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Because of their excellent thermal and mechanical properties, the efficacy of carbon nanotubes (CNTs) as a thermal interface material has recently been studied. Vertically oriented arrays of CNTs directly synthesized on substrates form dry and separable interfaces that have been demonstrated to achieve thermal resistances that compare favorably to state-of-the-art thermal interface materials. A transient photoacoustic (PA) technique is used to measure the total thermal resistances of different interface structures that comprise CNT arrays directly synthesized on various substrates, and on one and both sides of the interface and on thin metal foils inserted into the interface. The PA technique is also employed to measure the CNT-substrate (growth substrate and opposing substrate) resistances and the intrinsic resistance of the CNT arrays that sum to produce the total thermal resistance of the CNT array interface structures. The measurements reveal that CNT-substrate resistances are the largest local resistances in CNT array interfaces, and that the resistances at the CNT free ends are significantly larger than the resistances at the CNT-growth substrate interfaces.

X.1. INTRODUCTION The past decade has witnessed the advancement of high-power electronic components and devices with increasingly small dimensions. As a consequence of such advancements, the research community has been presented with a peremptory challenge to develop novel solutions that are capable of addressing the requirements for the present and future thermal management of electronic packages. Enhancing heat conduction across the solid contacts within these packages is of paramount importance as highlighted in the 2007 International 1 [email protected].

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Technology Roadmap for Semiconductors (ITRS) [1]. For example, in present high-power packages, thermal interface resistance can comprise more than 50% of the total thermal resistance [2], and over the next ten years, the significance of interface resistance will continue to grow because die-level power dissipation densities are projected to approach and to exceed 1 W/mm2 (100 W/cm2). Thus, the need for improved thermal management technologies – particularly focused on reducing contact resistance – is reaching a critical point, and it is unlikely that incremental improvements of existing technologies will satisfy future needs. Today, improved understanding of thermal energy transport at nanometer scales, combined with the burgeoning means to design new materials at the atomic level, has enabled a broad range of technological advances that can be applied to address the problem of reducing thermal interface resistance between electronic devices and heat sinks, or more generally, between any two solids in contact. In this chapter we discuss a particular class of such advancements – thermal interface materials (TIMs) based on carbon nanotube (CNT) arrays. Because of their extraordinarily high thermal conductivities [3-8] and mechanical conformability [9-11], CNTs offer a compelling alternative to traditional TIMs in electronics packages. We note that the conformability feature is particularly advantageous in addressing coefficients of thermal expansion mismatches, which are a primary cause of device failure. Also, in contrast to state-of-the-art thermal greases, CNT array interfaces are dry and chemically stable in air from cryogenic to high temperatures (~ 450°C), making them suitable for extreme-environment applications. We begin this chapter by discussing thermal transport through CNT array interfaces using a resistive network analogy, and then by briefly describing a transient photoacoustic (PA) measurement technique that is capable of individually resolving the components of this network. Next, we discuss a few promising interface structures that comprise CNT arrays directly synthesized via microwave plasma chemical vapor deposition on substrates of technical interest such as silicon (Si) and silicon carbide (SiC), and copper (Cu), aluminum (Al), and diamond. Finally, we present PA measurements of the thermal resistances of such CNT array interface structures and discus significant components in the resistive network.

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X.2 THERMAL TRANSPORT THROUGH CARBON NANOTUBE ARRAY INTERFACES In the traditional view, heat transfer across solid contacts is hampered by a thermal resistance that is predominantly caused by differences in bulk material properties and the inherent roughnesses of the interfacing surfaces, which creates a lack of intimate contact. Thermal contact resistance (R) manifests as a temperature drop across the interface and is mathematically expressed as

R=

ΔT , q"

(1)

where q˝ is the heat flux and ΔT is the temperature drop across the interface. For dry interfaces, conduction, primarily through solid contact spots, is the dominant heat transfer mechanism at room temperature (see Figure 1).

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Figure 1. Illustration of heat transfer across solid contacts.

Therefore, thermal interface resistance is reduced when the number and size of contact spots (i.e., the real contact area) and conduction through the contact spots are increased. Such improvements can be achieved by applying highly conductive and compliant CNT arrays to an interface as discussed below. For comprehensive coverage of thermal contact resistance between bulk materials, the reader is referred to the rich history of work in this area for bulk materials [12]. The geometric complexity of thermal interfaces comprised of dense carbon nanotube arrays creates a substantial modelling challenge. Relying to some extent on prior work in the area of thermal contact resistance between bulk materials and extensions to nanoscale contacts, Cola et al. [13] developed a simplified model for thermal transport through CNT array interfaces that we use here for the purpose of discussion. Figure 2 shows a candidate thermal network in which the thermal resistances are resolved at the individual nanotube level for true CNT-substrate interfaces, both at the growth substrate (with a nanotube number density of N, in contacts/mm2) and at the opposing interface (with a contacting nanotube number density of n, in contacts/mm2). For such a single-sided interface, the contact number density N on the growth surface must exceed the density (n) on the opposing substrate. At each local CNT-substrate interface, a substrate constriction resistance (Rcs) exists of the usual form: Ψ ( a, b) Rcs (a, b, k ) = (2) 4ka

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where k is the substrate thermal conductivity and a is the contact radius. The numerator in Eq. (2) is the alleviation factor, which accounts for the finite size of the flux tube diameter b, which depends on the density of contact spots [13].

Figure 2. (a) Schematic (not to scale) of a interface with the addition of a vertically oriented CNT array of thickness tarray. (b) Buckled CNT contacting an opposing surface with its wall. (c,d) Free tips contacting an opposing surface at different angles. (b), (c) and (d) also show that some CNTs do not make direct contacts with the opposing surface. (e) Resistance schematic of a one-sided CNT array interface between two substrates, showing constriction resistances (Rcsi), phonon ballistic resistances (Rbi), and the effective resistance of the CNT array (R”array).

When the contact radius a is comparable to or smaller than the mean free path of the dominant thermal energy carriers (phonons in the present case), an additional resistance must be included to account for the ballistic nature of thermal energy transport through the contact spots [14]. In the present case, values of a are typically of the order of 10 nm, while roomtemperature phonon mean free paths in the materials under study here are of the order of 100

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nm. Under such conditions, a phonon ballistic resistance (Rb) of the following form must be included [14]

Rb (a ) =

4 ( C1 ⋅ vg1 + C2 ⋅ vg 2 ) 1 T1 − T2 = ⋅ 2 q′′ ⋅ π ⋅ a ( C1 ⋅ vg1 )( C2 ⋅ vg 2 ) π ⋅ a 2

(3)

where we have employed Chen’s transmissivity approximation in the diffuse mismatch model of the interface [15], and C is the phonon specific heat and vg is the frequency independent group velocity. The remaining resistance (R”array) originates from heat conduction through the CNT array. While a network consisting of separate conductive paths through each of the billions of CNTs could potentially be defined, such an approach would require missing knowledge of the number and nature of CNT-to-CNT contacts within the intertwined array. To circumvent this issue, a simplification in which a single effective thermal resistance is defined for the entire array (including void spaces) is made, as this quantity has been measured in prior work for representative samples [16] and can be used to interpret experimental results that measure only overall thermal interface resistance. Once the foregoing component resistances have been defined, an overall or total interface resistance can be calculated, given knowledge of the contact number densities at the growth substrate (N) and the opposing substrate (n). The former density (N) can be estimated from scanning electron micrographs of synthesized arrays, and the latter density (n) can be estimated using a model that describes the contact mechanics of CNT arrays [13]. An effective resistance that combines constriction and ballistic effects at the interface between the growth substrate (GS) and CNT array can be defined as

R

" GS − CNT

⎡ ⎤ Ni = ⎢∑ ⎥ ⎣ i Rcs.GS −CNT (ai , bGS ) + Rb.GS −CNT (ai ) ⎦

−1

where Ni is the contact density of CNTs of radius ai and satisfies

(4)

∑N

i

= N . We also note

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i

that the statistical distribution of CNT diameters can be accounted for by assuming a standard distribution of nanotube diameters [17]. The effective resistance that combines constriction and ballistic effects at the interface with the opposing substrate (OS) can be defined as −1

⎡ ⎤ ni = ⎢∑ R ⎥ (5) ⎢⎣ i Rcs.CNT −OS (ax.CNT −OS ,i , a y .CNT −OS ,i ) + Rb.CNT −OS (ax.CNT −OS ,i , a y .CNT −OS , i ) ⎥⎦ where ni is accounted for by substituting into Eq. (5) an expression for the ratio of real to apparent contact area in the interface [13]. Considering CNT array contact mechanics [13], " CNT − OS

the total number density of CNTs in contact with the opposing substrate ( n =

∑ n ) can be i

i

expressed as

106

n = Φ⋅

Baratunde A. Cola, Timothy S. Fisher and Xianfan Xu

P 1 ⋅ 3 ⋅ bCNT ⋅ a y .CNT −OS ⎛ ax.CNT −OS ⎜ P +σR ⋅Φ⋅ bCNT ⎝

⎡ ⋅⎢ ⎞ ⎢ ⎟ ⎣ ⎠

(

⎤ ⎥ 2 − 1 ⋅ t ′ + to ⎥ ⎦ to − t ′

3

)

(6)

where Φ is the volume ratio of CNTs in the array (i.e., one minus the CNT porosity), P is the nominal contact pressure, σR represents the arrays resistance to mechanical compression, to is the ‘pressure-free’ array thickness, t' is the incompressible thickness of the CNT array, bCNT is the average CNT diameter, and ax.CNT-OS and ay.CNT-OS are the contact width and length, respectively [13]. Summation of the three effective resistances in this model gives a prediction of the overall resistance of an interface with a CNT array grown on one side (R”total = R”GS-CNT + R”array + R”CNT-OS). A similar approach can be used to model the total thermal resistance of structures with CNT arrays grown on both sides of an interface. For such details and additional model information, the reader is referred to previous work [13]. The above model applied to the interface between the CNTs and their growth substrate (Si) suggest that an array with a surface density of 108 CNTs/mm2 and CNT diameters of 20 nm could produce a local resistance of R”GS-CNT ≈ 0.1 mm2K/W [13]. This value represents an approximate limiting value of thermal transport because Rb essentially assumes perfect contact between a CNT and its underlying substrate [18], and the acoustic mismatch model used to derive Rb produces the lowest classical resistance for materials with reasonably wellmatched acoustic impedances [19]. Such idealizations can cause a significant underprediction of thermal resistance [13, 18]. In fact, as discussed below, experiments capable of resolving the three effective component resistances (R”GS-CNT, R”array, and R”CNT-OS) have shown measured values of R”GS-CNT ≈ 1 mm2K/W [20]. Such measurements enable critical insights into the behaviour and optimization of CNT array interfaces, and can facilitate further model refinements.

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X.3. PHOTOACOUSTIC CHARACTERIZATION OF THERMAL PROPERTIES In photoacoustic (PA) measurements, a heating source (normally a laser beam) is periodically irradiated on a sample surface. The acoustic response of the gas above the sample is measured and related to the thermal properties of the sample. The photoacoustic phenomenon was first explained by Rosencwaig and Gersho [21], and an analytic solution of the PA response of a single layer on a substrate was developed. A more general analytic solution derived by Hu et al. [22] explains the PA effect in multilayered materials.

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Figure 3. Schematic of the photoacoustic test setup used in measurements of a Cu-Si interface with CNT arrays grown separately on each substrate [20]. (a) The CNT arrays are not included as a layer in the PA model but rather as a constituent of interface resistance between the Si and Cu layers. (b) The CNT arrays are considered as layers in the model to enable the estimation of CNT-substrate resistances.

The sample in a photoacoustic measurement can be modelled one-dimensionally [23], and in accordance with the generalized theory of the photoacoustic effect in multilayer materials [22], can consist of an arbitrary number of layers, a backing material (0) and N successive layers (1, 2, ···, N), and is heated by a modulated laser beam with an intensity of 1/ 2 ⋅ I o (1 + cos(ωt )) . Absorption of the laser beam is allowed in any layer, and in more than

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one layer. An additional gas medium (N+1) is in contact with the surface layer (N). The backing material (0) and gas medium (N+1) are assumed to be thermally thick. A schematic of a two-sided CNT interface previously measured [20] and the labelling of layers used in the PA model are shown in Figure 3. In Figure 3(a), the CNT array is not included as a layer in the PA model, which greatly simplifies estimates of overall interface resistance. In Figure 3(b), the CNT layer is included, which allows the CNT-substrate ‘intra-interface’ resistances to be estimated. The fitting of experimental data with the two different models shown in Figure 3 are discussed more below. The transient temperature field in the multilayer sample and gas can be derived by solving a set of one-dimensional heat conduction equations, and the transient temperature in the gas is related to the pressure, which is measured experimentally. Because the transient temperature in the gas is related to the thermal properties of the sample, measuring the pressure allows determination of the thermal quantities – in this work thermal interface resistance. The solution of the complex temperature distribution θN+1 in the gas can be expressed as

θ N+1 = (1 − ρ ) ⋅ BN +1e −σ

e jω t ,

(5)

⎡ Em ⎤ ⎢⎣ Em +1 ⎥⎦ i =0 m =0 ; N ⎡0 ⎤ Ui ) ⋅ ⎢ ⎥ [0 1]⋅ (∏ i=0 ⎣1 ⎦

(6)

N +1 x

where

[0 BN +1 = −

N

m −1

1]⋅ ∑ ( ∏ Ui )⋅ V m ⋅

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and other variables are detailed in prior work [22]. The temperature in the gas layer is related to the phase shift and amplitude of the PA signal. The phase shift of the PA signal is calculated as Arg ( BN +1 ) − π / 4 , and the amplitude of the PA signal is

Abs[(1 − ρ ) ⋅ BN +1 Po / 2lN +1aN +1To ] , where Po and To are the ambient pressure and temperature, respectively. BN+1 is a function of the densities, thermal conductivities, specific heats, thicknesses, optical absorption coefficients, and interface resistances in the multilayered sample. When phase shift and amplitude are experimentally measured and known at several laser heating frequencies, the unknown values in BN+1 can be found by using a least-squares fitting algorithm in which the square of the difference between the measured and theoretical signals calculated using trial unknown values is adjusted by updating the values until a convergence criterion is satisfied. If only one parameter in BN+1 is unknown, as in estimating the total CNT interface resistance (see Figure 3 (a) – in this case the CNT array is not considered as a layer in the model but as a constituent of the interface resistance between layers), the model is linear with respect to the unknown value and, as a result, the regression analysis is greatly simplified [20]. To estimate CNT-substrate resistances, the CNT array(s) must be included in the PA model (see Figure 3 (b)). Such resistances are more difficult to estimate with the PA model due to additional unknown parameters associated with the CNT arrays such as thermal diffusivity, thermal conductivity, and thickness [20]. However, because the CNT-substrate resistances dominate the thermal response at different heating frequencies, using a wide frequency range for data fitting allows for such interface resistances to be estimated with a high degree of fidelity [20]. Furthermore, the thermal response in PA measurements is insensitive to the low intrinsic thermal resistance of the CNT array(s), which is expected due to the high thermal conductivity and number density of CNTs in the arrays typically used for TIM applications. Consequently, the raw PA signals (amplitude and phase shift) are insensitive to the thermal conductivity and the thickness of the CNT array(s) [20]. Therefore, the only parameters that can be reasonably estimated for CNT array interfaces are thermal interface resistance and thermal diffusivity. For the data presented in this chapter, the phase shift of the PA signal is used to fit for thermal properties because it was more stable in the experimental setup than the amplitude signal [20]. Uncertainty in the measured phase-shift signal, which usually ranges from ± 0.1 to 0.5°, is the primary determinant for the uncertainty in the estimated thermal properties, which usually ranges from ± 0.5 to 1 mm2K/W [20]. The reader is referred to previous studies for more details on the PA model and measurement technique [20, 22].

X.4 TYPES OF CARBON NANOTUBE ARRAY INTERFACES Polymer-CNT composites have been used in thermal interface material (TIM) applications [2, 24] with modest improvements in thermal performance. The lack of significant enhancement is likely the result of two dominant factors. First, an elastic medium surrounding CNTs has been shown to reduce effective thermal conductivity by altering phonon dispersion in CNTs [25]. Second, these composites, which are typically prepared through batch processes and then applied as a standalone film, lack the chemical bonding of

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CNTs to the bulk substrate, and as we will show later, this ‘true’ interface is the dominant local resistance in CNT array interface structures.

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Figure 4. CNT array interface structures. (a) An example one-sided interface. (b) An example two-sided interface. (c) An example CNT-coated foil interface.

More recently, several groups have investigated using vertically oriented CNT arrays directly synthesized on substrates as TIMs [16, 20, 26-43], and such structures have been demonstrated to achieve significant reductions in thermal interface resistance. Here we present three structures based on vertically oriented CNT arrays (see Figure 4) that have exhibited some of the most promising thermal performance characteristics to date. The first structure consists of CNT arrays directly synthesized on one side of an interface (i.e., a onesided CNT array interface). The second structure consists of CNT arrays directly synthesized on the surfaces of both sides of an interface (i.e., a two-sided interface), forming VelcroTMlike contact because of the strong van der Waals forces between CNTs and mechanical entanglement of CNTs. The third structure comprises vertically oriented CNT arrays directly and simultaneously synthesized on both sides of thin foil substrates that are inserted into an interface. The CNT-coated foil structures are particularly attractive in that they serve as a method for applying CNT arrays to interfaces between heat sinks and devices that would experience damage from exposure to the high temperatures normally required for high-quality CNT growth (≈ 800°C). CNT array structures similar to those illustrated in Figure 4 were synthesized on various substrates using microwave plasma chemical vapor deposition (MPCVD) [44]. The MPCVD process offers significant advantages over other synthesis techniques due to the volumetric addition of plasma energy near the deposition (substrate) surface. Variation of plasma energy input enables control of the plasma geometry and composition such that optimal gas-phase conditions can be achieved near the substrate. As a result, relatively low substrate temperatures can be maintained in this process, as demonstrated in recent publications [37, 38]. Low temperatures are particularly desirable for in situ deposition on pre-functionalized substrates. For example, MPCVD synthesis can occur at temperatures below the melting temperatures of common electrical interconnect metals, such as aluminium and copper, whereas alternative processes can require higher temperatures.

110

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The deposition of a metal catalyst layer is usually required before CNT arrays can be directly synthesized on substrates using MPCVD. Two different catalyst structures were used to synthesize the CNT arrays presented here. The first is a trilayer catalyst [29] that consists of a 30 nm-thick Ti barrier layer, a 10 nm-thick Al ‘buffer’ layer, and a layer of catalyst metal (Fe or Ni) that ranges from 1 to 6 nm in thickness. The other catalyst is an iron-containing dendrimer catalyst [35, 45] that delivers monodispersed nanoparticles to the substrate surface. Additional process and recipe details related to the synthesis of the CNT arrays on the substrates discussed below have been reported in previous work [20, 33, 36-39]. Achieving vertically oriented CNT array growth on substrates such as Si, SiC, Cu, Al, and diamond is important to several thermal management applications that are particularly relevant to the microelectronics industry. Figures 5 and 6 contain several scanning electron microscope (SEM) images of CNT arrays grown on different substrates. To assemble onesided interface structures that could be applied to Si microprocessors, CNT arrays have been successfully grown via MPCVD and the above mentioned catalyst techniques on Si at normal growth temperatures as well as at much reduced temperatures [38] as shown in Figs. 6(a) and (b). As shown in Figures 5(c) and (d), well-adhered CNT arrays have been directly synthesized on the carbon face of SiC [39] (SiC crystals are polar and therefore have a termination layer of carbon atoms on one face and Si atoms on the opposite face) and on CVD diamond substrates [36] (notably, both the diamond and CNT layers were grown in the same MPCVD reactor [41, 46]) to assemble one-sided interfaces that are particularly attractive for MEMs and power-electronics applications.

Figure 5. CNT arrays directly synthesized on various substrates. (a) CNT array on Si grown at 800°C [38]. The average CNT diameter is 40 nm. (b) CNT array on Si grown at approximately 500°C [38]. The average CNT diameter is 8 nm. The inset (scale bar = 1 μm) shows vertical orientation. (c) CNT array grown on a CVD diamond layer [36]. The average CNT diameter is 30 nm. (d) CNT array grown on the carbon face of SiC [39]. The average CNT diameter is approximately 40 nm. (e) CNT array grown on Cu using a trilayer catalyst [20]. The average CNT diameter is 30 nm. (f) CNT array grown on Cu using a different trilayer catalyst structure. The average CNT diameter is 15 nm.

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These structures are expected to be particularly suitable as thermal interfaces because their carbon-based gradient morphologies should promote efficient phonon transmission through matching of phonon statistics and dynamics (e.g., density of states and group velocities). Two-sided interfaces with CNT arrays directly synthesized on Si and Cu surfaces that approximate the contact between a Si die and Cu heat sink have been also assembled [20]. Growing dense CNT arrays on Cu is challenging because Cu can poison CNT catalyst, however, such growth has been accomplished using the trilayer catalyst [20]. Figures 5(e) and (f) contain SEM images that illustrate CNTs grown on Cu from two different trilayer catalyst structures, demonstrating a level of control over CNT array properties such as diameter, height, and porosity using the trilayer catalyst. Because of the large contact area established at the interface of matting CNT arrays in the two-sided configuration, and efficient phonon transmission across CNT-CNT contacts [13], two-sided CNT array interfaces have achieved the lowest thermal resistances to date as discussed later. Figure 6 contains SEM images of CNT-coated Cu and Al foil. Trilayer catalyst was deposited on both sides of the foils and the foils were elevated in the MPCVD growth chamber to allow simultaneous growth of the arrays [33, 37]. Because of the low melting temperature of Al (~ 660°C), CNT growth was carried out at reduced temperatures on these foil substrates [37]. The combination of compliant foil substrates and compliant CNT arrays is particularly attractive for alleviating adverse effects of surface roughness and can lead to significant increases in interfacial contact area – and as a result thermal conductance – because when the foil deforms it lifts the attached CNTs further into the microcavities of the contacted surfaces. Multiwalled CNTs (MWCNTs), with diameters ranging from 5 to 50 nm, were synthesized for each array presented here, and the CNT porosity of the arrays ranged from approximately 0.5 to 0.9. We note that, while most measurements show a higher inherent thermal conductivity of individual single-wall CNTs (SWCNTs) as compared to MWCNTs, the use of SWCNT arrays as thermal interface materials [40] is compromised by the fact that dominant phonon wavelengths in bulk materials are approximately 5 nm [47] while SWCNT diameters are typically 1-2 nm [48]; such a scale mismatch produces wave reflection at CNTsubstrate contacts that can significantly reduce thermal conductance.

Figure 6. CNT-coated foil interface structures. (a) CNT arrays on both sides of 10 μm-thick Cu foil [33]. The average CNT diameter for both arrays is approximately 20 nm. (b) CNT arrays on both sides of 25 μm-thick Al foil [37]. The average CNT diameter for both arrays is approximately 10 nm.

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Baratunde A. Cola, Timothy S. Fisher and Xianfan Xu

X.5. THERMAL RESISTANCES OF CARBON NANOTUBE ARRAY INTERFACES

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Xu and Fisher reported some of the earliest results in applying CNT arrays as thermal interfaces, with interface resistances less than 20 mm2K/W for dry one-sided structures [29] and less than 7 mm2K/W for CNTs directly synthesized on Si and then enhanced with a phase-change polymer [32]. Since then, several others have explored using CNTs (and carbon nanofibers (CNFs)) to improve contact thermal conductance, achieving good performance as well [16, 20, 26-43]. Ngo et al. [28] used electrodeposited Cu as a gap filler to enhance the stability and thermal conductance of CNF arrays and reported a thermal resistance of 25 mm2K/W under a pressure of 414 kPa for Si-Cu interfaces enhanced with such structures. At moderate contact pressures thermal resistances of approximately 12 mm2K/W were measured by Xu et al. [31] for a Si-CNT-Ni interface, and by Tong et al. [34] for a Si-CNT-glass interface; these values are very close to the result presented in [16]. Amama et al. [35] measured thermal resistance values of approximately 8 mm2K/W at a pressure 350 kPa for SiCNT-Ag interfaces, and Cola et al. [20] measured the resistances of a two-sided interface to be near 4 mm2K/W at moderate contact pressures. Zhang et al. [42] recently applied CNT arrays with optimized synthesis conditions to enhance the brightness and efficiency of lightemitting diodes and achieved resistances as low as 7 mm2K/W for a Si-CNT-Al interface at a contact pressure of 150 kPa. Resistances as low as 7 mm2K/W were also measure by Cola et al. [38] for a one-sided Si-CNT-Ag interface.

Figure 7. Summary of total thermal resistance as a function of pressure of one- and two-sided CNT thermal interfaces, and CNT-coated foil interfaces at room temperature. The presented results represent the best to-date performance of each type of interface structure.

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As summarized in Figure 7, vertically oriented CNT arrays directly synthesized on one or both sides of an interface have been measured using the PA technique to achieve total thermal resistances as low as 7 and 4 mm2K/W, respectively, and CNT-coated foil interfaces have been measured with the PA technique to achieve resistances as low as 8 mm2K/W. These resistance values are the lowest reported to date, and compare very favorably with state-ofthe-art thermal greases. Furthermore, the performance of the two-sided CNT array interface surpasses that of bonded solder joints [2]. The one-sided interface in Figure 7 is a Si-CNT-Ag interface with the CNT array directly synthesized on the Si surface (see Figure 5(a)) [38]. The Ag is used as the top contact to enhance PA measurements as described in [20]. The two-sided interface in Figure 7 is a SiCNT-CNT-Cu interface with CNT arrays directly synthesized on the Si and Cu (see Figure 5(e)) surfaces [20]. The CNT/foil interface in Figure 7 consists of CNT arrays directly synthesized on both sides of Cu foil as shown in Figure 6(a) [33]. After testing the interfaces were separated, and for each structure the CNT arrays remained well adhered to their growth substrate. Interfaces with CNT arrays directly synthesized on Si [39], diamond (see Figure 5(c)) [36], and the C-face of SiC (see Figure 5(d)) [39] using similar catalyst structures and growth recipes were measured with the PA technique and the results are illustrated in Figure 8. The Si-CNT-Ag interface (the top curve) gives the poorest results (i.e., the largest resistance) of the three for all pressures. The middle curve represents the diamond-CNT-Ag interface for which the resistances are slightly less than those of the Si curve. The bottom curve represents results from CNTs grown directly on the carbon face of SiC. These resistances are lower than the others by 15 to 30 percent and possibly indicate a strong matching of phonon dynamics between the CNTs and the SiC substrate. We believe that direct CNT growth on the carbon face of SiC creates a superior atomic-scale interface morphology that may enhance thermal transport at individual CNT-SiC contacts.

Figure. 8. Total thermal interface resistance at room temperature as a function of pressure for one-sided CNT array interfaces grown directly on Si, diamond, and SiC.

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Figure 9. Intra-interface resistances for a one-sided Si-CNT-Ag interface with CNTs directly synthesized on Si at 241 kPa measured at room temperature using the PA

When the CNT arrays are considered as layers in the PA model (see Figure 3(b)), intrainterface resistances that sum to produce the total resistance of the CNT array interface can be resolved. Figure 9 illustrates the intra-interface or component resistances of a one-sided SiCNT-Ag interface with CNTs directly synthesized on Si at a pressure of 241 kPa measured using the PA technique [20]. The room-temperature total thermal resistance of this interface is approximately 16 mm2K/W. The resistance at the CNT-growth substrate interface (RSi-CNT) is approximately 2 mm2K/W, and the resistance at the interface to the free CNT ends (RCNT-Ag) is approximately 14 mm2K/W. It is clear that the resistance between the free CNT ends and the Ag substrate dominates the overall thermal resistance, and that significant performance improvements can be achieved by reducing the resistance at this local interface [34]. Because of the high thermal conductivity and small thickness of the CNT array, its resistance was less than the measurement sensitivity of the PA technique [20]. Figure 10 illustrates the component resistances of a two-sided Si-CNT-CNT-Cu interface with CNT arrays directly synthesized on Si and Cu surfaces [20]. At a contact pressure of 241 kPa the total resistance of the two-sided CNT array interface was measured with the PA technique to be approximately 4 mm2K/W. The resistance at the contacting CNT ends was approximately 2 mm2K/W, and this dry contact was the largest component of the total resistance, as in the one-sided configuration. The lower resistance achieved at the CNT-CNT free end contacts as apposed to free end contacts to an opposing substrate is primarily the result of increased contact area at the interface of two highly compliant materials such as CNT arrays [13]. The resistances at the two growth substrate interfaces (RSi-CNT and RCu-CNT) were approximately 1 mm2K/W each, and the intrinsic resistances of the CNT arrays were measured to be practically negligible.

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Figure 10. Intra-interface resistances for a two-sided Si-CNT-Ag interface with CNTs directly synthesized on Si and Cu at 241 kPa measured at room temperature using the PA technique [20].

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Figure 11. Intra-interface resistances for an interface with CNT-coated Cu foil (10 μm thick) at 276 kPa measured at room temperature using the PA technique [33].

The component resistances of an interface comprised of Cu foil coated on both sides with CNT arrays were measured with the PA technique [33] and are illustrated in Figure 11. The interface resistance between a CNT array and its Cu growth substrate (RCNT-Cu), approximately 1 mm2K/W, and the effective thermal conductivity of CNT arrays synthesized under conditions similar to the ones of this study, approximately 80 W/mK (which corresponds to an intrinsic resistance, RCNT layer, of approximately 1 mm²·K/W for each relatively thick CNT array), have been measured in previous work [16, 20]. The combined resistance of both CNT arrays, both CNT-foil interfaces, and the Cu foil (< 0.03 mm2K/W) sums to approximately 4 mm2K/W. Therefore, the remaining resistance is produced by the two interfaces to the free CNT ends. Assuming similar contact conditions, each free end interface for the CNT-coated foil structure can be assumed to have a resistance of approximately 2 mm2K/W.

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X.6. CONCLUSION This chapter contains a detailed study of thermal transport through CNT array interfaces and includes measured thermal resistance data for several promising CNT array interface structures such as one-sided, two-sided, and CNT-coated foil that at moderate contact pressures achieve thermal resistances that compare favorably to state-of-the-art materials. The measurements were conducted using a transient PA technique that is capable of resolving the intra-interface resistances that sum to produce the total interface resistance. The measurements reveal that the total thermal resistance of CNT array interfaces is dominated by the CNT-substrate resistances, and that the resistances at the CNT-growth substrate interfaces are appreciably smaller than the resistances at the interfaces to free CNT ends. Therefore, the thermal performance of CNT array interfaces can be improved by reducing resistance at such contacts.

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International Roadmap for Semiconductors (2007). Assembly and Packaging. http://www.itrs.net/Links/2007ITRS/Home2007.htm. Prasher, R. Thermal interface materials: Historical perspective, status, and future directions. Proc. IEEE 2006, vol. 94, pp. 1571-1586. Kim, P.; Shi, L.; Majumdar, A.; McEuen, P. L. Thermal transport measurements of individual multiwalled nanotubes. Phys. Rev. Lett. 2001, vol. 87, p. 215502. Che, J. W.; Cagin, T.; Goddard, W. A. Thermal Conductivity of Carbon Nanotubes. Nanotechnology 2000, vol. 11, pp. 65-69. Berber, S.; Kwon, Y. K.; Tomanek, D. Unusually High Thermal Conductivity of Carbon Nanotubes. Phys. Rev. Lett. 2000, vol. 84, pp. 4613-4617. Osman, M. A.; Srivastava, D. Temperature dependence of the thermal conductivity of single-wall carbon nanotubes. Nanotechnology 2001, vol. 12, pp. 21-24. Hone, J.; Whitney, M.; Piskoti, C.; Zettl, A. Thermal conductivity of single-walled carbon nanotubes, Phys. Rev. B 1999, vol. 59, pp. 2514-2516. Shi, L.; Li, D.; Yu, C.; Jang, W.; Kim, D.; Yao, Z.; Kim, P.; Majumdar, A. Measuring Thermal and Thermoelectric Properties of One-Dimensional Nanostructures Using a Microfabricated Device, ASME J. Heat Transf. 2003, vol. 125, pp. 881-888. Cao, A.; Dickrell, P. L.; Sawyer, W. G.; Ghasemi-Nejhad, M. N.; Ajayan, P. M. Supercompressible foamlike carbon nanotube films. Science 2005, vol. 310, pp. 1307-1310. Deck, C. P.; Flowers, J.; McKee, G. S. B.; Vecchio, K. Mechanical behaviour of ultralong multiwalled carbon nanotube mats. J. Appl. Phys. 2007, vol. 101, p. 023512. Suhr, J.; Victor, P.; Ci, L.; Sreekala, S.; Zhang, X.; Nalamasu, O.; Ajayan, P. M. Fatigue resistance of aligned carbon nanotube arrays under cyclic compression. Nature Nano. 2007, vol. 2, pp. 417-421. Madhusudana, C. V. Thermal Contact Conductance; Springer-Verlag: New York, NY, 1996; pp. 23-97. Cola, B. A.; Xu, J.; Fisher, T. S. Contact mechanics and thermal conductance of carbon nanotube array interfaces. Int. J. Heat and Mass Transf., in review.

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[14] Prasher, R. Predicting the thermal resistance of nanosized constrictions, Nano Lett. 2005, vol. 5, pp. 2155-2159. [15] Chen, G. Size and interface effects on thermal conductivity of superlattices and periodic thin-film structures. ASME J. Heat Transf. 1997, vol. 119, pp. 220-229. [16] Hu, J. X.; Padilla, A. A.; Xu, J.; Fisher, T. S.; Goodson, K. E. 3-omega measurements of vertically oriented carbon nanotubes on silicon. ASME J. Heat Transf. 2006, vol. 128, pp. 1109-1113. [17] Cheung, C. L.; Kurtz, A.; Park, H.; Lieber, C. M. Diameter-controlled synthesis of carbon nanotubes. J. Phys. Chem. B 2002, vol. 106, pp. 2429-2433. [18] Zhong, H.; Lukes, J. Interfacial thermal resistance between carbon nanotubes: molecular dynamics simulations and analytical thermal modelling. Phys. Rev. B 2006, vol. 74, p. 125403. [19] Stevens, R. J.; Smith, A. N.; Norris, P. M. Measurement of Thermal Boundary Conductance of a Series of Metal-Dielectric Interfaces by the Transient Thermoreflectance Technique. J. Heat Transf. 2005, vol. 127, pp. 315-323. [20] Cola, B. A.; Xu, J.; Cheng, C.; Xu, X.; Hu, H.; Fisher, T. S. Photoacoustic characterization of carbon nanotube array thermal interfaces. J. Appl. Phys. 2007, vol. 101, p. 054313. [21] Rosencwaig, A.; Gersho, A. Theory of the photoacoustic effect with solids. J. Appl. Phys. 1976, vol. 47, pp. 64-69. [22] Hu, H.; Wang, X.; Xu, X. Generalized theory of the photoacoustic effect in a multilayered material. J. Appl. Phys. 1999, vol. 86, pp. 3953-3958. [23] Quimby, R. S.; Yen, W. M. On the adequacy of one-dimensional treatments of the photoacoustic effect. J. Appl. Phys. 1980, vol. 51, pp. 1252-1253. [24] Zeng, J. L.; Liu, Y. Y.; Cao, Z. X.; Zhang, J.; Zhang, Z. H.; Sun, L. X.; Xu, F. Thermal conductivity enhancement of MWNTs on the PANI/tetradecanol form-stable PCM, J. Therm. Analysis and Calorimetry 2008, vol. 91, pp. 443-446. [25] Prasher, R. Thermal conductance of single-walled carbon nanotube embedded in an elastic half-space. Appl. Phys. Lett. 2007, vol. 90, p. 143110. [26] Xu, J.; Fisher, T. S. Enhanced Thermal Contact Conductance using Carbon Nanotube Arrays. ITHERM 2004, vol. 2, pp. 549-555. [27] Chuang, H. F.; Cooper, S. M.; Meyyappan, M.; Cruden, B.A. Improvement of thermal contact resistance by carbon nanotubes and nanofibers, J. of Nanoscience and Nanotechnology 2004, vol. 4, pp. 964-967. [28] Ngo, Q.; Cruden, B. A.; Cassell, A. M.; Sims, G.; Meyyappan, M.; Li, J.; Yang, C. Y. Thermal interface properties of Cu-filled, vertically aligned carbon nanofiber arrays. Nano Lett. 2004, vol. 4, pp. 2403-2407. [29] Xu, J.; Fisher, T. S. Enhanced thermal contact conductance using carbon nanotube array interfaces. IEEE Trans. Comp. Pack. Tech. 2006, vol. 29, pp. 261-267. [30] Wang, X.; Zhong, Z.; Xu, J. Noncontact thermal characterization of multiwall carbon nanotubes. J. Appl. Phys. 2006, vol. 97, p. 064302. [31] Xu, Y.; Zhang, Y.; Suhir, E.; Wang, X. Thermal properties of carbon nanotube array used for integrated circuit cooling. J. Appl. Phys. 2006, vol. 100, p. 074302. [32] Xu, J.; Fisher, T. S. Enhancement of thermal interface materials with carbon nanotube arrays. Int. J. of Heat and Mass Transf. 2006, vol. 49, pp. 1658-1666.

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[33] Cola, B. A.; Xu, X.; Fisher, T. S. Increased real contact in thermal interfaces: a carbon nanotube/foil material. Appl. Phys. Lett. 2007, vol. 90, p. 093513. [34] Tong, T.; Zhao, Y.; Delzeit, L.; Kashani, A.; Meyyappan, M.; Majumdar, A. Dense vertically aligned multiwalled carbon nanotube arrays as thermal interface materials. IEEE Trans. Comp. Pack. Tech. 2007, vol. 30, pp. 92- 99. [35] Amama, P. B.; Cola, B. A.; Sands, T. D.; Xu, X.; Fisher, T. S. Dendrimer-assisted controlled growth of carbon nanotubes for enhanced thermal interface conductance. Nanotechnology 2007, vol. 18, p. 385303. [36] Cola, B. A.; Xu, X.; Fisher, T. S. Carbon nanotube array thermal interfaces on chemical vapor deposited diamond. IPACK2007: Proc. ASME Interpack Conf. 2007, vol. 1, pp. 967-969. [37] Cola, B. A.; Xu, X.; Fisher, T. S. Aluminum foil/carbon nanotube thermal interface materials. Proc. ASME/JSME Therm. Eng. Summer Heat Transf. Conf. 2007, vol. 2, pp. 901-903. [38] Cola, B. A.; Amama, P. B.; Xu, X.; Fisher, T. S. Effects of growth temperature on carbon nanotube array thermal interfaces. ASME J. Heat Transf., in press. [39] Cola, B. A.; Capano, M. A.; Amama, P. B.; Xu, X.; Fisher, T. S. Carbon nanotube array thermal interfaces for high-temperature silicon carbide devices. J. Nano. and Micro. Thermophysical Eng., in press. [40] Panzer, M.; Zhang, G.; Mann, D.; Hu, X.; Pop, E.; Dai, H.; Goodson, K. E. Thermal Properties of Metal-Coated Vertically Aligned Single-Wall Nanotube Arrays. ASME J. Heat Transf. 2008, vol. 130, p. 052401. [41] Hu, X. J.; Panzer, M. A.; Goodson, K. E. Infrared Microscopy Thermal Characterization of Opposing Carbon Nanotube Arrays. ASME J. Heat Transf. 2007, vol. 129, pp. 91-93. [42] Zhang, K.; Chai, Y.; Yuen, M. M. F.; Xiao, D. G. W.; Chan, P. C. H. Carbon nanotube thermal interface material for high-brightness light-emitting-diode cooling. Nanotechnology 2008, vol. 19, p. 215706. [43] Prasher, R. Thermal boundary resistance and thermal conductivity of multiwalled carbon nanotubes. Phys. Rev. B 2008, vol. 77, p. 075424. [44] Maschmann, M. R.; Amama, P. B.; Goyal, A.; Iqbal, Z.; Gat, R.; Fisher, T.S. Parametric study of synthesis conditions in plasma-enhanced CVD of high-quality single-walled carbon nanotubes. Carbon 2006, vol. 44, pp. 10-18. [45] Amama, P. B.; Maschmann, M. R.; Fisher, T. S.; Sands, T. D. Dendrimer-Templated Fe Nanoparticles for the Growth of Single-Wall Carbon Nanotubes by Plasma-Enhanced CVD. J. Phys. Chem. B. 2006, vol. 110, pp. 10636-10644. [46] Cola, B. A.; Karru, R.; Cheng, C.; Xu, X.; Fisher, T. S. Influence of Bias-Enhanced Nucleation on Thermal Conductance through Chemical Vapor Deposited Diamond Films. IEEE Trans. Comp. Pack. Technol. 2008, vol. 31, pp. 46-53. [47] Ziman, J. M. Electrons and phonons: the theory of transport phenomena in solids; Clarendon Press: Oxford, UK, 1962. [48] Dresselhaus, M. S.; Dresselhaus, G.; Eklund, P. C. Science of Fullerenes and Carbon Nanotubes; Academic Press: San Diego, CA, 1996.

In: Carbon Nanotubes: New Research Editor: Avery P. Ottenhouse

ISBN 978-1-60692-236-1 © 2009 Nova Science Publishers, Inc.

Chapter 5

COMPUTATIONAL ANALYSIS OF THE INTERFACIAL BONDING CHARACTERISTICS OF CARBON NANOTUBE/POLYMER COMPOSITES Qingzhong Xue∗ and Qingbin Zheng College of Physics Science and Technology, China University of Petroleum, Dongying, Shandong 257061, People’s Republic of China

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ABSTRACT Since the discovery of carbon nanotubes (CNTs) by Iijima in 1991, CNTs have attracted great research interest due to their unique properties such as high electrical and thermal conductivity, excellent stiffness against bending, and high tensile strength. Using carbon nanotubes (CNTs) as nanofibers to enhance the mechanical, electrical, thermal, and optical properties of composite materials has been pursued extensively. Molecular mechanics (MM) and molecular dynamics (MD) simulations have become increasingly popular in the theoretical investigations of reinforcement mechanisms in CNT-polymer composite systems. This paper is dedicated to conduct theoretical study on the interfacial characteristics of CNT reinforced polymer composites. Firstly, force-field-based MD simulations are performed to study the interaction between polymers and SWNTs. The “wrapping” of nanotubes by polymer chains was computed. The influence of temperature, nanotube radius and chirality on polymer adhesion was investigated. Furthermore, the “filling” of nanotubes by polymer chains was examined. The results show that the interaction between the SWNT and the polymer is strongly influenced by the specific monomer structure such as aromatic rings, which affect polymers’ affinities for SWNTs significantly. The attractive interaction between the simulated polymers and the SWNTs monotonically increases when the SWNT radius is increased. The temperature influence is neglectable for PE and PP but strong for PS and PANI. Secondly, our simulations indicate that the adhesion energy between the SWNT and the polymer strongly depends on the chirality. For SWNTs with similar molecular ∗

Corresponding Author. E-mail: [email protected], Tel: +86-0546-8392836, Fax: +86-0546-8392123

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Qingzhong Xue and Qingbin Zheng weights, diameters and lengths, the armchair nanotube may be the best nanotube type for reinforcement. The simulations of filling reveal that molecules of PE, PP and PS can fill into a (10, 10) SWNT cavity due to the attractive van der Waals interactions. The possible extension of polymers into SWNT cavities can be used to structurally bridge the SWNTs and polymers to significantly improve the load transfer between them when SWNTs are used to produce nanocomposites. Finally, the influence of chemical functionalization on the interfacial bonding characteristics of SWNTs reinforced polymer composites was investigated using MM and MD simulations. The simulations show that functionalization of nanotubes at low densities of functionalized carbon atoms drastically increase their interfacial bonding and shear stress between the nanotubes and the polymer matrix. This indicates that increasing the load transfer between SWNTs and a polymer matrix in a composite via chemisorption may be an effective way and chemical attachment of nanotubes during processing may be in part responsible for the enhanced stress transfer observed in some systems of the nanotube-polymer composites. Furthermore, this suggests the possibility to use functionalized nanotubes to effectively reinforce other kinds of polymer-based materials as well. The simulation results would be of important in the production of CNTs reinforced polymer composites.

Keywords: Carbon nanotube polymer composites, Molecular mechanics, Molecular dynamics, Interfacial bonding, Molecular interaction, Chemical functionalization.

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1. INTRODUCTION AND BACKGROUND Since the discovery of carbon nanotubes (CNTs) by Iijima in 1991 [1], CNTs have attracted great research interest due to their unique properties such as high electrical and thermal conductivity, excellent stiffness against bending, and high tensile strength [2]. Using CNTs as nanofibers to enhance the mechanical [3-10], electricitrical [11-14], thermal [15-17], and optical [18] properties of composite materials has been pursued extensively both in experimental and theoretical studies. Recently, experiments have shown remarkable enhancements in elastic modulus and strength of polymer composites with an addition of small amounts of CNTs [19-22]. It is well established, from the research on microfiber-reinforced composites over the past few decades, that the structure and properties of the fiber-matrix interface play a major role in determining mechanical performance and structural integrity of composite materials. However, due to difficulties in devising experiments to study the CNT-polymer interface, molecular mechanics (MM) and molecular dynamics (MD) simulations have become increasingly popular in the investigations of reinforcement mechanisms in CNT-polymer composite systems [23]. Many groups have investigated the interfaces in CNT-reinforced polymer composites using MD simulations. For example, Liao et al. [24] have studied the interfacial characteristics of a CNTreinforced Polystyrene (PS) composite system through MM simulations and elasticity calculations. They found that the fiber/matrix adhesion comes from electrostatic, van der Waals interaction, mismatch in the coefficients of thermal expansion and radial deformation induced by atomic interactions. Frankland et al. [25] have investigated the influence of

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chemical cross-links between a Single-walled nanotube (SWNT) and a polymer matrix on the matrix-nanotube shear strength using MD simulations. The results suggest that load transfer and modulus of nanotube-polymer composites can be effectively increased by deliberately adding chemical cross-linking and inadvertent chemical bonding between nanotubes and polymer matrices during processing may be in part responsible for the enhanced stress transfer observed in some systems of this type. Wong et al. [26] have studied local fracture morphologies of CNT/PS rod and CNT/epoxy film composites. Transmission and scanning electron microscopy examinations showed that these polymers adhered well to CNT at the nanometer scale. Some of the important interfacial characteristics that critically control the performance of a composite material were quantified through MM simulations and elasticity calculations. Multi-walled CNT morphology-related mechanical interlocking at nanometer scale, thermal residual stresses, as well as relatively cavity free surface for polymer adsorption are also believed to be contributing factors. Gou et al. [27] investigated the interfacial bonding of SWNT reinforced epoxy composites using a combination of computational and experimental methods. The interfacial shear strength between the nanotube and the cured epoxy resin was calculated to be up to 75 MPa, indicating that there could be an effective stress transfer from the epoxy resin to the nanotube. The following experimental results provided evidence of stress transfer in agreement with the simulation results. Yang et al. [28] has studied the interaction between polymers and CNTs using forcefield-based MD simulation. They found that the specific monomer structure plays a very important role in determining the strength of interaction between nanotubes and polymers. The polymers with a backbone containing aromatic rings are promising candidates for the noncovalent binding of CNTs into composite structures, which can be used as building blocks in amphiphilic copolymers to promote increased interfacial binding between the CNT and the polymeric matrix. Wei [29] has studied temperature dependent adhesion behavior and reinforcement in CNT-polymer composite. They found that the interfacial shear stress through van der Waals interactions increase linearly with applied tensile strains along the nanotube axis direction and a lower bound value for the shear strength is found ∼ 46 MPa at low temperatures. Direct stress-strain calculations show significant reinforcements in the composite in a wide temperature range, with ∼ 00% increase in the Young’s modulus when adding 6.5% volume ratio of short CNTs. However, most of the cited literatures considered the effect of only one or two factors on the adhesion properties. In this study, we focus on the physisorption of polymers on SWNTs and investigated the physical interactions between polymers and SWNTs in all conditions that we could think about using MM and MD simulations.

2. EXPERIMENTAL 2.1. Computational Method In this study, MM and MD simulations were conducted to explore the interfacial characteristics between SWNTs and polymers, through which we could get useful

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information for the development of nanotube-based polymeric composites. Here, MM and MD simulations were carried out using a commercial software package called Materials Studio developed by Accelrys Inc. The condensed phase optimization molecular potentials for atomistic simulation studies (COMPASS) module in the Materials Studio software was used to conduct force-field computations. The COMPASS was a parameterized, tested and validated first ab initio force-field [30, 31], which enables an accurate prediction of various gas-phase and condensed-phase properties of most of the common organic and inorganic materials [32-34].

2.2. Force Field The application of quantum mechanical techniques can accurately simulate a system of interacting particles, but such techniques often cost too much time and are usually feasible only in systems containing up to few hundreds of interacting particles. As we know, the main goal of simulations of the systems containing a large number of particles is generally to obtain the systems’ bulk properties which are primarily controlled by the location of atomic nuclei, so the knowledge of the electronic structure, provided by the quantum mechanic techniques, is not critical. Thus, we could have a good insight into the behavior of a system if a reasonable, physically-based approximation of the potential (force-field) can be obtained, which can be used to generate a set of system configurations which are statistically consistent with a fully quantum mechanical description. As stated above, a crucial point in the atomistic simulations of multi-particle systems is the choice of the force-fields, a brief overview of which is given in this section. In general, the total potential energy of a molecular system includes the following terms [35]:

Etotal = Evalence + Ecross−term + Enon−bond

(1)

Evalence = Ebond + Eangle + Etorsion + Eoop + EUB

(2)

Ecross−term = Ebond −bond + Eangle−angle + Ebond −angle + Eend −bond −torsion + Emiddle−bond −torsion + Eangle−torsion

(3)

+ Eangle−angle−torsion

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Enon−bond = EvdW + EColumb + EH −bond

(4)

The valence energy generally includes a bond stretching term, Ebond , a two-bond angle term, Eangle , a dihedral bond-torsion term, Etorsion , an inversion (or an out-of-plane interaction) term, Eoop , and a Urey–Bradlay term (involves interactions between two atoms bonded to a common atom), EUB . The cross-term interacting energy, Ecross −term , accounts for the effects such as bond lengths and angles changes caused by the surrounding atoms and generally includes: stretch– stretch interactions between two adjacent bonds, Ebond −bond , bend–bend interactions between

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two valence angles associated with a common vertex atom, Eangle−angle , stretch–bend interactions between a two-bond angle and one of its bonds, Ebond −angle , stretch–torsion interactions between a dihedral angle and one of its end bonds, Eend −bond −torsion , stretch– torsion interactions between a dihedral angle and its middle bond, Emiddle−bond −torsion , bendtorsion interactions between a dihedral angle and one of its valence angles, Eangle−torsion , and bend–bend–torsion interactions between a dihedral angle and its two valence angles, Eangle-angle-torsion . The non-bond interaction term, Enon−bond , accounts for the interactions between nonbonded atoms and includes the van der Waals energy, EvdW , the Coulomb electrostatic energy, ECoulomb , and the hydrogen bond energy, EH −bond . The COMPASS force-field uses different expressions for various components of the potential energy as follows [32, 33]:

Ebond = ∑ [ K 2 (b − b0 ) + K 3 (b − b0 ) + K 4 (b − b0 ) ]

(5)

Eangle = ∑ [ H 2 (θ − θ 0 ) + H 3 (θ − θ 0 ) + H 4 (θ − θ 0 ) ]

(6)

2

3

4

b

2

3

4

θ

Etorsion = ∑ [V1[1 − cos(φ − φ10 )] + V2 [1 − cos(2φ − φ20 )] + V3[1 − cos(3φ − φ30 )]] (7) φ

Eoop = ∑ K x χ 2

(8)

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x

Ebond − bond = ∑∑ Fbb ' (b − b0 )(b'−b0 ')

(9)

Eangle − angle = ∑∑ Fθθ ' (θ − θ 0 )(θ '−θ 0 ')

(10)

Ebond −angle = ∑∑ Fbθ (b − b0 )(θ − θ 0 )

(11)

Eend _ bond −torsion = ∑∑ Fbθ (b − b0 )× [V1 cosφ + V2 cos 2φ + V3 cos 3φ ]

(12)

b

b'

θ

θ'

b

θ

θ

b

E middle _ bond −torsion = ∑∑ Fb 'θ (b'−b0 ')(b'−b0 ')× [F1 cosφ + F2 cos 2φ + F3 cos 3φ ] (13) θ

b'

E angle−torsion = ∑∑ Fθφ (θ − θ 0 )× [V1 cosφ + V2 cos 2φ + V3 cos 3φ ]

(14)

E angle−angle−torsion = ∑∑∑ K φθθ ' cosφ (θ − θ 0 )×(θ '−θ 0 ')

(15)

θ

φ

φ

ECoulomb = ∑ i> j

qi q j

εrij

θ

θ'

(16)

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⎡ Aij Bij ⎤ EvDW = ∑ ⎢ 9 − 6 ⎥ rij ⎥⎦ i> j ⎣ ⎢ rij where q is the atomic charge,

(17)

ε is the dielectric constant, and rij is the i-j atomic separation

θ is the two-bond angle, φ is the dihedral torsion angle, and χ is the out of plane angle. b0 , ki (i = 2 − 4) , θ 0 ,

distance. b and b' are the lengths of two adjacent bonds,

H i (i = 2 − 4) , φi0 (i = 1 − 3) , Vi (i = 1 − 3) , Fbb ' , b0 ' , Fθθ ' , θ 0 ' , Fbθ , Fbφ , Fb 'θ , Fi (i = 1 − 3) , Fθφ , Kφθθ ' , Aij , and Bij are fitted from quantum mechanics calculations and are implemented into the Discover module of Materials Studio [36] , a powerful commercial atomic simulation program used in this paper.

3. INVESTIGATION OF MOLECULAR INTERACTIONS BETWEEN SWNT AND POLYETHYLENE/ POLYPROPYLENE/ POLYSTYRENE/ POLYANILINE MOLECULES 3.1. Molecular Model

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3.1.1. Molecular Model of SWNT In this study, we have used different kinds of SWNTs with diameters ranging from 7.83 to 27.12 Å and different chirality ranging from zigzag (10, 0) to armchair (10, 10). The electronic structures of the all carbon atoms in the SWNT models were sp2 hybridization. We have avoided the unsaturated boundary effect by adding hydrogen atoms at each end of CNT. Each C–C bond length was 1.42 Å and C–H bond length was 1.14 Å. The hydrogen atoms had charges of +0.1268 e and the carbon atoms connecting hydrogen atoms had charges of −0.1268 e, thus the neutrally charged SWNTs were constructed. The computer graphics picture of a (10, 10) SWNT model (with 400 carbon atoms and 40 hydrogen atoms) is shown in Figure 1. 3.1.2. Molecular Model of the Investigated Polymers The simulated polymers were polyethylene (PE), Polypropylene (PP), Polystyrene (PS), Polyaniline (PANI). The chemical structure and molecular models are provided in Figures 2 and 3. The simulated polymers had comparable numbers of atoms and molecular weight (PE 38 atoms, 170, PP 38 atoms, 170, PS 34 atoms, 204, and PANI 26 atoms, 184), hence the magnitude of the interaction energy gives a direct measure of the strength of their binding to the SWNT. Since the number of atoms and monomers used is small (about 35 atoms per molecule which corresponds to 6 monomers for PE, and 4 monomers for PP, 2 monomers for PS, 2 monomers for PANI), the molecules are better described as oligomers than polymers. However, we use the term “polymer” throughout the paper for simplicity, with the understanding that the results of our simulation describe the behavior of a small part (block)

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125

of a “long” polymer. PE is polymeric molecules with no side groups, whereas PP has side groups of methyl. PS and PANI are both molecules with side groups of aromatic groups.

Figure 1. Molecular model of a (10, 10) SWNT.

Polyethylene

Polypropylene

Polystyrene

Polyaniline

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Figure 2. Chemical structure of the investigated polymers.

Polyethylene

Polypropylene

Polystyrene

Polyaniline

Figure 3. Molecular model of the investigated polymers under minimum energy.

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3.2. Results and Discussion Generally speaking, wrapping and filling are two typical phenomena which would take place when the interactive process of the SWNT-polymer system is simulated [37]. We did a constant NVT simulation with undefined boundary conditions, which implies that the simulated volume is actually infinite. Also, it has to be noted that our simulation does not explore all the states of the ensemble because of the short simulation time (several nanoseconds). If the simulation time were long enough, then the polymer would move away eventually and very likely never interact with the CNT again, which is a direct consequence of the fact that we use infinite volume (no boundary conditions). However, it does not affect the results within our simulation time because this “escape” event is extremely rare. We do the simulation in a vacuum in order to simulate the effect of an ideal bad solvent and the thermostat in our simulation can be thought of as mimicking the action of the bad solvent. Here, the MD simulation for each case study was performed long enough to observe several cycles of thermal vibration. The interval of each MD simulation step was typically 1 femtosecond. All calculations were carried out at the initial temperature of 400 K except a special condition, using constant number of particles, constant volume and constant temperature (NVT) ensembles.

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3.2.1. Wrapping Polymer wrapping of CNTs has received attention as a promising way for manipulating and organizing CNTs into ordered structures. Recently, Chen et al. [38] found that a molecule containing a planar phenyl group can irreversibly adsorb to the surface of a SWNT and successfully immobilize proteins, DNA, and smaller biomolecules on the nanotube sidewalls. Experiments for the wrapping of SWNTs with poly(m-phenyleneviny-co-2,5-dioctyloxy-pphenylenevinylene) have also been reported [39]. To simulate the interactions between polymers and SWNTs, MD simulations were established with the polymers initially placed at the side of the SWNTs within a distance of 9.5 Å, which is the cutoff distance of van der Waals interactions in this study. 3.2.1.1. Interaction between Polymers and SWNTs Firstly, an armchair (10, 10) CNT (Figure 1) and four polymer models are selected as the representative elements for the simulation. Figures 4-7 show the snapshots of polymers and SWNTs observed at different time steps of the simulation. Initially, the polymer chains were put near the middle of SWNTs in a distance of about 8.5 Å. The simulation showed that all the four molecular chains would stretch and move toward the nanotubes until they finally wrapped on the surface of the helix of the nanotube and the equilibrium was achieved. Particularly, it cost about 70 ps for the wrapping of PE, PP and PS, but only 5 ps for PANI, which may be because of the strong polarity of PANI. We also noticed that the two aromatic rings of PS and PANI molecules gradually orientated to align their ring planes parallel to the SWNT surface during the dynamic interactions. The dynamic behavior of the polymer molecules can be illustrated by tracking the interaction energy of the SWNT-polymer molecules. Generally, the interaction energy is estimated from the difference between the potential energy of the composites system and the potential energies for the polymer molecules and the corresponding SWNTs as follows:

Computational Analysis of the Interfacial Bonding Characteristics…

ΔE = Etotal − ( ESWNT + E polymer )

127 (18)

where Etotal is the total potential energy of the composite at the end of equilibration, ESWNT is the energy of the nanotube without the polymer, and E polymer is the energy of the polymer without the nanotube.

0ps

5ps

10ps

15ps

35ps

55ps

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Figure 4. MD simulation snapshots of the SWNT–PE interactions.

0ps Figure 5. (Continued).

5ps

10ps

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Qingzhong Xue and Qingbin Zheng

15ps

35ps

70ps

Figure 5. MD simulation snapshots of the SWNT–PP interactions.

Copyright © 2009. Nova Science Publishers, Incorporated. All rights reserved.

In the other words, the interaction energy can be calculated as the difference between the minimum energy and the energy at an infinite separation of the nanotube and the polymer matix [23, 27, 40].

0ps

5ps

10ps

30ps

35ps

65ps

Figure 6. MD simulation snapshots of the SWNT–PS interactions.

Computational Analysis of the Interfacial Bonding Characteristics…

0ps

0.5ps

2.0ps

2.5ps

4.5ps

5ps

Figure 7. MD simulation snapshots of the SWNT–PANI interactions.

19200 Potential energy (Kcal/mol)

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19150 19100 19050 19000 18950

BSWNT-PANI BSWNT-PS BSWNT-PP BSWNT-PE

18900 18850 18800 18750 0

20

40

60

80

100

Time(ps) Figure 8. Potential energy evolution for SWNT-Polymer composites during 100 ps of wrapping simulation.

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Qingzhong Xue and Qingbin Zheng

Figure 8 shows the potential energies during the simulation and we can find that the potential energies of the four composites are almost the same during the simulations. Figure 9 shows the interactions during the wrapping process for PE, PP, PS, and PANI. Initially, for all the polymers the interaction between SWNTs and polymer chains gradually decreases. For PE and PP, the interaction decreases to -13 kcal/mol, while PS and PANI decreases to -20 kcal/mol, which is much stronger. Both PS and PANI are molecules with side groups of aromatic rings, so the interaction energy between polymers and SWNTs may be influenced by aromatic rings greatly.

Interaction energy (Kcal/mol)

0 SWNT-PANI SWNT-PP

-5

SWNT-PS SWNT-PE

-10 -15 -20 -25 0

20

40

60

80

100

Time(PS)

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Figure 9. Interaction energy evolution for SWNT-Polymer composites during 100 ps of wrapping simulation.

3.2.1.2. The Influence of Different Factors on Polymer Adhesion Firstly, we put different polymer chains near the nanotube in order to save simulation time, then the MD simulations were carried out to study the interactions between SWNTs and individual molecules of PP, PE, PS, and PANI for 200 ps. After this, the systems were minimized and the total interaction energies between the SWNTs and the polymers in equilibrium were recorded. Influence of the temperature on polymer adhesion. To assess the temperature dependence of the adhesion energy between the polymers and the SWNTs, some MD simulations were carried out at different temperatures, which varied from 300 K and 500 K in steps of 25 K. Figure 10 shows the temperature dependence of the intermolecular interaction. It was shown that the temperature influence is very small for all considered polymers except for PANI. Influence of the nanotube radius on polymer adhesion. In order to determine the influence of the nanotube radius on polymer adhesion, some MD simulations were carried out on SWNTs with PE, PP, PS, and PANI, respectively. The SWNT radius was varied from 8.14 to 27.12 Å in these simulations. The simulations show that the attractive interaction between the simulated polymers and the SWNTs monotonically increases when the SWNT radius is increased. Especially, for PS and PANI , the interactions is much stronger and increases rapidly than that of PE and PP. PS and PANI are both polymers with aromatic rings, which

Computational Analysis of the Interfacial Bonding Characteristics…

131

are therefore expected to possess a strong attractive interaction with the surface of the SWNTs and may play an important role in providing effective adhesion. When the SWNT radius are increased, aromatic rings in polymers can well align parallel to the surface, and thus the π − π interactions between the aromatic rings and the SWNTs increases significantly as shown in Figure 11.

Interaction energy (Kcal/mol)

-15

-20

-25

PE PS

-30 300

350

PP PANI

400

450

500

Temperature(K)

Interaction energy (Kcal/mol)

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Figure 10. Intermolecular interaction as a function of temperature.

-15

-20

-25

-30

PE PS 10

PP PANI 15

20

25

-10

SCNT diameter(10 )m Figure 11. Intermolecular interaction as a function of SWNT diameter.

Influence of the nanotube chirality on polymer adhesion. In this part of our study, the initial atomic configurations of SWNTs are obtained by creating the planar hexagonal carbon

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atom network corresponding to an (n, m) nanotube cut open axially. The corresponding chiral angle θ and diameter Dn of a SWNT with (n, m) indices could be determined by using the rolling grapheme model:

θ = arctan(

3m ), 2n + m

Dn =

3

π

b (n 2 + m 2 + nm) , (0 ≤ m ≤ n)

(19)

Copyright © 2009. Nova Science Publishers, Incorporated. All rights reserved.

where b is the C-C bond length23. Eleven types of SWNTs, with different chirality ranging from zigzag (10, 0) to armchair (10, 10), are generated as shown in Figure 1 and 12. The total number of atoms, diameters and lengths for each chiral nanotube are presented in Table 1.

10,0zigzag

10,1

10,2

10,3

10,4

10,5

10,6

10,7

10,8

10,9

Figure 12. Schematics of different chiral nanotubes.

Computational Analysis of the Interfacial Bonding Characteristics…

133

Table 1. Total number of atoms utilized in MD simulation for chiral SWNTs H

C

Nanotube diameter

Nanotube length

atoms

atoms

Å

Å

(10,0) SWNT zigzag

20

400

7.83

42.60

(10,1) SWNT

26

400

8.25

40.43

(10,2) SWNT

28

400

8.72

38.26

(10,3) SWNT

32

400

9.23

36.13

(10,4) SWNT

32

400

9.78

34.11

(10,5) SWNT

30

400

10.36

32.20

(10,6) SWNT

40

400

10.96

30.43

(10,7) SWNT

36

400

11.59

28.79

(10,8) SWNT

36

400

12.23

27.27

(10,9) SWNT

38

400

12.89

25.88

(10,10) SWNT armchair

40

400

13.56

24.60

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Figure 13 shows the adhesion energy of the composite versus the corresponding chirality of the nanotube. We can find that the adhesion energy increases slowly when the chirality becomes higher. However, it is clear that nanotubes with lower chirality indices tend to have smaller diameter and longer cylindrical axes compared to those with higher chirality, such as the armchair nanotube (10, 10). The longer the nanotube, the more nanotube surface area to form bonds between the nanotube and matrix, therefore, the adhesion energy between the CNT and the polymer strongly depends on the chirality. Thus, our simulations indicated that the lowest chirality nanotubes are the best nanotube type for reinforcement.

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Interaction energy (Kcal/mol)

-10

-15

-20

-25

PE PP PS PANI

(10,0)(10,1)(10,2)(10,3)(10,4)(10,5)(10,6)(10,7)(10,8)(10,9)(10,10)

Nanotube chirality

Copyright © 2009. Nova Science Publishers, Incorporated. All rights reserved.

Figure 13. Adhesion energy between different chiral nanotubes and polymer chains.

3.2.2. Filling The possibility of filling polymers into nanotubes during real-world composite processing would create the desired structure bridges between nanotubes and polymers. However, the reality of this filling will be mainly determined by van der Waals interactions between the polymers and the internal surface of the SWNT. To study the four polymer molecules’ filling phenomena, some MD simulations were set up with the polymer chains initially placed near the opening at one end of the nanotubes along the direction of the nanotube axis. The simulations show that molecular chains of PE, PP and PS would gradually moved the entire molecule body into the nanotubes, while PANI molecules can’t encapsulate into the nanotube even after a long time of simulation, which maybe caused by the strong polarity of PANI. The configurations of PE, PP and PS molecules filling into SWNTs, which is observed at different time steps of the MD simulations, are shown in Figures 14∼16. For PE and PP, the molecules were lingering around the opening firstly, then constantly changing their orientation to facilitate filling into the SWNT opening, and encapsulating into the nanotube within 100 ps. An equilibrium state of the system was also achieved when the polymer molecules were entirely in the nanotube. However, as shown in Figures 14 and 15, we also notice that the PE molecules will stay in the middle of the nanotube, while PP molecules will stay near the opening instead of going to the middle of the nanotube or the opposite opening, which maybe because of PP has side groups of methyl and is not as smooth as PE molecular chains. For PS, however, a very slow filling process is observed compared with the fast filling phenomenon of PE and PP, which cost about 2000 ps as shown in Figure 16. The PS chain has side groups of aromatic rings, which may be an important factor for the slow filling.

Computational Analysis of the Interfacial Bonding Characteristics…

0ps

20ps

30ps

40ps

55ps

80ps

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Figure 14. MD simulation of PE molecule filling into SWNT cavity.

0ps

30ps Figure 15. (Continued)

70ps

135

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Qingzhong Xue and Qingbin Zheng

80ps

85ps

95ps

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Figure 15. MD simulation of PP molecule filling into SWNT cavity.

0ps

100ps

300ps

400ps

1000ps

2000ps

Figure 16. MD simulation of PS molecule filling into SWNT cavity.

Computational Analysis of the Interfacial Bonding Characteristics…

137

19200 Potential Energy(Kcal/mol)

19150 19100 19050 19000

(SWNT-PS) (SWNT-PANI) (SWNT-PP) (SWNT-PE)

18950 18900 18850 18800 18750 0

20

40 60 Time(ps)

80

100

Figure 17. Potential energy evolution for SWNT-Polymer composites during 100 ps of filling simulation.

Interaction energy (Kcal/mol)

0 SWNT-PS SWNT-PP

-5 -10 -15 -20 -25 -30 -35 0

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SWNT-PANI SWNT-PE

20

40

60

80

100

Time(ps) Figure 18. Interaction energy evolution for SWNT-Polymer composites during 100 ps of wrapping simulation.

Figure 17 shows the potential energies and interaction energies during the simulations and we can see that the potential energies of the four composites are also almost the same during the simulations. Figure 18 shows the interactions during the filling process for PE, PP, PS, and PANI. Initially, just as in the wrapping process, for all the polymers the interaction between SWNTs and polymer chains gradually decreases till they encapsulated into the nanotube and achieved an equilibrium state. We also notice that the interaction energy will

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decreases rapidly for PE, PP and PS once they start filling the nanotube, which reveals that the filling can improve the load transfer between polymers and SWNTs significantly.

3.3. Conclusions In this study, some MD simulations are carried out to investigate the interactions of PE, PP, PS and PANI molecules with SWNTs in a vacuum. The results show that the interaction between the SWNT and the polymer is strongly influenced by the specific monomer structure such as aromatic rings, which affect polymers’ affinities for SWNTs significantly. The results also show that the attractive interaction between the simulated polymers and the SWNTs monotonically increases when the SWNT radius is increased while temperature influence is neglectable for all considered polymers except for PANI. The MD simulations also indicate that the adhesion energy between the SWNT and the polymer strongly depends on the chirality and the lowest chirality nanotubes are the best nanotube type for reinforcement. Lastly, the filling simulations reveal that molecules of PE, PP and PS can fill into a (10, 10) SWNT cavity due to the attractive van der Waals interactions. The possible extension of polymers into SWNT cavities can be used to structurally bridge the SWNTs and polymers to significantly improve the load transfer between them when SWNTs are used to produce nanocomposites.

4. INFLUENCE OF CHIRALITY ON THE INTERFACIAL BONDING CHARACTERISTICS OF CARBON NANOTUBE POLYMER COMPOSITES In this section, the influence of chirality on the interfacial bonding between the SWNTs and polymer were investigated using MM and MD simulations. In order to reveal the effect of the chirality on the interfacial bonding characteristics of the nanotube reinforced composites, several tubes with different chiralities but similar tube radii and lengths are selected.

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4.1. Molecular Model Poly(methyl methacrylate), (PMMA), is a well-known glassy polymer used in a variety of engineering areas from aircraft glazing to lightweight construction systems. Therefore, PMMA, with 10 repeating units in each chain, is chosen as a matrix in the study, which is also due to its simplicity and generic representation feature for polymer materials. Five types of SWNTs, with different chirality but similar molecular weights, diameters and lengths, are generated as shown in Figure 19. The total number of atoms, diameters and lengths for each nanotube are presented in Table 2. In the simulations, each of the composite systems was composed of a fragment of SWNT totally embedded inside the amorphous polymer matrix. A model of the composite system embedded by the pristine SWNT, which consisted of a supercell in the range of 57 Å×57 Å×62 Å, is shown in Figure 20. Each of the configurations was initiated by randomly generating 112 PMMA molecular chains surrounding the SWNT using an initial density of 1.2 g/cm3. The models were put into an NPT ensemble simulation with a pressure of 10 atm

Computational Analysis of the Interfacial Bonding Characteristics…

139

and a temperature of 300 K for 10 ps with a time step of 1 fs while holding the nanotube rigid. The purpose of this step was to slowly compress the structure of the matrix polymers to generate initial amorphous matrix with the correct density and low residual stress. The matrix polymers were then put into an NVT ensemble simulation and equilibrated for 20 ps with a time step of 0.2 fs with rigid nanotubes. After that, the composites systems were further equilibrated for 40 ps at a time step of 2 fs with non-rigid nanotubes to create a zero initial stress state using NVT ensembles. Table 2. Total number of atoms utilized in MD simulation for chiral SWNTs Type of

H

C

Nanotube diameter

Nanotube length

Chiral angel

SWNTs

atoms

atoms

Å

Å

θo

(10, 10) SWNT armchair

40

960

13.56

59.03

30.00

(12, 8) SWNT

40

960

13.65

58.64

23.43

(14, 5) SWNT

44

960

13.36

59.93

14.71

(16, 2) SWNT

44

960

13.38

59.83

5.82

(17, 0) SWNT zigzag

50

960

13.31

60.14

0.00

The energy of the composite systems was minimized to achieve the strongest bonding between the nanotubes and the polymer27, 40. Finally, the interfacial bonding energy and interfacial shear stress were calculated through pullout simulations.

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4.2. Results and Discussion The bonding strength between the SWNTs and the polymers can be evaluated by interfacial energy in the composites. Generally, the interaction energy is estimated from the difference between the potential energy of the composites system and the potential energy for the polymer molecules and the corresponding SWNTs as described in equation (18). The total interaction energy, ΔE , is twice the interfacial bonding energy γ scaled by the contact area A [41]:

γ=

ΔE 2A

(20)

The pullout simulations were performed to characterize the interfacial shear stress of the composites. The pullout energy, E pullout , is defined as the energy difference between the full

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Qingzhong Xue and Qingbin Zheng

embedded nanotube and the complete pullout configuration. The pullout energy was divided into three terms as follows [27]:

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Figure 19. Schematics of different chiral nanotubes.

a

b

Figure 20. Molecular model of The SWNT/PMMA composite system: (a) top view; (b) section view.

Computational Analysis of the Interfacial Bonding Characteristics…

E pullout = E2 − E1 = ( ΔE2 + ESWNT 2 + E polymer 2 ) − (ΔE1 + ESWNT 1 + E polymer1 )

= (ΔE2 − ΔE1 ) + ( ESWNT 2 − ESWNT 1 ) + ( E polymer 2 − E polymer1 ) The pullout energy can be related to the interfacial shear stress,

141

(21)

τ i , by the following

relation:

E pullout = ∫

x= L

x =0

τi =

2πr ( L − x)τ i dx = πrτ i L2

E pullout

πrL2

(22)

(23)

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where r and L are the outer radius and length of the SWNT, respectively, and x is the coordinate along the longitudinal tube axis [24.] In the first part of the study, the interfacial bonding for armchair SWNT was investigated. The pullout simulations of a SWNT were performed in order to characterize the interfacial shear strength of the composites. In order to demonstrate the statistical validity of the results, the pullout simulations were performed on five molecular models with different initial configurations and the error was calculated. Figure 21 shows the snapshots of the pullout simulations. The SWNT was pulled out of the PMMA matrix along the nanotube axis direction. The potential energy, interaction energy, and interfacial bonding energy were plotted against the displacement of the SWNT from the PMMA matrix, as shown in Figure 22. Figure 22a indicates that the potential energy of the SWNT/PMMA composite system was increased as the SWNT was pulled out of the PMMA.

Figure 21. Snapshots from the MD simulation of the pullout of the SWNT.

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Qingzhong Xue and Qingbin Zheng

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Figure 22. Energy plots during the pullout of the SWNT. (a) potential energy; (b) interaction energy; (c) interfacial bonding energy.

During the pullout, the interaction energy changed with the displacement linearly and decreased toward a value of zero, as shown in Figure 22b. This is due to the stable interfacial binding interaction and the decrease of contact area during the pullout. The interfacial binding energy kept constant with a value of 0.1 Kcal/mol Å2 during the pullout, as shown in Figure. 22c. After the SWNT was completely pulled out of the PMMA, the potential energy of the system was level off and the interaction energy then kept zero. The average potential energy of the composites was 42,122 Kcal/mol at the initial stage of the pull out and increased to 42,501 Kcal/mol after the pullout. From the pullout simulation, the interfacial shear strength between the pristine SWNT and the PMMA was about 36 MPa. Next, pullout simulations were performed on the other four kinds of SWNTs and the influence of chirality on the interfacial bonding has been investigated. In this part of the simulations, the interaction energy also changed with the displacement nearly linearly and decreased toward a value of zero during the pullout, as shown in Figure 23. Figure 24 shows the interaction energy, interfacial bonding energy and shear stress of the composite versus the corresponding chirality of the nanotube, all of which is the average value during the pullout. It was shown that the interaction energy, interfacial bonding energy and shear stress attain the

Computational Analysis of the Interfacial Bonding Characteristics…

143

highest value for the armchair system, while the zigzag nanotube composite produces the least value. Therefore, the binding energy between the SWNTs and the PMMA depends on the chirality and the armchair SWNT is the best nanotube type for reinforcement. Chirality dependent conformation of PMMA molecule at nanotube interface has been investigated through MD simulations by Wei [42]. Local wrapping angle θ is defined as the angel between the vector connecting the two ends of a three segment subchain on a polymer o

molecule and the nanotube axis. The simulations indicated that, while wrapping around 0 dominate on a small radius armchair SWNT, molecule wrapping shift to larger angels on a similar radius zigzag tube. The different conformations of polymer molecules at various SWNT interfaces may cause different interfacial bonding energy and the armchair SWNTs may have the strongest adhesion with the polymers.

Figure 23. Interaction energy plots during the pullout of the SWNTs from the matrix.

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4.3. Conclusions In summary, MM and MD simulations have been used to study the influence of chirality on the interfacial bonding characteristics between the SWNTs and the PMMA matrix. Several SWNTs, which include (10, 10), (12, 8), (14, 5), (16, 2), and (17, 0), with different chiralities but similar tube radii and lengths are selected. The simulations indicate that the interfacial bonding energy between the SWNT and the PMMA depends on the chirality. Substantial adhesion exists between the nanotube and PMMA when the nanotube has a higher chiral indices or larger chiral angel. For SWNTs with similar molecular weights, diameters and lengths, the armchair nanotube may be the best nanotube type for reinforcement. The general conclusions derived from this work may be of importance in devising advanced nanotube reinforced composites.

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Figure 24. Influence of chirality on the interfacial bonding characteristics of SWNT. (a) interaction energy; (b) interfacial bonding energy; (c) shear stress.

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5. EFFECT OF CHEMISORPTION ON THE INTERFACIAL BONDING CHARACTERISTICS OF CARBON NANOTUBE POLYMER COMPOSITES While chemically cross-linking or molecular entanglement method to strengthen the interface has been conducted [25,41], studies involving the influence of chemical attachment on interfacial properties of CNTs have not been reported. This section was about finding a viable way to get SWNT to go into the polymer matrix to act as reinforcement. The difficulties involved in doing this arise mostly from the fact that CNTs cannot interact well with other materials. The method pursued here for making the SWNTs capable of effectively interacting with the polymer was based on the covalent attachment of functional groups to the surface of SWNTs. By taking advantage of these functional groups, which could act as an effective interfacial bridge between the SWNTs and the polymeric matrix, an effective load transfer could be achieved between the SWNTs and the polymer matrix. In this study, the influence of chemical functionalization on the interfacial bonding between the SWNTs and polymer was investigated using MM and MD simulations.

Computational Analysis of the Interfacial Bonding Characteristics…

145

5.1. Molecular Model .

Poly(methyl methacrylate) (PMMA) and polyethylene (PE) are well-known polymers used in a variety of engineering areas. Therefore, PMMA and PE, with 10 repeating units in each chain, are chosen as matrixes in the study, which are also due to their simplicity and generic representation feature for polymer materials. The molecular model of PMMA and PE are shown in Figure 25. (10, 10) SWNTs, which have diameters of 13.56 Å and lengths of 59.03 Å, are selected for the simulations of the SWNT/PMMA composites except special conditions. The unsaturated boundary effect was avoided by adding hydrogen atoms at the ends of the SWNTs. The literature supplies numerous examples of addition reactions on nanotube surfaces43. Ying et al. [44] reported the grafting of aromatic rings on the side walls of SWNTs. In the present work, we used phenyl groups to functionalize the nanotube surface due to its simplicity and generic representation for the functionalization of CNTs. As we know, the dispersion degree of the SWNTs in the PMMA matrix can affect the interfacial bonding characteristics between the SWNTs and the PMMA matrix. However, if we consider the dispersion degree of the SWNTs, the computational system would be so large that it would cost too long a time for the simulation.

(a)

(b)

Figure 25. Molecular model of PMMA and PE.

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Also, since the main goal of our research is to investigate the interfacial bonding characteristics between the SWNTs and the PMMA matrix, the SWNTs were assumed to be well dispersed in the PMMA matrix and the simulation results would be useful for the production of SWNTs reinforced polymer composites as well.The composites, reinforced

by pristine SWNT and the SWNTs on which 0.5%, 2.5%, 5%, 7.5%, or 10% of the carbon atoms had a bonded phenyl group, were simulated by using MM and MD simulations. In the part of the influence of modification type, MM and MD simulations were performed on composites reinforced by pristine SWNT and the SWNTs on which 5% of the carbon atoms had bonded groups (carboxylic group COOH, amide group CONH2, alkyl group C6H11, or phenyl group C6H5). The functional groups were randomly end-grafted to the surface of the SWNTs. SWNTs with functional groups randomly chemisorbed to 5% of the carbon atoms are illustrated in the left panel of Figure 26. The chemical functionalization of the SWNTs has been performed by attaching functional groups to the surface of the CNTs through chemical covalent bonding and the functional groups were randomly end-grafted to the surface of the SWNTs. The associated change in geometry of the atoms on which the phenyl groups are bonded is illustrated in the right panel of Figure 26, where the bonded

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Qingzhong Xue and Qingbin Zheng

nanotube atoms are “raised” away from the nanotube axes and have hybridizations that change from sp2 to sp3 [45].

(a) with carboxylic groups (－COOH)

(b) with amide groups (－CONH2)

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(c) with alkyl groups (－C6H11)

(d) with phenyl groups (－C6H5)

Figure 26. Illustrating of a (10, 10) SWNT with functional groups randomly chemisorbed to 5% of the carbon atoms.

Computational Analysis of the Interfacial Bonding Characteristics…

147

5.2. Results and Discussion In the simulations, each of the composite systems was composed of a fragment of SWNT totally embedded inside the amorphous polymer matrix. A model of the composite system embedded by the pristine SWNT, which consisted of a supercell in the range of 57 Å×57 Å×62 Å, is shown in Figure 27. For SWNT-PMMA system, each of the configurations was initiated by randomly generating 112 PMMA molecular chains surrounding the SWNT using an initial density of 1.2 g/cm3. For SWNT-PE system, each of the configurations was initiated by randomly generating 247 PE molecular chains surrounding the SWNT using an initial density of 0.9 g/cm3.The models were put into an NPT ensemble simulation with a pressure of 10 atm and a temperature of 300K for 10 ps at a time step of 1 fs while holding the nanotube rigid.

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Figure 27. Cross-section view of SWNT/PMMA system before simulation.

(a)

(b)

Figure 28. Illustration of the composite embedded by a (10, 10) SWNT with phenyl groups randomly chemisorbed to 2.5% of the carbon atoms: (a) top view; (b) side view.

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Qingzhong Xue and Qingbin Zheng

The purpose of this step was to slowly compress the structure of the matrix polymers to generate initial amorphous matrix with the correct density and low residual stress. The matrix polymers were then put into an NVT ensemble simulation and equilibrated for 20 ps with a time step of 0.2 fs with rigid nanotubes. After that, the composites systems were further equilibrated for 40 ps at a time step of 2 fs with non-rigid nanotubes to create a zero initial stress state using NVT ensembles. The energy of the composite systems was minimized to achieve the strongest bonding between the nanotubes and the polymer shown in Figure 28 [24, 40]. Finally, the interfacial bonding energy and interfacial shear stress were calculated through pullout simulations.

) Energy (Kcal/mol) Energy (Kcal/mol)

Y

Energy (Kcal/mol

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5.2.1. Interfacial Bonding for Pristine SWNT The pullout simulations of a SWNT were performed in order to characterize the interfacial shear strength of the composites. The SWNT was pulled out of the polymer matrix along the nanotube axis direction. The potential energy, interaction energy, and interfacial bonding energy were plotted against the displacement of the SWNT from the polymer matrix, as shown in Figure 29 and 30. During the pullout, the interaction energy changed with the displacement linearly and decreased toward a value of zero, as shown in Figure 29a and 30a. This is due to the stable interfacial binding interaction and the decrease of contact area during the pullout. Figure 29b and 30b indicates that the pullout energy of the SWNT/ polymer composite system was increased as the SWNT was pulled out of the polymer. The interfacial binding energy kept constant with a value of 0.1 Kcal/mol Ǻ2 during the pullout, as shown in Figure 29c and 30c. After the SWNT was completely pulled out of the polymer, the potential energy of the system was leveled off and the interaction energy then kept zero. 0 -100 -200 -300 -400 -500 -600 400

(a)

0

300

10 20

30

40 50 60 70

(b)

200 100 0

0

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60

-0.06

(c)

-0.08 -0.10 -0.12 -0.14

0

10

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30

o

40

50

Displacement (A ) Figure 29. Energy plots during the pullout of the SWNT from the PMMA matrix. (a) interaction energy; (b) pullout energy; (c) interfacial bonding energy.

o

Y

Energy (Kcal/mol A )

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Energy (Kcal/mol)

Computational Analysis of the Interfacial Bonding Characteristics… 0 -100 -200 -300 -400 -500 -600 -700

149

(a)

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(b)

0

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50

Figure 30. Energy plots during the pullout of the SWNT from the PE matrix. (a) interaction energy; (b) pullout energy; (c) interfacial bonding energy.

5.2.2. Influence of Chemical Functionalization Degree The SWNTs and the polymer matrix were not held fixed in the pullout simulation. Therefore, the pullout energy has been influenced by the deformation of the nanotubes and polymer during the pullout. Figure 31 and 32 shows the interaction energy changed with the displacement nearly linearly during the pullout, which is due to the stable interfacial binding interaction between the SWNTs and the polymer.

Energy (Kcal/mol)

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0 -500 -1000

Unfunctionalized 0.5% functionalized 2.5% functionalized 5.0% functionalized 7.5% functionalized 10% functionalized

-1500 -2000 0

10

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Displacement (Å) Figure 31. Interaction energy plots during the pullout of the SWNT from the PMMA matrix.

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Qingzhong Xue and Qingbin Zheng

Energy (Kcal/mol)

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-2000 -2400 -2800 -3200 -3600 0

10

20

30

40

50

60

70

Displacement (Å)

Copyright © 2009. Nova Science Publishers, Incorporated. All rights reserved.

Figure 32. Interaction energy plots during the pullout of the SWNT from the PE matrix.

However, the interaction energy will keep zero after the nanotubes were completely pulled out of the polymer because there was no interaction between the nanotubes and the polymer [25]. Plotted in Figure 33a-b and 34a-b is the calculated interaction energy and interfacial bonding energy for SWNTs as a function of the degree of functionalization. When the degree of functionalization is increased, the interaction energy and interfacial bonding energy between the simulated SWNTs and the polymer monotonically increases toward a magnitude value, which is about four times the value for pristine SWNT. The interfacial bonding, which appears to be critically dependent on the nanotube-polymer interface surface area, will increase linearly with the total interface surface area [10]. When the SWNT is chemically attached with phenyl groups, the contact area between the nanotube and the polymer matrix will be drastically increased, which will cause the increase of the interfacial bonding between the nanotube and the polymer. Figure 33c and 34c shows the growth and saturation with higher degrees of functionalization. The results show that the shear stress of nanotube-polymer interface with weak nonbonded interactions can be increased by about 1000% with the introduction of a relatively low density ( ≤ 5%) of chemical attachment. However, the shear stress increases only weakly with the introduction of a relatively high density (>5%) of chemical attachment. When the functional groups of SWNT were successfully embedded into the polymer matrix, which may possibly link SWNTs with the polymer matrix, the shear stress could be effectively increased. The successful embedding could happen at a low density of functionalization and thus an effective enhancement of the shear stress could be attained.

Energy (Kcal/mol)

Computational Analysis of the Interfacial Bonding Characteristics…

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Copyright © 2009. Nova Science Publishers, Incorporated. All rights reserved.

o

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Energy (Kcal/mol A )

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Figure 33. Influence of chemical functionalization on the interfacial bonding characteristics of SWNT for SWNT/PMMA system. (a) interaction energy; (b) interfacial bonding energy; (c) shear stress.

-0.2 -0.4 -0.6

600 400 200 0 0 2 4 6 8 10 Degree of functionalization (%)

Figure 34. Influence of chemical functionalization on the interfacial bonding characteristics of SWNT for SWNT/PE system. (a) interaction energy; (b) interfacial bonding energy; (c) shear stress.

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However, when the density of functionalization becomes higher, some functional groups may only contact with the other functional groups, which may lead to a direct result that the effective contact surface area between the functional groups and the polymer matrix couldn’t be strongly increased any more, and thus there is only a weak increase of the shear stress. Although the covalent attachment of functional groups to the surface of nanotubes can improve the efficiency of load transfer, these functional groups might introduce defects on the walls of the perfect structure of the nanotubes, which will lower the strength of the nanotube filler. Some models predict that the change in mechanical properties of the SWNTs with lower level ( ≤ 10%) of functionalization is negligible [25]. So SWNT with 5% level of functionalization may be the feasible nanotube type for reinforcement, which could improve the efficiency of load transfer with negligible influence on the mechanical properties of the SWNT. It also supports suggestions that chemical attachment of nanotubes during processing may be in part responsible for the enhanced stress transfer observed in some systems of the nanotube-polymer composites.

5.2.3. Influence of Chemical Functionalization Type Figure 35 shows the interaction energy changes with the displacement nearly linearly during the pullout, which is due to the stable interfacial binding interaction between the SWNTs and the PE matrix. However, the interaction energy will keep zero after the nanotubes were completely pulled out of the PE matrix because there was no interaction between the nanotubes and the PE matrix.

Energy (Kcal/mol)

0 -500 -1000 -1500

Unfunctionalized With carboxylic groups With amide groups With alkyl groups With phenyl groups

-2000

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-2500 0

10

20 30 40 50 o Displacement ( A )

60

70

Figure 35. Interaction energy plots during the pullout of the SWNTs from the PE matrix.

Plotted in Figure 36 is the calculated interaction energy (Figure 36a) and interfacial bonding energy (Figure 36b) of the SWNT-PE system for SWNTs as a function of the type of functionalization. The figure shows that although the four types of functionalization could increase the adhesion with the polymer matrix, the special structure of the functional groups plays a very important role in determine adhesion to the matrix. We can observe that the SWNT functionalized with -C6H5 directly in the surface has the most strong interaction with

Computational Analysis of the Interfacial Bonding Characteristics…

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o

Shear Stress (MPa) Energy (Kcal/mol A x 10)

Energy (Kcal/mol)

the matrix (about 4 times as compared with that of pristine SWNT), whereas the SWNT with -COOH, -CONH2, or -C6H11 groups has increased only weakly than pristine SWNT. The interfacial bonding, which appears to be critically dependent on the nanotubepolymer interface surface area, will increase linearly with the total interface surface area [10]. When the SWNT is chemically functionalized, the contact area between the nanotube and the polymer matrix will be drastically increased, which will cause the increase of the interfacial bonding between the nanotube and the polymer. The aromatic ring (-C6H5) may has more contact area with the matrix than the other three functional groups for its special ring structure, which may cause the effective increase of adhesion energy. Figure 36c shows the interfacial shear stress between SWNTs and PE matrix as a function of the type of functionalization. The figure shows that the SWNT functionalized with -C6H11 or -C6H5 has increased the shear stress effectively (-C6H11: about 3 times as compared with that of pristine SWNT, -C6H5: about 17 times as compared with that of pristine SWNT), whereas the SWNT with -COOH, or-CONH2 groups has almost the same value as compared with that of the pristine SWNT. As shown in Figure 26, the backbones of -C6H11 and -C6H5 groups nearly parallel with the radial direction of the SWNT, while the -COOH, or-CONH2 groups nearly parallel with the SWNT axis direction. When the functional groups of SWNT were successfully embedded into the polymer matrix, which may possibly link SWNTs with the polymer matrix, the shear stress could be effectively increased. The successful embedding could be happen when the functional groups parallel with the radial direction of the SWNT, and thus the shear stress could be effectively increased when the SWNTs are functionalized with -C6H11 or -C6H5 groups. -2500 -2000 -1500 -1000

Interaction energy

-500 0 -50 -40 -30 -20

Interfacial bonding energy

-10 0 600 500 400 300 shear stress 200 100 0 Unfunctionalized Carboxyl Amide

Alkyl

Phenyl

Type of functionalization Figure 36. Influence of modification on the interfacial bonding characteristics of SWNT-PE system.

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Qingzhong Xue and Qingbin Zheng

The primary objective of this work was to select the appropriate functional groups that would provide a good interaction mechanism with the composite’s matrix and act as a load transfer conduit between the SWNTs and the composite matrix.

5.3. Conclusions In summary, we have used MM and MD simulations to study the effect of chemical functionalization on the interfacial bonding characteristics between the SWNTs and the polymer matrix. The simulations show that functionalization of nanotubes at low densities of functionalized carbon atoms drastically increase their interfacial bonding and shear stress between the nanotubes and the polymer matrix. This indicates that increasing the load transfer between SWNTs and a polymer matrix in a composite via chemisorption may be an effective way and chemical attachment of nanotubes during processing may be in part responsible for the enhanced stress transfer observed in some systems of the nanotube-polymer composites. Furthermore, this suggests the possibility to use functionalized nanotubes to effectively reinforce other kinds of polymer-based materials as well.

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CONCLUSIONS In this study, force-field-based MD simulations are performed to study the interaction between polymers and SWNTs. The “wrapping” of nanotubes by polymer chains was computed. The influence of temperature, nanotube radius and chirality on polymer adhesion was investigated. Furthermore, the “filling” of nanotubes by polymer chains was examined. The results show that the interaction between the SWNT and the polymer is strongly influenced by the specific monomer structure such as aromatic rings, which affect polymers’ affinities for SWNTs significantly. The attractive interaction between the simulated polymers and the SWNTs monotonically increases when the SWNT radius is increased. The temperature influence is neglectable for PE and PP but strong for PS and PANI. Also, our simulations indicate that the adhesion energy between the SWNT and the polymer strongly depends on the chirality. For SWNTs with similar molecular weights, diameters and lengths, the armchair nanotube may be the best nanotube type for reinforcement. The simulations of filling reveal that molecules of PE, PP and PS can fill into a (10, 10) SWNT cavity due to the attractive van der Waals interactions. The possible extension of polymers into SWNT cavities can be used to structurally bridge the SWNTs and polymers to significantly improve the load transfer between them when SWNTs are used to produce nanocomposites. Also, the influence of chemical functionalization on the interfacial bonding characteristics of SWNTs reinforced polymer composites was investigated using MM and MD simulations. The simulations show that functionalization of nanotubes at low densities of functionalized carbon atoms drastically increase their interfacial bonding and shear stress between the nanotubes and the polymer matrix. This indicates that increasing the load transfer between SWNTs and a polymer matrix in a composite via chemisorption may be an effective way and chemical attachment of nanotubes during processing may be in part responsible for the enhanced stress transfer observed in some systems of the nanotube-polymer composites.

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Furthermore, this suggests the possibility to use functionalized nanotubes to effectively reinforce other kinds of polymer-based materials as well.

ACKNOWLEDGMENT This work was supported by CNPC Innovation Fund under Contract No. 06E1024, and Shandong Natural Science Foundation under Contract No. Y2005A10.

REFERENCES [1] [2] [3] [4] [5] [6] [7] [8] [9] [10]

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[11] [12] [13] [14] [15] [16] [17] [18] [19] [20]

Iijima, S. Nature 1991, 354(7), 56-58. Cheng, Y.; Liu, G. R.; Li, Z. R.; Lu, C. Phys. A 2006, 367(15), 293-304. Schadler, L. S.; Giannaris, S. C.; Ajayan, P. M. Appl. Phys. Lett. 1998, 73(26), 38423844. Wagner, H. D.; Lourie, O.; Feldman, Y.; Tenne, R. Appl. Phys. Lett. 1998, 72(2), 188190. Zheng, Q. B.; Xue, Q. Z.; Yan K. Y.; Gao, X. L.; Li, Q.; Hao, L. Z. Polymer 2008, 49(3): 800-808. Zheng, Q. B.; Xue, Q. Z.; Yan K. Y.; Gao, X. L.; Li, Q.; Hao, L. Z. J. Appl. Phys. 2008, 103(4): 044302-1-4. Zheng, Q. B.; Xue, Q. Z.; Yan K. Y.; Hao, L. Z.; Li, Q.; Gao, X. L. J. Phys. Chem. 2007, C 111(12): 4628-4635. Cadek, M.; Coleman, J. N.; Barron, V.; Hedicke, K.; Blau, W. J. Appl. Phys. Lett. 2002, 81(27), 5123-5125. Dalton, A. B.; Collins, S.; Munoz, E.; Razal, J. M.; Ebron, V. H.; Ferraris, J. P.; Coleman, J. N.; Kim, B. G.; Baughman, R. H. Nature 2003, 423(6941), 703. Cadek, M.; Coleman, J. N.; Ryan, K. P.; Nicolosi, V.; Bister, G.; Fonseca, A.; Nagy, J. B.; Szostak, K.; Beguin, F.; Blau, W. J. Nano Lett. 2004, 4(2), 353-356. Kilbride, B. E.; Coleman, J. N.; Fraysse, J.; Fournet, P.; Cadek, M.; Drury, A.; Hutzler, S.; Roth, S.; Blaw, W. J. J. Appl. Phys. 2002, 92(7), 4024-4030. Kim, B.; Lee, J.; Yu, I. J. Appl. Phys. 2003, 94(10), 6724-6728. Ramasubramanjam, R.; Chen, J.; Liu, H. Appl. Phys. Lett. 2003, 83(14), 2928-2930. Sandler, J. K. W.; Kirk, J. E.; Kinloch, I. A.; Shaffer, M. S. P.; Windle, A. H. Polymer 2003, 44(19), 5893-5899. Biercuk, M. J.; Llaguno, M. C.; Radosavljevic, M.; Hyun, J. K.; Fischer, J. E.; Johnson, A. T. Fischer, J. E. Appl. Phys. Lett. 2002, 80(15), 2767-2769. Wei, C. Y.; Srivastava, D.; Cho, K. Nano Lett. 2002, 2(6), 647-650. Pham, J. Q.; Mitchell, C. A.; Bahr, J. L.; Tour, J. M.; Krishanamoorti, R.; Green, P. F. J. Polym. Sci. B 2003, 41(24), 3339-3345. Kymakis, E.; Amaratunga, G. A. J. Appl. Phys. Lett. 2002, 80(1), 112-114. Shaffer, M. S. P.; Windle, A. H. Adv. Mater. 1999, 11(8), 937-941. Lozano, K.; Barrera, E. V. J. Appl. Polym. Sci. 2000, 79(1), 125-133.

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[21] Sen, R.; Zhao, B.; Perea, D.; Iktis, M. E.; Hu, H.; Love, J.; Bekyarova, E.; Haddon, R. C. Nano Lett. 2004, 4(3), 459-464. [22] Li, X. D.; Gao, H. S.; Scrivens, W. A.; Fei, D. L.; Xu, X. Y.; Sutton, M. A.; Reynolds, A. P.; Myrick, M. L. Nanotechnology 2004, 15(11), 1416-1423. [23] Al-Haik, M.; Hussaini, M. Y. J. Appl. Phys. 2005, 97(7), 074306-1-5. [24] Liao, K.; Li, S. Appl. Phys. Lett. 2001, 79(25), 4225-4227. [25] Frankland, S. J. V.; Caglar, A.; Brenner, D. W.; Griebel, M. J. Phys. Chem. B 2002, 106(12), 3046-3048. [26] Wong, M.; Paramsothy, M.; Xu, X. J.; Ren, Y.; Li, S.; Liao, K. Polymer 2003, 44(25), 7757-7764. [27] Gou, J.; Minaie, B.; Wang, B.; Liang, Z. Y.; Zhang, C. Comp. Mater. Sci. 2004, 31(34), 225-236. [28] Yang, M. J.; Koutsos, V.; Zaiser, M. J. Phys. Chem. B 2005, 109(20), 10009-10014. [29] Wei, C. Y. Appl. Phys. Lett. 2006, 88(9), 093108-1-3. [30] Maple, J. R.; Hwang, M. J.; Stockfisch, T. P.; Dinur, U.; Waldman, M.; Ewig, C. S.; Hagler. A. T. J. Comput. Chem. 1994, 15(2), 162-182. [31] Sun, H. J. Comput. Chem. 1994, 15(7), 752-768. [32] Sun, H. J. Phys. Chem. B. 1998, 102(18), 7338-7364. [33] Sun, H.; Ren, P.; Fried, J. R. Computat. Theor. Polym. Sci. 1998, 8(1), 229-246. [34] Rigby, D.; Sun, H.; Eichinger, B. E. Polym. Inter. 1998, 44(3), 311-330. [35] Grujicic, M.; Cao, G.; Roy, W. N. Appl. Surf. Sci. 2004, 227(1-4), 349-363. [36] http://www.accelrys.com/products/mstudio/modeling/polymersandsimulations/discover. html. [37] Xie, Y. H.; Soh, A. K. Mater. Lett. 2005, 59(8-9), 971-975. [38] Chen, R. J.; Zhang, Y. G.; Wang, D. W.; Dai, H. J. J. Am. Chem. Soc. 2001, 123(16), 3838-3839. [39] Steuerman, D. W.; Star, A.; Narizzano, R.; Choi, H.; Ries, R. S.; Nicolini, C.; Stoddart, J. F.; Heath, J. R. J. Phys. Chem. B 2002, 106(12), 3124-3130. [40] Gou, J.; Liang, Z.; Zhang, C.; Wang, B. Compos. B. 2005, 36(6-7), 524-533. [41] Lordi V.; Yao N. J. Mater. Res. 2000, 15(12), 2770-2779. [42] Wei C. Y. Nano Lett. 2006, 6(8), 1627-1631. [43] Banerjee S.; Hemraj-Benny T.; Wong S. S. Adv. Mater. 2005, 17(1), 17-29. [44] Ying Y. M.; Saini R. K.; Liang F.; Sadana A. K.; Billups W. E. Org. Lett. 2003, 5(9), 1471-1473. [45] Padgett C. W.; Brenner D. W. Nano Lett. 2004, 4(6), 1051-1053.

In: Carbon Nanotubes: New Research Editor: Avery P. Ottenhouse

ISBN 978-1-60692-236-1 © 2009 Nova Science Publishers, Inc.

Chapter 6

MECHANICAL PROPERTIES OF CARBON NANOTUBES Q. Wang1 and K. M. Liew2 1

Department of Mechanical and Manufacturing Engineering, University of Manitoba, Winnipeg, Manitoba, Canada R3T 5V6 2 Department of Building and Construction Engineering, City University of Hong Kong, China

ABSTRACT

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Molecular mechanics calculations for the in-place stiffness, shear modulus, and bending rigidity of both single- and double-walled carbon nanotubes are reported by calculating the strain energy of carbon nanotubes and graphite sheets subject to various types of loading. Elastic rod and plate theories are employed to link the material properties of carbon nanotubes directly to the molecular mechanics calculations. The length dependence of these material properties is reported and investigated via nonlocal elasticity theory. In addition, the van der Waals effect on the differences between the material properties of double- and single-walled carbon nanotubes is also examined. The diminishment of such differences in large sizes of carbon nanotubes is revealed from the simulations.

INTRODUCTION Carbon nanotubes (CNTs), which were discovered by Iijima in 1991 [1], are macromolecules of carbon in a periodic hexagonal arrangement with a cylindrical shell shape. As a new type of nano-scale material, CNTs have aroused great interest among researchers because of their remarkable mechanical, thermal, electrochemical, piezoresistive, and other physical properties [2-5]. They can be viewed as one (or more) graphite sheet(s) rolled into a seamless tube. The way this graphite sheet is wrapped is represented by a pair of indices (n, m) that are called the chirality. When m = 0, the nanotubes are called “zigzag,” and when n = m, they are called “armchair.” Research findings have revealed extremely strong mechanical properties in these materials [6-7]. Of the mechanical properties of CNTs, accurate estimates

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of the Young’s modulus, shear strength, and bending rigidity are critical for their potential application. Experimental endeavors have been undertaken to estimate the mechanical properties of CNTs. Treacy et al. [8] obtained the Young’s modulus of multi-walled CNTs (MWCNTs) in a wide range, from 0.4 to 4.15 TPa, with an average of 1.8 TPa, by measuring the amplitude of their intrinsic thermal vibrations in a transmission electron microscope. Salvetat et al. [9] used an atomic force microscope to conclude that the elastic and shear modules of a singlewalled CNT (SWCNT) were of the order of 1 TPa and 1 GPa, respectively. Krishman et al. [10] calculated the Young’s modulus of SWCNTs to be 0.9 ~ 1.7 TPa by observing their freestanding room-temperature vibrations in a transmission electron microscope. Wong et al. [11] experimentally studied the Young’s modulus of individual, structurally isolated silicon carbide nanorods and MWCNTs that were pinned at one end to molybdenum disulfide surfaces and found the values to be 0.7 ~ 1.9 TPa. Poncharal et al. [7] used a transmission electron microscope to observe the static deformation of an MWCT and indicated that the Young’s modulus of the materials was about 1 TPa. The wide variety of experimentally obtained mechanical properties of CNTs is mainly due to the uncertainty and uncontrollable environmental effects on the measurements in the experiments. Although a rough estimate of the order of the mechanical properties of CNTs is available, a more accurate prediction is still necessary and is, in fact, indispensable for capturing the extensive potential of these materials. In addition to experimental endeavors, theoretical evaluations of the material properties of CNTs have also been undertaken. Theoretical modeling is usually classified into two main categories. The first is atomic modeling, and it includes such techniques as classical molecular dynamics [12-13], tight-binding molecular dynamics [14], and density functional theory [15]. Because these atomic methods are limited to systems with a small number of molecules and atoms, they are restrained to small-scale modeling. Continuum mechanics modeling, in contrast, is practical for the analysis of CNTs for large-scale systems. Thus, both continuum modeling and molecular dynamics have been employed to estimate the mechanical properties of CNTs. Closed-form expressions for the axial elastic properties of chiral CNTs were recently presented by Chang et al. [16-17]. In their work, a nonlinear stick-spiral model was developed to investigate the material behavior of SWCNTs, especially the estimates of the Young’s modulus and shear modulus of CNTs based on a molecular mechanics concept. The major conclusion based on this nonlinear model was that the elastic properties are chirality-independent for SWCNTs with a diameter of less than 2 nm, thus demonstrating an obvious scale effect. An attempt to estimate the material properties of achiral CNTs was also made via the concept of a representative volume element of the chemical structure of a graphite sheet [18-19]. In addition to measurements of the Young’s modulus and shear modulus of CNTs, their bending rigidity has also been investigated. Adams et al. [20] applied quantum molecular dynamics, using both empirical and local density functional methods, to evaluate the energies of a number of ball-shaped and tubular fullerenes of various sizes and suggested that the value of bending rigidity was D = 1.62 eV. Lucas et al. [21] estimated flexural rigidity D to be 1.78 eV by comparing the dispersion relation of the out-of-plane acoustic phonons in graphite with the flexural vibrational frequency of a continuum plate. Odegard et al. [18] introduced a representative volume element of the chemical structure of a graphite sheet and predicted bending rigidity D ≈ 1.12eV for armchair nanotubes and D ≈ 1.22eV for zigzag nanotubes, which was supported by the results of Wang [19]. Kudin

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et al. [22] reported ab initio calculations of the mechanical properties of two-dimensional lattices of carbon, boron-nitride, and fluorine-carbon composites. It has been pointed out that atomic methods are limited to systems with a small number of molecules and atoms and that continuum mechanics modeling is practical in the analysis of CNTs for large-scale systems. However, the classical continuum models themselves are not universally applicable, even for macro-engineering structures. For example, the Euler buckling load is only valid for steel columns with aspect ratios greater than 30 [23]. Continuum mechanics modeling is also unable to capture the atomic structures of nano-materials, and hence further verification of its applicability is necessary. Therefore, it can be concluded that continuum mechanics models are essential in the study of large-sized CNTs, but that the effectiveness of any proposed model should be verified through either atomic modeling or ab initio simulations to justify its applicability. From the aforementioned divergent results on the material properties of CNTs via different methods, it can be seen that a simple, effective, and efficient modeling method is necessary to find a reasonable and accurate estimate of the elastic modulus, shear modulus, and, especially, the bending rigidity of CNTs in a systematic way. Such a simple and explicit modeling method is expected to employ the classical continuum mechanics theory while being able to maintain the nature of the atomic structures in the modeling. The scale effect on CNTs has been an interesting topic in the nano-community. The modeling of such a size-dependent phenomenon has become an active and interesting subject for research [24]. Sun and Zhang [25] pointed out the limited applicability of continuum models in nanotechnology. They indicated the importance of a semi-continuum model to analyze nanomaterials. In their semi-continuum model for nano-structured materials with plate-like geometry, results that contrast with those of classical continuum models were observed. The values of the material properties were found to be completely dependent on the thickness of the plate structure. Geng and Chang [17] developed a nonlinear stick-spiral model to investigate the mechanical behavior of SWCNTs. They discussed the elastic properties, paying special attention to the effects of tube chirality and tube size. However, the dependence of the material properties of CNTs on their length has not yet been reported in the available research findings. Nonlocal elasticity was proposed by Eringen [26-27] to account for the scale effect on elasticity by assuming the stress at a reference point to be a function of the strain field at every point in the body. In this way, the internal size scale could be considered in the constitutive equations simply as a material parameter. The application of nonlocal elasticity in micro- and nano-materials has received a lot of attention from the nanotechnology community recently. Peddieson et al. [28] investigated the potential for applying the nonlocal elastic beam theory to micro- and nano-materials by formulating and applying a nonlocal version of the Euler-Bernoulli beam theory to the study of a cantilever beam. The small-scale effect on the wave propagation dispersion relation of a CNT was explicitly revealed [29] for different CNT wavenumbers and diameters via the nonlocal elastic beam and shell theories. The scale coefficient in nonlocal continuum mechanics was then roughly estimated for CNTs from the obtained asymptotic frequency. This research proved effective in predicting the small-scale effect on CNT wave propagation with a qualitative validation study based on the published experimental reports. Zhang, Liu, and Han [30] developed a nonlocal multiple-shell model for the elastic buckling analysis of MWCNTs under uniform external radial pressure in which the effect of small length scale was incorporated in the formulation of the buckling pressure. Duan and Wang [31] studied the axisymmetric bending of micro- and nano-scale circular plates and obtained exact nonlocal

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solutions under general loading conditions using a variable transformation technique. To the best of the authors’ knowledge, the application of nonlocal elasticity to the estimation of the material properties of CNTs, especially the verification of the theory with molecular dynamics, has not yet been explored. The verification of this theory with molecular dynamics simulations is indispensable if it is to be further developed in the analysis of CNTs. This manuscript is intended to introduce and summarize the progress that the authors have made in the modeling of the mechanical properties of CNTs. A simple, effective, and efficient modeling method for the calculation of the in-plane stiffness, shear modulus, and bending rigidity of CNTs via molecular mechanics simulations and elastic theory is proposed and discussed. In particular, the strain energy of CNTs and graphite sheets subject to various types of loading is used to evaluate all of the material properties via elastic rod and plate theories. A tight link between the molecular mechanics calculations on the strain energy and the corresponding second derivative and estimate of the mechanical properties of CNTs is uncovered, particularly for the derivation, and physical interpretations of the results are provided. In addition, the length-dependent stiffness of SWCNTs is investigated via nonlocal elasticity by employing an elastic rod that is subject to axial compression to derive the closeform solution of this material property. Verification of the obtained stiffness from the nonlocal elastic rod theory is obtained from the molecular simulation results, and a suggestion for the scale coefficient that is employed in nonlocal elasticity is also proposed. Finally, the length dependence of the mechanical properties of double-walled carbon nanotubes (DWCNTs) is explored, and the van der Waals effect on the differences between these properties in DWCNTs and SWCNTs is investigated.

MECHANICAL PROPERTIES OF SWCNTS In-plane stiffness, shear modulus, and bending rigidity are investigated using continuum mechanics and the molecular dynamics principle through calculations of the strain energy for CNTs and graphite sheets subject to various types of loading. Elastic rod and plate theories are employed to link the material properties of SWCNTs directly to the molecular mechanics calculations.

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Theoretical Foundation First of all, t = 0.34 nm, the thickness of a grapheme sheet, is normally assumed for CNT thickness. However, Yakonson et al. [32] concluded that the effective thickness of CNTs should be taken to be t = 0.066 nm rather than t = 0.34 nm if the bending rigidity D = 0.85

eV and in-plane stiffness Et = 360 J / m 2 are consistent with the classical shell bending theory. This discussion of the wall thickness of CNT can also be found in Yakobson and Avouris [33]. The definition of in-plane stiffness is thus defined here as Et (similar to the definition in solid mechanics) to avoid argument over the value of the effective thickness of CNTs. The physical interpretation of the in-plane stiffness of an SWCNT is the rigidity of the material to the axial loading that is subject to it. Elastic rod theory is employed to link the in-

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plane stiffness to the strain energy stored in the structure. From the mechanics of the materials, an elastic rod that is subject to axial uniform compression or tension can be simply modeled or represented by a fictitious spring element, with the stiffness given as [34]

k = AE / L ,

(1)

where A is the area of the cross section, E is the Young’s modulus, and L is the length of the elastic rod. For an SWCNT, A = πdt is set, where d and t are the medium diameter of the SWCNT’s cross section and wall thickness, respectively. Therefore, the relationship between the in-plane stiffness of the SWCNT, Et , and the stiffness of the fictitious spring is obtained by

Et =

k (L / d )

π

.

(2)

However, it is also known that spring stiffness is normally viewed as the second derivative of the strain energy restored in the spring with respect to the corresponding elongation or compression, i.e., U ′′ . Hence, the in-plane stiffness of the SWCNT can be directly obtained as follows in terms of the second derivative of the strain energy stored in the SWCNT, subject to axial loading [35]:

Et =

U ′′( L / d )

π

.

(3)

Eq. (3) directly links the in-plane stiffness to the calculations of strain energy and the corresponding second derivative via molecular dynamics. Similarly, an elastic rod under torsion can be directly modeled by a rotary spring with the stiffness kγ given by [34]

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kr = GI p / L ,

(4)

where I p is the polar moment of the inertia of the circular cross section, and G is the shear modulus. It has been acknowledged that the thickness of CNTs is normally considered to be very thin compared to their diameters. For example, the diameter of (8,8) armchair CNTs is d = 1.085 nm, whereas the thickness of the SWCNT is used as 0.076 nm. Hence, the polar moment of inertia for a thin circular rod can be approximately given by I p = πd t / 4 . 3

Similar to the spring that is subject to axial loading, the rotary spring stiffness, k r , is equivalent to the second derivative of the strain energy with respect to the torsion angle in the spring, or, equivalently, the strain energy stored in the CNTs, with respect to the rotation angle applied to them, i.e., U r′′ . Hence, the shear modulus of SWCNTs can be easily obtained from [36]

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Q. Wang and K. M. Liew

4U r′′L / d 3

π

.

(5)

The limited estimates available on bending rigidity are almost all from studies of graphite sheets [15, 37]. Finally, bending rigidity D is evaluated by applying point loading at the center of a square graphite sheet with a length of L and the four edges clamped. Based on the elastic plate theory, the relationship between the loading, P , and the deformation at the loading position, δ , is governed by [38]

P

δ

=

D . 0.0056 L2

(6)

Because the work done by the point loading is completely transferred to the strain energy, the plate is again modeled by a fictitious spring whose stiffness, P / δ , can be calculated from the second derivative of strain energy U δ′′ , as measured from the molecular mechanics simulations. The expression for D can thus be given as [35]

D = 0.0056 L2U δ′′ . (7) Eqs. (3), (5), and (7), by virtue of elastic theory, represent the relationship between the mechanical properties of CNTs and the calculations of the second derivative of strain energy via molecular dynamics. The measurements of these properties will thus be obtained through molecular dynamics simulations of CNTs subject to axial loading, torsion, and graphite sheets by point loading, as shown in the following sections.

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Molecular Dynamics Molecular dynamics is a form of computer simulation wherein atoms and molecules are allowed to interact for a period of time under the known laws of physics, thus giving a view of the motion of the atoms [39]. Molecular dynamics simulations are conducted via Materials Studio, which was developed by Accelrys to study chemicals and materials, including crystal structure and crystallization processes, polymer properties, catalysis, and structure-activity relationships. In these simulations, the interatomic interactions are described by the condensed-phased optimized molecular potential for atomistic simulation studies [40]. This is the first ab initio force field that was parameterized and validated using condensed-phase properties, and it has been proved to be applicable in describing the mechanical properties of CNTs [35-36]. In molecular dynamics, the potential energy of a system can be expressed as the sum of the valence (or bond), cross-terms, and non-bond interactions: Etotal = Evalence + Ecrossterm + Enon-bond.

(8)

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The energy of valence, Evalence, is generally accounted for by terms that include bond stretching, valence angle bending, dihedral angle torsion, and inversion. The cross terms, Ecrossterm, account for such factors as the bond or angle distortions caused by nearby atoms to accurately reproduce the experimental vibrational frequencies and, therefore, the dynamic properties of molecules. The energy of interactions, Enon-bond, between non-bonded atoms is primarily accounted for by the van der Waals effect. The molecular simulations are carried out at a temperature of 1 K to avoid the thermal effect with an adiabatic process. The molecular dynamics procedure involves the stepwise integration of Newton’s equations. The constant volume ensemble, also known as the microcanonical ensemble, is obtained by solving the standard Newton equation without any temperature or pressure control. Energy is thus conserved when this (adiabatic) ensemble is generated. The time step in all dynamics simulations is 1 fs . Once every molecular dynamics process has finished, the configuration of CNTs or graphite sheets is achieved through a minimizer processor that enables the atoms in the structures to rotate and move in relation to one another to minimize the potential energy so that an equilibrium state can be recognized. The simulations are run in parallel for the four processors on a Sun workstation. In molecular dynamics simulations of the compression motion of CNTs, the strain energy 0

is collected at every incremental displacement step 0.1 A . Once the strain energy at every compression step is available, the second derivative of the strain energy with respect to the compression can easily be obtained through a simple direct finite difference method. Then, the in-plane stiffness of the SWCNT can be directly determined by Eq. (3). The shear modulus of CNTs is investigated through a similar procedure. The strain energy at an incremental step rotation angle, φ = 1 degree, is collected to calculate the corresponding second derivative and the shear modulus according to Eq. (5). In the estimate of the bending rigidity of SWCNTs, the boundary of the graphite is updated with hydrogen to cease the dangling bonds on the edges of the sheets. This is to make the simulation more stable. After the initial minimization process, the four edges of the sheets are clamped, and the deformation 0

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with incremental step 0.02 A at the loading is applied to find the strain energy data of the plate sheet and the corresponding second derivative of the energy with respect to the incremental step of the deformation. Then, the bending rigidity can be extrapolated via Eq.(7).

Simulations Table 1 lists the in-plane stiffness of achiral (8,0) and (8,8) and chiral (8,4) CNTs. The diameters and unit cell lengths are 0.626nm and 0.426nm for zigzag (8,0) SWCNTs, 1.085 nm and 0.246 nm for armchair (8,8) SCNTs, and 0.829nm and 1.127 nm for chiral (8,4) SWCNTs, respectively. Table 1 shows that the in-plane stiffness of (8,0) CNTs increases from Et = 354.01J / m to Et = 375.18 J / m from the shorter size, L = 2.22nm , to the larger size, L = 11.99nm . As for the armchair (8,8) CNTs, it can again be seen that the in-plane stiffness increases with the increase of the tube length from 2

2

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Q. Wang and K. M. Liew

Et = 354.08 J / m 2 for the (8,8) CNT with L = 2.66nm to Et = 377.58 J / m 2 for the CNT with L = 14.37 nm . Table 1. Molecular dynamics simulation calculations of in-plane stiffness and shear modulus of SWCNTs

(8,0) SWCNT L (nm) Et (J/m^2) 2.22 354.01 4.16 363.91 6.10 369.73 8.04 373.31 10.12 374.90 11.99 375.18

In-Plane stiffness (8,8) SWCNT L (nm) Et (J/m^2) 2.66 354.08 4.35 362.89 6.28 369.99 8.69 375.17 11.57 377.58 14.37 377.58

(8,4) SWCNT L (nm) Et (J/m^2) 2.20 353.31 4.42 368.65 6.63 373.61 8.84 376.69 10.11 378.96 12.15 379.70

Shear stiffness (8,8) SWCNT L (nm) Gt (J/m^2) 2.66 116.75 4.35 118.87 6.28 121.83 8.69 123.31 11.57 123.79

The asymptotic values of the stiffness for the achiral CNTs are all found for tubes larger than 12 nm from the simulations. An obvious scale effect for the in-plane stiffness is secured for tubes shorter than 10nm . The asymptotic value of the in-plane stiffness of (8,8) armchair CNTs is found to be larger than that of (8,0) zigzag CNTs. A similar observation was also indicated by Geng and Chang [17] via their nonlinear molecular mechanics model. The measurements of the in-plane stiffness of chiral CNTs are more tedious to obtain than are those of achiral CNTs, as the repeated units display themselves in a helical direction, rather than in a straight longitudinal direction as in achiral tubes, thus leading to inaccurate measurements of the tube lengths. Therefore, a more careful identification of the exact locations of the repeated units is necessary for accurate measurements of the lengths. The asymptotic value for the in-plane stiffness of the chiral CNTs is Et = 379.70 J / m , and the 2

lower value is found to be Et = 353.31J / m for a tube with L = 2.20nm . The noticeable length dependence of the stiffness of the chiral tubes is clearly identified through the simulations. Our molecular simulations reveal that the length-dependent in-plane stiffness of CNTs is 2

in the range of 352 − 380 J / m , which is close to the estimate of Yakobson et al. [32], 360 2

J / m 2 , based on data provided by Robertson et al. [41]. Gupta et al. [42] used a similar Copyright © 2009. Nova Science Publishers, Incorporated. All rights reserved.

method to evaluate the Young’s modulus and found the in-plane stiffness to be about 420

J / m 2 , which is fairly close to our prediction. In addition, other estimates of the Young’s modulus based on experimental results [7,9-10] have also confirmed the range of this mechanical property when the thickness of CNTs, t = 0.34nm , is employed in the calculations. Such good agreement in the predictions of in-plane stiffness also demonstrates the effectiveness of the present method. The in-plane shear modulus is investigated by applying torsion motions to the CNTs. The last two columns of Table 1 show the variation of the stiffness versus the length of (8,8) armchair CNTs. The shear modulus increases from Gt = 116.75 J / m

2

for a CNT with

L = 2.66nm to the asymptotic value Gt = 123.79 J / m for CNTs longer than 12nm . The 2

length-dependent shear modulus is also found in the simulations. Our results are in good

Mechanical Properties of Carbon Nanotubes

165

agreement with some of the existing predictions, such as those from lattice dynamics by Popov et al. [43]. A square graphite sheet subject to point loading at its center is employed to measure the bending rigidity of SWCNTs [35]. This value was found to be largely length-dependent for the sheets less than 6.5 nm that we tested. The simulations [35] for bending rigidity are 1.47, 1.30, and 0.99 eV for square sheets with lengths of 6.42, 5.08, and 3.64 nm , respectively. However, very consistent results are obtained for bending rigidity with a length of 8.48 nm , and the average of the values is 1.778 eV . A further measurement attempt was made on a square plate with a length of 9.4 nm . The calculated bending rigidity is 1.783 eV , which is very close to the estimate for the previous sheet. The minor difference in the estimates of the two sheets of different sizes indicates the converged value for the bending rigidity of graphite sheets larger than 8.48 nm in size. A value of 1.78 eV is thus recommended for the bending rigidity of SWCNTs and graphite sheets. Such a prediction is in excellent agreement with the estimate of Lucas et al. [21] and also quite close to that of Adams et al. [20], in which quantum molecular dynamics methods were applied. The novelty of the method developed here, however, is that it enables a quick and effective calculation of bending rigidity by employing the simplicity of continuum mechanics while maintaining the accuracy of molecular dynamics modeling.

Application of Nonlocal Theory

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The length-dependence of in-plane stiffness was revealed in the previous section based on molecular dynamics simulations. Nonlocal elasticity that employs an elastic rod subject to axial compression is here introduced to investigate this length-dependent property [44]. According to the theory of nonlocal elasticity [27], the stress at a reference point x is considered to be a function of the strain field at every point in the body. The basic equations for a linear, homogeneous, isotropic, nonlocal elastic solid with zero body force are given by

σ ij , j = 0 ,

(9)

σ ij ( x ) = ∫ α ( x − x ′ ,τ )Cijkl ε kl ( x ′ )dV ( x ′ ) , ∀x ∈ V ,

(10)

ε ij =

1 (ui , j + u j ,i ) , 2

where Cijkl is the elastic module tensor of classical isotropic elasticity;

(11)

σ ij and ε ij are the

stress and strain tensors, respectively; and ui is the displacement vector.

α ( x − x ′ ,τ ) is

the nonlocal modulus or attenuation function that incorporates into the constitutive equations the nonlocal effects at the reference point x produced by the local strain at source x′ .

x − x ′ is the Euclidean distance, and τ = e0 a / l is defined, where l is the external characteristic length (e.g., crack length or wavelength). Parameter a describes the internal

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Q. Wang and K. M. Liew

characteristic length. For example, the length of a C-C bond is chosen for the analysis of CNTs [30]. The parameter e0 was given as 0.39 by Eringen [27]. Wang [29] estimated the scale coefficient as e0 a < 2.1nm based on a vibration analysis via the nonlocal Timoshenko beam theory. Wang and Hu [45] estimated the value to be around 0.28 using the strain gradient method. To obtain the length-dependent in-plane stiffness of an SWCNT subject to axial loading, a nonlocal elastic rod theory is here established based on nonlocal elasticity [44]. Hooke’s law for a uni-axial stress state by nonlocal elasticity was proposed in reference [27] and is given as

σ ( x ) − (e0 a )2

d 2σ ( x ) = Eε ( x ) , dx 2

(12)

where x is the coordinate with its origin at the left end of the rod structure. Thus, the nonlocal elastic rod theory can be derived as follows, considering the kinematics relation

ε ( x) =

E

∂σ du ( x) and the equilibrium equation + q ( x) = 0 . ∂x dx

2 d 2u ( x ) 2 d q ( x) ( ) + ( ) − =0, q x e a 0 dx 2 dx 2

(13)

where u ( x) is the compression displacement of the elastic rod under compression, and

q( x) is the distributed axial force applied to the rod. At the limit where the effects of the strains at points other than x are neglected, or e0 a = 0 , the local or classical theory of elasticity is obtained from the nonlocal elasticity. In our molecular simulations, the CNTs were subject to compression displacement ΔL on one clamped end. The general equation (13) can then be re-written as follows, involving the Dirac Delta function and the Heaviside function to model the molecular simulation process of a CNT with its left end clamped and its right end subject to “point” loading P = AEΔL / L and based on the local elastic rod theory, Copyright © 2009. Nova Science Publishers, Incorporated. All rights reserved.

covering the domain from L− < x ≤ L .

E

d 2u ( x ) P (H (x − L− ) − H ( x − L) ) − P (e0 a )2 (δ ′(x − L− ) − δ ′( x − L)) = 0 , + 2 dx AL AL

(14)

where L− is assumed to be very close to L to model a very small portion of the point loading

on

the

right

end

of

the

CNT.

⎧ 1, x ≥ x0 H ( x − x0 ) = ⎨ and ⎩0, otherwise

⎧ ∞, x = x0 are the Heaviside function and the Dirac Delta ⎩0, otherwise

δ ( x − x0 ) = H ′( x − x0 ) = ⎨

Mechanical Properties of Carbon Nanotubes

167

function, respectively, and the prime indicates the derivation of the function with respect to x . Solving these mechanics problems based on the boundary conditions u (0) = 0 and

u ( L) = ΔL leads to the displacement at the edge of the enforced domain x = L− as u=

PL ⎛⎜ ⎛ e0 a ⎞ 1+ ⎜ ⎟ AE ⎜⎝ ⎝ L ⎠

2

⎞ ⎟, ⎟ ⎠

(15)

which shows the equivalent size-dependent Young’s modulus in the form of

⎛ ⎛ e0 a ⎞ 2 ⎞ ⎟ . Figures 1-3 show the ratios of the in-plane stiffness of the aboveE ′ = E / ⎜1 + ⎜ ⎜ ⎝ L ⎟⎠ ⎟ ⎝ ⎠ studied SWCNTs (see also Table 1) at every specific length to the corresponding asymptotic in-plane stiffness, thus demonstrating this length-dependent mechanical property. Figure 1 displays the ratio variation of the zigzag (8,0) SWCNTs from the molecular simulations based on the data in Table 1 as a solid line by employing the asymptotic value

Et = 375.18 J / m 2 . This asymptotic value is independent of CNT size and hence can be viewed as the in-plane stiffness of the structure based on local elastic rod theory. The stiffness ratio versus the length of the SWCNTs is also plotted with the different markers shown in the figure at scale coefficients of e0 a = 0.35nm , e0 a = 0.65nm , and e0 a = 0.95nm , respectively. The ratio is shown to be less than unit for shorter CNTs, but to approach unit at larger sizes, thus indicating the obvious scale effect of length on the measurements of stiffness. The molecular simulations show that the ratio at a smaller scale coefficient always provides a higher value. Of the three scenarios, the variation of the ratio at e0 a = 0.65nm fits the molecular simulation results with the least difference. Overall, the comparison of the ratio between the nonlocal theory and the molecular simulation results verifies the applicability of the nonlocal elastic rod theory to the estimation of length-dependent stiffness. A comparison of the measurements of stiffness based on the nonlocal theory with those via molecular dynamics, which are shown by solid lines, for the armchair (8,8) SWCNTs is illustrated in Figure 2. Similarly, the stiffness ratio is calculated by the ratio of the in-plane stiffness of CNTs at every specific length to the asymptotic value, Et = 377.58 J / m , as shown in Table 1. The ratio via the nonlocal elastic rod theory is displayed by various markers at e0 a = 0.35nm , e0 a = 0.75nm , and e0 a = 1.05nm , respectively. The variation

Copyright © 2009. Nova Science Publishers, Incorporated. All rights reserved.

2

of this ratio can again be observed from the figure, thus indicating a lower level of stiffness for shorter SWCNTs and an asymptotic stiffness for longer CNTs. In addition, the result obtained via the nonlocal elastic rod theory at e0 a = 0.75nm is found to be best fitted to that obtained via molecular simulations for the armchair SWCNTs. The applicability of the nonlocal elastic rod theory is further verified by the measurements of the in-plane stiffness of the chiral (8,4) SWCNTs. From the molecular simulations, the asymptotic value for the in-plane stiffness of the chiral CNTs is

Et = 379.70 J / m 2 .

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Q. Wang and K. M. Liew

Stiffness ratio

1 0.95

Molecular simulations e0a=0.35 nm

0.9 e0a=0.65 nm e0a=0.95 nm

0.85 0.8 1

3

5

7

9

11

13

Tube length (nm)

Figure 1. In-plane stiffness ratio of zigzag (8,0) SWCNTs.

Stiffness ratio

1 Molecular simulations e0a=0.35 nm

0.95

0.9

e0a=0.75 nm e0a=1.05 nm

0.85

0.8 1

3

5

7

9

11

13

Tube length (nm)

Figure 2. In-plane stiffness ratio of armchair (8,8) SWCNTs.

Stiffness ratio

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1

0.95

Molecular simulations e0a=0.35 nm

0.9

e0a=0.70 nm e0a=0.95 nm

0.85

0.8 1

3

5 7 9 Tube length (nm)

Figure 3. In-plane stiffness ratio of chiral (8,4) SWCNTs.

11

13

Mechanical Properties of Carbon Nanotubes

169

From the comparison between the stiffness ratio via the nonlocal elasticity and that via the molecular simulations, the length-dependent stiffness for shorter CNTs can again be examined. In addition, the scale coefficient e0 a = 0.7 nm is found to be a more adequate value for the application of nonlocal elasticity in the estimation of the stiffness of chiral CNTs.

MECHANICAL PROPERTIES OF DWCNTS In this section, the calculations of the in-plane stiffness and shear modulus of DWCNTs via the elastic rod theory and molecular simulations, which are similar to the calculations of SWCNTs presented above, are briefly introduced [46]. The length-dependence of the mechanical properties is explored, as is the van der Waals effect on the differences between the material properties of DWCNTs and SWCNTs. For a DWCNT, the cross section A = π (d i + d o )t is set, where t is the wall thickness of the DWCNT, and d i and d o are the medium diameters of the cross section of the inner and outer CNTs, respectively. According to Eq. (3), the in-plane stiffness of the DWCNT, Et , is obtained by

Et =

U ′′L . π (d i + d o )

(16)

Similarly, the shear modulus of DWCNTs can easily be obtained as follows, based on Eq. (5).

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Gt =

4U r′′L . π d i3 + d o3

(

)

(17)

In building a DWCNT, we choose the inner and outer constituent nanotubes and pick zigzag (8,0) @ (17,0) and armchair (8,8) @ (13,13) DWCNTs with various lengths. The outer tubes of the two zigzag and armchair DWCNTs are 1.331 nm and 1.763 nm, respectively. Five armchair DWCNTs, with lengths of 2.657 nm, 4.351 nm, 6.286 nm, 8.697 nm, and 11.353 nm, respectively, are simulated. The CPU used for the largest calculation for the initial minimization process of the (8,8) @ (13,13) DWCNT with a length of 11.353 nm and 4116 atoms is 1237.55 seconds. The in-plane stiffness versus the length of the zigzag (8,0) @ (17,0) DWCNTs is plotted in Figure 4 by the curve marked with triangle symbols. The stiffness increases from an initial value of Et = 344.92 J / m to an asymptotic value of Et = 375.43 J / m for DWCNTs of a shorter size, 2.092 nm, and those of a larger size, 11.717 nm. Figure 5 depicts the in-plane stiffness versus the length of the armchair (8,8) @ (13,13) DWCNTs, showing an increased 2

2

variation in the stiffness from an initial value of Et = 347.38 J / m to an asymptotic value 2

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Q. Wang and K. M. Liew

of Et = 376.72 J / m for DWCNTs of a shorter size, 2.657 nm, and those of a larger size, 11.353 nm.

In-plane stiffness (J/m^2)

2

375

(8,0) SWNTs

360

(8,0)@(17,0) DWNTs 345

330 0

3.5

7

10.5

14

Length (nm)

Figure 4. Comparison of in-plane stiffness between zigzag DWCNTs and SWCNTs [46].

In-plane stiffness (J/m^2)

380

365

(8,8) SWNTs (8,8)@(13,13) DWNTs

350

335 Copyright © 2009. Nova Science Publishers, Incorporated. All rights reserved.

1

4

7

Length (nm)

10

13

Figure 5. Comparison of in-plane stiffness between armchair DWCNTs and SWCNTs [46].

In both scenarios, an obvious scale effect on the in-plane stiffness is secured for tubes shorter than 12 nm, which is similar to the calculations for SWCNTs. For comparison purposes, the results of the stiffness of zigzag (8,0) and armchair (8,8) SWCNTs are also shown by the curves marked with square symbols in Figs. 4-5. By comparing the stiffness of the DWCNTs with that of the SWCNTs, it can clearly be seen that the stiffness of the former is obviously less than that of the latter at shorter sizes. Such a difference is diminished only in longer CNTs. An interpretation of this observation was made based on the van der Waals effect that occurs between the two walls of the DWCNTs [46]. The interaction of the atoms

Mechanical Properties of Carbon Nanotubes

171

Shear stiffness (J/m^2)

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between these two different walls is the non-bond van der Waals effect based on the molecular dynamics principle. The role of this effect is briefly illustrated here by the axial compression process of a DWCNT. When a DWCNT is subject to compression, the expansion of its outer wall is greater than that of its inner wall. This is because a larger diameter leads to a larger gap between the two walls of a DWCNT, and this gap increases during compression. Because of the widened gap between the two walls, attraction is initiated due to the van der Walls effect. The force of this attraction means the outer wall is prone to expand in the length direction, whereas the inner wall contracts further in the longitudinal direction. With a smaller diameter, the magnitude of the reduction of the inner wall in the longitudinal direction is greater than that of the extension of the outer wall, thus shortening the DWCNT further as a whole. This decreasing trend during compression obviously weakens the resistance of a DWCNT structure that is subject to compression, and hence leads to the lower in-plane stiffness of the DWCNT. For a longer DWCNT placed under the same compression as a shorter one, the change in the gap between the two walls becomes less because of the smaller amount of strain in the radial direction. This results in less attraction between the two walls due to the van der Walls effect. Therefore, the difference between the material properties of DWCNTs and SWCNTs is negligible for larger sizes, which can be seen from the convergence of the two curves in Figs. 4-5. The difference in the stiffness diminishes for zigzag DWCNTs larger than 12 nm, although only for armchair DWCNTs larger than 5 nm. A lower level of stiffness was also reported for MWCNTs from experimental observations [7], and attributed to the occurrence of wavelike ripples. Figure 6 shows the in-plane shear moduli of armchair (8,8) @ (13,13) DWCNTs, varying from a value of Gt = 115.11J / m 2 for those with a length of 2.657 nm to an asymptotic value of Gt = 123.83 J / m 2 for those with a length of 11.353 nm. It should again be noted that the van der Waals effect leads to the smaller shear modulus of DWCNTs, as compared with SWCNTs, and that the difference in this shear modulus diminishes for DWCNTs of larger sizes. For armchair DWCNTs, the size effect on the difference between the shear modulus of DWCNTs and SWCNTs becomes negligible when the length of the CNTs is greater than 6 nm.

124

(8,8) SWNTs

120

(8,8)@(13,13) DWNTs 116

112 1

4

7

Length (nm)

10

13

Figure 6. Comparison of shear modulus between armchair DWCNTs and SWCNTs [46].

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Q. Wang and K. M. Liew

CONCLUSION A comprehensive continuum mechanics and molecular dynamics method for the measurement of the mechanical properties of both SWCNTs and DWCNTs has been introduced based on the research findings of the authors’ group. This tight link between the principles of the two methods enables accurate and efficient measurement because of the simplicity of maintaining atomic structures in the continuum mechanics modeling and the ability to do so via the molecular dynamics principle. The length-dependence of the mechanical properties of both SWCNTs and DWCNTs is reported and investigated via the nonlocal elasticity theory. The van der Waals effect on the difference between the material properties of DWCNTs and SWCNTs is also examined, with the diminishment of that difference at large sizes of CNTs revealed in the simulations.

ACKNOWLEDGMENTS This research was undertaken, in part, thanks to funding from the Canada Research Chairs Program, the National Science and Engineering Research Council (NSERC), and the Canada Foundation for Innovation (CFI).

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[14] Hernandez, E.; Goze, C.; Bernier, P.; Rubio, A.; Phys. Rev. Lett. 1998, Vol. 80, pp. 4502-4505. [15] Sánchez-Portal, D; Artacho, E.; Soler, J.M.; Rubio, A.; Ordejón, P. Phys. Rev. B. 1999, Vol. 59, pp. 12678-12688. [16] Chang, T.; Geng, J.; Guo, X.; Proc. R. Soc. A. 2006, Vol. 462, pp. 2523-2540. [17] Geng, J.; Chang, T.; Phys Rev B, 2006, Vol. 74, pp. 245428. [18] Odegard, G.M.; Gates, T.S.; Nicholson, L.M.; Wise, K.E.; NASA/TM-2002-211454. 2002. [19] Wang, Q.; International Journal of Solids and Structures. 2004, Vol. 41, pp. 54515461. [20] Adams, G.B.; Sankey, O.F.; Page, J.B.; O’Keeffe, M.; Drabold, D.A. et al., Science. 1992, Vol. 256, pp. 1792-1795. [21] Lucas, A.A.; Lambin, P.H.; Smalley, R.E.; J Phys. Chem. Solids. 1993, Vol. 54, pp. 587-593. [22] Kudin, K.N.; Scuseria, G.E.; Yakobson, B.I.; Phys. Rev. B. 2001, Vol. 64, pp. 235406. [23] Johnston, B.G.; Guide to design criteria for metal compression members; 2nd edition, Wiley: New York, 1966. [24] Sheehan, P.E.; Lieber, C.M.; Science. 1996, Vol. 272, pp. 1158-1161. [25] Sun, C.T.; Zhang, H.; Journal of Applied Physics. 2003, Vol. 93, pp. 1212-1218. [26] Eringen, A.C.; Nonlocal polar field models; Academic: New York, 1976. [27] Eringen, A.C.; J. Applied Physics. 1983, Vol. 54, pp. 4703-4710. [28] Peddieson, J.; Buchanan, G.R.; McNitt, R.P.; Int. Journal of Engineering Science. 2003, Vol. 41, pp. 305-312. [29] Wang, Q.; Journal of Applied Physics. 2005, Vol. 98, pp. 124301. [30] Zhang, Y.Q.; Liu, G.R.; Wang, J.S.; Physical Review B. 2004, Vol. 70, pp 205430. [31] Duan, W.; Wang, C.M.; Nanotechnology. 2007 Vol. 18, pp. 385704. [32] Yakobson, B.I.; Brabec, C.J.; Bernholc, J.; Phys. Rev. Lett. 1996, Vol. 76, pp. 25112514. [33] Yakobson, B.I.; Avouris, P.; Topics in Applied Physics. 2001, Vol. 80, pp. 287- 329. [34] Gere, J.M.; Mechanics of Materials, Brooks/Cole Thomson Learning, 2001. [35] Wang, Q.; Liew, K.M.; Journal of Applied Physics. 2008, Vol. 103, pp. 046103. [36] Wang, Q.; Han, Q.K.; Wen, B.C.; Journal of Computational and Theoretical Nanosciences. 2008. [37] Falvo, M.R.; Clary, G.J.; Taylor II, R.M.; Chi, V.; Brooks Jr., F.P.; Washburn, S.; Superfine, R.; Nature (London). 1997, Vol. 389, pp. 582-584. [38] Timoshenko, S.P.; Woinowsky, S.; Theory of plates and shells, McGraw-Hill Kogakusha, Ltd., 1959. [39] Molecular dynamics-Wikipedia, the free encyclopedia. http://en.wikipedia.org/wiki/ Molecular_dynamics. [40] Rigby, D.; Sun, H.; Eichinger, B.E.; Polymer International. 1997, Vol. 44, pp. 311-330. [41] Robertson, D.; Brenner, D.; Mintmire, J.; Phys. Rev. B. 1992, Vol. 45, pp. 1259212595. [42] Gupta, S.; Dharamvir, K.; Jindal, V.K.; Phys. Rev. B. 2005, Vol. 72, pp. 165428. [43] Popov, V.N.; Van Doren, V.E.; Balkanski, M.; Phys. Rev. B. 2000, Vol. 61, pp. 30783084.

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[44] Wang, Q.; Han, Q.K.; Wen, B.C.; Advances in Theoretical and Applied Mechanics. 2008, Vol. 1, pp. 1-10. [45] Wang, L.F.; Hu, H.Y.; Physical Review B. 2005, Vol. 71, pp. 195412. [46] Wang, Q.; Molecular simulation. 2008, http://www.informaworld.com.

In: Carbon Nanotubes: New Research Editor: Avery P. Ottenhouse

ISBN 978-1-60692-236-1 © 2009 Nova Science Publishers, Inc.

Chapter 7

ELECTRICAL PROPERTIES OF A CARBON NANOTUBE/POLYMER NANOCOMPOSITE AND ITS APPLICATION AS HIGHLY SENSITIVE STRAIN SENSORS Ning Hu1, Zen Masuda and Hisao Fukunaga Department of Aerospace Engineering, Tohoku University, Aramaki-Aza-Aoba 6-6-01, Aoba-ku, Sendai 980-8579, Japan

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ABSTRACT Carbon nanotubes (CNTs) of high aspect ratio possess excellent electrical conductivity. Therefore, with a little amount of CNTs, which are dispersed into insulating polymers, it is possible to manufacture CNT/polymer nanocomposites with very high electrical conductivity. This kind of conductive nanocomposites can be employed in various applications, such as highly sensitive strain sensors and electromagnetic interference materials. In this Chapter, we will mainly describe our research outcomes about the electrical properties of CNT/polymer nanocomposites from experimental and theoretical studies. First, in this work, based on the statistical percolation theory, we proposed a three dimensional (3D) numerical model to predict the electrical properties of a nanocomposite made from an insulating polymer with filled CNTs. In this model, with the assumption of randomly distributed CNTs in the polymer, the percolation threshold was estimated at the volume fraction of CNTs when the first complete electrically- conductive path connected by some CNTs is formed. Furthermore, to predict the electrical conductivity of the nanocomposite after the percolation threshold, a 3D resistor network model was constructed, in which Kirchhoff’s current law was adopted to set up the system algebraic equations at different nodes in the network formed by CNTs. The macroscopic current of the nanocomposite under the applied external voltage was calculated by solving these equations, and then Ohm’s law was employed to predict the macroscopic electrical conductivity of the nanocomposite. The influences of curved shapes of CNTs, aggregates 1

To whom all correspondence should be addressed:Email: [email protected] (Ning Hu) Fax: +81-22-7954109.

176

Ning Hu, Zen Masuda and Hisao Fukunaga of CNTs and tunnel effect among CNTs on the percolation threshold and the electrical conductivity have been investigated in detail. To verify the above numerical model, a lot of experiments have also been performed by the authors. The effects of various factors in the in situ polymerization fabrication process on the electrical performances of the nanocomposite were explored. The present experimental results plus some previous experimental results by other researchers were found to agree with the present numerical results very well. Moreover, a simple yet reliable empirical percolation theory has been obtained based on the detailed numerical investigations. For the application of this nanocomposite as highly sensitive strain sensors, by considering the tunnel effect among CNTs and the rigid-body movement of CNTs in the polymer caused by the prescribed strain, the above numerical model was further extended for modeling the electrical resistance change of the nanocomposite due to the strain. The relation between the applied strain and the electrical resistance change was estimated numerically and measured experimentally. Both numerical and experimental results, which are in very good agreement, demonstrate that the CNT/polymer sensors possess much higher sensitivity or gauge ratio compared with the traditional strain gauge. The tunnel effect was found to be a key factor to control the performance of this new-type strain sensor.

Keywords: carbon nanotube; polymer; electrical property; nanocomposites; statistical percolation model

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1. INTRODUCTION Recently, much attention has been paid to the fabrication of nanocomposites with the use of carbon nanotubes (CNTs) in polymer materials to harness the exceptional intrinsic properties of CNTs. In particular, polymers with the incorporation of CNTs show great potential for electronic device applications, such as organic field emitting displays, photovoltaic cells, highly sensitive strain sensors, electromagnetic interference materials, etc. Generally, for the different applications, the different electrical properties of nanocomposites are employed. For instance, for the application of strain sensors, direct current (DC) properties of nanocomposites are needed. Meanwhile, for the application of electromagnetic interference materials, alternate current (AC) properties of nanocomposites are needed. In the recent decade, numerous experimental studies on the electrical properties of nanocomposites made from insulating polymers filled by CNTs have been carried out [1-19]. In this work, we will focus on the DC properties of nanocomposites. To prepare this kind of nanocomposites, currently, melt mixing compounding [1-4], curing/in situ polymerization [5-17] and coagulation [18, 19] are widely used. Depending on the polymer matrix and processing technology as well as the type of nanotube material used, percolation thresholds ranging from less than 1.0 % to over 10.0 wt% of CNTs loading have been observed experimentally [12]. For example, for single-wall carbon nanotubes (SWNTs), Nogales et al. [5] applied in situ polycondensation reaction to prepare SWNT /PBT nanocomposites and achieved an electrical percolation threshold as low as 0.2 wt% of SWNTs loading. Ounaies et al. [6] have investigated the electrical properties of SWNTs reinforced polyimide (CP2) composites. The obtained conductivity obeys a percolation-like power law with a low

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percolation threshold of around 0.1 wt%. The bundling phenomenon of SWNTs within the matrix has been identified in experimental analysis. Park et al. [7] have shown that it is possible to control the electrical properties of SWNT/polymer composites through the techniques of alignments of SWNTs. Kymakis et al. [8] studied the electrical properties of SWNTs filled in the soluble polymer poly (3-octylthiophene) (P3OT). The reported percolation threshold is around 11 wt%. In their latter work [9], purified SWNTs were used, which lead to a much lower percolation threshold at around 4 wt%. For multi-wall carbon nanotubes (MWNTs), Sandler [10] have employed MWNTs with an epoxy polymer based on bisphenol-A resin and an aromatic hardener, and they got a lower percolation threshold at around 0.04 wt%. The formation of aggregates was also identified. Sandler et al. [11] reported the lowest percolation threshold up to the present date, i.e., 0.0025 wt% using MWNTs. To obtain a low percolation threshold, using MWNTs and epoxy, Martin et al. [12] investigated the influence of process parameters employed in the in situ polymerization fabrication process, such as stirring rate, resin temperatures and curing temperatures. It was found that the electrical properties of nanocomposites strongly depend on the choice of these parameters. Using the in situ polymerization process, the MWNT/polymer nanocomposites were prepared in [13-15], and the obtained percolation thresholds were found to be lower than 1.0 wt%. Hu et al. [19] prepared the MWNT/PET nanocomposites by means of coagulation process. Uniform dispersion of MWNTs throughout PET matrix was confirmed by transmission electron microscopy (TEM) and scanning electron microscopy (SEM). The obtained percolation threshold is around 0.9 wt%. Generally, there are two issues addressed in many previous studies: dispersion of CNTs in polymer matrix and interaction between CNTs and polymer. For the first issue, due to the high surface-to-mass ratio of CNTs, molecular scale forces and interactions should be considered among CNTs. Van der Waals forces usually promote flocculation of CNTs, whilst electrostatic charges or steric effects lead to a stabilization of the dispersion through repulsive forces [6, 12]. As a consequence, by considering the nature of percolating network formed by very fine filler, e.g., CNTs, the balance of the two factors of reverse effects outlined above should be taken into account. For the second issue, the fact, that the nanotubes in the composites are coated or encapsulated with a thin insulating polymer layer was identified for SWNTs [9] and MWNTs [19]. This encapsulation acts as a barrier to the electrical charge transfer between nanotubes [9]. As mentioned above, although a lot of experimental studies have been performed recently, whereas, except the study in [12], there is little literature covering the detailed influences of various factors in the fabrication process on the electrical properties of CNT/polymer nanocomposites using in situ polymerization method to our knowledge. Moreover, there has been almost no systematically theoretical or numerical work for comprehensively understanding the electrical characteristics of the nanocomposites at and after the percolation threshold except that the percolation threshold was determined by a numerical model [6] with randomly distributed CNTs in a polymer and by an empirical formula from the extruded volume approach based on the statistical percolation theory [12]. Generally, by gradually filling some traditional conductive filler particles, such as carbon short fibers, into insulating polymers, the variation of electrical conductivity of composites can be divided into three stages as shown in Figs 1.1 and 1.2. In the first stage, the electrical conductivity is very low since there are few filler particles in matrix as shown in Figure 1.1(a) and Figure 1.1(b). In Figure 1.1(b), some large clusters connected by fillers are gradually

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formed. In this first stage, the electrical conductivity of composites is close to that of the polymer as shown in Figure 1.2. In the second stage, as the amount of filler particles increases, the first complete electrically-conductive path connected by some filler particles is formed as shown in Figure 1.1(c). In this second stage, the electrical conductivity will increase remarkably following a percolation power law as shown in Figure 1.2. This process is called as percolation process. The volume fraction of filler particles at this stage is called as the percolation threshold, i.e., φ c . In the final stage, with the further addition of filler particles into the polymer, a lot of electrically-conductive paths, which forms a conductive network, can be constructed as shown in Figure 1.1(d), and the electrical conductivity further increases gradually, until leveling off at a constant, which is close to that of the element or filler of conductive network in Figure 1.2. From the previously published experimental results, it was found that the electrical behavior of nanocomposites using CNTs as conductive filler particles in polymer matrix follows the same percolation phenomenon. For some traditional electronic composites with fillers [20-22], e.g. carbon short fibers or carbon flakes, there have been some theoretical or numerical studies based on the traditional statistical percolation model, especially for predictions of percolation threshold. It is therefore natural to ask if the statistical percolation model is still valid to describe the electrical behaviors of the nanocomposites with such a fine filler, as CNTs. In this study, for an insulating polymer with random distribution of CNTs, first, based on the statistical percolation model, we developed a three dimensional (3D) numerical model with two stages for investigating the electrical properties of nanocomposites at and after the percolation threshold. In the first stage, the percolation threshold was predicted at the volume fraction of CNTs when the first complete electrically-conductive path connected by some CNTs is formed in matrix. In the second stage, a 3D resistor network model was constructed to predict the macroscopic electrical conductivity of nanocomposites after the percolation threshold. This model demonstrates remarkable success in capturing the main features of electrical behaviors of nanocomposites. The influences of various factors, such as the curved shapes of CNTs, the aggregates of CNTs in matrix and tunnel effect among CNTs on the electrical properties of nanocomposites have been studied. Then, the verified numerical model was employed to construct a simple and reliable empirical percolation theory. Next, we experimentally investigated the electrical properties of MWNT/polymer nanocomposites. The specimens were prepared by in situ polymerization method. For the case of 2 wt% of MWNTs loading, the effects of various factors in the fabrication process on the electrical behaviors of the nanocomposites have been studied. It was found that the bulk conductivity of the nanocomposites is significantly sensitive to some factors in the fabrication process, such as curing temperature and mixing process. The experimental results plus some other previous experimental results have been employed to validate the proposed numerical model. Finally, the currently fabricated MWNT/polymer nanocomposites have been applied as highly sensitive sensors. Moreover, by considering the tunnel effect, the present numerical model was further extended into the case of nanocomposites with prescribed strains. The relation between the strain and the electrical conductivity was estimated numerically and experimentally. Finally, both numerical and experimental results demonstrate that this newtype sensor possesses much higher sensitivity or gauge ratio compared with the traditional

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strain gauge. Moreover, it was found that the tunnel effect among CNTs plays a key role in determining the performance of this new-type sensor.

Figure 1.1 Percolation process in electronic composites

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2. A STATISTICAL PERCOLATION MODEL FOR PREDICTION OF PERCOLATION THRESHOLD OF NANOCOMPOSITES In this section, we will mainly describe several key steps to create a statistical numerical model for predicting the percolation threshold of nanocomposites based on the assumption of that CNTs are randomly distributed in a polymer. First, we will show how to generate this numerical model with the different features what we need. Second, we will employ the generated model as well as a powerful algorithm to find the value of percolation threshold. Finally, this model will be used to obtain the percolation threshold and to investigate the influences of various factors.

2.1. Generation of Model of Randomly Distributed CNTs in Matrix First, as shown in Figure 2.1, we consider a 3D representative unit element, which is only a small and local portion of the whole nanocomposite body. However, there are enough CNTs contained in this 3D element, which can effectively represent the macroscopic and bulk

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electrical properties of nanocomposites. Our goal is to find the volume fraction or weight fraction of CNTs when the first complete conductive path is formed by some CNTs, e.g. from the left side to the right side of the 3D cube in Figure 2.1. Three kinds of cases which may be possibly encountered in the practical nanocomposites are considered in this research. This first one is a model with the uniform random distribution of straight CNTs, which is a simplest model for the ideal dispersion of CNTs in matrix. The second one is a model in which the shape of practical CNTs is considered, e.g., the curved CNTs considered here. The third one relates to the fabrication process of nanocomposites, where the perfect dispersion cannot be realized practically. Therefore, in this model, the aggregates of CNTs are modeled. We will introduce these models one by one and state the main steps to construct them.

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Figure 1.2. Electrical conductivity of electronic composites as a function of filler fraction.

2.1.1. Model of Uniform Random Distribution of Straight CNTs In this study, to predict the percolation threshold of this nanocomposite numerically, as shown in Figure 2.1, we consider the 3D element with uniform random distribution of straight CNTs. The so-called ‘soft-core’ CNTs of the length of L and the diameter of D are considered as capped cylinders, which are allowed to penetrate each other. This assumption can lead to the tremendous reduction in the computational cost, which results in a proper solution method suitable for the Monte-Carlo procedure used here. The capped cylinders are randomly put in the 3D cube and their orientations in space are chosen randomly. This procedure for numerical prediction of percolation threshold is similar in principle to the ones in [6, 22]. For this ideal state of uniformly dispersed straight CNTs in matrix, the following method can be employed. The coordinates of two ends of a CNT, i.e, ( x1 , y1 , z1 ) and ( x 2 , y 2 , z 2 ) can be set as

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x1 = rand × L x

(1a)

y1 = rand × L y

(1b)

z1 = rand × L z

(1c)

x 2 = x1 + L ⋅ v1 ⋅ cos(w1 )

(1d)

y 2 = y 1 + L ⋅ v1 ⋅ sin (w1 )

(1e)

z 2 = z1 + L ⋅ u 1

(1f)

where as shown in Figure 2.1, Lx, Ly and Lz are the lengths of the 3D element along x, y and z axes, respectively, and rand is a random number located in [0,1), which is uniformly generated. Also, the alignment directions of CNTs, i.e., u1, v1 and w1 are expressed as follows

u1 = 1.0 − 2.0 × rand

v1 = 1.0 − u1

(2a)

2

(2b)

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w1 = 2π × rand

(2c)

2.1.2. Model of Uniform Random Distribution of Curved CNTs As shown in Fig 2.2 from our SEM observation for a specimen of 13 wt.% MWNTs loading, practically, CNTs are not perfectly straight. To model this curved shape of CNTs, a very simple method is proposed in this study. First, as shown in Figure 2.2, we divide each CNT into several segments (10 segments are used in this research). The angle in 3D space between arbitrary two adjacent segments can randomly vary within a circular cone with a top angle θmax. For the divided CNTs, the coordinates of the first end, i.e., x1, y1 and z1, can be determined using Eqs (1a)-(1c), and the coordinates of the following points can be determined as follows one by one

xi +1 = xi + L ⋅ vi +1 ⋅ cos(wi +1 ) N

i = 1, N

(3f)

y i +1 = y i + L ⋅ vi +1 ⋅ sin (wi +1 ) N

i = 1, N

(3g)

z i +1 = z i + L ⋅ u i +1 N

i = 1, N

(3h)

where

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Ning Hu, Zen Masuda and Hisao Fukunaga

wi +1 = wi ± θ max × rand

i = 1, N

(3c)

⎧⎪ ⎛u u i +1 = sin ⎨tan −1 ⎜⎜ i ⎪⎩ ⎝ vi

⎞ u′ ⎫ ⎟⎟ + tan −1 ⎛⎜ ⎞⎟⎪⎬ ⎝ v ′ ⎠⎪⎭ ⎠

i = 1, N

(3d)

⎧⎪ ⎛u v i +1 = cos ⎨tan −1 ⎜⎜ i ⎪⎩ ⎝ vi

⎞ u ′ ⎪⎫ ⎟⎟ + tan −1 ⎛⎜ ⎞⎟⎬ ⎝ v ′ ⎠⎪⎭ ⎠

i = 1, N

(3e)

where

u′ = sin(θ max ) ⋅ (1.0 − 2.0 × rand)

(3a)

v ′ = 1.0 − u ′ 2

(3b)

where θ max is the angle of the cone top, N is the number of divisions. Also, u1, v1 and w1 are determined using Eqs (2a)-(2c).

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2.1.3. Model of Aggregates of Straight CNTs Usually, due to the high surface-to-mass ratio of CNTs resulting in strong absorption energies among CNTs, there are some aggregates or bundling formed by CNTs caused by a poor dispersion process. Especially, for SWNTs, due to their much smaller sizes compared with those of MWNTs, this phenomenon may be more obvious. To generate these aggregates numerically, the well-known Box-Muller method using two random numbers is employed. The aggregates of CNTs with normal distribution are artificially created in matrix. This method is briefly described here. First, the coordinates of the starting point of a CNT, i.e., x1, y1 and z1, are determined as

x1 = Lxc + Lx μ − 2 log(U x1 Lx ) ⋅ cos(2π U x2 L x )

(4a)

y1 = Lyc + Ly μ − 2 log(U y1 Ly ) ⋅ cos(2π U y2 L y )

(4b)

z1 = Lzc + Lz μ − 2 log(U z1 Lz ) ⋅ cos(2π U z 2 L z )

(4c)

where Lxc, Lyc and Lzc are the coordinates of the center of an aggregate, respectively, and μ is a parameter to determine the extensity of the aggregate with normal distribution. A higher means the larger volume of the aggregate with lower density of CNTs, and

U x1 = rand × L x

U x 2 = rand × L x

(5a)

μ

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U y1 = rand × L y

U y 2 = rand × L y

(5b)

U z1 = rand × L z

U z 2 = rand × L z

(5c)

In our analysis, for the sake of simplicity, only four aggregates are modeled in the 3D representative element, and the coordinates of their centers are

(L 3 4, L x

y

(L

x

4, L y 4, L z 2 ) ,

4, Lz 2) , (L x 4 , L y 3 4 , L z 2 ) and (Lx 3 4, Ly 3 4, Lz 2) , respectively.

After obtaining the coordinates of the starting end of the CNT in Eqs (4), for the coordinates of another end of the CNT, Eqs (1d)-(1f) and (2a)-(2b) can be simply applied. Naturally, this model is not a practical one, for example, due to the small number of aggregates modeled here, the isotropy of electrical properties of the 3D element cannot be guaranteed. However, we can still employ it to qualitatively investigate the influences of aggregates on the electrical properties of nanocomposites.

2.1.4. Judgment of Contact Between CNTs In our numerical model, CNTs are randomly put into the 3D cube one by one. It is a key step to judge if the dispersed CNTs are in the state of contact, which may lead to the formation of possible conductive clusters as shown in Figure 1.1(b). To determine if the generated CNTs using the techniques outlined in the above section are in the state of contact, we consider three possible contacting patterns between two CNTs shown in Figure 2.3. For the case of Figure 2.3(a), from the coordinates of two ends of CNT1 and CNT2, we can calculate the distance between CNT1 and CNT2. First, we consider the differences of three coordinates of two ends of CNT1 and CNT2 as follows: (x1 , y1 , z1 ) − ( x 2 , y 2 , z 2 )

and

(x3 , y 3 , z 3 ) − (x 4 , y 4 , z 4 ) . Then, the vectors of alignment

directions of CNT1 and

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CNT2, i.e., d1 and d2 are determined as follows

d 1 = (x 2 − x1 , y 2 − y1 , z 2 − z1 )

(6a)

d 2 = (x 4 − x 3 , y 4 − y 3 , z 4 − z 3 )

(6b)

Also，we define the difference of coordinates of the starting ends of CNT1 and CNT2 as follows

p1 − p 3 = (x1 − x3 , y1 − y 3 , z1 − z 3 )

(7)

Then, by using Eqs. (6a)-(6b) and Eq. (7), the shortest distance d between CNT1 and CNT2 can be evaluated as follows

d=

p1 − p 3 , d 1 , d 2 d1 × d 2

(8)

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Next, for the contacting pattern shown in Figure 2.3(b), the shortest distance d between CNT1 and CNT2 at the point 3 can be simply calculated as follows

d = a−

a , d1 d , d1

d1

(9)

where a = ( x3 − x 2 , y 3 − y 2 , z 3 − z 2 ) , and d1 is evaluated by Eq. (6a). Finally, for the contacting pattern shown in Figure 2.3(c), the shortest distance d between CNT1 and CNT2 at the point 3 can be simply calculated as

d=

(x1 − x3 )2 + ( y1 − y 3 )2 + (z1 − z 3 )2

(10)

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When the estimated distance between two CNTs is lower than the diameter of CNTs, it can be thought of that two CNTs are in the state of contact. Note that in our numerical model, the ‘soft-core’ CNTs are used, which are allowed to penetrate each other. Therefore, in our numerical model, there may be overlapping among CNTs to a certain extent. However, when the volume fraction of CNTs is low and the aspect ratio of CNTs is large, the error caused by this overlapping is negligible.

2.1.5. Union/Find Algorithm for Searching for Cluster Formation The tree-based union/find algorithm [23] was adopted to detect the first complete conductive path connecting two sides of 3D cube (as red CNTs marked in Figure 2.1), and then the percolation threshold can be determined using the total volume of CNTs at this point. This algorithm is very quick, which is suitable for a Monte-Carlo procedure used here. When two CNTs are in the state of contact, a cluster can be formed. As the amount of filled CNTs in matrix increases, the number of CNTs, which are in the state of contact, will also increase, which results in some larger clusters gradually as shown in Figure 1.1(b). With the further addition of CNTs in matrix up to a critical volume fraction, one of the clusters will connects the two sides of the 3D element, which finally form the first complete conductive path or network within the 3D element. At this point, the electrical conductivity of nanocomposites will remarkably increase and the volume fraction of CNTs can be thought of as the percolation threshold what we need. Generally, with the addition of one cylinder (here, a CNT) into matrix, to search for if two clusters are amalgamated, the tree-based union/find algorithm can be adopted, which was proposed by Newman et al. [23] for the percolation problem in a square lattice. In this research, we just extend this algorithm to the case of the 3D element with randomly distributed CNTs, as schematically shown in Figure 2.4. In Figure 2.4(a), represents a newly added CNT into matrix. In Figure 2.4(b), the sequence number of happening of CNTs is labeled. Also, ○ marks the ‘child’ of a tree, and ● represents the ‘root’ site of the tree. The basic steps involved in the union/find algorithm are briefly stated as follows

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i)

As shown in Figure 2.4(a), each CNT without contact with other clusters is considered to be an independent ‘root’ site of a tree or a cluster in matrix, respectively, e.g., CNT2 in Figure 2.4(b). ii) For a 3D element with sizes of Lx, Ly and Lz, one CNT is randomly added into it. iii) For the added CNT, its root is recorded to be a cluster of size of 1. Also, the happening number of this CNT is labeled and its maximum and minimum x coordinates, i.e., the x coordinates at two ends are recorded. iv) For the newly added CNT in step (ii), the judgment of contact state between it and other CNTs is performed. If there is no contact, return to (ii) (for instance for CNT1 and CNT2 in Figure 2.4(b)). If there is only one contacting point, the root of the cluster contacted by the newly added CNT is searched for (e.g. CNT8 and CNT10). If there are more than one contacting points, such as two contacting points, the roots of two clusters connected by this CNT (e.g. CNT12) are searched for. At this point, the roots are searched by following the pointers shown in Figure 2.4(b). v) For the case of one contacting point outlined in (iv), the size of the pre-existing cluster should be at least equal to or larger than that of the newly added CNT of the size of 1, the size of this cluster is increased by 1 and the root of the added CNT is relabeled as that of the cluster. For the case of two or more contacting points, e.g. two contacting points here, if the roots of two clusters connected by the added CNT are the same one, the root of the added CNT is relabeled as it. The size of this cluster is increased by 1. vi) If the roots of two clusters are different, the comparison of the sizes of two clusters is performed. The root of the cluster with a smaller size should be relabeled as the root of the cluster with a larger size (e.g., see CNT5 and CNT7 in Figure 2.4(b)). The root of the added CNT is also relabeled as the one of the cluster with the larger size. The size of the cluster should be also changed into that of the final amalgamated one. vii) If the maximum and minimum x coordinates of the cluster formed at steps (v) or (vi) change, the new data about cluster coordinates should be recorded as well as the root site. viii) If the maximum x coordinate of the cluster formed at steps (v) or (vi) achieves at

L x , and the minimum x coordinate of the cluster is equal to 0. At this point, the total

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volume of all CNTs is calculated. Otherwise, return to the step (ii). The volume VCNT of all CNTs of the number of M is expressed as follows

1 1 VCNT = ( πD 3 + πD 2 L) M 6 4

(11)

The total volume of CNTs obtained in (viii) is used to predict the percolation threshold,

φ p (vol%) as follows φp =

VCNT × 100 Lx ⋅ L y ⋅ Lz

(12)

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Figure 2.1. Schematic view of a representative 3D element with randomly dispersed CNTs.

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Figure 2.2. Definition of divided segments of CNTs for modeling curved CNTs.

Figure 2.3, Contact between two CNTs: (a) skew of CNT1 and CNT2; (b) CNT1 and node 3 of CNT2; (c) node 1 of CNT1 and node 3 of CNT2.

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Figure 2.4. An example of the tree structure for CNT fillers.

2.2. Numerical Results of Percolation Threshold and Investigations

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In this section, we will focus on the numerical investigation of percolation threshold using the statistical percolation model outlined previously. The influences of various factors, such as the shapes and aggregates of CNTs will be explored.

Determination of Sizes of Representative 3D Element Before entering into the stage of the detailed investigations, to determine the sizes of the representative 3D cube, which can represent the macroscopic and bulk electrical properties of nanocomposites, the following two aspects have to be considered. The first one is about the anisotropy of percolation threshold. It means that the electrical properties along three axis directions of 3D cube in Figure 2.1 should be approximately the same to guarantee the bulk electrical properties to be correct. We have calculated the percolation thresholds along three axis directions of the 3D cube. As shown in Figure 2.5(a), we can find that for the case of Lx/L=Ly/L=Lz/L=1, there is obvious anisotropy along different directions. However, when Lx/L ≥ 2, Ly/L ≥ 2 and Lz/L ≥ 2, the anisotropic characteristic of percolation threshold is negligible. The percolation thresholds along three axis directions are almost identical. The second one is about the convergence of results. For the aspect ratio (L/D) of 100, Figure 2.5(b) shows that the sizes of Lx/L=Ly/L=5 and Lz/L= 2.0 of the 3D cube can yield sufficiently stable results. Moreover, Figure 2.5(c) illustrates that the percolation thresholds at the different simulation runs in our Monte-Carlo procedure. Again, Lx/L=5 and Lz/L= 2.0 can generate the converging results with very small standard deviation. The percolation thresholds generated at the different random simulation runs are almost constant. By considering the isotropy and convergence of results, the sizes, i.e., Lx/L=Ly/L=5 and Lz/L= 2.0, were used consistently later. By fixing the length of CNTs, we adjust the diameter of CNTs to achieve the different values of aspect ratios of CNTs. We have also provided the results of a 2D model in Figure 2.5(b). From it, it can be found that the results of the 2D

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Ning Hu, Zen Masuda and Hisao Fukunaga

model are quite higher than the converging results of the 3D model. It means that a 2D model may be improper for this kind of simulations. Finally, a Monte-Carlo procedure of 100 simulations has been performed to obtain the average percolation threshold at each volume fraction of CNTs.

Percolation Threshold of Straight CNTs First, for the uniform random distribution of straight CNTs, the results of percolation threshold versus the aspect ratio of CNTs are shown in Figure 2.6. In fact, for the traditional statistical percolation theory, it is well-known that the percolation threshold strongly depends on the aspect ratio of filler. The results estimated from an empirical statistical percolation theory are also plotted in this figure for comparison. From Figure 2.6, we can find that our numerical results agree with the theoretical ones [20] very well although the slopes of two kinds of results are slightly different, which may be caused by some simplifications in the empirical statistical percolation formula. By using the numerically obtained results and the least-square fitting, we can obtain the percolation threshold

φc

for straight CNTs with uniform random distribution in matrix as

follows

⎛L⎞ ⎟ ⎝D⎠

−1.1± 0.03

φc = ⎜

(13)

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This formula is of much simpler form compared with some traditional empirical theories, e.g. [20], from which the percolation threshold can be estimated effectively based on the aspect ratio of CNTs only. Naturally, it should be noted that this formula is obtained from the fitted results of numerical simulations for the filler of high aspect ratio, at least larger than 10 from our numerical experiences. For the cases of lower aspect ratio, this formula is invalid.

2.2.3. Influences of Shapes and Aggregates of CNTs on Percolation Threshold Next, we will investigate the influences of shapes and aggregates of CNTs on the percolation threshold of nanocomposites. First, for curved CNTs, when θ max defined in Fig 2.2 is equal to 15o, 30o, 45o and 60o, respectively, the configurations of the 3D element containing curved CNTs are shown in Figure 2.7. From it, we can see that as θ max increases, the CNTs are more curved. Also, we can find that the curved CNTs can be modeled properly using the proposed technique. In these models, the number of divisions of CNTs is fixed to be 10. Figure 2.8 demonstrates the influence of θ max on the percolation threshold when the aspect ratio of CNTs is taken as 100. In this figure, θ max = 0 relates to the results of straight CNTs. From this figure, it can be found that as

θ max increases, the percolation threshold

increases gradually. This result is intuitively reasonable. If we consider a simple conductive path, which is from the left side to the right side of the 3D cube, it is more difficult to form this path using the curved CNTs due to their projected lengths in the horizontal plane (x-y plane in Figure 2.1) are shorter compared with those of straight CNTs. Moreover, the effect of

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θ max on the percolation threshold seems to be quite stable, and the percolation threshold changes continuously with the variation of θ max . Another important factor, which may influence the electrical properties of nanocomposites significantly, is aggregation of CNTs. Although as shown later in our SEM observations, we have not identified the obvious aggregates in our experimental specimens when using MWNTs, this factor is still important for modeling these nanocomposites since there may be serious aggregates or bundling of CNTs caused by the improper dispersion process as reported in many previously studies [6], especially for SWNTs. As shown previously, we employ the well-known Box-Muller method to form the aggregates with gathered CNTs of normal distribution. For the sake of simplicity, only four aggregates in our model are considered. The generated aggregation models of CNTs are schematically shown in Figure 2.9. To qualitatively investigate this problem, we define the following parameter:

δ=

Vagg V1 4

(14)

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where Vagg is the approximate volume of a sphere containing one aggregate, and V1/4 is one quarter of the total volume of the 3D element shown in Figure 2.9(a). Therefore, δ can approximately and qualitatively describe the extensity of aggregates although it is not so strict. For different values of δ in Figure 2.9, we can find that as δ increases, the aggregates extend more widely, but with the lower density of CNTs included in them. The influence of aggregates on the percolation threshold is shown in Figure 2.10. From it, we can find that very serious aggregates may lead to very high percolation thresholds. However, when δ is larger than a critical value, i.e. 0.05 in our model, the aggregates have no obvious influence on the percolation threshold of nanocomposites. It means that, unless there are serious aggregates corresponding to a very small value of δ, the influence of aggregates on the percolation threshold is almost ignorable. Naturally, it should be noted again that this investigation is only of the qualitative meaning, not quantitative one. Moreover, for the different types of aggregates, such as chain-like aggregates of CNTs, the result should be different. However, it does tell us how important to avoid the serious aggregates of CNTs through a proper dispersion process when fabricating this nanocomposite.

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Figure 2.5. Verification of isotropy and convergence of representative element: (a) Percolation thresholds along x, y and z directions; (b) Size dependence of percolation threshold (L/D=100); (c) Percolation threshold versus simulation number for Lz/L =2

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Figure 2.6. Percolation threshold versus aspect ratio of straight CNTs.

Figure 2.7. Schematic top view of models with curved CNTs for various θ max.

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Figure 2.8. Influence of θ max on percolation threshold.

Figure 2.9. Schematic top view of agglomerated model generated by normal distribution.

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Figure 2.10. Influence of δ on percolation threshold.

3. PREDICTION OF ELECTRICAL CONDUCTIVITY OF NANOCOMPOSITES In this section, we will proceed to the contents about the electrical conductivity of nanocomposites after the percolation threshold. First, we will introduce a 3D resistor network model for estimating the electrical conductivity of the 3D element with randomly distributed CNTs. Then, we will investigate the influences of various factors, such as the shapes of CNTs, aggregates of CNTs and the tunnel effect among CNTs on the electrical conductivity of nanocomposites.

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3.1. A 3D Resistor Network Model for CNT/Polymer Nanocomposite Traditionally, for the cases of a square lattice or a cubic lattice, if considering the sites occupied by fillers as conductors, and sites being not occupied by fillers as insulators, the electrical conductivity of composites can be evaluated by varying the volume fraction of filler from 0 to a value close to 1 [24, 25]. For the electrical conductivity after the percolation threshold, except the work in [22], there have been almost no numerical studies based on a fully 3D statistical network model, even for traditional electronic composites with filler materials such as short fibers or flakes. In this research, we will try to construct a continuum system with randomly distributed CNTs. Unlike the studies [24, 25], in which the conductivity of a matrix phase is also modeled, in this research, the electrical paths in the matrix phase are completely neglected. Since the CNTs are randomly distributed in the matrix, for the matrix among CNTs, there are infinite paths if it is conductive. Here, to simplify our numerical model, the electrical conductivity of the matrix is taken as 0 S/m since the electrical conductivity of epoxy in this

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study is around 10-12 S/m (resistivity is 1014 Ωcm), which is much smaller than that of MWNTs. As outlined above, we only consider the electrically-conductive paths or network formed by CNTs. A part of the network is shown in Figure 3.1(a). As shown in this figure, for two pre-existing CNTs i and i+1, a new CNT j is added into. Using the contact search algorithm stated previously, the contact state between CNT j and CNT i and CNT i+1 can be easily confirmed. The node numbers of two ends of CNT j are k and k+1, respectively. The intersections between CNT j and CNT i and CNT i+1 are numbered as k+2 and k+3, respectively. In this case, and CNT j is divided into three segments. As shown in Figure 3.1(b), the conductance (inverse of resistance) of one segment between two adjacent nodes of the four nodes from k to k+3 is represented by

g k , k + 2 , g k + 2 , k +3 and g k +1, k + 3 , respectively.

For instance, the conductance between k and k+2, i.e.,

g k , k + 2 = σ CNT where

g k , k + 2 can be expressed as

S CNT lk ,k +2

(15)

σ CNT is the electrical conductivity of CNTs, l k , k + 2 the distance between the node k

and the node k+2, and S CNT is the cross-sectional area of CNTs. Usually, it is very difficult to measure the electrical conductivity of a single CNT. For a SWNT, as reported previously, its electrical conductivity ranges from 17.2 S/m to 3.0×109 S/m [26-28]. For a MWNT, its electrical conductivity ranges from 5×103～5×106 S/m [29, 30]. There is a lack of uniformity of electrical conductivity of SWNTs, which strongly depends on the atomic structural parameters, such as the chiral vector. In this research, we employ σ CNT of MWNTs as 1×103, 104, 105, 106 S/m, respectively. Next, for the nanocomposite containing randomly distributed CNTs, as shown in Figure 3.2, the applied voltage is V, therefore, the electrical potentials of electrodes 1 and 2 are V and 0, respectively. Note that our model is a 3D one, for simplicity, only a 2D model is demonstrated. In our numerical computation, when the applied voltage is known, and the macroscopic current I of the nanocomposite can be calculated. As shown in Figure 3.2, at an Copyright © 2009. Nova Science Publishers, Incorporated. All rights reserved.

arbitrary node i, the current is I i , which is expressed as

I i = ∑ g ij (Vi − V j ) N

j , j ≠i

(16)

where N is the total number of nodes in the network, and g ij is the conductance between the node i and the node j, Vi and Vj are the electrical potentials at the nodes i and j, respectively. Moreover, the following relationship g ij = g ji holds. For those nodes, which are not directly connected to the node i by a CNT, we can set g ij = 0 since the conductivity of matrix phase is taken to be zero.

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By constructing Eq. (16) for all nodes, we can summarize the following linear algebraic equations as

{I } = [G ]{V }

(17)

where {I } is the vector of electrical currents,

[G ] of dimension of

{V } is the vector of electrical potentials, and

N × N is the conductance matrix, which is described as

N

Gij = ∑ g ij and G ij = G ji j , j ≠i

(18)

When the nodes are not located on the two electrodes of the both sides of the nanocomposite in Figure 3.2, based on Kirchhoff’s current law, there is

Ii = 0

(19)

Also, for those nodes located on the two electrodes, their sum can be set up as

I = ∑ Ii

− I = ∑ Ii

(Electrode1) (Electrode2)

(20a) (20b)

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For the components in the electrical potential vector corresponding to those nodes located on electrodes 1 and 2, they are set by

Vi = V

(Electrode1)

(21a)

Vi = 0

(Electrode2)

(21b)

By substituting Eqs (19), (20) and (21) into Eq. (17), we can finally get the following equation

[A]{x} = {B}

(22)

Where the vector {x} contains the unknown electrical currents and potentials, [ A] is still

a symmetric matrix, and the vector {B} contains the known electrical currents at the inner

nodes, which are equal to zero as shown in Eq. (19), and potentials at the two electrodes as shown in Eqs (21). The obtained I i is substituted into Eq. (20) to get the total electrical current of electrodes, i.e., I. Since Eq. (22) is a large-scale linear algebraic equation, here we employ an

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iterative solver, i.e., ICCG (Incomplete Cholesky Conjugate Gradient) to solve it. The obtained I as well as the applied known voltage V is then used in the following Ohm’s law to get the macroscopic electrical conductivity of nanocomposite

σ com =

σ com

I Lcom V S com

as follows

(23)

where Scom and Lcom are the cross-sectional area and the length of the nanocomposite, respectively.

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Figure 3.1. Modeling of electrical resistance in network formed by CNTs.

Figure 3.2. Random resistor network of CNTs.

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3.2. Numerical Results of Model of Uniform Random Distribution of Straight Cnts in Matrix First, for the case of uniformly and randomly distributed straight CNTs of L/D=100, the electrical conductivity of nanocomposites is shown in Figure 3.3(a) for various electrical conductivities of CNTs. This figure reveals that the electrical conductivity of nanocomposites increases as the electrical conductivity of CNTs increases. If we consider the following traditional percolation theory for the electrical conductivity

σ com

of composites [31] as follows

σ com = σ 0 (φ − φ c )t

for

φ > φc

(24)

where t is the critical exponent, φ the volume fraction of filler, φc the percolation threshold, and σ0 is a parameter. Usually φc and σ0 are determined experimentally. By using the electrical conductivities at two volume fractions of CNTs obtained from numerical simulations, we can identify the critical exponent t as follows

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t=

log (σ com 1 σ com 2 )

log {(φ1 − φ c ) (φ 2 − φ c )}

(25)

Here, for an ideal state of uniform random distribution of straight CNTs in a polymer, by using Eq. (25) and the least-squares fitting, from the numerical results for various σCNT (103 S/m~105 S/m), we have identified that the average value of t is 1.8±0.05 (see Figure 3.3(b)), which is universal and depends on the dimensionality of the system [32]. In a 3D system, the expected value is 2. Figure 3.4 shows the results of electrical conductivity with respect to the different aspect ratios of CNTs (L/D) when σCNT =104 S/m. For the case of L/D=100, the computation can be carried out up to around 6.0% volume fraction of CNTs. However, for the case of L/D=1000, the computation can only be performed up to 0.5% volume fraction of CNTs. The reason is that as L/D increases, the diameter and volume of CNTs should be decreased since the length of CNTs is fixed in our numerical models as stated in Section 2.2.1. For the high volume fractions of CNTs of high aspect ratios, the number of CNTs increases remarkably, which results in a large-scale amount of computation. This tremendous computational amount is already over than capacity limit of a personal computer. Also, in Figure 3.4, it can be identified that the percolation threshold tends to decrease as L/D increases. When the electrical conductivity of nanocomposites attains at 10 S/m (red line in Fig 3.4(a)), the corresponding volume fraction of CNTs for L/D=100 is around 1.3 vol%, meanwhile, the volume fraction of CNTs for L/D=1000 is only around 0.3 vol%. It means that for the applications, such as electromagnetic interference materials, it is better to use CNTs with the high aspect ratio under the condition of uniform dispersions. Of course, it is well-known that practically it is more difficult to disperse the longer CNTs uniformly in matrix. The fitted critical exponent t in this figure is still equal to 1.8 as shown in Figure 3.4(b), which means that the aspect ratio of CNTs does not influence the value of critical exponent.

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3.3. INFLUENCE OF SHAPES AND AGGREGATES OF CNTS ON ELECTRICAL CONDUCTIVITY OF NANOCOMPOSITES Next, the influence of the curved shape of CNTs is investigated, which is shown in Figure 3.5(a) for the case of σCNT =104 S/m and L/D=100. The number of divisions of straight CNTs is 10. From this figure, it can be found that the electrical conductivity of nanocomposites decreases as that when

φ − φc

θ max increases. Furthermore, from Figure 3.5(b), we can find

ranges from 0.003 to 0.01, the slope of the results of curved CNTs is

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almost same as that of straight CNTs, i.e., t=1.8. However, when

φ − φ c is larger than 0.01,

the slope of the results of curved CNTs tends to be slightly lower, i.e., t=1.6. It means that over a limit of the volume fraction of CNTs, the formation of network by the curved CNTs is more difficult than that by the straight CNTs. We further explore the influence of aggregates of CNTs in matrix for the case of σCNT =104 S/m and L/D=100, which is shown in Figure 3.6(a). Here, δ is a parameter to represent the extensity of aggregates in Eq. (14). As δ decreases, the electrical conductivity of nanocomposites becomes lower. Also, for the cases of δ = 0.065 and δ = 0.056 , the continuous electrical conductivity with respect to the volume fraction of CNTs can be obtained, whereas, when δ ≤ 0.048 , there are strong discontinuities in the results. When δ =0.035, the electrical conductivity of nanocomposites almost remains to be constant. The reason can be found from Figure 2.9. When δ =0.065 as shown in Figure 2.9(c), there are a lot of CNTs located between the isolated aggregates, which connect aggregates together and form the network easily. However, when δ =0.035, as shown in Figure 2.9(a), there are very few CNTs located between isolated aggregates, which leads to the difficult formation of conductive network, and the low and constant electrical conductivity of nanocomposites. Even with the addition of new CNTs, due to the limit from the formation of aggregate model with centered normal distribution, it is hard for these newly added CNTs to play a bridge between two aggregates. For the discontinuities in the results of δ =0.042, which happens at 2.5 vol% and 3.5 vol%, the reason may also be from that the addition of only a few CNTs, which however connect isolated aggregates together, can result in a sudden increase of electrical conductivity of nanocomposites. From the above results, we can find that the influence of aggregates is more significant than that of the curved shape of CNTs. Moreover, in Figure 3.6(b), the influence of aggregates is obvious, which leads to the much lower t.

3.4. Influence of Tunnel Effect Among CNTs on Electrical Conductivity of Nanocomposites Usually, in the stage just before the percolation threshold, although a complete electrically-conductive path has not been formed, there may be a very weak electrical conductivity due to the short distances among CNTs as shown in Figure 1.1(b). These short distances among CNTs can result in the possible tunnel effect to transfer electric charges among CNTs. A lot of the situations of CNTs of short distances have been identified through our SEM observations as shown in Figure 3.7.

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For this tunnel effect, as shown in Figure 3.8, we can approximately evaluate the resistance between two separated CNTs with a short distance as [33]:

(26) where J is tunnel current density, V the electrical potential difference, e the quantum of electricity, m the mass of electron, h the Planck’s constant, d the barrier width (i.e., the distance between CNTs), λ the height of barrier (for epoxy, 0.5 eV~2.5 eV), and A the crosssectional area of tunnel (we simply use that of CNTs here). The influence of tunnel effect is shown in Figure 3.9. From it, we can find that the tunnel effect leads to the increase of electrical conductivity, but its effect is limited to a very narrow band around the percolation threshold. This finding highlights that the application of this nanocomposite for highly sensitive strain sensor should be focused in the region around the percolation threshold, which was also experimentally verified by other researchers, e.g. [34].

3.5. An Empirical Percolation Theoretical Model To obtain a simple percolation theory from the numerical results with the assumption of the uniform random distribution of straight CNTs in the polymer, we need to identify some important terms. For the critical exponent t, as shown above, it is a constant, i.e., 1.8, which does not depend on the aspect ratio of CNTs. Also, for the percolation threshold

φc ,

as

shown in Eq. (13) in Section 2.1, it relates to the aspect ratio in a very simple form. Now, we still need to find σ0 in Eq. (24). Usually, from the explanation of traditional percolation theory, σ0 is the conductivity of the element of a percolating network [31], i.e., the conductivity of CNTs here. Here, we explore σ0 again from Figure 3.4. If we use the identified t and

φc

into Eq.

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(24), we can obtain the following equation

σ com

⎧⎪ ⎛ L ⎞ −1.1±0.03 ⎫⎪ = σ 0 ⎨φ − ⎜ ⎟ ⎬ ⎪⎩ ⎝ D ⎠ ⎪⎭

where

φ

1.8+ 0.05

(27)

is the volume fraction of CNTs.

By fitting the results of various aspect ratios to determine σ0, the results of σ0 normalized by σCNT are shown in Figure 3.10. From this figure, we have surprisingly found that σ0 is a parameter, which not only depends on σCNT, but also on the aspect ratio of CNTs as follows

σ0 = 10 0.85{log ( L D )−1} σ CNT

(28)

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Ning Hu, Zen Masuda and Hisao Fukunaga Finally, the percolation theory in Eq. (24) can be re-cast into the following simple form,

σ com = σ CNT ⋅10

0.85 {log ( L D )−1}

⎧⎪ ⎛ L ⎞ −1.1± 0.03 ⎫⎪ 1.8± 0.05 ⋅ ⎨φ − ⎜ ⎟ ⎬ ⎪⎩ ⎝ D ⎠ ⎪⎭

for

φ > φc

(29)

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We note that the percolation threshold expression, i.e., (L/D)-1.1 is only valid for filler particles of high L/D, such as over 10. This model is of great significance by which the macroscopic electrical conductivity of nanocomposites can be predicted simply if we know σCNT and L/D of CNTs. The theoretically predicted results by Eq. (29) are compared with those obtained numerically as shown in Figs 3.11(a) and 3.11(b) for various aspect ratios of CNTs and various electrical conductivities of CNTs. As shown in Figure 3.11, both results agree with each other very well. This model is also useful for predicting the electrical properties of traditional electronic composites using short fibers of high L/D (e.g., higher than 10) as filler particles.

Figure 3.3. Electrical conductivity of nanocomposite for various conductivities of CNTs: (a) Electrical conductivity versus volume fraction of CNTs; (b) Electrical conductivity versus reduced volume fraction of CNTs.

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Figure 3.4. Electrical conductivity of nanocomposite for various aspect ratios of CNTs: (a) Electrical conductivity versus volume fraction of CNTs; (b) Electrical conductivity versus reduced volume fraction of CNTs.

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Figure 3.5. Electrical conductivity of nanocomposite for various θ max of CNTs: (a) Electrical conductivity versus volume fraction of CNTs; (b) Electrical conductivity versus reduced volume fraction of CNTs.

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Figure 3.6. Electrical conductivity of nanocomposite for various δ of aggregation model: (a) Electrical conductivity versus volume fraction of CNTs; (b) Electrical conductivity versus reduced volume fraction of CNTs.

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Figure 3.7. Configurations of some close CNTs in nanocomposite.

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Figure 3.8. Modeling of tunnel effect among CNTs.

Figure 3.9. Influence of tunnel effect on electrical conductivity of nanocomposite.

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Figure 3.10. Relation between σ0 /σCNT and aspect ratio of CNTs.

Figure 3.11. Verification of proposed percolation theory by numerical results: (a) Comparison of theoretical results of Eq. (29) and numerical results for various aspect ratios of CNTs; (b) Comparison of theoretical results of Eq. (29) and numerical results for various electrical conductivities of CNTs

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4. EXPERIMENTS In this section, we will report our experimental results for the electrical properties of this nanocomposite, which was fabricated using in situ polymerization method.

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4.1. Fabrication Process of Nanocomposites A kind of MWNTs made from chemical vapor deposition (CVD), which was provided by Nano Carbon Technologies Co. (NCTC) in Japan, was used. The reasons to choose MWNT as filler are from that they are generally conducting and their dispersion is comparatively easier due to their much lower absorption energy compared with that of SWNTs (around one order of magnitude lower). Furthermore, the price of MWNTs is much cheaper than that of SWNTs. The purity of these MWNTs is higher than 99.5%. The diameter of MWNTs ranges from 20 nm to 80 nm, and the average length of MWNTs is around 5 μm, respectively. The average aspect ratio of MWNTs is around 100. The reported electrical conductivity of MWNTs ranges from 5×103 S/m to 5×106 S/m [20, 21]. A kind of insulating epoxy (bisphenol-F resin) was employed here. The electrical conductivity of epoxy is around 10-12 S/m. The reason for using bisphenol-F resin instead of bisphenol-A resin [10, 11] is that its viscosity is lower. An amine hardener (polyaminoamides) was used in our experiments, which cures epoxy resins by reacting with the epoxide groups or by promoting selfpolymerization of the epoxy by catalytic action. The epoxy and hardener are in the liquid state at room temperature. A planetary mixer with two rotation axes is shown in Figure 4.1. A cup containing the mixture of epoxy and CNTs is in an orbital motion around the X1 axis. Also, the cup rotates around its central axis, i.e., the X2 axis, which is vertical to the top and bottom planes of cup. Usually, the rotation speed ω2 around the X2 axis is comparatively very slow, which is 2.5 times lower than ω1 around the X1 axis. The highest rotation speed of ω1 is 2000 rpm. In the mixing process, the shear forces provided by the planetary mixer can be much higher than that of a conventional propeller stirrer. Originally, in our preparing process of nanocomposites, we pre-treated the CNTs in a solvent using a sonication bath. However, it was found that the effect of this step on the final electrical performance of nanocomposites is not so obvious. Therefore, MWNTs without further treatment were employed directly. For the fixed amount of MWNTs loading, i.e., 2.0 wt%, 5 samples were prepared using the different parameters in the fabrication process, which are described as follows: Sample A: The epoxy and hardener were first poured into the cup. They were mixed using the mixer for 20 seconds with ω1 at 2000 rpm. Then, CNTs were added into the mixture, which was mixed again for 1 minute with ω1 at 800 rpm. Sample B: The epoxy and hardener were first poured into the cup. They were mixed using the mixer for 20 seconds with ω1 at 2000 rpm. Then, CNTs were added into the mixture, which was mixed again for 1 minute with ω1 at 2000 rpm. Sample C: The epoxy was poured into the cup, and then CNTs were added into the epoxy. They were mixed using the mixer for 1 minute with ω1 at 2000 rpm. Then, the hardener was poured into, and the mixture was mixed again for 1 minute with ω1 at 2000 rpm.

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Sample D: The epoxy was poured into the cup, and then CNTs were added into the epoxy. They were mixed using the mixer for 4 minutes with ω1 at 2000 rpm. Then, the hardener was poured into, and the mixture was mixed again for 1 minute with ω1 at 2000 rpm. For all above samples, after the mixing process, the liquid was cast in a silicon mold to form the nanocomposites, which was cured in a vacuum oven at 80oC for 3 hours to remove excess air. Sample E: The steps are the same as those in Sample D, except the different curing process, where the final mixture was cured at room temperature for 48 hours. After the curing and deforming process, the surfaces of two sides of specimens were covered with sliver paste to ensure good contact of the sample surfaces with the electrodes as shown in Figure 4.2. Copper wire was used as electrode material. The conductivity was measured in dry air at ambient temperature by a four-terminal method using a LCR meter (HIOKI 3522-50) as shown in Figure 4.2. The applied voltage ranged from 0.01 V to 5 V to investigate the dependence of DC electrical properties on the applied voltage. For each sample, five specimens were prepared for obtaining the average electrical properties of nanocomposites. To check the uniformity of resistance distribution, 4 vertical wires are inserted into the specimen of Sample D along the length direction as shown in Figure 4.3. As shown in Figure 4.4, the resistance distribution along the length direction is almost constant. The isotropy of electrical resistance of specimen of Sample D along length, width and thickness directions was also checked.

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4.2. Effect of Parameters in Fabrication Process on Electrical Properties of Nanocomposites The effects of curing process on the electrical conductivity of nanocomposite are shown in Figure 4.5. Note that the resistance of Sample E is too large, which exceeds the measurement limit of the LCR meter of 200 M Ω used. It means that the electrical conductivity of Sample E is lower than a value at the order of 10-6 S/m if we consider the dimensions of specimen. This result is not shown in this figure. The obtained electrical conductivity of various specimens ranges from the order of 10-6 S/m to the order of 1.0 S/m depending on the different fabrication processes used. By comparing the result of Sample D shown in Figure 4.5 and the result of Sample E (lower than 10-6 S/m), we can find that the result of Sample E cured at room temperature for 48 hours is much lower than that of Sample D cured in the vacuum oven at 80oC for 3 hours. This finding is coincident with that in [12], where it was shown that high curing temperature enhances the conducting network formation of nanotube clusters by enhancing mobility of CNTs in the accelerated diffusion process. Next, we investigate the influence of mixing time of the mixture of epoxy containing MWNTs. From the results of Samples C and D, we can find that the result of Sample D with a longer mixing time (4 minute) is 3 times lower than that of Sample C (1 minute). It means that too long mixing time is not beneficial for enhancing the electrical properties of nanocomposites. Generally, it may be helpful to keep the state of small-scale aggregates of MWNTs in the dispersion process, which make the formation of macroscopic conducting network more easily in the reaggregation process of MWNTs after adding hardener [12].

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Ning Hu, Zen Masuda and Hisao Fukunaga

Therefore, this phenomenon may be explained from that a too long mixing process may break up the small aggregates by overcoming the effect of Van der Waals forces among CNTs, which has a negative impact on the formation of network. For the mixing speed, from Figure 4.5, we can find that the result of Sample A is around 10 times higher than that of Sample B although the mixing speed of Sample A is much lower than that of Sample B. The reason is that with the addition of hardener, small nanotube aggregates are formed, which subsequently agglomerate to form a macroscopic network covering large volume fractions of the epoxy as shown in Figure 4.6(a). In this case, low shear forces, which provide the particles with sufficient kinetic energy to overcome the repulsive interactions of the electrostatic charging, are helpful to induce the agglomeration [12]. However, using higher shear forces in this step can disrupt the agglomerates as shown in Figure 4.6(b). Similarly to that shown previously for the effect of longer mixing time, the effect of higher mixing speed on the electrical performance of nanocomposites can be negative. We further explore the influence of the timing for adding the hardener. Note that all of previous studies employed the similar procedure of Samples C and D, in which the hardener was added after the dispersion process of MWNTs in epoxy. By comparing the results of Samples C and B, we can interestingly find that the result of Sample B is around 3 times higher than that of Sample C. Therefore, like the process used in Sample B, it is at least harmless to mix the epoxy and hardener first with the subsequent addition of MWNTs. It is very difficult to clearly explain this phenomenon. One reason may be from the easier formation of macroscopic network in the polymerization process accompanied by the dispersion process of MWNTs. But another reason may be that the procedure of Sample B can partially avoid the encapsulation or coating phenomenon of CNTs. Although the exact mechanism of how MWNTs interact with polymer is still unclear, the practical encapsulation of nanotubes by polymer chains has been identified in many previous studies [9, 19], which retards the conducting between CNTs. Therefore, avoidance of possible encapsulation of nanotubes by polymer chains is a very important issue. Some fractured cross sections for Samples A, B, C and D were observed using a SEM (HITACH S-4300E) as shown in Figs 4.7 and 4.8. From these figures, it can be found that there is no obvious difference on the fractured surfaces in various samples by different processes although the electrical conductivities of these samples are much different, e.g., the result of Sample D is around 100 times lower than that of Sample A. In these figures, as observed in [19], the comparatively homogeneous dispersion of CNT in polymer without very serious aggregates can be identified clearly. Therefore, unlike SWNTs [6], serious aggregates or bundling between MWNTs in matrix due to attractive Van der Waals forces do not exist if a proper mixing process is employed. Finally, the above investigations indicate that the high curing temperature accelerates the formation of agglomeration, which is beneficial for enhancing the electrical properties of nanocomposites. However, an excessive long and powerful mixing process has a negative impact on the electrical performance of nanocomposites due to the difficult formation of macroscopic conducting network. Naturally, a mixing process with shear forces of a certain level is still necessary to stably disperse MWNTs in matrix by overcoming the serious bundling of CNTs caused by high attractive Van der Waals forces, and to induce agglomeration by overcoming the repulsive forces among CNTs contributed by the electrostatic effect after addition of the hardener.

Electrical Properties of a Carbon Nanotube/Polymer Nanocomposite…

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Figure 4.1. Description of a planetary mixer with two rotation axes.

Figure 4.2. Schematic view of measurement of nanocomposite resistance (unit of length: mm).

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Figure 4.3. Specimen for checking resistance distribution (unit of length: mm).

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Figure 4.4. Resistance distribution between two adjacent wires.

Figure 4.5. Electrical conductivities of various samples.

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Figure 4.6. Comparison of two kinds of macroscopic networks.

Figure 4.7. SEM images of nanocomposites for Samples A, B, C and D (2000 times magnification).

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Figure 4.8. SEM images of nanocomposites for Samples A, B, C and D (10000 times magnification).

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5. COMPARISON BETWEEN NUMERICAL AND EXPERIMENTAL RESULTS To investigate the electrical conductivity versus MWNTs loading, finally, we prepared the specimens using the process of Sample B consistently. Specimens corresponding to 0.1, 0.3, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 5.0, 6.0, 8.0, 10.5, 13.0 and 15.0 wt% of MWNTs loading, respectively were prepared. Although the electrical conductivity of Sample A is much higher than that of Sample B (around 10 times higher), the reason for not using the process of Sample A is that for higher volume fractions of MWNTs, the viscosity of the mixture containing MWNTs is very high. Therefore, it is hard to mix it using only 800 rpm as that in the procedure of Sample A. The present numerical and various experimental percolation thresholds versus the aspect ratio of CNTs are compared in Figure 5.1 in the volume fraction of MWNTs. The result of an empirical extruded volume approach [20] was also plotted. In our experiments, at first, the weight fraction of MWNTs was measured easily, and then the conversion between the volume fraction of MWNTs and the weight fraction of MWNTs was carried out as follows

Electrical Properties of a Carbon Nanotube/Polymer Nanocomposite…

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φ vol =

1 ⎞ ρ ⎛ 1 1 + CNT ⎜⎜ − 1⎟⎟ ρ Poly ⎝ φ wt ⎠

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(30)

where φvol is the volume fraction of MWNTs, and φwt is the weight fraction of MWNTs, and the mass density ρCNT of MWNTs and ρPoly of epoxy are 2100 kg/m3, and 1100 kg/m3, respectively. Our experimental percolation threshold is 0.055 vol% (i.e., 0.1 wt%), which is quite low although it is not the lowest one as shown in Figure 5.1. If the procedure for Sample A was employed, a further lower percolation threshold could be expected since as shown in Figure 4.2, the electrical conductivity of Samples A is around 10 times higher than that of Sample B. From Figure 5.1, it can be found that there is a large scattering in experimental results, which may be caused by the different properties of phase materials, different manufacturing processes, unclear definition of percolation threshold in experimental measurements and inaccurate data of the aspect ratio of CNTs. A clear phenomenon in Figure 5.1 is that on the whole, various experimental percolation thresholds tend to decrease as the aspect ratio of CNTs increases although there are some exceptions. As pointed out in [12], the statistical percolation model may be insufficient to address the inter-particle or the matrix-particle interactions, and a model based on colloid theory may be helpful. In Figure 5.1, however, the theoretical and numerical predictions from the statistical percolation model still pass through the middle area of various scattered experimental data. This result may be reasonable since the traditional percolation model only provides the average possibility of the formation of the first conducting network under the assumption of uniform random distribution of fillers. Obviously, even for traditional electronic composites with carbon short fibers, the experimental results cannot always match the theoretical ones well since the perfect uniform random distribution of carbon short fibers in matrix cannot be always realized practically. Naturally, the extent of scattering in the experimental data of the traditional electronic composites is not as large as that of nanocomposites using CNTs as filler. Also, in Figure 5.1, an interesting phenomenon in various experimental results is that the percolation thresholds using SWNTs are comparatively higher than the numerical and theoretical values. The reason may be from: difficult dispersion of SWNTs due to easier formation of serious aggregates or bundling caused by their much higher absorption energy as shown in Figure 5.2 [35], where the absorbability of SWNTs is around 10 times higher than that of MWNTs. Moreover, generally, there is a lack of uniformity of electrical conductance in SWNTs, which strongly depends on the atomic structural parameters such as the chiral vector. In contrast, the percolation thresholds using MWNTs except that in [19] are lower than the numerical and theoretical ones. The reason may be from the practical small-scale aggregates of MWNTs in the macroscopic conducting network as shown in Figure 4.3(a). In this case, if we consider a chain-like small aggregate formed by MWNTs as a single filler, its effective aspect ratio should be higher than that of one MWNT, which consequently results in the lower percolation thresholds compared with the theoretically predicted value using the original lower aspect ratio of MWNTs. Especially for longer MWNTs, these small aggregates may be formed more easily, it may be a reason of why the results in [10, 11, 12] are much lower than the numerical and theoretical ones.

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When CNTs possess L/D and σCNT as 100 and 104 S/m, respectively, the comparison of the present numerical and various experimental results are shown in Figure 5.3. It should be noted that CNTs used in our experiments and in [14, 15] are the same, which are of L/D as 100. This figure demonstrates that the numerical results obtained from the 3D resistor network model agree with the experimental results very well. The influence of curvature of CNTs is insignificant in this case. Again, it confirms the effectiveness of the statistical percolation model for the nanocomposites with MWNTs as filler particles. The main reason can be that the dispersion of MWNTs is comparatively good as shown in Figs. 4.4 and 4.5. Therefore, like the traditional short fiber, each MWNT can be treated as an independent filler particle and the effects of aggregates of MWNTs can be neglected. Naturally, it is further needed to verify the cases of SWNTs as filler particles, since the adsorption energy among SWNTs is much higher that that among MWNTs (around one order higher), which can easily result in the serious bundling or serious aggregates of SWNTs. Also, another issue is about the interactions between CNTs and polymer, such as coating of polymer on CNTs, which has to be considered and reflected in an improved numerical model in the future.

Figure 5.1. Comparison of experimental and numerical results for percolation threshold.

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Figure 5.2. Relation between particle size and absorbability by Van der Waals force [35].

Figure 5.3. Comparison of experimental and numerical results for electrical conductivity.

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6. APPLICATION OF NANOCOMPOSITES TO HIGHLY SENSITIVE STRAIN SENSOR In this section, we will describe a highly sensitive strain sensor, which was developed based on the nanocomposite fabricated previously. The experimentally obtained results indicate that the sensitivity of this new-type sensor is much higher than that of traditional strain gages. Also, an improved numerical model with the consideration of tunnel effect among CNTs will be described and the working mechanism of the sensor will be explored.

6.1. Experiments By using the fabrication process of Sample B in the section 4, a strain sensor of thickness of around 170 μm was fabricated from this nanocomposite as shown in Figure 6.1. To measure the electrical resistance change of this sensor caused by the prescribed strain, this sensor was attached on the surface of an insulating cantilever beam as shown in Figure 6.2. Also, the traditional strain gage was employed, which was attached on the opposite surface of the beam at the same position of the CNT/polymer sensor. This strain gage was used to measure the strain of the beam at this position. The electrical resistance change of the CNT/polymer sensor was measured using the LCR meter. For the traditional strain gage, the strain is measured from the resistance change of gage caused by its deformation. The gage ratio can be expressed approximately as follows

(31)

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where ν is the Poisson’s ratio This equation indicates that the gage ratio of the traditional strain gage is around 2. Also, it should be noted that usually the minimum measurement ability of the traditional strain gage is around 10 με.

6.2. Numerical Model with Consideration of Tunnel Effect for Resistance Change Caused by Prescribed Strains Usually, from the results of currently existing studies, the mechanisms of CNT/polymer sensors can be clarified into three aspects: (1) breakup of CNT network due to strain; (2) electrical resistance change of CNTs due to deformation of CNTs; (3) increase of electrical resistance of tunnel effect among CNTs due to the increase of distances among CNTs. In our study, we only consider the effects of (1) and (3) outlined above. The stretch or compressive deformation in CNTs and the corresponding resistance change of CNTs are neglected due to their much higher Young’s modulus than that of epoxy (more than 300 times higher if we take the Young’s modulus of CNTs as 1 TPa and the Young’s modulus of epoxy as 2.4 GPa). Moreover, in our specimens, the interface between the polymer and CNTs seems

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to be weak as shown in Figure 6.3, where a trace of a CNT, which is completely removed from the polymer, is clearly illustrated. The tunnel effect seems to be a very important factor which controls the performance of the CNT/polymer sensor. By seeing Eq. (26), if there is 1Å increase of d, i.e., the distance between two CNTs, the tunnel current will be 10 times lower. Especially in the region around the percolation threshold, there are a lot of situations where there are very short distances among CNTs as shown in Figure 3.7. In this case, the electrical charges can still be transferred between two close CNTs without contact, if the distance between them is sufficiently small. When this nanocomposite is under the prescribed strain, we reconstruct our 3D resistor network by considering the rigid-body movement of CNTs in the nanocomposite as shown in Figure 6.4. The changes of position and orientation of CNTs caused by the strain and effect of Poisson’s ratio are modeled. By considering the effects of (1) and (3) outlined above, we have numerically investigated the electrical resistance change of the CNT/polymer sensor under the prescribed strains for the cases of 2.0 wt%, 3.0 wt% and 5.0 wt% of MWNTs loading. From the numerically obtained results, it was found that the electrical resistance change of the sensor is very small if only considering (1), i.e., the breakup of CNT network caused by the strains. The influence of this factor seems to be very tiny at least for small strains under 1% in our numerical simulations. For higher strains, the obtained results may be different. On the other hand, it was found that the tunnel effect leads to the remarkable resistance increase of the sensor under the prescribed strain. It implies that the tunnel effect is a key factor to control the performance of CNT/polymer sensors. However, its effect is limited to a very narrow band around the percolation threshold. It means that the application of this nanocomposite for highly sensitive strain sensor should be focused in the region around percolation threshold.

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6.3. Comparison Between Numerical and Experimental Results The experimental measured results for the resistance change of this new-type sensor is shown in Figure 6.4, where the gage ratio of the traditional strain sensor is K=2. The numerical results are shown in Figure 6.5. Both figures show that the sensitivity of this newtype sensor is much higher than that of the strain gage. As the volume fraction of CNTs decreases, which is gradually close to the percolation threshold of the nanocomposite (i.e., 0.1 wt% here), the sensitivity of sensors becomes higher gradually. It verifies our speculations as stated above. Moreover, our numerical results with the consideration of the tunnel effect among CNTs agree very well with the experimental results. Therefore, the modeling of tunnel effect is very important in our numerical simulations. Moreover, it can be concluded that the tunnel effect among CNTs is a key factor for controlling this phenomenon although other factors such as the electrical conductance change of CNTs themselves may also be important (we have not modeled this effect here). Another interesting phenomenon is that the behavior of resistance change of the CNT/polymer sensor becomes non-linear when the strain is higher as shown in the numerical results in Figure 6.5. For the experimental results shown in Figure 6.4, this non-linear behavior can also be identified although it is not as clear as that in the numerical results. The reason can be found from Eq. (26), where the resistance of tunnel effect depends on the distance between two CNTs in the form of nonlinearity. Due to the existence of this non-

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linear behavior, the calibration of this new-type sensor becomes more important and more complex.

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Figure 6.1. Strain sensor fabricated from CNT/polymer nanocomposite.

Figure 6.2. Experimental setup for measuring resistance change in strain sensors.

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Figure 6.3. Modeling of CNTs movement as rigid-body in sensor.

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Figure 6.4. A trace of a removed CNT (evidence of weak interface between polymer and CNTs).

7. CONCLUSIONS In this study, the electrical behaviors of a nanocomposite made from an insulating polymer with filled CNTs have been numerically and experimentally investigated. Based on the statistical percolation theory, we proposed a 3D numerical model to predict the electrical properties of the nanocomposite at and after the percolation threshold. In this model, with the assumption of randomly distributed CNTs in the polymer, the percolation threshold was predicted at the volume fraction of CNTs when the first complete electrically-conductive path connected by some CNTs is formed. Furthermore, a 3D resistor network model for electrical conduction problems of composites was proposed to predict the macroscopic electrical

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conductivity of the nanocomposite after the percolation threshold. The influences of the shapes of curved CNTs, aggregates of CNTs and the tunnel effect among CNTs have been studied in detail. In experiments, it was found that the electrical behaviors of the nanocomposite are very complex practically, which strongly depends on the manufacturing process. The different macro-structures of CNTs in the polymer caused by the different fabrication processes are crucial to determine the electrical properties of the nanocomposite. Moreover, the undesirable coating of the polymer on CNTs formed in the manufacturing process may be another key factor controlling the macroscopic electrical performances of the nanocomposite. Although there are a lot of complexities needed to be tackled, based on the traditional statistical percolation theory with some simplifications, the present numerical model for predicting the electrical properties of the nanocomposite was verified to be powerful and effective by comparing the numerical results with the experimental results. The main reason is that the very serious aggregates of MWNTS are not identified in our experiments. The verified and reliable numerical simulations finally help us obtain a simple empirical formula for predicting the electrical properties of the nanocomposite with sufficient accuracy. Moreover, a highly sensitive sensor was practically developed from this nanocomposite. Both experimental and numerical results verify its high sensitivity compared with that of the traditional strain gage. When the volume fraction of CNTs is gradually close to the percolation threshold, the sensitivity of this new-type sensor increases gradually. An extended numerical resistor network model by considering the rigid-body movement of CNTs in matrix caused by the strains and the tunnel effect among CNTs is very effective to predict the electrical resistance change of this sensor caused by the strains, which implies that the tunnel effect is a key factor to control the sensor performance.

REFERENCES [1] [2]

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[3]

[4]

[5]

Seo MK, Park SJ. Electrical resistivity and rheological behaviors of carbon nanotubesfilled polypropylene composites. Chem Phys Lett 2004; 395(1-3): 44-8. Meincke O, Kaempfer D, Weickmann H, Friedrich C, Vathauer M, Warth H. Mechanical properties and electrical conductivity of carbon-nanotube filled polyamide6 and. its blends with acrylonitrile/butadiene/styrene. Polymer 2004; 45(3): 739-48. P &o& tschke P, Abdel-Goad M, Alig I, Dudkin S, Lellinger D. Rheological and dielectrical characterization of melt mixed polycarbonate-multiwalled carbon nanotube composites. Polymer 2004; 45(26): 8863-70. McNally T, P &o& tschke P, Halley P, Murphy M., Martin D., Bell SEJ, Brennan GP, Bein D, Lemoine P, Quinn JP. Polyethylene multiwalled carbon nanotube composites. Polymer 2005; 46(19): 8222-32.

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Nogales A, Broza G, Roslaniec Z, Schulte K, S ics I, Hsiao BS, Sanz A, GarcíaGutiérrez, MC, Rueda DR, Domingo C, Ezquerra TA. Low Percolation threshold in nanocomposites based on oxidized single wall carbon nanotubes and poly(butylene terephthalate). Macromolucules 2004; 37(20): 7669-72.

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Ounaies Z, Park C, Wise KE, Siochi EJ, Harrison JS. Electrical properties of single wall carbon nanotube reinforced polyimide composites. Compos Sci Technol 2003; 63(11): 1637-46. Park C, Wilkinson J, Banda S, Ounaies Z, Wise KE, Sauti G, Lillehei, PT, Harrison JS. Aligned single wall carbon nanotube polymer composites using an electric field. J Polym Sci, Part B: Polym Phys 2006; 44(12): 1751-62. Kymakis E, Alexandou I, Amaratunga GAJ. Single-walled carbon nanotube-polymer composites: electrical, optical and structural investigation. Synthetic Metals 2002; 127(1-3): 59-62. Kymakis E, Amaratunga GAJ. Electrical properties of single-wall carbon nanotubepolymer composite films. J Appl Phys 2006; 99: 084302. Sandler J, Shaffer MSP, Prasse T, Bauhofer W, Schulte K, Windle AH. Development of a dispersion process for carbon nanotubes in an epoxy matrix and the resulting electrical properties. Polymer 1999; 40(21): 5967-71. Sandler JKW, Kirk JE, Kinloch IA, Shaffer MSP, Windle AH. Ultra-low electrical percolation threshold in carbon-nanotube-epoxy composites. Polymer 2003; 44(17): 5893-9. Martin A, Sandler JKW, Shaffer MSP, Schwarz MK, Bauhofer K, Schulte K, Windle AH. Formation of percolating networks in multi-wall carbon-nanotube-epoxy composites. Compos Sci Technol 2004; 64(15): 2309-16. Ogasawara T, Ishida Y, Ishikawa T., Yokoda R. Characterization of multi-walled carbon nanotube/phenylethynyl terminated polyimide composites. Composites: Part A 2004; 35(1): 35-67. Ono U, Aoki T, Ogasawara T. Mechanical and electrical properties of MWNT reinforced composites. Proc. of the 48th Conference on Structural Strength in Japan, July 2006, Kobe, 141-3 (in Japanese). Research Report, Nano Carbon Technologies Co., Ltd, 66-2 Horikawamachi, Saiwaiku, Kawasaki shi, Kanazawa, 2004 (private communication) Jiang X, Bin Y, Matsuo M. Electrical and mechanical properties of polyimide–carbon nanotubes composites fabricated by in situ polymerization. Polymer 2005; 46(18): 7418-24. Kilbride EB, Coleman JN, Fraysse J, Fournet P, Cadek M, Drury A, Hutzler S, Roth S, Blau WJ. Experimental observation of scaling laws for alternating current and direct current conductivity in polymer-carbon nanotube composite thin films. J. Appl. Phys. 2002; 92(7): 4024-30. Du F, Fisher JE, Winey KI. A coagulation method to prepare single-walled carbon nanotube/PMMA composites and their modulus, electrical conductivity and thermal stability. J Polym Sci, Part B: Polym Phys 2003; 41(24): 3333-8. Hu G, Zhao C, Zhang S, Yang M, Wang Z. Low percolation thresholds of electrical conductivity and rheology in poly(ethylene terephthalate) through the networks of multi-walled carbon nanotubes. Polymer 2006; 47(1): 480-8. Celzard A, McRae E, Deleuze C, Dufort M, Furdin G, Marêché JF. Critical concentration on percolating systems containing a high-aspect-ratio filler. Phys. Rev. B 1996; 53: 6209-14. Balberg I, Anderson CH, Alexander A, Wagner N. Excluded and its relation to the onset of percolation. Phys. Rev. B 1984; 30: 3933-43.

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[22] Balberg I, Binenbaum N. Cluster structure and conductivity of three-dimensional continuum systems. Phys. Rev. A 1985; 31: 1222-5. [23] Newman MEJ, Ziff RM. Fast Monte Calro algorithm for site or bond percolation. Phys. Rev. E 2001; 64: 016706. [24] Kirkpatrick S. Classical transport in disordered media: scaling and effective-medium theories. Phys. Rev. Lett. 1971; 20: 1722-5. [25] Kirkpatrick S. Percolation and conduction. Rev. Mod. Phys. 1973; 45: 574-88. [26] Thess A, Lee R, Nikolaev P, Dai H, Petit P, Robert J, Xu C, Lee YH, Kim SG, Rinzler AG, Colbert DT, Scuseria GE, Tomanek D, Fischer JE, Smalley RE. Crystalline ropes of metallic carbon nanotubes. Science 1996; 273: 483-7. [27] Ebbesen TW, Lezec HJ, Hiura H, Bennett JW, Ghaemi HF, Thio T. Electrical conductivity of individual carbon nanotubes. Nature 1996; 382: 54-6. [28] Fischer JE, Dai H, Thess A, Lee R, Hanjani NM, Dehaas DL, Smalley RE. Metallic resistivity in crystalline ropes of single-wall carbon nanotubes. Phys. Rev. B 1997; 55: R4921-4. [29] de Heer WA, Bacsa WS, Châtelain A, Gerfin T, Humphrey-Baker R, Forro L, Ugarte D. Aligned carbon nanotube films: production and optical and electronic properties. Science 1995; 268: 845-7. [30] Hobara R, Yoshimoto S, Ikuno T, Katayama M, Yamauchi N, Wongwiriyapan W, Honda S, Matsuda I, Hasegawa S, Oura K. Electronic transport in multiwalled carbon nanotubes contacted with patterned electrodes. Jpn J Appl Phys 2004; 43: L1081-4. [31] Deutscher G. Disordered systems and localization. in Percolation and Superconductivity, ed. by A.M. Goldman and S.A. Wolf, Plenum Press, New York, 95113, 1984 [32] Stauffer D. Introduction to Percolation Theory, Taylor and Francis, London, 1985. [33] Simmons JG. Generalized formula for the electric tunnel effect between similar electrodes separated by a thin insulating film. J. Appl. Phy. 1963; 34: 1793-1803. [34] Kang I, Schulz MJ, Kim JH, Shanov V, Shi D. A carbon nanotube strain sensor for structural health monitoring. Smart Mat. Struct. 2006; 15: 737-48. [35] Kondo T, Suzuki S. Introduction of Colloid Theory and Interface Science. Sankyo Press, Tokyo, 2000 (in Japanese).

In: Carbon Nanotubes: New Research Editor: Avery P. Ottenhouse

ISBN 978-1-60692-236-1 © 2009 Nova Science Publishers, Inc.

Chapter 8

THE FERROCHEMISTRY OF CARBON NANOTUBES, DIAMOND, NUCLEIC ACIDS AND PROTEINS: THE MAGNETIC SYNERGISM OF MACROMOLECULES AND LIFE’S CHEMICAL PATTERNS Reginald B. Little Department of Chemistry Elizabeth City State University Elizabeth City, North Carolina

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ABSTRACT Magnetic and electric phenomena have been known in matter for over 2 millennia. The existence of magnetism and electricity in both living and nonliving materials and the intrinsic relationship between electricity and magnetism suggest intrinsic magnetic effects on the chemistry and chemical dynamics of both inorganic and organic substances. Such a magnetic role in matter is supported by the different types of bonds: ionic, covalent, metallic and hydrogen bonding. The internal charges and charge motions for atomic structure further support the magnetic role in the structure and dynamics of matter. In this perspective, an electromagnetic interpretation by cooperative selfinteractions is given for the quantum and wave descriptions of internal charges of the atoms of matter. By considering such magnetic effects, the nature of valence, covalent bond, and catalysis is explained. The photophysics of organic molecules and transition metal complexes are given more meaning by this magnetic perspective. Such a magnetic consideration allows the chemical reaction dynamics to be explained in a more general manner for organic, organometallic, nonmetal, ionic, transition metal and complexes substances thereof. New chemistry by the nonpreservation of orbital symmetry becomes meaningful. The ferrochemistry (the Little Effect) is discovered wherein the bond rearrangements and bonds of many atoms between reacting substances are transformed by many polarized spins during the interactions. Such ferrochemistry was discovered while determining the mechanism of carbon nanotube formation. Ferrochemistry has resolved the two hundred year old diamond synthesis problem. Unconventional nuclear phenomena have been understood by ferrochemical effects. In this perspective, ferrochemistry is further developed among the branches of chemistry. By correlated and

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Reginald B. Little exchanged fermions during macromolecular reactions, a quantum/wave consideration of ferrochemical reactions in plasma, liquids and solids is presented. Such a quantum/wave nature of ferrochemical dynamics determines the basis of resonance and tautomerism. On the basis of the uniqueness of compositions of biomacromolecules and their aqueous environments, the quantum/wave natures of many, varied, nano-arrayed, ferrochemically reacting functional groups of proteins and nucleic acids and complexes thereof are considered to determine emerging structures, dynamics and properties of proteins and nucleic acids. The magnetism, magnetic order and ferrochemistry arise within and between the biomacromolecules due to the many coupled varied weak acid - weak base reactions by p+ transfers among the many functional groups and the continual shift and magnetic p+ currents for their dis-equilibriums by the quantum/wave internal motions and interactions.

I. THE HISTORY OF MAGNETISM AND THE RECENT DISCOVERY OF FERROCHEMISTRY A. Ferrochemistry and the Little Effect

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The Little Effect is phenomena wherein polarized spins and associated magnetism of fermions act coherently to alter many orbital motions of the fermions for multiple alterations of chemical bonding symmetry [1-8]. The Little Effect is in general the magnetic organization of chemical patterns. Such magnetic organization of chemical dynamics determined a new field in chemistry and physics. Traditionally such orbital changes and spin changes have not been considered during chemical reactions. In this perspective, such spin induced orbital dynamics are presented for accounting for prior unknown reaction mechanisms of carbon nanotubes, diamond, protein, and nucleic acid chemistry. Here in this section, such changes in spins for changing multiple orbital dynamics and chemical patterns (ferrochemistry) in atoms, molecules, and lattices are fitted within the general history of e-, p+ and neutron and their magnetic phenomena. Although the Little Effect was discovered in 2000 while determining the mechanism of carbon nanotube (CNT) nucleation and growth [1,2], magnetic and nonmagnetic (as well as electric) phenomena have been observed, reasoned and probed for over 2 millennia. In this perspective, the magnetic ordering effects of e-, p+, and neutrons are extended to chemical reactions (ferrochemistry) in general to better understand biochemical reactions.

B. Some of the First Reports of Magnetism and Electricity in Matter The ancient Chinese reported the earliest observations of attraction and repulsion between iron ores (lodestone), which were probably magnetized by lightning strikes. The mineral magnetite (lodestone) and its directional alignment with the earth were discovered around 600 BC. In 560 BC, Thales of Miletus discovered that rubbed amber pieces electrically repel and that rubbed amber pieces attract a magnetic lodestone. The Chinese developed compass technology around 1086 AD on the basis of the orienting effect of these magnetic needles relative to each other and relative to the surface of the earth. So from the outset on the basis of such magnetism in lodestone and earth and there organization, why

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shouldn’t magnetism orient chemical reaction dynamics? In this perspective, such ferrochemistry is introduced. But back in history, in 1600 AD William Gilbert developed a theory of electricity and a theory of magnetism. Gilbert even interestingly attempted to explain the planetary motions magnetically. Gilbert performed some of the first scientific experiments on electricity and magnetism. Stephen Gray in 1729 discovered the conduction of electric charge and force. Charles du Fay in 1734 proposed a two fluid theory of electricity. Benjamin Franklin in 1750 developed an important theory of electricity and a theory of magnetism. Franklin proposed a one fluid theory of electricity. In 1752 Franklin determined that electricity magnetizes metal needles. Galvani during the 1770s discovered “animal electricity” (electric effects in living matter) whereby substances of living materials possess internal electricity. Volta in 1796 discovered intrinsic electrical differences in nonliving substances such that different metals have different charge affinities and generate currents between them for the effect that different elements have different electrical properties. Franklin, Coulomb and Cavendish measured the electric forces between charges to determine the inverse square law with distance (force is proportional to 1/r2). The inverse square law between magnetic poles was also determined. Therefore the electric nature of matter in the living and nonliving matter was established. These electric and magnetic natures will be considered later to play important roles in chemical bonds and bond resonance and bond rearrangement in CNT, diamond, organic and biomolecules.

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C. Relationship between Magnetic and Electric Phenomena in Matter Stephen Gray discovered the motion of charges and electric conduction. Then Oersted (1820) and Romagnosi (1802) discovered that moving charges generate magnetic field. Fresnel and Ampere then in the 1820s proposed internal currents in iron (Amperean currents) for causing its ferromagnetism. The earth itself therefore has some type of charge flow to account for its magnetism. Therefore in addition to matter having an electrical nature it also possesses an associated magnetic nature due to the motion of the charges within matter. In 1808 Etienne Malus discovered that crystals polarize reflected light in consistency with the later discovered internal electric and magnetic nature of matter and light. Roemer in 1676 discovered that light has a finite speed and observed it to travel at about 3 X 108 m/s. Faraday, ironically, discovered both benzene and the effect that changing magnetic fields exert mechanical force on conductor (1831)(later RBL considered both of Faraday’s discoveries to himself discover that changing magnetic fields exert forces on subatomic conductors to organize carbon into aromatic rings, which fuse into CNT formation). In 1845 Faraday also discovered that a magnetic field rotates polarized light. Although electricity can produce magnetism and magnetism can produce electricity, it is important to note that the electric force was observed to be 2 about orders of magnitude greater than the magnetic force. It is this relative strength of electric to magnetic forces and in particular the feebleness of manmade magnetic fields that has caused many to ignore magnetic effects on physical and chemical phenomena. But here in this perspective, the greater internal electricity in atoms relative to the feeble man-made electricity is shown to produce non-trivial magnetic fields for substantially affecting many physical and chemical events. In 1864 Maxwell theoretically unified electric, magnetic and light phenomena. Light itself became understood as a propagating electric and magnetic wave pulse. Electric and magnetic fields in motion are the

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essence of light. This relationship between electricity, magnetism and light will be shown below to have significance to CNT, diamond and biomolecular bonds and bond rearrangements.

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D. Living and Nonliving Matter and its Magnetism and Electricity So now whatever matter is, it can possess these effects of electricity and magnetism. But what are the physical and chemical bases for matter? Dalton in 1803 proposed a new theory of matter as being made of atoms (element), molecules (compound) and/or mixtures of elements and compounds wherein compounds exist with definite stoichiometry with the transforming ability by chemical reactions. In 1799 Prost proposed the law of invariance of the elemental constitutions of compounds. At this point in time, the non-elemental nature of air, earth, water, and fire were observed. Johannes van Helmont in 1630 discovered that air is not a single element but it can contain a second substance CO2 (by fixing carbon in air) for fixed air produced by burning wood. So air can have carbon. John Black in 1756 showed that fixed air or CO2 can combines with other chemicals to form other compounds. Torbern Bergman in 1770 suggested differences between living and nonliving materials for organic and inorganic matters. A vital force was proposed to operate in living matter to explain the complexity of substances formed in living matter and the organization and controlled motion and replication of living matter relative to the simplicity and more static nature of nonliving chemical transformations. But then Michel Chevreul in 1816 used alkali (nonliving) + animal fat (living) to synthesize soap, demonstrating the seemingly non-necessity of vitalism. And then in 1828, F. Wohler synthesized ammonium cyanide (living substances) from inorganic substances. It is interesting to consider further the prior electricity in animals (Galvani) and the prior electricity in nonliving (Volta) in order to physically unify living and nonliving matter and grasp the implications for existence or nonexistence of vitalism. Thereby in 1848, the existence of the vital force was questioned and no line of distinction between organic and inorganic compounds was proposed. Therefore in addition to the physical relationship between magnetism, electricity, light and matter, a chemical relationship was determined between living materials, nonliving materials, their forces and energies. At this point in history, living and nonliving materials were determined to contain some of the same elements with the ability to involve the same compounds and the same forces of electricity and magnetism therein. In this perspective, the physical and chemical relations between inorganic and living materials are further developed by extending magnetic, organizing effects recently discovered in nonliving, inorganic substances like CNT and diamond to living substances like proteins and nucleic acids. In this perspective, the greater complexity of the same varied mixed compounds of organic and inorganic for biomolecules is shown to emerge effects in biochemistry not observed in the simpler inorganic and organic parts. But first here the historical understanding of these magnetic, electric, light and matter is further developed. So related magnetic and electric phenomena exist in the related living and nonliving matter and also in light. In 1802 Davy showed that electricity can break chemical bonds for electrical changes during compound and elemental chemical reactions. At this point, the author wonders why the role of magnetic field in chemical reactions was not reasoned, being electricity is related to magnetism and electricity causes chemical decomposition then magnetism should also cause chemical combinative reactions as later discovered by the

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author for ferrochemistry. In 1803, Berzelius proposed the ionic bond for electrical attraction between atoms for holding atoms in compounds.

E. Compounds of Atoms in Matter by Valance, Bonds and their Geometry The characteristic holding capacity and stoichiometry of different elements among their different possible compounds were determined during early mid nineteenth century. Valence was discovered during this time. Edward Franklin found that for specific metals certain numbers of organic groups are required for saturation capacity of the metal of its valence. Alexander Williamson determined the idea that certain atoms hold certain other atoms together in molecules. Different elements have different characteristic valence as by Mendeleev’s periodic table (1869). Kekule and Couper in 1858 discovered the tetravalence of carbon. The ability of elements to fulfill valence by more than one bond with another atom for multiple bonding was discovered. Such tendency to reach bonding capacity was disputed later by Gomberg’s synthesis of triaryl methyl radicals. The ability of atoms of the same element to bond themselves more than once was discovered. Erlenmeyer in 1862 discovered the C≡C triple bond. Brown in 1864 discovered C=C double bond. Kekule in 1861 conceived ring structure of benzene although no determination of the nature of the ring was given. Van’t Hoff and Le Bel in 1874 discovered the 3 dimensionality of carbon bonds and stereochemistry. So different types of valence for different elements and different structures and geometry for different compounds and valence were at this time discovered but what is the nature of the valence and the bond? And what is the basis of 3D structures in compounds?

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F. Insufficiency of the Ionic Bond for Molecules Berzelius’ ionic bond could not explain the bonds, valence, structure and 3D geometry between atoms in molecules. The ionic bond of Berzelius and its electric nature could not at this time fully account for many bonding phenomena, especially the vital structures involving carbon. If the electric, ionic nature cannot explain the bonds then why not consider the magnetic nature to explain bonds, valence, stereochemistry and as demonstrated here molecular reactions. Such consideration of magnetism is done here in this work to determine the better magnetic explanation of the existence and characteristics of bonds; valence; structures; stereochemistry; and dimensionality of different compounds, chemical reactions, energetic, and kinetics. This does not negate the important role of the Coulombic, electric forces in chemical reactions but this important magnetic revelation expands upon the Coulombic factor. In 1894, Ostwald conceived catalysis, which is the acceleration of chemical reaction by foreign body. The ionic bond of Berzelius also could not alone explain the catalytic effect. Although the electricity cannot fully account for catalysis, in this work magnetism is put forth for reasoning catalysis. Magnetism causes 3D structures and stereochemistry. It is quite beautiful that magnetisms from different motions exist in different directions for determining the 3 dimensional vectorial nature of bonds. Electrically a charge is a charge so 3D is irrelevant. But magnetically the current directions create 3D relevance. This introduction of

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magnetism for explaining bonds, valence and symmetry will be shown to increase the understanding of CNT, diamond and biomolecular properties.

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G. The Atom and its Electric and Magnetic Nucleus and Electrons for Magnetic Orbitals Old valence was based on the number of ligands; but until GN Lewis (during 1902-1916) no one specified the nature of the chemical bond. In 1897 Thompson discovered the electron and proposed the plum pudding model of the atom. In 1911 Rutherford discovered the nucleus in the atom as a tiny subatomic space containing all the positive charges with electrons occupying most of the space about the tiny nucleus. Bunsen and Kirchhoff in 1860 had already discovered that substances absorb characteristic wavelengths of light. Thereby the atoms within matter were shown to possess characteristic internal electric and magnetic fields and particles. In 1896 Zeeman discovered that external magnetic fields shift the characteristic spectra of substances. The Lorentz Rule determined that a magnetic field torques a moving eand determined the law of the right hand rule which follows from the currents causing magnetic field. Electrons in atoms are currents. e--e- currents in an atom and between atoms torque each other magnetically by Lorentz Law. Different elements have atoms containing different numbers of charges so the electron currents in different elemental atoms experience different internal torques and accelerations by their mutual e--e- magnetic interactions. Moreover external magnetic fields and magnetic currents of other elements can torque the electrons within an atom if the external fields are strong enough. Therefore matter is made of atoms which are made of positive and negative electricity and therefore it is reasonable that external magnetic fields even of other atoms can magnetically torque charge motion and internal magnetism of atoms. After Thompson discovered the e- and Rutherford discovered the nucleus, then Lewis proposed the e- covalent bond or shared e- bond. Planck in 1900 discovered the quanta of vibration of electrons and nuclei within atoms and between atoms sharing electrons. At this time, scientists did not realize the small size, rapid motion, short times and quick field effects cause internal self-interactions for more restricted motions and momenta relative to bulk dynamics. Here such quantum motion is explained by internal magnetic and electric patterns. Electron sharing occurs by e- --- e- internal magnetism. GN Lewis proposed chemical valence and covalence for electricity within and between atoms. About the same time of GN Lewis representing molecules by atoms sharing electrons even at the corner of cubes, Gomberg in 1900 reported the generation of the first organic free radicals, the triaryl methyl radicals, by the reaction of silver with chlorotriaryl methane. The odd e- radical of Gomberg’s radical received strong criticism for over 10 years. In 1913, Bohr proposed the physical e- orbit. Bohr’s orbits work well for hydrogen atom but not for many electron atoms. Bohr reasoned based on his electronic orbits that charges in atoms balance their motions so no net Amperean currents can exist for ferromagnetism. Bohr’s reasoning concerning ferromagnetism does not follow, considering his model concerned one electron atoms and his consideration of ferromagnetism considered multi electron atoms. Bohr orbits were based on electric force but here the magnetic factor is shown to accelerate orbits of many electrons into what would be called orbitals. These many electron magnetic accelerations are here shown to explain the inability of Bohr’s atomic model to

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explain many electron atoms. It is magnetism that torques electrons from Bohr orbits to orbitals into Schrödinger orbitals. Internal magnetism causes quantum mechanics. In 1915 Parson proposed the magnetism of electricity of Bohr electron orbit (currents) of Lewis valence-covalence for internal magnetism in the valence and covalence of atoms and between atoms. But Parson did not go far enough to consider more intimate orbit-orbit magnetic interactions for more complex motions as demonstrated here to determine orbitals. The magnetic nature of orbitals in atoms and molecules will be shown to play a crucial role in CNT, diamond, organic and biomolecular structures and structural dynamics.

H. Atoms and Their Magnetic and Electric Fields for Self Interacting Particles and Waves

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In 1905 Einstein discovered the photon (if it originates from finite it can be observed as finite), proposing that matter absorbs light in chunks, moreover light itself is a chuck of electric and magnetic impulse. So now a paradigm shift occurred from the classic matterparticle and lights waves to Fourier transformation of matter (waves) and light (particles). So which is matter: wave or particle? They both (matter and field) are localized in motion and delocalized in motion so particles in motion have light and light in motion has particles. Matter is energy. And light arises from particles and is particulate. The wave nature of matter should refer to the fields associated with it. The particle nature of light refers to its origination at some space-time from charges. In 1905 and 1916, Einstein discovered special and general relativity, respectively. de Broglie in 1924 discovered matter waves for the fields associated with particles, which later RBL determined further that coupled chemical reactions are waves. So although many have the perspective that matter has a wave nature itself, here the perspective is that matter has a wave nature due to the fields associated with its charges. Coupled chemical reactions manifest such extended wave fields associated with chemical reactions for ψ of the chemical reactions. RBL proposed ψ is electric and magnetic fields associated with fermions. It is the fermions’ internal magnetic and electric fields and their existence over short space-time and speed of light that cause quantum mechanics. Submesoscopic charges move over small spaces in short times and self-interact with their own fields unlike bulk objects which are not as subject to such strong influential self interactions.

I. Self Interacting Mechanics of the Waves of Particles and The Particles Causing Waves Quantum mechanics of Heisenberg (1926) is the consideration of these particles of atom by their associated magnetic, electric and photons of particles rather than the waves themselves and their motion. From bulk to submicroscopic, the physical effect of increasing the speed yet reduces the space of motion with stronger electric fields and magnetic fields of smaller space results in the ability of the particles to interact with themselves (self-interacts) constructively and destructively, these cooperative, self-interactions cause quantum mechanics. For such, only specific energies and specific momenta of the self interacting

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particles are allowed for cooperative particle synchronized, stimulated and organized selfinteractions and are the essence of Heisenberg’s quantum mechanics. On the other hand, from the wave mechanical perspective of Schrödinger (1925), the atoms may be considered in terms of the fields associated with their interior electrons and nuclei and their motions. As a result of the nonlinear, relativistic motions of electrons, the various electric and magnetic fields and light waves interfere constructively and destructively before they can escape the space-time of the atom. Such patterns of electric and magnetic fields actually determine the wave functions of Schrödinger. The electron should not be considered as a wave but it should be considered as the wave associated with a moving negative particle. The actual stationary stable ψ wavefunctions are those that meet the conditions of such constructive/destructive magnetic, electric or electromagnetic patterns. Other patterns are not stable constructively and destructively so the net magnetic, electric or electromagnetic waves are relativistically absorbed or emitted from the atom. This perspective is consistent with Einstein’s field perspective of the Hamiltonian (KE +PE).

J. Continuum and Spinrevorbital Motions for Einstein’s Hidden Variables

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Thus on the basis of the wave mechanics, the wave function represents stable constructive and destructive magnetic and electric fields in space-time about the nucleus that confine the e- in space-time within the atom. The allowed discontinuum regions are regions of positive charge and regions of attracting high speed magnetic currents, fields and exchange or correlated motions where electrons are allowed. On the other hand, forbidden continuum regions (unstable orbitals) are regions of negative charge and regions of repulsive, high speed magnetic currents, fields and exchange or correlated motions where electrons are not allowed. Hence on the basis of this model, Einstein is correct; the field theory is a better more exact theory, uniting relativity and quantum mechanics. Quantum mechanics becomes the continuum of possible energies and momenta if it is taken into consideration that the relativistic, unbalanced revolutionary motions of e- in orbitals with addition of spin causes continuum motions. Such revolutionary motion is the hidden variable of Einstein. Dirac combined the relativistic and wave mechanical motions of the electron in the atoms to derive the e- spin theoretically (1928). By using general relativity with uniting the other forces as space-time curvatures may theoretically yield such relativistic revolutionary fermionic motions within atoms.

K. The Discoveries of Wave Mechanics on the Basis of Magnetic Electron Motions In 1926 Schrodinger discovered orbitals by applying de Broglie wave to electrons in atoms; later RBL determined that changing orbitals during multiply coupled chemical reactions manifest a wave nature. In 1913 Starke discovered that external electric fields shift spectra for electrically, externally perturbing internal charge, charge motion and internal fields within atoms. Stern in 1921 discovered that external magnetic fields shift some atom beams of elements with unbalanced e- motions thereby detecting this internal unbalanced charge motion for observing Amperean currents in some atoms, showing the internal atomic

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magnetism. Weiss in 1907 determined that wave mechanics (as opposed to Bohr mechanics) allows the Amperean currents for ferromagnetism and also determined the theory of magnetic domains arises due to unbalanced charge motion due to wave mechanics. This reconsideration of Amperean currents includes magnetism of orbitals and spins. In 1895 Curie discovered that high temperature alters ferromagnetism. Later RBL determined that similar thermal perturbation of diamagnetism during multi chemical reactions have wave nature, involving Amperean current nature between many atoms for magnetically coupled unbalanced fermion motions and ferrochemistry.

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L. The Iron Catalyzed High Pressure High Temperature Fixation of N2 to NH3 In different elements like heavy metals, the nuclei are packed with more positive protons held strongly in nucleus, but the surrounding electrons have to do more to overcome their repulsions relative to electrons in lighter elements. In the heavier metals, the electrons move faster, generating stronger magnetic fields to attract and to overcome their repulsions. For example, such high speed magnetic electrons in iron magnetically disrupt covalence of carbon to form diamond and CNT. Electrons in iron disrupt the valence of H to form neutrons. Electrons approach nuclear speeds in heavy transition metals. Haber in 1909 first discovered that the iron can catalyze fixation of N2 into ammonia. Haber observed nitrogen fixation but RBL explains this nitrogen fixation magnetically. High temperature alone is insufficient to break N≡N triple bond and form N-H bonds. It is not just an electric effect of the bonds but also a magnetic effect of high speed torqueing electrons in the iron. On the basis of the Little Effect, the nitrogen fixation needs iron catalyst (which is magnetic) to magnetically catalyze the bond rearrangement or shift of the magnetic orbital current from N≡N triple bond to N-H bonds. Iron magnetically breaks the strongest possible chemical bond N≡N. The Hedvall Effect was discovered in 1934 as the change in catalytic kinetics about Curie temperature. The Hedvall Effect is a kinematical effect of catalytic rates about the Curie temperature, but the Little Effect is dynamical phenomena of spins and associated magnetic fields for organizing, stimulating and synchronizing orbital dynamics during chemical reactions, even explaining the Hedvall Effect. The discovery of superconductivity was in 1911 and the Meissner Effect was discovered in 1933. It is interesting to consider the iron alloy engine and its effect on the internal combustion chemistry in its cylinders. Does the iron hinder the oxidation reactions? Can the iron alloy engine break the N2 in the engine or can the engine be engineered to break N2 in the cylinder via the iron catalyzing walls to give more power to the engine? Can magnetizing the engine fix N2 to NH3 or N-O compounds which are energy sources? Iron exists in the human body, iron exists in the earth’s core. What ferrochemistry does iron provide in the human body and within the earth’s interior?

M. The Discovery of Electron Spin Magnetism Pauli proposed an intrinsic spin of the electron for more magnetic considerations to explain atomic structure spectroscopy, ferromagnetism and chemical covalence. Pauli proposed electron spin based on the Zeeman Effect and the number of possible electronic

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states for one electron elements (alkali) in a magnetic field. The number of states is better described by 4 quantum numbers rather than 3 quantum numbers. Thereby the new spin motion explains elemental chemical properties. In 1925 Goudsmit and Uhlenbeck physically determined electron spin from the hydrogen spectrum. Intrinsic e- spin momentum is ½ of the smallest electron orbital momentum first observed by Stern and Gerlach. RBL realized that spectra cannot discern intra-orbital relativistic revolutionary e- motion; such revolutionary motion of electrons in matter is the hidden variable of Einstein. The relativistic acceleration of electrons causes the indiscernible continuum states in matter. Dirac relativistically determined electron spin from both the theory of QM and the theory of special relativity.

N. The Wave Mechanics of the Covalent Bond In 1927 Heitler and London applied the wave nature of electrons in molecules to compute molecular orbitals just as Schrödinger computed the atomic orbitals of atoms for the electronic valence and covalence of Lewis from wave applications to the electrons in the atoms. Photons can excite electrons between atomic and molecular orbitals. In 1925 the La Porte rule determined that Δl ≠ 0 for such photophysics processes. The La Porte Rule follows from the momentum and magnetism in light and its magnetization and torque of fermions on absorption/emission by matter. Later chemical reactions will be shown to require similar magnetic torques and shifts! In 1948 Pauling used wave mechanics and discovered that mixing atomic orbitals causes hybridization for more complex molecular orbitals and molecular structures. But such mixing of atomic orbitals requires some torquing, from where does the torquing come? RBL later shows that magnetic, high spins, mixing and torque of electrons cause such hybridization on the basis that there is a stronger polarized spin-torque on orbital motions than unpolarized diamagnetic orbital torque on orbital motions. Thereby such multiple spin orbital dynamics during chemical reactions give a wave nature to multiply organized reactions and biomolecular reactions.

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O. Photo-Excited Magnetic Orbital Motion and Changing Spin in Molecules In 1944 Lewis and Kasha discovered new distributions (so-called forbidden distributions) of electronic spin motions in molecular matter as high spin, photo-excited states for triplet states and photomagnetism. Lewis and Kasha determined that the electrons can be excited to exist unpaired but in different orbitals with the same spin. After the triplet discovery, Kasha discovered new ways to generate the triplet state by molecular excited state - heavy metal interactions as Kasha Effect. Also Kasha and El-Sayed showed how internally orbital interactions can torque T→S. In 1963 Kasha determined that the metal can torque the e- spin in photoexcited molecules (Kasha Effect). In 1968 Kasha and El-Sayed discovered that orbital-orbital electronic interactions can torque e- spin T → S in photoexcited molecules. Later RBL discovered many polarized spin---spin interactions can torque orbital motion, even adiabatically. In 1950 Kasha Rule determined faster nonradiative to radiative transitions in molecules here explained on the basis of the excited state being less self-interacting than the ground state, therefore the ground state is more quantum /wave mechanical with lower density of states. Thereby the internal dissipation of upper-levels, electronic states is more of

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a classical nature relative to the more quantum nature of lower level relaxations on the basis of Kasha Rule. RBL discovered exceptions and modifications of Kasha Rule in very strong magnetic fields. In very strong magnetic fields, the ratio of nonradiative to radiative relaxation rates is diminished. Moreover, in this perspective RB Little demonstrates modification of Kasha Rule in chemically reacting systems in strong exchange with strong lattice magnetism of ferrometals. Moreover, molecules in water via proton exchange and currents manifest slower nonradiative relaxation for energy accumulation and focusing. Kasha and El-Sayed discovered internal, orbitally induced photoexcited T → S (El-Sayed Rule) ( Δl ≠ 0, Δs ≠ 0 supplementing La Porte). The Kasha Effect discovered that transition metals can flip spins in excited molecules for S → T intersystem crossing. In 1960, Rashba Effect discovered electric field effects can act as magnetic field in the rest frame of the electron as in the transport across interfaces for changing electronic spins. In 1955 Dresselhaus Effect discovered asymmetric orbital motions of conduction can induce singlettriplet transition.

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P. Photo-Excited Magnetic Orbital and Spin Motions in Transition Metal Complexes Within transition metal complexes and bulk transition metals different couplings of spin to orbital motions were discovered even relative to nonmetals and molecules. In 1925 Russell Saunders coupling was determined for 3d metal complexes and jj coupling (1930, Bakker and de Bruin) was determined for 4d and 5d transition metal complexes (ji = si + li ;J = Σji). Different spin-orbital interactions occur in 3d vs 4d and 5d transition metal complexes. 3d orbitals mix s and l separately for the whole mixing of S and L for J in 3d metals by Russell Saunders coupling. But 4d and 5d transition metals have jj coupling in transition metal complexes by spectral terms. In jj coupling, j=l+s mix individual spins with individual orbitals. Russell Saunders (LS) coupling and jj coupling of electronic states occur in transition metal complexes. The Paschen-Back Effect was discovered in 1912 and it occurs when a very strong magnetic field is applied to spectra of 3d transition metal complexes. In 2000, RBL discovered that strong external magnetic field causes Paschen-Back Effect on Fe which can allow many spins to act collectively on orbitals during chemical reactions thereby discovering the Little Effect! Here it is demonstrated that these couplings apply also during chemical reactions. So not just within the photo-excited compound but also during chemical transformations within chemical reactions, different spin-orbital couplings apply for different transition metals and nonmetals. jj chemical reactions cause Suzuki C-C coupling reactions (1997), but Russell Saunders or LS couplings cause diamond and CNT formation of Smalley (1996) on the basis of the Little Effect. RBL also determined that both local and delocalized chemical reactions occur; likewise jj coupling and LS coupling explain transport during low temperature superconductivity and high temperature superconductivity, respectively. Bardeen, Schrieffer, Cooper in 1957 developed BCS theory of low temperature superconductivity electrons in which paired electrons move without resistance (phonons scatter) by the antiferromagnetic pairing, keeping spins ordered during transport and phonon scattering. Landau in 1937 and Peierls in 1923 and 1935 determined that 2D crystals are thermodynamically unstable and cannot exist. They state “divergent contributions of thermal fluctuations lead to displacements of atoms that are comparable of interatomic distances at all

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temperatures.” Mermin in 1968 confirmed the work of Landau and Peierl, concluding: “no long range order in 2D dislocations should appear at any finite temperature”. But in 2000, RBL determined that the magnetic field of a ferrocatalyst can stabilize the 2D film formation as in graphene even at very high temperatures. Peierl, Landau and Mermin did not consider magnetism as an out of plane organizing force (electric cannot act out of plane nor out of line) to counter thermal fluctuations. But in 2000 RBL determined that magnetism can stabilize the graphene and magnetism can distort graphene into CNT. Out of plane deformations are suppressed by internal magnetism of the carbon atoms of the graphene. But the external magnetism of ferrocatalyst can distort the graphene. Electric fields cannot account for the internal stabilization of 2D graphene, but magnetism can account for the internal C-C stabilization of the plane. Also the electric field cannot explain the CNT formation from graphene. It is interesting to compare such magnetic stabilization of 2D films to the magnetic role in countering instability of superconductivity against thermal fluctuations. Therefore spin-orbital dynamics are important in transition metal, in transition metal complexes and in molecules. RBL extends here spin-orbital interactions for new understanding of aqueous molecules in chemical reactions.

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Q. Preservation of Orbital Symmetry/Momenta During Chemical Reactions In 1970 Woodward and Hoffman discovered that electronic orbital momentum is conserved (Δl = 0) during chemical reactions (Woodward-Hoffmann Effect). RBL later discovered non-Woodward-Hoffman Effects during chemical dynamics under extreme conditions of strong magnetization whereby Δl electronic states mix with Δs electronic states during chemical reactions for the nonpreservation of orbital momentum. In 1933 Gabiano demonstrated and observed the magnetic rotation of intact molecules. Later RBL shows that very strong magnetic fields can rotate parts of big molecules and even internal shells, subshells and orbtials within atoms for novel chemical dynamics. The significance of such magnetic and spin organization of biomolecular reactions will be consider in the later sections of this perspective. But the importance of such spin organization of orbital bond rearrangement and non-Woodward-Hoffmann reactions is realized by the difficulty of conventional organic synthesis for many biomolecular syntheses. Over the last 40 years, EJ Corey has developed a huge organic chemical synthetic arsenal by the conventional orbital preservation with the consequent limitations of conventional organic synthesis. Such conventional orbital preservation chemistry is the source of the difficulty in synthesizing many natural products and biomolecules which are synthesized in living organisms by nonWoodward Hoffmann chemistry on the basis of this presented ferrochemistry. Nonpreservation of orbital dynamics gives greater understanding of biochemical reactions, explaining the difficult syntheses of many biomolecules by conventional approaches. In addition to chemical syntheses, electronic transport and superconductivity will be advanced by taking into account such spin alterations of orbital motions. High temperature superconductivity was discovered in materials of complex ionic lanthanide-actinide + transition metal + polyoxoanions parts. The nonpreservation of orbital symmetry by strong spin-orbital interactions will allow even higher temperature superconductors in ferromagnetic materials on a non-BCS, ferromagnetically coupled theoretical basis. During the 1930s, Bitter of MIT developed the Bitter electrical, solenoidal magnet, which uses large electric current

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loops via copper plates (for higher current flow) with cooling holes (for water coolant flow) rather than copper wires to produce very high currents and strong magnetic fields within the coiled plates. RBL use such magnetic currents from Bitter style magnets to impose 20 Tesla magnetic fields on iron catalyst to affect magnetic chemistry in 2002.

P. Magnetic Orbital Resistance Effects on Transport and Chemistry In 1982 Ertl demonstrated the existence of N atoms on the surface of iron during the Haber process. Under chemical reacting conditions, iron can alter electron orbital motions in nitrogen bonds to prevent nitrogen atoms rebonding. Chemical reactions are charges in transport so similar effects of magnetic field on transport cause effects on chemical reactions. Under applied voltage in magnetic field, small magnetic fields resist electronic transport. In 1988 Fert and Grunberg demonstrated that rather small magnetic fields can really alter electronic motions in excited states. The giant magneto resistance of spins for even bulk electronic motions was discovered. Similarly the ability of iron to alter carbon valence orbital motion was later developed by RBL to form carbon nanotube and diamond and explain metabolism in FeS clusters of metabolism. So if the internal magnetic spin resistance to transport is large enough by very weak fields then by the Little Effect the magnetic spins can torque each other into different chemical symmetry under very strong fields like within the iron lattice.

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Q. Magnetic Orbital Resistance for Radical Pair Effect Just as Lewis and Kasha have shown spin slowing photorelaxation, Turro (1983) Buchachenko (1984) and Haysihi (1993) have shown that antisymmetry can slow chemical relaxation of radical pairs for the radical pair effect. Internal magnetic repulsion between polarized spins of broken bonds slows rebonding for radical pair effects. But RBL goes further than Turro, Buchachennko, Hayashi and the radical pair effect. RBL not only considered the magnetic slowing of chemical relaxation of the two radicals, but RBL also discovered that many spins between many interacting radicals can torque their orbital symmetries during their chemical reactions and also during the superconductivity. It has recently been observed that iron complexes exhibit high temperature superconductivity [9]. But ferrochemistry involves many interacting spins of radicals and atoms for nonpreservation of orbital symmetry among the many reactions. Woodward Hoffmann Rules involves isolated spin pairs of chemical reactions whereby the orbital symmetry is preserved. Turro, Hayashi, Buchachenko and their radical pair effect involve spin motion between 2 radicals of a broken isolated chemical bond. Buchachenko discovered the magnetic isotope effect wherein nuclear spins internally torque spins of a broken bond such that the antisymmetry resists motion of rebonding. Just as the photochemistry of Buchachenko, Turro, Hayshi shows that spin antisymmetry slows chemical bond, RBL goes further by showing spins can alter the momentum and symmetry course and outcome of chemical reactions. In Woodward Hoffmann effects, orbital symmetry is preserved across course of chemical reactions. But with the Little Effect, it is the internal spins that can alter the course of chemical reactions

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from orbit to orbital so external spin can alter the orbital motion for chemical reactions and structural changes!

R. Discovery of Nanocarbon, Spheres of Fullerenes and CNT In 1985 Kroto, Curl, Smalley discovered fullerenes as curved graphene spheroids [10]. In 1991 Iijima discovered tubular nanographene [11]. In 1998 Smalley discovered nanoferrocatalyst for tubular nanographene [12]. But the mechanisms of fullerene and CNT formations were unknown in 2000. In 1998 Stein observed the femtosecond radical pair effect [13].

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S. Changing Orbital and Spin Motions During Chemical Reactions for Magnetic Organization of 3D Graphene, Fullerene, CNT and Diamond Chemistry In 2000 RBL discovered that magnetic field can shift electronic spins to induce orbital shifts during chemical reactions for the magnetism of chemical reaction. Thereby magnetic spins can shift orbital symmetry in addition to the spin pairs slowing their rebonding of Turro, Hayashi, and Buchachenko. RBL discovered the magnetic shift in hybridization and molecular structure. RBL showed that a magnetic field can cause the distortion of graphene to change orbital direction and hybridization during the chemistry for magnetic torque of e- into different dimension 0D to 1D to 2D to 3D to 4D. Since magnetism is intrinsic to all matter, why should it not influence chemical bond dynamics and symmetry of matter? By the Little Effect, the magnetism torques electrons into van’t Hoff/Le Bel three dimensions. Thereby many spins, radicals and many orbital dynamics are coupled magnetically. The magnetic field can accumulate, organize, synchronize, stimulate, cohere and concentration energy contrary to the second law of thermodynamics. Laser light can excites atoms for inverted nonequilibrium states which also disobey second law [14]. Protein and nucleic acids can excite broken chemical bonds in non-equilibrium states and likewise disobey second law under physiological conditions in non-equilibrium. At low temperatures under equilibrium, the system obeys the second law for forming more disorder. But even at high temperature or high potential fields if the system never equilibrates then it can organize and lower its entropy for an energy sinks into chemical bond or sink into a nucleus reaction. The Little Effect involves spin alterations of orbital dynamics during chemical reactions for shifts in bonds in substances containing elements like boron, carbon, nitrogen, oxygen, chromium, manganese, iron, cobalt, nickel, copper and lanthanides. CNT chemistry, diamond chemistry, and biochemistry involve bond rearrangements of carbon atoms wherein such shifts result in change in hybridization which cause and are caused by magnetism. RBL discovered magnetic carbon and first proposed that chemical dynamics cause carbon magnetism. On this basis magnetic field was used to control carbon chemistry in CNT and diamond. Esquinazi [15], Rode [16] and Makarova [17] later independently (on the basis of RBL) determined that p+ bombardment, laser irradiation, and HPHT can alter carbon lattices for unconventional magnetism in carbon. RBL discovered the inverse beta on the basis of such magnetic shift in

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e- orbital. Now in this perspective, the ferrochemistry of carbon macromolecules with multiple functional groups in nanowater is used to explain biochemistry. RBL used the internal Amperean currents in iron plus Bitter type solenoidal magnetic to demonstrate strong magnetic alteration of carbon chemistry. In analog to prior technology of steam engine to internal combustion engine, RBL put the magnetic field directly (as iron) in the chemical reaction rather than having a weak magnetic effect surrounding the chemical reaction. This direct magnetization of chemistry is like the 19th century putting the fire in the cylinder for steam engine to internal combustion engine technological development, putting iron in the chemical reactions while others are currently using steam engines of weaker solenoidal magnets. Chemical reactions, the iron lattice, fire, hydrogen plasma, and aqueous solutions of biomolecules are in this perspective shown to manifest similar ferrochemical phenomena. Inherently when bonds break or valence changes, there is magnetism. Using Amperean Currents in iron plus external magnetic field from a solenoid this inherent magnetism is modified during the bond breakage, bond rearrangement and valence changes to first demonstrate ferrochemistry. On this basis such noncovalent magnetic interactions are inherently demonstrated to pull atoms together.

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II. THE DISCOVERY OF FERROCHEMISTRY This ferrochemistry and the Little Effect were discovered in June 2000 [1-3]. This work of determining the mechanism of CNT formation was inspired by RE Smalley during the Out of the Box and Into the Future Conference at the Potomac Institute. Smalley emphasized the unknown mechanism of CNT formation during this time. I was inspired to study the mechanism of CNT formation from his presentation. At this time, I worked at the NRL in Gaithersburg, MD during summer 2000 on magnetic nanostructures. During July 2000, RBL developed a ferromagnetic mechanism of carbon nanotube nucleation and growth. It is important to note that although Smalley inspired me to work on the mechanism of CNT formation, the magnetic role in the mechanism of CNT formation was determined solely by the author. Smalley had previously employed magnetic field to align preformed existing CNT based on their diamagnetic interactions. But RBL first proposed the intrinsic magnetism during the CNT genesis itself and the use of external magnetic fields to explain and to enhance the chemical formation. In this mechanism, the various adsorption, decomposition, transport, nucleation and growth steps of CNT were explained magnetically by the decomposing hydrocarbon, absorbed carbon, diffusing carbon, and combinative chemical bonding of carbon which are coupled, stimulated, synchronized, organized and energized magnetically by the catalyst. Magnetic order was conceived in the carbon network during the growth process as the forming carbon atomizes, diffuses, nucleates, anneals and grows on ferrocatalyst (Fe, Co and/or Ni). Such magnetic organized formation of the carbon nanotube was also extended to the autocatalysis of CNT by carbon itself at higher temperatures by laser vaporization and arc vaporization [2]. The autocatalyzed process by magnetic carbon itself was a further determination of ferromagnetism in carbon itself. On the basis of magnetism in the catalyst and magnetism in growing CNT, a magnet-magnet coupled chemical and transport process was proposed. Under the growth conditions, the temperature fluctuates about the Curie temperature so a dynamical organizing process was determined as organized

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by the fluctuating magnetism and spin density wave and current under the growth conditions. In addition to spin density and spin currents, charge density was included as a basis for catalytic activity at lower temperature. A strong interaction of the charge and spin (Dirac Spins) currents was conceived with the orbital momentum in order to explain the magnetic mechanism. The dynamics magnetic environment stimulates, organizes and synchronizes the bond rearrangements (the Little Effect). Furthermore, a more static magnetic environment on the nano-length scale was reasoned by RBL to stimulate, organize and synchronize a change to diamond condensation. I contacted Dr. Jack Crow in Aug 2000 and proposed experiments to explore this model at the National High Magnetic Field Laboratory [3]. Subsequently fererocarbon was developed independently on the basis of my model by: Esquinazi [15], Makarova [17], Rode [16], and Mombru [18]. I inspired subsequent work on magnetic carbon nanotubes, Landau levels in graphene [19] and Dirac spins [20] in carbon nanotubes, graphene and magnetic diamond formation.

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III. Ferrochemistry of Carbon Nanotube Formation The ferrochemistry in 3 inorganic systems has been determined and will be considered in the next 3 sections. The carbon nanotube nucleation and growth were first determined to be governed by ferrochemistry (the Little Effect). The magnetically organized nucleation and growth were first determined in the ferrocatalyzed (Fe, Co, and Ni) formation of CNT. Subsequently the ferromagnetic mechanism was extended to laser vaporization (LV) and arc vaporization (AV) methods of CNT formation. In these inorganic systems, the magnetic organization of the ferrocatalysts (iron, cobalt and/or nickel) was introduced to ferrochemically organize the CNT formation. In the autocatalyzed method, the H+, He+, eplasma was proposed magnetic and analogous to the metal lattice for ferrochemically organizing CNT formation, autocatalytically. The spin currents and spin waves in the gaseous H/He plasma were proposed to ferrochemically torque hydrocarbon decomposition, C transport, C rehybridization and C-C bonding to form the CNT. Therefore the magnetism of eorbital currents was determined in both condensed and uncondensed systems for organizing CNT formation. This ferrochemical catalytic activity of lattice e- in metals and the H/He plasma will be compared later to p+ catalysis in p+ orbitals of water lattice for ferrochemical nucleic acid and protein dynamics, structure and properties. By considering these various methods of forming carbon nanotubes along with this ferrochemical model, a comprehensive ferrochemical mechanism of carbon nanotube nucleation and growth was determined for both condensed and uncondensed systems. This comprehensive magnetic mechanism was expanded from the catalytic CVD to the autocatalytic laser and arc vapor depositions. The plasma plume has magnetic properties. The vapor vortex is magnetic carbon, hydrogen, electrons and protons for magnetic carbon chemistry. This comprehensive, ferrochemical model has led to better CNT syntheses. On the basis of this work, synthetic environments for magnetically achieving better size and helical control were proposed. It is important to note that prior to this magnetic determination of the CNT formation, the magnetic influence on chemical reactions was missing. But by considering matter as both magnetic as well as electrical, the CNT chemistry was rationalized. This magnetic factor during the CNT formation involves changes in spin and orbital motions of C, H, and M atoms during chemical reactions that form carbon nanotubes. The magnetic changes in the metal

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associated with the rehybridization of bonding of more metal orbitals with lower net magnetization for the compression and/or rarefaction of M-M bonds by e –screening, thereby ferrochemically allowing C atom diffusion thru the metal catalyst. This magnetic screening effect during C diffusion is in analog with e- screening during lattice transmutations and fusion [20]. The charge flows associated with the bond rearrangements of the metal lattice also ferrochemically torque C bonds for C atomic rehybridization to C-C sp2 hybridization for conjugated π bonding, cyclization, aromatization and ring fusion. Such e- motion in the nanocatalyst and forming CNT determined strong spin orbital interactions and the Dirac nature of e- in such systems. Such electronic currents in the lattice for magnetism have also determined Hall Effect, Landau excitations and Berry phases during the catalyzed CNT formation. The strong spin and orbital magnetic effects on the chemistry of the CNT and the catalyst are manifested in recent observations that attached Fe or Co atoms (on CNT) cannot be oxidized to until the CNT collapses [21]. It is interesting to note the electric field and magnetic field screening in MWCNT only after a few layers and screening chemical bond by CNT [22]. Iron gives life to the heat in carbon and the burning bush is slow to consume. Charge flow and magnetically interacting currents bend and torque each other to torque large molecules, rotate subunits, rotate functional groups, rotate bonds, and rehybridize torque ebetween bonds. Breaking bonds and compression cause high magnetism and correlation. A metal lattice with negative e- magnetic cloud can alter carbon bond into CNT. In H plasma the e- and p+ of the plasma alter C bonds into CNT. Just as p+ of H plasma interacts with C to organize CNT, p+ in water organizes chemistry of proteins and nucleic acids in water. Next I will consider how analogous p +cloud in water alter organic bonds and alter biomolecules of nucleic acids and proteins by coupling e- and p+ of water to the protein and nucleic acid for dynamics on larger length and longer time scales. As a metal lattice loses magnetism, the carbon becomes magnetic with magnetic compression and/or rarefaction by e -motion for allowing carbon diffusion. The energy in bonds goes into surrounding bonds to allow lattice openings for carbon atomic diffusion by the magnetic field stretching and compressing metal bonds. The magnetic field further stretches and compresses C-C bonds of the growing graphitic net with holding of carbon atoms to organize C-C sp2 bonding and knitting. From the metal lattice catalyst to H plasma catalyst to e -arc plasma catalyst, the magnetics of polarized spins organize the bond rearrangement during decomposition, diffusion and rebonding of carbon. The magnetic torque of chemical bonds is demonstrated so now the torque of the bonds to smaller electronic orbitals as in sp3 organization to diamond and then larger organization of proton orbitals in aqueous solution of biochemistry are considered. Protein and nucleic acid backbones have alkene-aryl like bonds. The same spin effects for CNT apply to biomolecules.

IV. FERROCHEMISTRY OF DIAMOND FORMATION In addition to the inorganic chemical dynamics of CNT formation, another interesting chemical mechanism better determined by ferrochemistry (The Little Effect) is diamond synthesis. On the basis of ferrochemistry, the 200 year old diamond problem has been resolved. During the synthesis of diamond by both HPHT (direct and indirect) processes and H plasma processes, conditions are created whereby the magnetic field and spin polarization

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are more static over length scales greater than the size of C-C double bond and in particular over sizes greater than the diameter of aromatic rings. Such static magnetic fields polarize spin currents and spin waves to ferrochemically disrupt the hybridization of π electrons into aromatic ring, conjugated π bonds and even the π bond of C=C double bonds. The π electrons are off the internuclear axis and more easily influenced by external magnetic fields relative to the σ C-C bonds. The resulting pz off internuclear axial electrons are more easily ferrochemically spin polarized, organized, stabilized and synchronized by the external spin currents and associated magnetic fields. The accumulation and stabilization of the C(pz) electron currents allow many interactions for torqueing their magnetic orbitals from sp2 → sp3 geometry for nucleating and growing diamond. It is important to note that such magnetic environments are created by raising the pressure to 5 GPa on hot carbon-iron for the indirect catalytic method or by raising the pressure even more to 20 GPa on pure carbon for the direct autocatalytic method of diamond formation. Although the high temperatures beyond the Curie temperature diminish the ferromagnetism of the catalyst, by also increasing the high pressure (5 GPa) stronger interactions between the atoms occur so that the ferromagnetism is sustained in the iron during the indirect diamond forming processes, even above its Curie temperature. However, higher pressures and higher temperatures on pure carbon are required (20 GPa) to induce carbon magnetism for diamond formation. Here it is further suggested that by employing external strong magnetic fields on these HPHT processes, the molten iron can of its more broken bonds exhibit even stronger internal lattice magnetic fields on the order of 10,000 Tesla relative to the 1,000 Tesla fields in solid iron below the Curie temperature. Such 10,000 Tesla transient magnetic fields of the liquid iron catalyst magnetically, ferrochemically torque electrons about radii less than the aromatic ring radius and even torque radii less than the C=C double bond radius to accelerate sp2 to sp3 rehybridization of the carbon atoms and radicals. In the uncondensed H plasma process, the magnetic currents of p+ and e- in the plasma ferrochemically torque sp2 to sp3 rehybridization of carbon into diamond but on a smaller length scale relative to the iron catalytic process for polycrystalline diamond formation by the H plasma process. It is interesting to note that in the ferrocatalytic process the magnetic field correlates electrons of the catalyst for their electric and magnetic fields to ferrochemically break, rehybridize, orient, synchronize and stimulate the carbon knitting into the diamond on larger length scales. But in the gas phases H plasma, both e- and p+ magnetically rehybridize and synchronize the C knitting into polycrystalline diamond. The magnetic polarized proton spins can organize ferrochemistry just as the magnetic polarized electrons. Recently Little has independently discovered the use of lightning bolts [23] for a source of high energy polarized spin currents to accelerate sp2 to sp3 diamond formation. Therefore during both HPHT and/or H plasma processing conditions polarized magnetic spins are created wherein sp2 carbon is torque to sp3 carbon. This role of magnetic polarized p+ and e- currents for novel dynamics led RBL to discover new mechanism for inverse beta processes in the iron metal lattices and new magnetic explanations for low temperature nuclear reactions [24, 25]. It is quite beautiful that the electron screening effects for low temperature nuclear reactions [20] also screen Coulombic repulsive and attractive forces for C diffusion thru the metal catalyst and screening Coulombic attractive forces between carbon atoms during carbon bonding into both CNT and diamond formations. Moreover considering the role of both polarized p+ with polarized e- ferrochemistry allowed RBL to determine the ferrochemical basis for biochemical processes to be discussed later.

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V. FERROMAGNETISM OF LOW TEMPERATURE NUCLEAR REACTIONS The ability of strong magnetization to overcome Coulombic forces to ferrochemically accelerate and pinch CNT and diamond formations was a seed by which RBL discovered a new basis for understanding low temperature nuclear reactions. It was realized that the huge transient magnetism in metal lattices can pinch magnetic e- orbitals and p+ orbitals for inverse beta processes at low temperatures. It was further realized that deuterium in some metal lattices can be magnetically pinched by surrounding, screening magnetic electron orbitals to form helium. Recently, experimental evidence of low temperature fusion in metal lattices has been acquired by Arata [26]. Salzmann has given computational basis for the electron screening for low temperature fusion [20]. Some people call these phenomena low energy nuclear reactions, but I prefer to call them low temperature nuclear reactions, because although the temperature is low, the energy is not low. The energy of these novel unconventional nuclear phenomena is in the form of potential energy of electric and magnetic fields rather than the kinetic energy of high temperatures of the conventional nuclear processes. The lattice is able to affect the nuclear reactions by the strong high energy magnetic and electric fields it ferrochemically accumulates, organizes, focuses and stimulates. Across and down the periodic table the atoms of heavier elements have more and more positive charges in the nucleus and more valence electrons. The strong force of the nucleus binds protons and neutrons in the nucleus, but how do the electrons handle their strong repulsions. In heavy metals, lattice electrons manifest high speeds and directional acceleration for magnetic correlation and exchange to magnetically attract electrons to electrons to counter their Coulombic repulsion. It is such high magnetic fields of electrons in the metal lattices that act on hydrogen solute atoms to screen and to disrupt the electronic orbitals and ferrochemically compress them inside the Bohr radius for inverse beta processes to form neutrons. Furthermore such high magnetic electronic fields in metals can magnetically and ferrochemically screen hydrogen and deuterium nuclei for low temperature fusion in the metal lattice. One of the central themes of ferrochemistry is the ability of high magnetic field and polarized spin currents to organize and focus energies into fewer spins like a Lawrence cyclotron. Low speed spins can torque faster spin to even faster cyclic motion but the high speed smaller radial spins cannot give their energy as efficiently to spins of slower, larger spin radii. So many slow moving spins focus their energies magnetically into a few higher energy spins for high energy nuclear processes. Although high speed cyclotrons cannot give their energy to slower moving spins of larger radii, they can couple magnetically to many spins to give small quanta each to many slower spins and vice versa many slower spins can magnetically give their small quanta as a sum to a big quanta to excite a higher speed spin. There have been plenty of evidence for such low temperature nuclear reactions consistent with this magnetic model dating back over 80 years ago with Wendt [27] and Rutherford [28] works on exploding wires. Other subsequent data from Stephanakis [29], Winterberg [30] , Rahman [31] give clear evidence of neutron formation during exploding wires. For over 80 years this has not been understood. About the same time in 2005, RBL [24] and then Widom and Larsen [32] offered similar models for this inverse beta process. RBL in April 2005 proposed many e- spins in the metal collectively, magnetically and ferrochemically pinch e- and p+ into neutrons. Widom and

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Larsen in May 2005 proposed that surface e- plasmons cause inverse beta during such processes. RBL in May 2005 obtained data to support his model by driving huge currents 75,000 amps through Ag-Cu coils for many months to observe inverse beta and nuclear reactions in the magnetic coils. In these experiments in electromagnets, such currents are comparable to the currents in a weak lightning bolt. Hereby RBL proved his magnetic pinch mechanism of inverse beta and low temperature nuclear reactions. It is interesting to note Uman has determined experimentally that lightning produces X-rays [ 33]. The magnetic model of RBL explains Uman’s observed X-Rays produced at low temperatures. Although the temperature is 1000 times too low to generate X-rays, the magnetic and electric fields in lightning are huge for tremendous potential (rather than kinetic) energies to generate X-Rays. Other investigators have observed gamma rays formed in lightning bolts [34]. Just as the magnetic fields of lightning bolts can organize X-ray and gamma ray production, core electrons dynamics in the metal lattice can occur for causing nuclear reactions in the metal lattice. The strong magnetic iron lattice can withhold the strongest chemical bond N≡N triple bonds. The experimental evidence has been given by Mosier-Boss and Szpak [35] and Arata [26].

VI. FERROMAGNETIC BASIS OF THE COVALENT BOND

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A. Magnetic Chemical Bonds With the magnetic spin and orbital dynamics established during the chemical changes, now chemical reactions and bonds are considered from this magnetic perspective. Since 2000 on the basis of this work with CNT, I have demonstrated these magnetic effects on chemical bonds to many areas of chemistry including the magnetic nature of the chemical bond itself. On the basis of this work, I have forged a reconsideration of the nature of the bond, bond rearrangements, and chemical reactions. In this reconsideration, the chemical bond is determined to be magnetic in and of itself. The ionic bond is electrical, but the magnetism of the ionic bond is internal to the ions and between the moving ions of the bond. But, the covalent bond is both electric and magnetic in its nature having high speed electron motions (magnetic field) across two or more atoms across the ions of the bonds. Berzelius first proposed the ionic bond and the Coulombic interactions for understanding compounds. GN Lewis discovered the covalent bond with a lot of controversy surrounding its physical nature, which was later expanded on quantum mechanically by Heitler-London and Linus Pauling. The binding nature of the covalent bond is the source of the controversy. But how can shared electrons produce the electric, Coulombic binding between atoms of the same element like carbon to form molecules on an ionic basis? After here considering important milestones in magnetism; electricity; the theory of matter; and atoms and molecules, now a more detail magnetic consideration of bonds and bond dynamics between atoms in molecules is given. For such a covalent bond, the Berzelius ionicity is diminished by the sharing of the electrons. Here, it is suggested that magnetism makes up for the lowered ionic, Coulombic binding by the magnetism of electronic motion contributing to holding the atoms together in bondage! Two or more atoms having odd electrons can attract by the magnetic force between the odd electron orbitals of the involved atoms. The nuclei of the

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atoms are in addition Coulombically bound by the negative charges of the magnetically exchanged electrons. The controversy surrounding the Lewis covalent bond surrounds this missing magnetic interpretation as presented here. The covalent bond has been perceived by the conventional theory as a mutual attraction of two or more nuclei to shared electrons, relative to the lab frame with stationary nuclei and stationary electrons attracting Coulombically. But RB Little notes that relative orbital motions of the electrons of the covalent bond and the magnetism of such relative charge motion for bonding. In the relative motion, the chemical bond can be interpreted as a magnetic attraction of the electrons to each other and to the nuclei and a magnetic gluing of the electrons in the bond. Therefore here it is proposed, that the covalent bond is both magnetic and electric phenomena. Valence is magnetic and electric phenomena. On the basis of the Hamiltonian, various energy terms determine the atomic, molecular and lattice structures. Magnetic electrons Coulombically bind to a nucleus causing the atom. The magnetic electrons also Coulombically repel causing the shells. The Coulombic electronic repulsion is balanced and countered by a magnetic attraction of the electrons in their orbital motions in their relativistic revolutionary motions and in their spin motions. The relative energies of these interactions reflect that the Coulomb energy is 100 times the magnetic energy and the relative size of the systems, the number of charges, the relative kinetic to potential energy and the times involved. In general, the energy of Coulombic attraction of e- to nucleus is greater (>) than the energy of e--e- Coulombic repulsion > e--eorbital magnetic attraction > e--e- orbital to spin magnetic attraction> e--e- spin --spin magnetic attraction > e--nuclear orbital spin attraction> e--e- spin spin attraction> e- – nuclear spin---spin attraction. In different atoms, molecules and lattices the relative order of magnitudes of these electromagnetic interactions can vary. e- accelerates different speeds “l” (azimuthally). e- accelerate different directions “ml” (magnetically).

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B. Magnetic Valence Magnetism causes quantum mechanics, wave mechanics and valence and covalence. So the motions (currents) of the electrons within the valence of the atom cause magnetism and symmetry of valence, and the attraction (potential) of the positive nucleus to the negative magnetic electron cloud causes valence. The magnetic pairings of electrons in atoms balance their motions for balanced magnetism or diamagnetism. The octet rule is evidence of this magnetic effect on valence, because Coulombic forces alone cannot rationalize the octet rule, i.e... e--e- Coulombic repulsion cannot explains O2- ion and its stability. In electron deficient elements, there is not enough positive nuclear charge to Coulombically fill the subshell, but a magnetic electronic attraction (although weaker but still involved) (in addition to their Coulombic electric attraction to the nucleus which is opposed by their Coulombic e--ereupulsions) of these valence electrons can fill the valence shells for octet rule. Here it is suggested that the electrons in valence exhibit finer, immeasurable magnetic motions than orbital motions, called magnetic revolutional motions. The e- relativistically revolves within the magnetic orbital and it magnetically spins within its magnetically, relativistically revolving motion. The magnetic revolutionary motion is not finer than the magnetic spin motion but the relativistic revolutionary motion is a finer motion than the orbital e- motion. It is such increase relativistic revolutionary e -motion by photon absorption within the orbital

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that causes changes in orbital states or photo excitation or emission of the valence, covalence or lattice. The increased revolutionary motion and its magnetism interact with the spin and orbital motions of itself and other valence/core electrons to kick the electron into outer excited motions or relax it into lower levels. So the e- in the valence of the atom exhibits magnetic spin + magnetic revolutionary + magnetic orbital motions = magnetic spinrevorbital motion. Within the magnetic spinrevorbital motion, the electron on the basis of Maxwell’s equation radiates photons. But the e- does not collapse on the nucleus because of its confined interactions. The confined interacting electrons reabsorb the released photons (virtual) before they can collapse on the nucleus. Here it is suggested that quantum mechanics is an electromagnetic effect of electrons in the electric and magnetic fields within the atom and internal photons of their self-interactions and interactions with the nucleus and other electrons. Only certain momenta and magnetic spinrevorbital motions (discontinuum states) are allowed for constructive self-interactions of the valence electrons for allowed states. Other interactions and magnetic spinrevorbital motions (continuum states) can exist but the magnetic motions are not balanced (forbidden states) for allowed constructive/destructive self-interactions, so photons are released and/or reabsorbed to form discontinuum stable (allowed) states of cooperative self-interactions. The time-independent wavefunctions (Ψ) are patterns of electric and magnetic fields confined about the nucleus that allow these constructive/destructive self-interactions of the particles and/or fields. The time-dependent wave functions are patterns of electric and magnetic fields plus photons associated with changing fields that allow self-interactions of the electrons and nuclei. Photophysics involves an atom absorbing external photons with change in magnetic valence or the atom emitting a photon with change in magnetic valence. Here it is suggested that the magnetic relativistic revolutionary motions within the orbital are the basis of continuum states in atoms and molecules. The magnetic revolutionary motions are so rapid (relativistic) within the magnetic orbitals that they cannot be observed experimentally due to the limiting speed of light and the speed limit of light, the very small confining distance, and the short time intervals pertinent to the interior atom. Here it is suggested that this magnetic revolutionary motion within orbitals is Einstein’s hidden variable and the connection between quantum mechanics and relativity.

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C. Magnetic Covalence and Stereochemistry Chemical bonds are a moving charges and electric quanta of currents, having magnetism and responding to internal and external magnetic fields. Covalence involves magnetism. Magnetic diamond formation has already been discussed and is evidence of this ferrochemistry in inorganic chemistry. Magnetic hydrocarbon chemistry and biochemistry will be discussed later. The magnetism of covalence is due to electron flow and consequent magnetism across two or more atoms. Net magnetism occurs during changing covalence between atoms, because the balanced electronic motions of the bonds are altered for unbalanced e- motions and hence net magnetism. This is essentially the basis for unconventional magnetism in carbonaceous substances first conceived by the author [1-3]. Magnetism is also relevant for ionic chemical reactions as transient magnetic pulses during the reactions. The Berzelius ionic bond has the magnetism confined to the valence of ions (cations and anions) with the Coulomb binding of the ions for the ionic lattice. Electrons are

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more localized in ionic bonds. But the covalent bonds delocalize the electrons and extend the currents and magnetism across two or more atoms in confined space and directions (momentum). In the covalence, the magnetism causes specific momentum of electrons for symmetry of bonds. The structures of molecules are determined by e--e- magnetic interactions between the magnetically bound atoms. Coulombic forces alone cannot explain the symmetries and structures in molecules. Different elements have different abilities to accelerate the electron currents across many atoms with consequent different electronic symmetries and structures and different compounds and lattice symmetries. Metals have high speed electrons (e-) with intense e--e- magnetic interactions are very unique in iron (Fe) for interesting ferromagnetic lattice, nuclear and chemical processes. Next such magnetic effects on valence, covalence, covalence dynamics and pycnonuclear processes are extended to biological systems in this perspective. This extension to biological systems is done by considering the H atom in metal lattices in analog to H atom in water and nonmetal nanolattices of aqueous solutions of biomolecules.

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D. Magnetic Acceleration of Orbital Symmetry Nonmetals have lower electronic speeds with stronger nuclear ---e- interactions, as in the unique carbon atom having no core p subshell electronic momenta. Carbon atoms act as an electron and/or a proton source-sink for its role in the center of life. p+ in antibonding orbitals of molecules can strengthen bonds. The magnetism of the acceleration of the electrons across the valence of many atoms increases with the number of electrons in the valence of each involved atom, causing internal magnetism of the orbital currents across many atoms. Electron deficient elements have rehybridization constraints due to the limited number of valence magnetic electrons to accelerate the hybridization and the Little Effect. Electron precise carbon has the high bonding capacity but lacks the sufficient internal magnetic currents under ambient conditions to rehybridize its electrons to higher bond order sp3. The electron excess elements nitrogen, oxygen and fluorine have less difficulty in the rehybridization of their valence electrons due to them having more valence electrons relative to carbon. Completing octet is a magnetic effect. It is important to note that relative to hydrocarbons, functional groups containing nitrogen, oxygen, phosphorus, sulfur and some transition metal cations assist the rehybridization chemistry of carbon by providing their orbital electronic/protonic motions to assist carbon in rehybridizing its valence electrons. Such rehybridizing roles of these functional groups result from internal base catalysis and/or acid catalysis! These functional groups help carbon magnetically twirl its electrons into various covalence symmetries. Third row and heavier nonmetals have less difficulty magnetically rehybridizing their electrons due to their inner shell core electrons for internal patterns. Such issues of magnetic rehybridizing also play a role in 3d transition metals and their lower bond order and ferromagnetism. By magnetically accelerating ml, protons can also assist rehybridization for explaining acid catalysis. The magnetism within atoms accelerates orbits into orbitals. The magnetic orbitals (l) accelerate ml. The orbital – orbital interactions can magnetically accelerate hybridization, however polarized spins more strongly magnetically accelerate orbital rehybridization, magnetism of atomic orbitals and hybrid orbitals accelerate magnetic molecular orbitals. Magnetic mixing molecular orbitals accelerate resonance, tautomerism and conjugation.

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Magnetically mixing, cyclic, conjugated orbitals yield aromaticity for odd number of electron pairs of ring for the consequent magnetic lowering of energy by magnetic motions of the unbalanced odd e- pair. Magnetic mixing of molecular orbitals yields lattices and bands. Magnetic mixing and hybridization therefore are involved in chemical reactions. Bosonic, magnetic hybridization causes Woodward Hoffmann chemical dynamics. But fermionic, magnetic hybridization causes the Little Effect and non-Woodward Hoffmann chemical dynamics.

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E. Magnetic Chemical Reactions and Chemical Equilibriums Chemical reactions are currents of magnetic electron(s). Electric fields of nuclear attractions and electric fields of e--e- repulsions drive chemical reactions. But in many chemically reacting systems, internal and external magnetic fields can influence and drive chemical reactions also. The magnetic, correlational e- and/or p+ speeds can compete with Coulombic and exchange energies. The chemical bond involves electrons bound by protons of the nucleus and magnetic e--e- interactions of these bound electrons. A new kind of bonding in this perspective of bonding in water is described by p+ orbitals in water with its hydrogen bonding. Bond rearrangements occur by magnetic electron flows or magnetic proton flows (electric currents within and on the lattice, molecular, atomic, and subatomic scales) during chemical reactions of such charge flow. Davy demonstrated electricity can alter chemical bonds by activating decomposition. Here it is wondered and realized that the magnetism can organize chemical construction of molecules. Here in this perspective, strong and weak acid and base reactions are shown to inherently have magnetic fields associated with their chemical dynamics. Strong acid-base reactions have strong magnetic field pulses occurring during the rapid charge flows associated with their reactions. During weak acidbase reactions with their oscillating equilibriums, associated magnetic fields oscillate with the oscillating charge flows to induce cycles when many such interacting non-equilibrating chemical reactions are magnetically coupled and intermixed. Equilibrium and cyclic processes can yield different states. Structures of molecules arise due to magnetic e--einteractions or magnetic current - current interactions or magnetic spin-spin and orbital-spin interactions, which lower repulsion of e- currents between atoms in molecules. Both dipole moments and magnetic moments exist and are important in molecules and molecular dynamics. Stronger magnetic effects occur at the mesoscopic and submesoscopic levels. On the basis of such molecular magnetic moments, external magnetic fields have been demonstrated to rotate molecules and rotate functional groups [36]. Since structures are due to internal magnetic (spin-orbital) current interactions; then structural changes can be induced by changing magnetic currents. Both internal and external spin currents and associated and magnetic fields can drive such chemically dynamic currents. External polarized charges can flow into antibonding orbitals to weaken bonds and to cause/prevent rotation of coordinates for bond symmetry alterations for magnetically organized structures and altered structures, geometries and stereochemistries. Unlike the electric force, the magnetic force acts perpendicular and out of line and out of plane to internuclear motions and e- motions to explain the 3 dimensional accelerated magnetic orbitals and orbital dynamics in atoms, hybrids, molecular orbitals for conjugation, aromaticity, resonance, tautomerism of lattices and during chemical reactions. Here magnetic currents (both external and internal) are shown

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important for ferrochemically organizing these chemical bonds and lattice rearrangements. This is the essence of the Little Effect of spin polarized and associated magnetic fields organizing chemical and nuclear bond rearrangements.

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F. Magnetic Catalysis On the basis of this magnetic consideration of electrons in atoms, molecules, and lattices, catalysis can be reasoned as a result of the catalyst presenting more complex magnetic patterns of electronic (protonic) motions not inherent in B, C, N, O or other atoms! Also the p+ in aqueous solution have similar abilities to accelerate complex magnetic patterns of other p+, e- and H bonds for protein and nucleic acid structures and structural dynamics. Magnetic environments can thereby change the Hamiltonian in un-precedented manners! By RBL, metals by magnetic electron transfer take the nonmetals’ electrons and magnetically accelerate them into complex orbital patterns and then give the electrons back to the nonmetal elements but with altered orbital symmetry to shift the covalent bonding! Furthermore by RBL, ferrometals catalyze many carbon atoms by spin polarized electrons for ferrochemically stimulated, concerted, and synchronized orbital dynamics (Little Effect). It is interesting to compare this ferrochemistry of the Little Effect to the photophysics of LaPorte and echanging orbitals S1 → S2 and/or T1 → T2 for Δl ≠ 0, and also to compare this ferrochemistry to the photophysics of Kasha/El-Sayed Ti → Si Δ l ≠ 0. Whereas in chemistry the Woodward Hoffmann rule determines Δl = 0 during chemical reactions for the preservation of orbital symmetry, the Little Effect considers novel dynamics of spin-orbital mixing during chemical reactions whereby Δs ≠ 0 and/or Δl ≠ 0 for Δl = Σ si along the chemical reaction trajectory. For polarized magnetic currents and polarized spins, the interactions can polarize other electrons to exist within the same orbital symmetry with like spins but in different orbitals. For unpolarized currents, the spins are unpolarized so electrons exist in same orbitals with paired unlike spins moving in opposite directions or the electrons exist in different orbital symmetry with different spin symmetries. So electrons in the same orbitals attract by both orbital-orbital attraction and spin - spin magnetic attraction. Such interpretations explain the radical pair effect as the bonding of radicals requires the antiferromagnetically coupling of their lone electron orbitals. The Little Effect considers such effects during many chemically reacting reactions with the added many spin-orbital interactions. Rather than the pair of radicals, the Little Effect considers many spins with the emergence that many radicals can self interact to alter the orbital symmetry. The analogies of polarized spins not being able to unpolarize spin, to change orbital current, for orbital exchange of physical and chemical events are evidenced in Kasha/El-Sayed Effect, Woodward Hoffman Effect, and La Porte Rule. But RBL discovered the interactions of many spins for altering orbital motions. Therefore, by the Little Effect unpaired electrons in correlated currents can by spin exchange transform the paired electrons in exchange currents and vice versa. Moreover such spin dynamics can shift the symmetries of correlated molecular and lattice currents and exchange molecular and lattice currents.

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G. First Experimental Magnetic Organized Chemical Dynamics Since Lewis, no one has been able to explore the magnetic influence on the valence, covalence and alteration (reaction) of covalence, computationally or experimentally until now. Density functional theory has limitations for strongly magnetic systems [37]. The technology of electromagnets [38] has not advanced enough to alter valence or covalence. But unlike other investigators, RB Little first experimentally probed the ability of strong magnetic field on chemical reactions by using the inherent huge internal magnetic fields in iron rather than being limited only to the feeble external man-made magnetic field. Using such strong fields in iron lattice with some perturbation by strong external DC magnet, Little predicted and observed magnetic driven valence and covalence alterations during chemical reactions! The Little Effect was discovered by RB Little! Whereas others only used the currently available solenoidal magnets [38] to study its weaker effects on the transport and optical properties, RBL combines the much stronger lattice fields of iron with the solenoidal external magnet to demonstrate that the stronger magnetic field can alter valence and covalence during chemical reactions for ferrochemistry. RBL put the magnetism directly in the chemical dynamics by putting the iron in chemical reaction for stronger effects on the chemical dynamics in analog to the nineteenth century development of the internal combustion engine whereby the fire was directly put into the cylinder to replace the steam engine with the fire outside the cylinder. By the iron in the fire, the catalyst directly ferrochemically exchanges spin with covalence of the carbon to bind Fe-Fe atoms, to loosen C-C bonds and to shift the symmetry of C-C bonds to ferrochemically catalyze chemical reactions of carbon. The technology of external solenoidal magnetic fields has not advanced for strong enough fields to cause such modulation of chemical reactions. It is interesting to wonder if the iron in the engine reduces the combustion efficiency and also if the engine can be magnetically modified to break atmospheric nitrogen for a new source of power?

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H. Extension of Fermions in Biochemical Reactions Unlike inorganic chemistry and organic chemistry, biochemistry involves many varied functional groups bound by alkane-alkene-aryl (graphitic-diamond like) polymeric backbones with nano-aqueous regions and nano-nonpolar regions for multiple competing nucleophilic and electrophilic magneto-reactions and currents. Such many body, many weak acid-weak base reactions in non-equilibriums cause varied equilibriums, interacting chemical cycles, resonance and tautomeric phenomena in biochemistry to be discussed later. In this perspective, a wave nature with relativistic aspects is given to biochemical processes. Biochemical reactions are moving electric and magnetic fields and light. In such biosystems, the import of lone e- pairs, of p+ in antibonding orbitals, of p+, and of polyoxoanion is stressed to play important roles in the biochemical reactions. Biochemical molecules may be considered as continuously transforming large basis sets that continuously organize smaller basis sets.

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I. Wave Nature of Biochemical Reactions and Lattice Reactions On the basis of the magnetism during chemical reactions, it is quite interesting to note the emergence of chemically reactive wavefunctions, which arise in the confined many body chemically reacting systems in biochemistry, wherein many weak acid-weak base combinations and p+ transfer reactions occur via the surrounding water and the magnetic interactions between the many chemical equilibriums causing a ferrochemically synchronized, coherent, stimulated and organized many-bond rearrangements for chemically reactive, time dependent wavefunctions. Magnetic oscillations distinguish living from nonliving chemical systems. Such chemically reactive time dependent wave functions are quantized and explain the specificity of biochemical processes and stereochemistry and macromolecular mechanics of protein enzymatic activity; nuclei acid replication, transcription and translation; anabolic processes of photosynthesis, gluconeogenesis; and catabolic processes of glycolysis and citric acid cycle. During such processes the many p+ transfer reactions and many p+ orbitals extend in space for wave natures and wave functions of biochemical reactions. Such biochemical reactions are moving electric and magnetic fields. Charges (electric fields) and charge motions (magnetic fields) determine spatially, temporally extended Ψ wavefunctions, which strengthen or weaken bonds for stereochemical dynamics of structural changes, bond rearrangements, conformational changes, folding, coiling and supercoiling.

VII. FERROMAGNETISM AND ORGANIC CHEMISTRY

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A. Setting On the basis of this established internal ferromagnetic nature of the chemical bond, the ferromagnetic nature and reactivity of common organic classes of compounds are considered in this section. Organic compounds have a variety of different compositions and structures which have traditionally within organic chemistry been explored in bulk homogenous amounts within nonpolar or slightly polar solutions. Whereas organic chemistry has explored bulk homogeneous amounts, the life emerging aspects of nanoscale heterogeneous portions are considered in the following biochemistry section. But for now, the magnetic aspects of various electronic structures of some of these compounds are considered in new ways in this section. The differing internal magnetism and magnetic changes during the reactions of common organic compounds are introduced and demonstrated in this section.

B. Magnetic Alkanes Alkanes form a relatively inert class of molecules, having carbon and hydrogen, which have similar electronegativities. The similar electronegativities point toward very similar charge affinities and lack of charge differences of C and H for difficult ionic and Coulombic accounts of hydrocarbon bonding and reactions. The hydrocarbons therefore form nonpolar covalent bonds. With very little electric resistance to e- flow between the C and H, the e- flow

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between the atoms form magnetism and covalence. The hydrocarbon covalent bonds consist of two internal magnetic electron currents from each atom of the bond from collective spinpaired charge motions (diamagnetism) of spinrevorbital motions of electrons with the associated attraction to the e- pairs by the positive nuclei to the resulting diamagnetically balanced moving electron pairs. As a result of their nonpolar bonds, hydrocarbons require extreme conditions of high temperature and high pressure, UV irradiation, and/or chemical induction by electronegative halogens for their activations for chemical reactions. The hydrocarbon inertness is associated with the lack of internal electric dipole (C and H having similar electronegativities) for electrophiles or nucleophiles to attack. However, in this perspective external magnetization is introduced as a basis for activating alkyl hydrocarbon where by external magnetic fields exploit and disrupt the balanced internal currents/magnetism of C-C and C-H bonds of alkanes for magnetically and ferrochemically polarizing the bonds to induce chemical reactivity under lower temperature conditions. External polarized charges and magnetic fields can thereby ferrochemically bend, compress and rarefy the internal currents of the covalent bonds to activate chemical reactions: 1) as during CNT and diamond formations from hydrocarbon sources under ferromagnetic, catalytic transition metals [1,2,4,6]; 2) as during the functionalization of the nanodiamond surface; 3) as during terrestrial HPHT conversion of CO2 + H2O to hydrocarbons [39]; 4) as during the FeS cluster catalyzed de-fixation of CO2 from air into H2O to form sugars by enzymes during photosynthesis. Such conditions for chemical reactions of these systems are better understood on this basis of magnetic activation of hydrocarbon chemistry. The internal, balanced magnetism in the alkyl compounds subjects them to radical reactions and the magnetics of radicals and magnetically induced reactions by stimulating, orienting, and synchronizing many hydrocarbon radicals by external polarized spins or magnetic fields for their combinative and condensation reactions or bond rearrangements. The backbones of many biomolecules have alkyl portions, which contribute to greater stability and inertness as in the strong diamond-like backbone of protein relative to the reactive side chains.

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C. Magnetic Alkenes and Alkynes Alkenes have C=C double bonds, containing σ and π bonds between the carbon atoms. The multiple bonds contain 4e- or 2e- in the pairs for greater charge density in the bonds and more e- motions between the two carbon atoms of the bonds for greater internal magnetism in C=C double bond relative to the single C-C σ bond. Such faster electronic motion can lead to relativistic-like motion in the π bond of graphene. Just as in the hydrocarbon, the two carbon atoms have very little electric resistance to currents between them and for π symmetry even less resistance relative to σ symmetry. The π electrons are accelerated off the internuclear axis relative to the on nuclear axial acceleration of σ electron pairs. Such off internuclear axial electronic motions require and acquire faster internal motion to pair the two negative charges of the π bond for a greater internal magnetic binding of the π electron pair bonds relative to the σ electron pair bonds. The 2 carbon nuclei assist binding the σ electrons Coulombically, but the π electrons are more magnetically bound by high speed internal electronic motions. Such high speed, internal magnetic π electrons are in analog to d electrons in transition metals due to their high speeds and momenta and off internuclear axial motions. Indeed, this is the basis for some of the observed similar properties (conductive, magnetism, quantum Hall

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Effect, and Dirac particles) of graphite, graphene and CNT relative to transition metals. Such magnetic π electrons are thereby more subject to external magnetic fields and are the basis of the original conception of carbon’s ferromagnetism in distorted, defective, and disordered graphene by RBL in 2000 [1-3]. This magnetic nature of the π electrons was reasoned to allow the ability of ferrometals to stimulate, synchronize, energize and organize the carbon bonds and symmetry into graphene and CNT. The magnetic π electrons in graphene are ferrochemically subject to both electrophilic (Coulombically) and nucleophilic (Coulombically) reactions of alkenes and these reactions surely require a magnetic interpretation. For these reasons, the unconjugated alkenes tend to be more reactive than alkanes. The stereospecificity during alkene addition can be beautifully interpreted in biochemistry by magnetic patterns of enzymes organizing the electrophilic paths for syn and anti addition/elimination reactions. Alkynes have similar properties to alkenes. The triple bond in alkynes causes even denser e- regions, faster motions and stronger internal magnetism. The stronger magnetism in alkynes leads to greater acidity of alkyne hydrogens relative to alkene and alkyne hydrogens due to the magnetic stabilization and motions of the resulting formed negative charge of the conjugated base of the alkyne. The backbones of many biomolecules have alkene portions which contribute both to reactivity and flexibility of the backbone and also to the great stability and strength of the backbone relative to the more reactive side chains.

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D. Magnetic Resonance and Tautomerism and Superconductivity Indeed, such stabilization of the base anions of alkynes in the strong internal magnetic field of the multiple bonds in the molecules is an excellent new basis for understanding resonance. The internal magnetic fields of the π bonds stabilize the resulting charged anion. Resonance is the internal ferrochemical motions of the incipient negative charges in the internal magnetic fields of molecules. Magnetism ferrochemically holds, stimulates, integrates and synchronizes reversible resonating, self-interactions of the resonant electronic distributions. Protons and cations can also move in the internal magnetic fields of molecular structures, for ferrochemically explaining tautomerism. Magnetism ferrochemically stimulates, holds, integrates, blends and synchronizes the resonating, reversible selfinteractions of e- and nuclei motions of the tautomeric distributions. Resonance and tautomerism are consequences of the internal and net magnetism and the internal magnetism to ferrochemically organize reversible, internal bond rearrangements in carbonaceous structures. Magnetism causes a ferrochemical synchronization of e- and p+ motions by selfinteractions of internal nucleophiles and/or electrophiles. Such internal magnetism and its acceleration of internal π bonds cause the unique properties and chemical distinction of conjugated alkenes and alkynes relative to unconjugated structures. Similar π bonded resonant and/or tautomeric systems can involve other nonmetals in particular of the second row (N, O) as in NO3-, SO42- PO43- and NH4+. The electron excess nature of these elements (O and N) and H bonds contribute net charge (e-,p+) and charge motions (magnetism) for couple internal charge and coupling internal charge motions, which can be tossed about by the internal magnetism for strong resonance and tautomeric effects. The oxidizing power of polyoxoanions can be ferrochemically understood in this way. High temperature superconductivity in polyoxoanions can be understood ferrochemically in this way as a

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macroscopic magnetic effect for bulk resonance and tautomerism among many atoms in charge transport. High temperature superconductivity can be understood as a macroscale resonance and tautomeric effect of the charge transport.

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E. Magnetics of Aromaticity Similar magnetic effects of multiple conjugated π bonds in ring lead to their greater stability relative to branched unconjugated π bonds. A net magnetism and unbalanced motion of conjugated π electrons in rings containing an odd numbers of e- pair (2n+1) arise due to the added energetic stability of the unbalanced π electron pair motion causing what has been called aromaticity. The Kekule rule for aromaticity is that the ring contains (2n+1) conjugated electron pairs, which is an odd number of ring e -pairs. The odd number of e- pairs of the ring allows an unbalanced magnetic motion of one of the e----e- pairs for possible high speed and strong internal magnetism of the odd electron pair for consequent greater internal magnetic attraction of all the π electrons to counter their e----e- Coulombic repulsion between all the 2n+1 pairs for magnetically denser e- regions for shorter bond lengths and greater orbital overlaps for stronger bonding (greater stability) of the carbon nuclei of the ring on a magnetic basis. Such high speed π electrons of aromaticity explain the recent relativistic-like nature in graphene and the Landau levels in graphene. The extremely, high kinetic energy (relativisticlike speeds) of the odd e----e- pair and its internal magnetism effectively compete with attacking electrophiles and entering nucleophiles for greater ring stability relative to noncyclic alkenes. Such effects are important for aromatic rings to ferrochemically organize, stimulate, and synchronize multiple electrophiles or nucleophiles during the breakage and reformation of aromatic systems with relevance for biochemical systems like nucleic acids. The magnetic chemistry of the odd π ring systems ferrochemically organizes, stimulates and synchronizes multiple electrophiles and nucleophiles of addition-elimination reactions for organizing effects in biochemical reactions. The internal magnetism of such aromatic and fused rings is further exemplified by iron’s ability to ferrochemically catalyze their transformations. The internal ferromagnetism of iron nicely ferrochemically couples to the internal magnetism in the aromatic ring. The internal magnetism in alkenes explains pericyclic reactions. The internal magnetics in these aromatic compounds explain the carcinogenic nature of PAH and heterocycles [40]. This strong internal π electron magnetism also explains the excellent ability of external magnetic fields to align CNT [41] and the ability of uncollapsed CNT to resist the oxidation of attached iron [22]. The magnetic aspects of π aromatic rings should be kept in mind in CNT chemistry and functionalizations. The hydrogen absorption of CNT just as H2 absorption by metals is magnetic in nature and is better explained on a ferrochemical basis. This magnetic nature of the aromatic π rings is consistent with recent ferrocarbon observations. Esquinazi damage these graphitic bonds by proton bombardment for his subsequent observations of ferromagnetic carbon [15]. Makarova also damaged graphene bonds in fullerenes by high pressure high temperature treatment for her subsequent observations of ferromagnetic carbon in fused C60 polymer [17]. Rode used very intense laser pulses to disrupt the graphite lattice to observe unbalance orbital motions for net magnetism [16]. This internal magnetic nature of aromatic rings is demonstrated by the proton’s ability to ferrochemically disrupt the balanced magnetic currents (diamagnetism) of the bonds for net magnetism after intense p+

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bombardment of graphite (Esquinazi). The high temperature, high pressure bond rearrangement and polymerization of C60 with its consequent stressed and strained bonds and unbalanced currents cause its ferromagnetism (Makarova). The bond disorder, stress and strain in graphite by intense laser ablation cause net magnetism in carbon nanofoam (Rode).

F. Magnetic Polar Covalent Bonds Whereas hydrocarbons, alkanes, alkenes, alkynes and aromatic compounds have nonpolar bonds, carbon bound to more electronegative nonmetals like halogen, oxygen, nitrogen, sulfur, phosphorus results in polar covalent bonds with positively biased carbon. This difference in the electronegativities causes bond dipole in addition to the internal magnetism of the shared electron currents. The polar covalent bond involves separated, magnetic, fractional charges within the magnetic electron cloud of the polar current bond. The resulting magnetic electric bonds accelerate the separated electric poles internally to the bond. Such magnetic, partially Coulombic polarized orbital currents within the bond more readily subject the internal dipoles to chemical dynamics of attacking nucleophiles and electrophiles during polar reactions relative to nonpolar bonds of hydrocarbons. Moreover, the magnetically coupled poles of the polar bonds are ferrochemically subject to external spins and magnetic fields. It is important to emphasize that changing solvent polarity as in biomolecular complexes causes physically driven changes in the internal magnetic circulations of these dipoles for emerging properties in proteins and nucleic acids. Polar organic molecules exhibit some solubility in water depending on the size of the molecules. Water has one of the largest dipoles for its size and mass for explaining its uniqueness and electronic, magnetic, thermal, optical and chemical properties. Water is amphoteric, possibly acidic or basic. The motion of the water dipole has resulted in its observed magnetism [42]. Moreover the unusual properties of nanovolumes of water have been reported [43]. The integration of water with both many, varied polar and nonpolar organic substances on the nanoscale is presented as the basis and essence of biochemistry in Section VIII.

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G. Magnetic Alcohols and Thiols Thiols and alcohols can be understood as organic derivatives of water but with smaller dipoles with the ability to form magnetically weaker hydrogen bonds for bigger p+ orbitals relative to water. Alcohols and thiols by their weak dipoles are weak acids. Due to the larger difference in electronegatives, thiols are stronger nucleophiles than alcohols. The magnetic nature of the valence and covalence gives stability to the conjugate negatively charged conjugate base anions of thiols and alcohols. The two lone e- pairs on O and S of alcohols and thiols contribute more internal nucleophilic dynamics relative to other types of functional groups. The internal magnetic motion of the charge separation of the bond dipole causes reactivity of alcohols and thiols by subjecting them more to nucleophiles and electrophiles relative to alkanes. The stronger magnetism of the internal electric dipoles between alcohols and thiols with attacking electrophiles and nucleophiles causes synchronization and organization of the reactants and the orbital dynamics.

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H. Magnetics of Carbon Nucleophiles and Electrophiles In addition to positive biased C centers of polar magnetic bonds, negatively biased C centers can be formed by C bonded to less electronegative elements: C-B, C-Mg, C-Li. Such compounds have negatively biased carbon with partial electric poles under the magnetism of the bonds for causing nucleophilicity of the carbon center. Indeed, Grignard reagent may be interpreted as a negatively biased magnetic C center. The reaction of Grignard reagent (MgC-X) with an alcohol involves magnetic and electrophilic carbon of alcohols binding a magnetic and nucleophilic carbon of Grignard reagent. Here, the new magnetic consideration is relevant for such reactions in particular for understanding the stereochemistry when many such nucleophiles and electrophiles are chiral centers and act concertedly and interactingly as in biochemical systems. The different magnetisms about the chiral centers cause different enantiomeric products. Ethers are also water derivatives and they are slightly polar with the capacity for hydrogen bonding and strong dipolar interactions.

I. Magnetic Amines

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The inversion ability of nitrogen via the intra atomic nucleophilic attack contributes unique features to amines. The amines are not as acidic as the alcohols. Amines are organic derivative of ammonia. Amines are basic highly polar and strongly interacting. They are basic nucleophiles. The lone e- pair of the amines is magnetically capable of internally inverting about the N nucleus by an internal nucleophilic attack within the N atom. Such internal lone e- pair dynamics and magnetism attribute interesting properties to amines. It is interesting to note the energy of internal magnetic N inversion is 2 times the C-C magnetic bond rotation. Such similar energy quanta allow similar magnetic torque of the nitrogen e- lone pair of its inversion and this inversion energy is twice the magnetic torque about C-C bond. Therefore such magnetic, internal inversion about the N of amines in proteins can couple with rotation about carbonyl carbon-carbon bond and C alpha – to C-N bonds. Being nucleophilic and basic due to the lone e- pairs, the amines are chemically reactive with electrophiles. The magnetic modulated internal electric dipole of the N-C bond of amines allows strong magnetic synchronizing, organizing and coupling of amines to nucleophiles and electrophiles. Such magnetic organization of many electrophilic and nucleophilic reactions including amines plays important roles in chemical patterns in biochemistry.

J. Magnetic Carbonyls and Nitriles Just as polarizing the magnetic σ electron cloud increases chemical reactivity, polarizing the π magnetic electron clouds results in even greater chemical reactivity about carbonyl and nitrile double bonds. Traditionally, the greater chemical lability of the polar π carbon systems such as C=O carbonyls and C≡N (nitriles) has been attributed to the lesser steric hindrance about the carbon center to nucleophilic attack. But here, further magnetic factors are given for the greater reactivity about the ferrochemically polarized magnetic π carbon centers of C=O and C≡N. Just as was the case of the polar σ bonds, the magnetic field of the polar double bond ferrochemically torques the charge separation within the bonds but in the polarized π

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bond case, off internuclear axial asymmetry of the electric polar and magnetic π cloud allows easier external magnetic and electric influence by surrounding, approaching nucleophiles and electrophiles and external spins and associated magnetic fields. Such internal magnetically modulated motions of the π cloud and the σ cloud are important for providing magnetic and ferrochemical coupling of the π cloud to approaching magnetic nucleophiles and/or magnetic electrophiles in addition to the conventional electric dipolar coupling. Here it is shown that the magnetic coupling between internal magnetic and electric polar electron clouds is important for stimulating, orienting and synchronizing the electrons between the molecules of the reactants in order to ferromagnetically couple them into antibonding molecular orbitals during decomposition or in order to antiferromagnetically couple them into the molecular orbitals during combinations to form the products. Without the magnetic synchronization of the multi-electronic motions between the reactants, the bonds of the products cannot form. Such synchronization and stimulation of electrons in multiple reactants become even more nontrivial and important for many, many coupled reactants and macromolecular chemistry. Such ferrochemical magnetic stimulation, synchronization and organization of reactants are considered in depth in the biochemical section next. Such magnetic interactions of nucleophiles with the polar π cloud of C=O controls the stereochemistry. Such magnetic stimulation and synchronization of multiple bond rearrangements when many bonds are selfinteracting is the physical basis for conjugation, resonance, tautomerism, hyperconjugation, aromaticity and as well as suggested here superconductivity. High temperature superconductivity is a chemical effect as well as a physical effect. The polyoxoanionic structures of common high temperature superconductors are consistent with the theory proposed here. Such magnetism of attacking nucleophiles and electrophiles and the carbonyl center determines the stereochemistry of syn or anti addition reactions.

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K. Magnetic Carbonyl Resonance and Tautomerism Just as resonance and tautomerism are magnetically driven in alkenes, aromatics and polar covalent bonds by the internal magnetism ferrochemically torqueing electronic orbitals, p+ orbitals and/or internal electric dipoles between atoms and about atoms, magnetism plays important roles in resonance and tautomerism in polar π bonded systems. The internal magnetism readily tosses the π bond dipole between the atoms and on the atoms of the compounds for various resonant and tautomeric structures. Relative to the polar sigma bond, the polar π bond allows the more facile torque of the dipole across the two atoms as in the C+O- ↔ C=O resonance. The resonance of a carbonyl (C+-O- ↔ C=O) may be understood ferrochemically as the C+-O- polar magnetic σ bond magnetically sucking the lone e- pair of the O- into the π magnetic orbital of C=O to electrically drive the rehybridization internally. The magnetic moment of the σ bond of C+-O- ferrochemically torques the lone e- pair of oxygen into π molecular orbital symmetry. The electronic crowding about oxygen of C+-Oalso Coulombically assists the push of the lone e- pair of O- into π bonding for the C=O formation. The consequent magnetic energy of e- circulation between the C+-O- in the π bond also drives the π bonding. The reverse process of the magnetic π e- cloud of C=O ferrochemically accelerating into compressed atomic orbital of O to form lone electron pair on oxygen O- is driven by the internal electric field of the more positive O of the C=O double bond, but the π to lone pair transition is organized by internal e- --- e- magnetic interactions on

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the O. Protons can break such internal π magnetism and resonance, which explains why water and acidic solutions slow CO2 and N2 formations in biochemical systems. These dynamics determine the magnetic importance of lone e- pairs of O and N in organic chemistry and biochemistry. The C=C double bond and C≡C triple bond lack such lone pairs for such internal magnetic dynamics. This difference explains the greater reactivity of aldehydes, ketones and carbonylic acids relative to alkenes and alkynes. The lone e- and p+ pairs thereby ferrochemically push and torque atomic orbitals and molecular orbitals during both internally and externally driven bond rearrangements about carbonyls for both acid catalyzed and base catalyzed migrations and bonding dynamics. It is important to note that the C=O bond polarity is greater in aldehyde than in ketones for greater reactivity of aldehydes in the conventional sense. Furthermore, here it is suggested that the magnetically induced hyperconjugation by the H of the C=O in aldehyde enhances the aldehyde reactivity relative to ketones.

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L. Magnetic Carboxylic Groups Just as the lone pair on the O- of the resonating carbonyl C+-O- pushes electrons from Ointo π bond for resonating the π bonds (C+-O- ↔ C=O), an additional O on the C center (as with carboxylic acids) extends the resonance over an additional O for resonating over three atoms -COO- for more stability and delocalization of π symmetry and CO2 formation ferrochemically. The resonance phenomena are reversible, equilibrium-like, self interacting, and internal subshell magnetic torques of electrons between orbitals of bound atoms where in two or more orbitals of many atoms exchange spin and ml momenta magnetically in the resonance. The lone e- of the involved atoms act as internal nucleophiles to ferrochemically push and torque the atomic orbitals and molecular orbitals of the atoms involved in the resonance. Such internal rehybridizations by these magnetic currents are in analog to spin torque rehybridizations during the CNT and diamond formations via metal catalyst. The electric dipoles drive the magnetism and torques in analog to external overpotential for electrochemical processes. Such internal currents of O and N extend spins and fields of catalysts and are important for fixing and coupling about many electrons of many C centers. In the case here, such internal magnetics of the resonance about carbonyls cause such efficient internal lone electron pair magnetic fixation, explaining the ease of CO2 (g) release from carboxylic acids. Just as protons modulate the lone e- pair and the π electron magnetic current of C=O for alcohol condensation, the protons modulate the lone e- pair and π magnetic e- cloud and lone e- pair resonance in COO- to condense carboxylic acids and slow CO2 release. The protons of aqueous solution suppress the complete oxidation to CO2 and convert CO2 into H2 CO3.

M. Proton Orbital Magnetic Torque of Carbonyls Protons magnetically, ferrochemically torque sp2 carbon centers to sp3 carbon centers. This p+ torque is very important in living organisms. So by low pH the lone pairs of carbonyls

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and carboxylic acids magnetically and ferrochemically torque entering groups into and out of the carbonyl centers. It is on this basis of such p+ modulated internal magnetic dynamics of carbonyl centers (as esters, amides, anhydrides, nitriles, carboxylic acids, ketones, and anhydrides) that they are the fundamental building blocks of life. The esters and amides play important roles in biochemistry as they have more reactive than aldehydes (H- leaving groups) and ketones (R- leaving group). The ester and amides have OR- leaving groups and NR- leaving groups and the strong magnetic fixing capacity of O and N for the carbonyl center. It is on this basis that the C≡N (nitrile) chemistry is similar to C=O chemistry but the N has only one lone pair for less lability relative to the O of C=O.

N. Magnetic Carbonyl Condensations

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Just as the magnetic π cloud of alkynes contributes to acidity of local p+ by the magnetic delocalization of the resulting negative of the conjugate basic anion, stronger acidic effects are observed for hydrogen at the C alpha position of carbonyl due to the magnetic π cloud ferrochemically interacting with the resulting conjugate basic carbanion to effect resonance, enolate-enol tautomerism for greater stability of the negative charge by its ferrochemical delocalization to the electronegative oxygen of the carbonyl. It is important to note the significance of this internal magnetism to the resonance and tautomerism for the acidity of the alpha hydrogen of the carbonyl. The magnetic π bond ferrochemically torques the lone e- pairs of alpha carbon into π bond in synchronization with torqueing carbonyl π into the O atomic orbital: C-C=O ↔ C=C-O-. Such magnetic factors are important for generating carbanion centers in biological systems for effecting aldol condensation forming C-C bonds. It is important to consider the internal magnetic nature of the entering and leaving nucleophiles about the carbonyl center, the self-interactions, the magnetic interactions and the magnetism leading to resonance and tautomerism and the internal magnetism of the carbonyl and nitrile polar π clouds synchronizing and organizing the incoming nucleophiles and electrophiles. Such magnetic stimulation, synchronization and organization are very meaningful in better understanding the many coupled perpetual weak acid-weak base reactions of carbonyls in biochemistry. Such magnetic resonance stabilizations are the essence of life. Many of such resonances, and tautomerisms, couple and extend in space as in the alpha carbon flanked by two carbonyls for many body effects on its acidity and delocalized carbanion charge, which contribute important magnetic effects in biochemistry All carbonyls undergo such alpha carbon deprotonation for such condensation reactions.

O. Magnetic Aryl Amines and Aryl Alcohols In addition to the influence of π magnetism on the reactivity of a polar π bond, we may further consider the influence of aromaticity on the reactivity of a polar bond. Aryl amines and phenols are examples of this ferrochemistry. The magnetism of the aromatic ring ferrochemically alters the chemical properties of aryl amines and phenols relative to the aliphatic amines and alcohols. Aryl amines are less basic than aliphatic amines. Phenols are more acidic than aliphatic alcohols. On the one hand, the acidity in phenols is increased due to constructive synergistics of the negative, magnetic, ring aromatic cloud with the incipient negative charge of phenoxide anion. On the other hand, the basicity of aryl amines is diminished due to the incipient destructive positive charge disrupting the negative aromatic

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ring magnetism. The magnetic aromatic electron cloud lowers the e---- e- repulsive Coulombic interactions in the aromatic phenoxide anion more than the alkyl stabilization of the conjugate alcoxide anion. However, the resulting positive charge in the conjugated acid of aryl amine Coulombically interferes with the magnetic, aromatic ring for lower basicity of aryl amines relative to aliphatic amines. Just as the magnetic π bonds ferrochemically delocalize the charge and give resonance in polar π covalent bonds, the magnetic, aromatic ring ferrochemically delocalizes partial and full negative charges during internal resonances and reaction pathways. Positive charges tend to Coulombically interfere with the ferromagnetic, aromatic, ring currents. Such Coulombic, destructive, interfering interactions of positive charges (as in protonated aryl amines) with aromatic ring currents are in analog to p+ disruption of magnetic π bonds and magnetic, aromatic rings. The internal magnetism ferrochemically organizes the charge oscillations and internal currents for various important resonances and transitory states in aryl amines and phenols.

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P. Magnetic Heterocycles Furthermore, we may consider the even stronger interactions of nucleophilic lone electrons of N and O when the N and O are directly part of the magnetic, aromatic ring, as opposed to them just being attachment as a functional group for indirect interactions with the magnetic ring as in aryl amines and phenols. N and O aromatic rings are heterocycles, having unique properties and playing important roles in organic and biochemistry. The heterocycles have their lone electron pairs and bond polarities directly coupled to the magnetic, aromatic ring for different properties relative to pyridine, phenol and aryl amines. The magnetic, aromatic rings directly influence the attack of electrophiles on lone pairs of ring N and O and the magnetic ring influences the nucleophilicity of the ring O and N. In these heterocycles there is a much stronger shift of the charges, for resonance and tautomerism. This stronger shift in aromatic heterocycles is the basis of their roles in biochemistry. The resonance and tautomerism are much better quantized and wave-like relative to the aromatic alcohols and amines. The magnetic ring can slow its internal current to lower charge effects, and also the magnetic ring can accelerates its internal current to enhance charge. Such magnetic ring effects lead to magnetic differences in electrophilic substitution on 5 membered vs 6 membered aromatic rings. The magnetic 5 membered heterocycles like pyrroles, furans and thiophenes have distinct ferrochemical properties relative to the amines, alcohols, sulfides, conjugated dienes, 6 membered herocycles, and even benzene. Unlike these compounds, the lone e- pairs of the 5 membered heterocycles are directly in the magnetic ring. The magnetic currents of the rings of 5 membered heterocycles cause them to resist electrocyclic addition but allow them to undergo electrophilic substitution on the ring. The magnetic exchange and correlation of the ring of the 5 membered heterocycles also cause their lower nucleophilic nature and the lower basicity of the lone e- pairs of ring N, O, and S. But the 5 membered heterocycles are more reactive toward electrophilic substitution than benzene. 6 membered heterocycles like pyridine are more basic and more nucleophilic than the 5 membered heterocyclic rings like pyrrole. The lone e- pairs of N, O, or S in the 6 membered rings are not directly in the magnetic ring. But pyridine is weaker base than alkylamines. Unlike 5 membered magnetic, heterocyclic rings, 6 membered magnetic, heterocyclic rings are less subject to electrophilic

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substitution than benzene. On the basis of such properties of 5 membered and 6 membered heterocyclic rings, novel ferrochemical properties arise in fused 5 membered and 6 membered heterocycles. The fused rings cause synergistic magnetic effects of different properties from benzene, 5 membered rings and 6 membered rings. Electrocyclic substitution occurs in the fused rings more readily than in pyridine but less readily than in benzene. The 5 membered part of the fused rings contributes electrophilic ring substitution tendency and the 6 membered part of the fused rings contributes basicity and nucleophilicity to the fused system. These combined effects synergistically allow fused rings to organize and synchronize multiple attacking electrophiles like p+ for important emerging effects in biochemistry. Purines are fused heterocyclic rings in nucleic acids and pyrimidines are 6 membered heterocyclic rings in nucleic acids. The comparisons explain the toxicity of benzene and polyaromatic hydrocarbons and carbon nanotubes [40]. These aspects of heterocycles contribute significance to biochemistry where multi heterocyclic groups are pertinent and are ferrochemically coupled. Biochemistry involves multiple N and O atoms on the rings and fused rings. Such multi ring N and O are important for ferrochemically synchronizing and organizing many electrophiles (protons) which will be considered in the next section on biochemistry in the sections on nucleic acids and proteins. Therefore on the basis of the demonstrated internal magnetism of the chemical bonds and valence, the compounds and their reactions in organic chemistry are internally magnetic, their chemical reactions are net magnetic.

VIII. FERROMAGNETISM AND BIOCHEMISTRY

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A. Preface to Biochemistry Currently biochemical reactions are not understood. The magnetic factors introduced here are just as important as the conventional electrical aspects for increasing the understanding of the biochemical reactions. It is useful to think of biomolecules as made of many varied small functional units of nonmetals and nonmetal molecules that are held strongly by a alkanealkene-aryl (graphene-diamond) like backbone, that are confined and moved by the backbone and that are forced to organize in water environments. Such nonmetals and nonmetal molecules typically exist as gases and liquids in bulk amounts thereof. But in biochemistry, life emerges by attaching these gaseous and liquid molecules on solid, backbone polymers. How do the molecules come to life? How do they come together and organize together to make life? In this perspective, the already considered magnetism within and between molecules is shown to play an important role in organizing and actuating life. A molecule may be static but inside it moves, its electrons move, and its nuclei moves. Where does life start and where does life ends: life inside the nucleus, life inside the atom, life inside the molecule? How does life exist between molecules? Life involves motions, controlled motions and replications. So how can molecules move between each other for life? Temperature makes the molecules move but not with organized motions for life. But temperature plus magnetism can allow organized motions. Why not temperature and electric force, well electric is involved but the electric interaction is a static force. But magnetism is superior in this dynamical regard to static electric force for the organization of life. Magnetism is a

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consequence of motion itself and it causes self organization under motions. Electric force organizes static objects, but cannot organize dynamic objects. Life requires motions so electric cannot alone organize and explain life. Life requires organization under motions. Magnetism organizes under motions. Therefore magnetism can explain the organizing aspects leading to life. Magnetism is required for life, but how do molecules acquire magnetism? As already discussed in this perspective, the molecules are intrinsically magnetic but the internal magnetism is balanced and cancelled. However through their motions and interactions, the molecular compressions, rarefactions, distortions, bending, stressing and straining disrupt the balanced internal charge motions and magnetism within and between biomolecules for net magnetism and organization for life processes. Both kinetic and potential effects of electron and proton motions between molecular orbitals cause the distortion and magnetism of these molecules. Magnetism of p+ motions between lone e- pairs causes magnetism. p+ orbital rearrangements are the chemistry for magnetism and organization of these aqueous biomolecules. So by strongly e- binding the varied functionals by backbones, the gaseous molecules (polar and nonpolar) (electrophiles and nucleophiles) (acids and bases) immersed in the water can then attract and repel Coulombically and magnetically (physically); they exchange charges (chemically). These chemical interactions alter the physical interactions in cyclic, organized manners. The physical interactions also alter the chemical interactions in cyclic, organized manners. This is the essence of life. These phenomena cause cyclic, internal, controlled, patterned motions within/between proteins and within/between nucleic acids. Life is organized by magnetism from the motions and consequent magnetism causing the organization. Magnetism organizes life. Metals are solid. It is interesting to compare aqueous biomolecules to the inorganic systems of CNT and diamond and the metal catalysts of their syntheses. It is interesting to compare metal lattices to aqueous nonmetal molecules attached to a flexible strong C-C (N,O) backbone. The flexible yet strong C-C backbone gives strength yet fluidity to biomolecules and the varied, attached functional groups give electronic and protonic dynamics on a larger scale in analog to metal lattices. But the metal lattices have electronic motions and dynamics on a smaller scale. The solid proteins, carbohydrates and fats exhibit such life bearing dynamics due to various physical effects of the functional groups trying to evaporate but condensed by the holding backbone, the functional groups trying to separate and mix yet modulated by the backbone and the functional groups trying to chemically equilibrate by pertinent acid-base reactions yet the backbone moving the acid and bases together and apart. So that the functional groups are yet perpetually falling toward these physical and chemical equilibriums but the equilibrium states are continually shifting. The nonmetals and molecular functional groups want electrons and they exchange electrons and protons reversibly between themselves via backbone and surrounding water for various characteristic, recognizing resonance and tautomeric states. The electrons of the resulting saturated states of the various functional groups complex proton orbitals! The many, varied complexes of functional groups by p+ orbitals determine dynamic hydrogen bondings of many weak acids and bases reversibly. Many such weak acid base pairs result in continuous flux of p+ among the many varied functional groups for perpetual currents and associated continuous magnetism.

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B. Magnetic Macromolecules After considering the magnetism of the chemical bonds and discussing the importance of organic compounds and the internal magnetism within organic structures and changing magnetism during their chemical reactions, now the ferromagnetic nature of biomolecular and biochemical reactions will be presented. Where as organic chemistry focused on single, isolated irreversible chemical reactions, the essence of biochemistry is in many, simultaneously interacting, and reversible chemical reactions in buffered environments. Unlike traditional organic and inorganic chemistry, biochemistry involves many body phenomena of these many reactions extended from subatomic to macro scales of space-time. The varied nonmetal compounds of organic chemistry (which are usually gaseous or liquid) are more fixed in space-time on carbonaceous backbones in macrobiomolecules in biochemistry. The backbones of biomolecules are alkane-alkene-aryl (graphene-diamond) like and strongly hold these nonmetal molecules in space-time yet strongly, rapidly nonrandomly displaces the varied functional groups for distinct emerging behavior unlike the bulk, gaseous phase reactions and liquid phase reactions of the conventional organic and inorganic chemistry. These many held varied molecular side chains (function groups) in the biomolecules magnetically share electrons with the alkane-alkene-aryl (graphene-diamond) backbone for varying polarization in their magnetic, covalence electron clouds. The different functional groups of such magnetic polar electron clouds (many such magnetic polarized eclouds and their motions cause attraction) exchange charges thru the holding alkane-alkenearyl (graphene-diamond) backbone with backbone bond rearrangement dynamics and associated motions during such charge flow and magnetism with interactions with the side chain functional groups. These big macromolecular structures may be in analog to a bulk chemical stockroom of functional groups yet characteristically nano-arrayed along the backbone.

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C. Structures of Magnetic Macromolecules and Water It is interesting to compare the gas phases of such molecules versus their condensed structures in these aqueous nanosolutions of the biomolecules. The primary structures of the resulting biomacromolecules are determined by the sequence of many monomers of differing side chains and functionalities. In the gas phases, such biomacromolecules may partially, internally hydrogen bond to give some structures beyond their primary structures. In the gas phases, such biomacromolecules are not as able (relative to the aqueous phase) to conduct charges between functional groups, except by the backbone and regions where the backbone has compressed some functional groups together. On the other hand, the dissolution of these biomacromolecules into water allows more complete internal, organizing interactions and dynamics via p+ orbitals with the surrounding water relative to the interactions of functional groups in the gas phases via the backbone. Here the essential role of water to life [44] is explained on the basis of magnetics of p+ currents and associated magnetics with functional groups of biomolecules. The water behaves as a coherent, organizing, orchestrating, and stimulating lattice for relaying the magnetic and electric fields and charge flows among the various side chains and functional groups of the biomolecules. The surrounding water is here suggested a plasma in analog to an ionized gas and an electric lattice of a metal.

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D. Magnetic Water Plasma Water about the biomolecules is like magnetic p+ plasma due to its nanosize regions; its autoionization (2H2O ↔ H3O+ + OH-); fluidity; and the self-interactions of its ions and charges. The magnetic water plasma is however much different in being less fluidic than the gaseous plasma of ionized gases or the e- plasma of the metal lattice. By considering water in this way, here a direct comparison is made between biochemistry to carbon nanotube and diamond synthesis and the chemistry of aqueous biomolecules. We may consider the water as delocalized p+ orbitals about negative nuclei like OH- for something of an inverted atom. Water consists of inverted atoms of negative nuclei surrounded by p+ orbitals which bind these negative nuclei (the varied functionals held to the backbones). Why does water supports life? The distinction between the metal lattice and its electronic band structure and the water lattice and its protonic band structure would be a Fourier Transformation. In general, there exists matter (particles) and fields. The matter can be Fourier transformed into the fields or the fields can Fourier transform into the matter. It is on this basis that here the wavefunction Ψ may be reasoned a Fourier transformation of the particles of matter to yield the more accurate interpretation as the patterns of Ψ as the electric and magnetic fields and electromagnetic waves in space-time that give self-interactions, cooperative, confinement of the fermions comparing matter.

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E. Water Molecules Inverted Atoms and the Water Lattice The water molecule may be considered inverted atoms with negative nuclei (OH-) bound by positive charges (p+) or p+ orbitals. p+ orbitals thereby bind two OH- nuclei. The p+ therefore exists in p+ orbitals in the water lattice. Water clusters can be considered bound nuclei or molecules of OH- bound by protons. The interesting consideration of water in this way allows us to consider nonmetal solutes or molecular solutes in water as other types of nuclei, which bind to OH- of water via p+ orbitals. So various classes of organic and inorganic chemical solute species can exist in water bound to the OH- (negative nuclei) by the p+ orbitals. These other species are functional groups which are like big atoms bound by p+ orbitals to OH- like atoms. Alcohols would exist in water via p+ bond to OH groups of alcohols. Alkanes would be gases in water or unbound by p+ orbitals. Alkenes, alkynes and aromatics would be like magnets in water. Esters, aldehydes, ketones, amides, amines and carboxylic acids would exist like some analogous nuclei bound to OH- nuclei by p+ orbitals. Such nano-aqueous solutions (water lattice) would thus consist of various anions (negative nuclei) with various properties all bound by p+ orbitals in analog to metal nuclei bound by ein metal lattices. But unlike the jade metal lattice containing only one type positive nucleus bound by e- plasma lattice, the aqueous protein or nucleic acid plasma contains varied negative functional groups (atom-like) bound by p+ plasma with flexible, many-body physical and chemical interactions and perpetual organizing motions for life. Therefore by this type of inverted atoms for p+ bound molecules, the aqueous biomolecules assume definite structures, coupled, stimulated, organized and synchronized by interacting and dynamic proton orbitals just as electron orbitals assume structures in atoms and metal lattices with synchronized and organized motions in a metal lattice. The p+ orbitals of the aqueous biomolecules are spin

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polarized for magnetic stimulation, orientation and synchronization for nonrandomly moving functional groups about for emerging structures, properties and dynamics.

F. Proton Orbitals for Structures and Properties for Biomolecules Large water clusters of OH- nuclei interact with these varied many functional groups via p orbitals, forming various molecules with specific structures. The various anions are bound by shared magnetic p+ orbitals for net magnetic properties due to the p+ spin and its motional currents and associated magnetism. On the basis of this ferrochemical model of big aqueous biomolecules, the internal composition, structure, properties, reactivities and enzymatic activity of various biomolecules can be rationalized. The rapid folding of proteins and replication, transcription and translation of nucleic acids and proteins are easily explained by this ferrochemical model. The structures of biomolecules depend thereby on the type of functional groups, their sequences and the p+ bonds between these varied side chain residues, water and the backbone within biomolecules and between biomolecules. The p+ orbital dynamics of currents and magnetism move the array of functional groups around for structural changes. The p+ orbitals couple to e- orbitals of the side chains and functional groups to alter the bonding within biomolecules. Thereby in this ferrochemical model both Lewis acid and Lewis base and Bronsted-Lowery acid and Bronsted-Lowery base concepts are important for rationalizing the structures and dynamics of the biomolecules. Structural conformational changes and chemical reactions may be reasoned as due to the magnetic p+ flux and currents (magnetic) and changes in p+ orbitals within and between biomolecules. The magnetic p+ currents drive magnetic e- currents for many biochemical reactions and vice versa the biochemical reactions drive magnetic currents causing macromolecular motions. The magnetic p+ orbital is bigger than conventional magnetic e- orbitals, and the magnetic p+ motion is slower than the conventional magnetic e- motion. Magnetic p+ orbitals are quantized and many self-interactions of magnetic p+ orbitals exhibit wave natures so aqueous biomolecules manifest bigger, slower wave functions and extended slower chemical dynamics that extend in space-time involving big (inverted) atoms (functional groups) relative to conventional e- orbitals. Magnetic p+ orbitals ferrochemically modulate the lone epairs, σ bonds, π bonds and even aromatic ring currents in the backbone to couple backbone domains to side chain dynamics and to ferrochemically modulate backbone structural and motional dynamics with the side chains and to ferrochemically modulate side chain structural and motional changes with the backbone. In this way, the resonating e- bond rearrangements and e- currents in the backbone magnetically organize to couple with the p+ orbitals in surrounding side chains and water to cause changing circuitry for open and closed circuit patterns in the backbone and side chains. Enzymatic activity and macromolecular templation may be explained by various magnetic patterns of p+ orbitals and magnetic synchronized, oriented, stimulated and accumulated p+ orbitals, currents and energetics. Thereby, the whole structures of biomolecules are involved in organizing their organic chemistry and inorganic chemistry, involving multiple functional groups with polar reactions and e- and p+ radical reactions with variety from alkanes to heterocycles and with various K+, Na+, Ca2+, Fe2+, Cu+, Mn2+, Zn2+, and Mg2+ ions and clusters, respectively. Organic chemistry is usually done in nonpolar solvents. But biochemistry involves p+ transfers between these varied functional groups of both organic and inorganic natures with mediation by the surrounding nano-water

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and modification of e- currents between the varied function groups via the holding alkanealkene-aryl (graphene-diamond) backbone. Thereby life consists of large scale quantized electric currents and spin domains with associated electric fields and magnetic fields. Recently investigators have measured the huge nature of electric fields in humans.

G. Nanosize Effects in Biochemistry It is important to further note the mix phases in biochemistry. Both polar and nonpolar phases exist together with interesting interactions and dynamics on nanoscale dimensions. The nanosize regions within biomolecules alter concentration and alter pH relative to bulk aqueous and nonaqueous solutions used in conventional organic and inorganic chemistry. The nanosize also alters properties of the various functional groups, relative to bulk amounts of these functional groups. The nanosize and submesoscopic sizes heighten magnetic effects relative to bulk sizes. It is interesting to imagine the energy created by forcing oil to dissolve in water on the molecular level. This forced mixing of immiscibles actually occurs and contributes to the dynamics of life as the strong alkane-alkene-aryl (graphene-diamond) backbone forces and moves these nonmixing phases together creating high energies of dynamic electric and magnetic fields for reversible chemical and physical dynamics; this is vitalism! The huge surface energies on the nanoscale allow the energies of the various physical events to sum to activate chemical events. Also such collective effects may allow chemical events to sum their energies to cause nuclear events. The surface energies and changing surface energies shift the many equilibriums in biochemical systems.

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H. Many Weak Acid Weak Base Equilibriums for Induced Macromolecular Rearrangements for Many Equilibriums Living organisms physically consist of large scales of many sub-volumes of nanoregions of quantized electric currents and spin domains with their associated cooperative selfinteractions of electric and magnetic fields. These spin currents and spin waves are produced by many perpetual non-equilibrating, self-interacting, cyclic chemical reactions and consequent nanoscale resonance and tautomerism. The delocalized, cyclic, resonating, many body, varied chemical reactions are wave mechanical in nature for chemical wave reactions. These perpetual, non-equilibrating chemical reactions arise from many varied functional groups in biomacromolecules and the many possible Bronsted-Lowery weak acid and weak base reactions between these various combinations in the aqueous environment. The many such weak Bronsted-Lowery acid and base combinations are all weak acids and weak bases for affecting many body reversible weak acid-weak base reactions, of complex patterns of p+ motions and associated magnetic patterns, causing net magnetism due to chemical reactions and their attempted many equilibriums between the various weak acid-base combinations. These many coupled reactions involve p+ currents and are therefore both magnetic and electric in nature, but these many body chemistries cannot all simultaneously equilibrate so they magnetically shift each others’ equilibriums. This magnetic shifting of the equilibriums of many physical and chemical dynamics is the essence of life. This emergence in biochemistry is due to these varied many functional groups and their chemical dynamics involving the intermixing, interacting and separating of these many chemical equilibriums so

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that these many functional groups are continually falling toward many equilibriums but their internal interactions and intermixings continuously perturb, shift and alter the equilibriums. It takes extended time for their equilibrations (death).

I. Perpetual Shifting Physical and Chemical Equilibriums Chemical equilibrations take time but the physical dynamics (of mixing, separating, gasifying, liquefying, and solidifying) within and between the macromolecules occur on short enough time scales to disrupt the chemical equilibrations. Likewise the chemical dynamics of p+ orbital rearrangements and motions (and e- orbital rearrangement of side chains and backbone) disrupt the physical dynamics of polar-nonpolar mixing-separating, gasification, liquefaction and solidification. The p+ orbitals dynamics both move the side chains and mediate the chemical kinetics and physical kinetics and non-equilibrations. Therefore the time scale for mixing is about that for chemical equilibrations. So the mixings disrupt the chemical and physical equilibrations and the chemical and physical equilibrations disrupt the mixings for both many physical and many chemical dis-equilibriums within and between aqueous biomolecules. The resulting non-equilibrations allow macroscale resonance and tautomerism along the backbone and side chains of macromolecules and macroscale resonance and tautomerism of the side chains, backbone and functional groups. The strong alkane-alkenearyl (graphene-diamond) backbone holds the functional side chains and prevents their physical and chemical equilibrations. The backbone magnetically moves functional side chains by p+ orbital dynamics, and also the many functional side chains cooperatively move the backbone by the p+ orbital dynamics. The magnetic p+ currents further disrupt the equilibrations of reactive centers to destablize the formations of CO2, H2O, N2, S8, P4 and hydrocarbons. This proposed many body, many gas, many liquid, many solid, many polar, many nonpolar, many acid, and many base non-equilibrating ferrochemical model for biochemistry is consistent with the buffering environments in organisms.

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J. Energetics and Kinetics of Multiple Weak Acid-Base Equilibriums It is important to consider the energetics of such multiple weak acid-weak base chemical dynamics and resulting magnetic patterns in biomolecules. Relative to alkanes, the alkanealkene-aryl (graphene-diamond) backbone and the many functional groups are highly activated with large potential energies. The dynamics of the many functionals involve continuous introversions of potential energy to kinetic energy via the weak acid-weak base reactions and the many physical mixings/separations as they are ferrochemically modulated by the magnetic p+ currents. These many body, chemical reactions about carbon centers involve only small energy changes between reactant and product states. The magnetic p+ currents provide important rehybridizations of internal e- orbitals during the physical and chemical dynamics within and between the biomolecules for lowering the activation barriers of the chemical dynamics, even explaining enzymatic activity.

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Such reversible kinetic to potential energy interconversions within and between the biomolecules determine catalyzed (enzymatic) cyclic processes of many small steps and coupled, interacting enzymatic, cyclic processes involving many biomolecules. Different biomolecules and interacting biomolecules thereby have different magnetic patterns and electric patterns in space-time. Such interacting, biochemical cycles in and between biomolecules are the magnetic gears of biochemical molecules, these are the magnetic gears whereby biomolecules act as motors and energy transducers for their internal and interdependent dynamics. Such biochemical cycles and electromagnetic synchrony are the chemical patterns of life. The competing nucleophiles (functional groups) and electrophiles (p+) with p+ currents and their organizing magnetism cause the internal electricity and magnetism of life for the animal electricity of Galvani.

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L. Proton Currents Within and between Biomolecules Different biomolecules and combinations have different magnetic patterns in space-time due to these many cyclic chemical equilibriums and their magnetic interactions and intermixings. Such cyclic, many equilibriums of many chemical functional groups involving many magnetic p+ transfers for many interacting magnetic currents involve spin torque of p+ orbitals and e- orbitals (the Little Effect) for many rotating chemical currents. These interactions within and between the big molecules allow synchronization of e- and p+ orbitals of the transforming molecules. The charge flow of e- and p+ into antibonding orbitals can strengthen and/or weaken various chemical bonds and organized currents of bonds. So in biochemistry many groups are involved in charge transfer for reversible, flexible bonds. The many charge transfers and their magnetism spin torque molecules, functional groups, atoms, valences, shells, subshells and orbitals. The charge flows on larger scales via p+ orbitals torque bend and alter structures in biomolecules. By these magnetic currents, bonds are broken, stretched and compressed in functional groups causing high magnetic fields. The many electric currents of such many bond dynamics interact magnetically to torque each other. The coupling of such many bond dynamics allow some bond breakages to hold higher order magnetism and correlation in coupled activated bonds to focus the energy for higher energy activations of bond cleavage rehybridizations and rebondings. During such coupled bond dynamics e -screening and p+ screening and associated magnetism play an important role in lowering the Coulombic bond attraction and repulsion along the reaction trajectories. These cyclic, magnetic, physical and chemical processes interact between different systems so as to fit lock into key (and furthermore as revealed her) even to turn the key within the lock. Big magnetic reactions of biomolecules (bigger basis sets) organize (template) and catalyze smaller monomer magnets (smaller basis sets) to replicate, transcribe, and translate for the anabolism and construction. Computationally, the big magnets act as basis sets providing the organization and energy for enzymatic catalysis for constructing the smaller basis sets. Just as magnetism of electronic interactions in atoms and between atoms accelerate orbits to orbitals to molecular orbitals to lattice, so likewise p+ orbits accelerate p+ orbitals to H-bonds to organize structures in the biomolecules. Protein and nucleic acid structures emerge from p+ orbital magnetic interactions just as atomic orbitals and molecular orbitals emerge due to the magnetic e- charge interactions within conventional atoms and molecules.

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IX. FERROCHEMISTRY OF PROTEINS

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A. Magnetic Backbone of Proteins In proteins, the polypeptide backbone holds various side chains residues of the 20 possible, different amino acids. The polypeptide backbone is a polymerization of the same peptide backbone with repeating backbone (-N-Cα-C-) units and 20 varying possible side chains. This polypeptide backbone of the protein consists of Cα-N and C-Cα bonds with resonant structures, involving resonating conjugated C=Cα and Cα=N bonds. The C-C, C-N, C=C and C=N bonds are some of the strongest possible chemical bonds, contributing primary and secondary structures, stabilities and reactivities to the protein, polypeptides. The backbone has the bond character of a resonating alkane-alkene-aryl (graphene-diamond) chain. The very strong resonating graphitic-diamond like backbone powerfully holds and ferrochemically moves the 20 possible side chains of Cα about during the physiology of the protein’s physical and chemical dynamics. The alkane-alkene-aryl (graphene-diamond) resonating nature of the backbone gives both conducting and semiconducting characters to the backbone. The alkane-alkene-aryl (graphene-diamond) oscillating, resonating backbone also determines magnetic and ferrochemical character in the backbone. The alkane-alkene-aryl (graphene-diamond) resonance of the backbone ties the protein to research discussed in this perspective on graphene, carbon nanotube and diamond. It is important to consider that magnetic p+ orbitals and p+ currents between the backbone, surrounding water, side chains and possibly nucleic acids or sugars or lipids can ferrochemically protonate the carbonyls and amino groups of the backbone, ferrochemically driving magnetic, resonating π currents from carbonyl C=O to amino C-N groups with deprotonation of Cα-H for conjugated N=Cα {C(OH)-N(H)-C(R)(H)-C(OH)) and on the other side of C-OH along the polypeptide chain for resonant, conjugative and tautomeric π and hydrogen bonds along the backbone. Such magnetic resonance and tautomerism of the backbone ferrochemically contribute structural and conformational dynamics to the backbone by polarized magnetic p+ currents (by the Little Effect) with the associated magnetically driven motions (and compression/rarefaction) in surrounding side chains, proteins, nucleic acids, sugars and/or lipids during biological activity. The p+ orbitals ferrochemically induce resonance in the backbone for also magnetically modulating the electronic nature of the backbone for conducting (graphitic) and insulative (diamond) resonance, tautomerism and transport from and thru the backbone to the attached side chains. Such powerful electrically induced magnetic motions (modulated and organized by the magnetic orbitals of the backbone) ferrochemically confine, move, mix and separate polar and nonpolar side chains with their associated chemical reactions, electric power and with the strength of the alkane-alkene-aryl (graphene-diamond) backbone. Recently, scientists measured electric fields as powerful as lightning bolts inside the living organisms [45]. The backbone powerfully, ferrochemically pushes hydrophobic and hydrophilic regions of side chains together, ferrochemically overcoming their physical repulsive interactions, ferrochemically accelerating the magnetic e- orbitals in the hydrophobic side chains and also ferrochemically accelerating the polar clouds in the hydrophilic side chains for magnetically overcoming the Coulombic differences between the immiscible side chains.

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B. Magnetic Side Chains of Proteins The alkane-alkene-aryl (graphene-diamond) peptide backbone is arrayed by its alpha carbons with 20 various different amino acid residues (for chemical stockrooms) with the firmness of the alkane-alkene-aryl (graphene-diamond) backbone. Some of the side chains are polar: serine, threonine, tyrosine, cysteine, glutamine and asparagine. Some of the side chains are nonpolar: alanine, glycine, valine, leucine, isoleucine, proline, phenylalanine, tryptophan and methionine. Some of the side chains are weak acids: glutamic acid and aspartic acid. Serine, cysteine and tyrosine also exhibit very weak acidity. Some of the side chains are weak bases: hystidine, lysine and arginine. Asparagine, glutamine, methionine, and tryptophan also exhibit very weak basicity. These side chains manifest many of the functional groups considered in the organic section [Section III]: alkyl, amines, alcoholic, aromatic, thiolic, carboxylic, phenolic, amides, and heterocyclic. But in biochemistry these different functional side chains are variously arrayed and held in nano-regions of varied environments for emerging properties. The chemical bonds of these various side chain residues to the alkane-alkene-aryl (graphene-diamond) backbone give even tremendous ferrochemical compression and rarefaction of these side chain residues and internal substrates to affect various protein activities and enzymatic chemistry. Magnetic p+ currents from the surrounding promoters and inhibitors modulate the backbone resonance to compress or rarefy bonds in substrates and side chains. The very strong backbone magnetically prevents the chemical equilibration of the magnetic side chains to thermodynamically stable CO2, H2O, N2, P4, hydrocarbons and S8 products. Unlike 3D diamond and 2D graphene, the backbone is ferrochemically, plastically activated by the p+ current induced resonance and tautomerism of its C=O groups and C-N groups. The alkane-alkene-aryl (graphene-diamond) like backbone magnetically modulates motions of side chains by internal p+ currents and p+ currents with the side chains for magnetically tossing the many side chains around for changing their physical (nonpolar/polar) and chemical (acidic/ basic) environments. Such compression, rarefaction, and/or bending of the magnetic side chains by the magnetic backbone motions and modulated mixing by the backbone motions ferrochemically create changing nanoscale volumes of side chains for emerging a variety of physical and chemical effects (vitalism) from the transient mixing and separating of the side chain residues and the changing chemical-physical environments by backbone motions about possible internal substrates and other nearby external biomolecules for explaining the quaternary structures and dynamics. The different internal magnetic patterns in these biomolecules by the magnetic p+ driven backbone motions allow their biorecognition. Internal to a given protein, the backbone magnetically modulates mixing and separating side chains continually and perpetually for the disruptions of the many possible weak acid - weak base chemical equilibriums between the 20 amino acid residues, surrounding water, other substrates, surrounding sugars, nucleic acids and lipids. Such nonequilibrating, continually, cyclic magnetic, and/or tautomeric magnetic p+ currents via p+ orbitals within the protein and between surrounding biomolecules cause the life of the protein, nucleic acid, and lipid membrane. It is here that life exists for the physical basis of organisms by their proteins, nucleic acids, lipids, nucleus, cytoplasma, ribosomes, lysosomes, endoplasmic reticulars, cells, tissues and organisms.

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C. Magnetic p+ Orbitals for Protein Activity The activities of the magnetic p+ currents extend over larger spaces and occur over longer times relative to magnetic e- current organization in Fe catalysis of CNT and diamond. Unlike conventional molecules which are held together by the much smaller e- orbitals, the proteins are bigger molecules and are ferrochemically held and moved by nonrandomly bigger, slower p+ orbitals. By the p+ orbitals, the folding, coiling and conformations in proteins are ferrochemically in analog to electronic, vibronic, and rotations in smaller molecules. The p+ orbitals electrically and magnetically trigger the motions and organization in proteins. p+ orbitals and p+ orbital dynamics explain the observed rapid, organized folding and coiling of proteins. Just as in Esquinazi’s p+ triggered magnetism in graphite [15], here p+ orbitals ferrochemically trigger magnetism and order in the proteins during side chain backbone p+ and e- exchanges. Just as in Makarova [17], the alkane-alkene-aryl (graphene-diamond) like backbone of these biomolecules and its compression and rarefaction of side chains causes their nanoscale magnetization.

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D. Characteristic Magnetic Patterns in Amino Acids It is the composition of the protein that causes magnetically induced structures and properties. Just as the peptide backbone contributes to magnetically induced structures and properties, the compositions of the 20 various side chains contribute compositely to the structure and properties of the proteins. The side chain compositions and sequences determine tertiary and quaternary structures and reactivity of proteins. It is important to note the p+ orbitals extending from the side chains interact magnetically with the backbone p+ orbitals to ferrochemically modulate the secondary (alpha helical or beta pleated) and primary (polypeptide formation or decomposition) structures and reactivities. The magnetic p+ currents ferrochemically accelerate the different dimensionalities of the biomolecules. The p+ orbitals of the side chains also interact with the other side chains for magnetic induced motions and activities. The 20 different side chains of the 20 amino acids have varying physical and chemical properties. Some are hydrophobic. Some side chains are hydrophilic. Some side chains are weakly basic. Some side chains are weakly acidic. The hydrophobic residues of the protein try to aggregate together under the restriction and modulation of the backbone and the hydrophilic residues try to aggregate together under the restriction and modulation of the backbone, causing tertiary structure of the proteins. The weakly acidic portions of the proteins tend to react with the weakly basic portions for a motley of Bronsted weak acid - weak base reactions, each such weak acid weak base reactions attempt to reach equilibriums but the backbone and side chain motions and the intermixing and magnetism continually ferrochemically perturb, disrupt and shift the many physical and chemical equilibriums for perpetual magnetism and chemical-physical dynamics within and between the proteins by magnetic p+ currents between the parts.

E. Nano-Regions in and about Proteins Each of the 20 different amino acids has different p+ currents and different magnetic signatures. So different sequences of amino acids along the polypeptide chains determine different magnetic and ferrochemical patterns for selective interactions and specific

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recognitions. It is further important to note the effects of the nanosize hydrophobic regions and hydrophilic regions on the equilibriums by the surface energies. The surface energies between these regions can cause the summing of physical interactions to be magnetically, ferrochemically organized to cause chemical events. The backbones of proteins can ferrochemically force hydrophobic regions into hydrophilic regions to raise the free energy for activating chemical reactions. The backbones can also ferrochemically force basic regions together and acidic regions together for raising the chemical potentials for accumulating and focusing chemical energies into specific bonds for enzymatic reactivities. Such ferrochemical forcing of basic away from acidic regions and polar into nonpolar regions is driven stimulated and organized by magnetic correlational motions with consequent magnetic attraction to overcome the Coulombic repulsion between polar and nonpolar regions and to overcome the Coulombic attraction between acidic and basic groups. The magnetic correlational motions are in analog to the magnetic electron screening to overcome Coulombic forces during CNT and diamond formations and inverse beta processes.

F. Magnetic p+ Orbitals Organize Proteins Structures

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All these aspects cause the native structures of protein by these internal magnetic p+ current orbitals. On the basis of structure emerging from dynamical magnetic p+ currents of the many acid-base reactions, the structure can change by changing the many acid-base reactions and the consequent p+ currents and magnetism. Disrupting p+ orbitals or changing internal magnetic currents, ferrochemically causes changes in the structure, folding, conformation and nature of the protein. By injecting energy, kinetic energy (KE) or potential energy (PE) into the biomolecules, the p+ orbital currents can change for transducing the energy magnetically for changing the proteins’ structures. The breakage of p+ orbitals of the native structures ferrochemically excites the protein so that the energy in the many excited magnetic p+ bonds can be ferrochemically organized, synchronized, accumulated, focused and/or dissipated for various enzymatic activities of the protein. Proteins are not static but magnetically dynamical, chemical structures. In these magnetically coupled p+ currents, the chemical bonds of many bodies get compressed and/or rarefied for various uncoiling, enzymatic and transport activities. Many magnetic p+ orbital currents can ferrochemically couple to many e- orbitals of the backbone to drive e- transport chains. The p+ orbitals can ferrochemically couple to ions in solution to pull ions across membranes.

G. p +Orbitals Induced Enzyme Activity It is important to note that within the proteins, p+ orbitals magnetically polarize the inner parts of the proteins. Within such magnetically polarized inner parts, the ferrochemical activation and excitation of motion and/or enzymatic activities can occur by the absorption of energy of less excited functional groups to focus the energy magnetically into specific active sites. In this way, interacting ferrochemical cycles about the active site can ferrochemically focus the energy into one of the cycles for hot spots for extreme motions and/or enzymatic activities. These ferrochemical cycles involve many side chains and the many reversible magnetic weak acid-weak base reactions so the many bodies cause tautomerism and

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resonance among the many extended reactions for p+ orbitals wavefunction in space-time for wave nature of the biochemical dynamics and reactions.

H. Wave Nature of Multi p+ Orbital Rearrangements The vant’ Hoff/Le Bel three dimensional bond is extended in space not only for stable compounds but here the extension in space (and also time) is expanded across many reacting compounds of biomolecules to embrace the dynamics of many chemical bonds and their simultaneous rearrangements. Therefore, many body chemistry extends in space-time quantum mechanically for Frank-Condon type effects during biochemical reactions with spin alterations and the explanations of chemical specificity, stereospecificity and high catalytic factor of 1020 of biochemical reactions (relative to 104 for inorganic catalyzed processes). Just as photophysics of molecules can be treated quantum mechanically, here RBL treats the multiply coupled chemical reactions in biomolecular systems and other lattices quantum mechanically for chemical reactive wavefunctions. It is on this magnetic basis that allosteric effects are explained magnetically as one substrate develops within the enzyme a magnetic pattern of magnetic p+ orbital alterations by which the enzyme can magnetically use this pattern as a basis to readily adopt another substrate or catalyze another reaction, cooperatively. Thereby the protein folding, uncoiling, enzyme activity and transport are quantized due to the internal self magnetic interactions. Functional groups in proteins are just as interdependent as the electrons in a many electron atom. Thereby the enzymatic activity by external chemical Ψ is as specific and characteristic as an electronic transition in an atom or molecule as described quantum mechanically by the bracket about the transition. In this way, control mechanisms are further understood magnetically as covalent modifications and promoters/inhibitors alter native p+ currents and orbitals for structural and energetic alterations of enzyme activities.

X. FERROCHEMISTRY OF NUCLEIC ACIDS

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A. Magnetic Nucleotides in Analog to Magnetic Amino Acids The compositions of nucleic acids and their internal dynamics cause their structures. The nucleic acids are polymers of nucleotides. The nucleotides have phosphate-sugar-base structures. The phosphates link (ester linkages) sugars which are decorated by 5 possible bases. It is interesting to ferrochemically compare the nucleotides with the amino acids. The parts of the nucleotides are bigger ferrochemical analogs of the parts of the smaller amino acids. The phosphate of nucleotides is ferrochemically in analog to the amine group in amino acids. The pentose sugar of the nucleotides is ferrochemically in analog to the carboxylic group of the amino acids. The base of the nucleotides is ferrochemically in analog to the Cα of the amino acids. The nucleotides are bigger than the amino acids. Such ferrochemical analogs of nucleotides and amino acids explain the p+ orbital coupling, magnetism, consequent interactions and dynamics between proteins and nucleic acids. The same dynamics in proteins are in nucleic acids but on larger scales. The 5 common bases are adenine, guanine, cytosine,

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thymine, and uracil. Three base combinations (codons) are equivalent to one specific amino acid. Magnetic patterns (e- currents) in the bases are bigger than the magnetic patterns (p+ currents) in the amino acids. The bases consist of fused complex heterocycles (e- aromatic rings) containing multiple ring nitrogens and oxygens on the fused rings.

B. Magnetic Interactions of Nucleic Acids and Proteins It is interesting to compare the backbones of proteins versus the backbones of nucleic acids. Nucleic acids have more inert backbones relative to protein backbones. Proteins have more flexible and dynamic yet stronger backbones relative to nucleic acid backbones. The side chains of amino acids and nucleotides have ferrochemical relations via the magnetic p+ orbitals for the coding of proteins by ribosomal nucleic acid (RNA). The ferrochemical compatibility of protons and nucleic acids results from p+ orbitals and currents between the ecirculating in protein side chains and backbones and the p+ coupling of these protein ecirculations with the e- circulations in coding bases. Within the protein, the carbonyls and amines ferrochemically modulate the side chains and within the nucleic acids the phosphates ferrochemically modulate the p+ orbitals of the bases. In complexes, these ferrochemical modulations within the proteins and nucleic acids are mixed for intramolecular magnetic p+currents and intramolecular modulated reactions and motions.

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C. Magnetic Bases in Nucleotides Nucleosides are arrayed with bases. There are 5 different bases. The bases are fused heterocyclic compounds with multiple ring nitrogens and oxygens for the lone electrons to strongly correlate p+ orbitals within the nucleic acids and between nucleic acid and protein complexes. The five different base pairs have varying physical and chemical properties. Two are purines are fused 6 membered ring and 5 membered ring. Two are pyrimidines or 6 membered heterocyclic rings. The rings are heterocyclic with multiple ring nitrogens and oxygens. The ring nitrogens and oxygens give stronger coupling of their lone e- pairs to the aromatic, magnetic π ring currents. The p+ currents from these magnetic heterocycles are thereby more strongly correlated, synchronized, organized and stimulated. Such magnetic p+ currents (magnetic) between bases, nucleosides, water, proteins cause double helical structures of deoxyribose nucleic acids (DNA). Changes in p+ orbital currents magnetically alter the nucleic acid structures of the helical coils. p+ orbital currents magnetically affect and are influenced by the reversible weak Bronsted acid-base reactions between the nucleotides, water, and surrounding proteins for chemical stability of nucleic acids from equilibrating to CO2, H2O, N2, P4, S8 and hydrocarbon products. Shifts in the many weak acid weak base reactions within nucleic acids and between nucleic acids and surrounding proteins cause magnetic patterns that alter the structures of nucleic acids. The nucleoside backbones are magnetically activated for various nucleic acid biological functions via the phosphate (PO4-) and pentose-sugar p+ orbital currents with surrounding proteins in the aqueous environment. The resulting p+ orbitals induce rehybridizations of pentose backbones (with possible resonating aromatization of pentose ring) with coupling to the bases to affect p+ orbital currents between the bases.

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D. p+ Orbital Induced Structures of Nucleic Acids It is the compositions of the nucleic acids that cause their magnetically induced structures and properties. Just as the pentose-phosphate backbone contributes to magnetically induced structures and properties of the nucleic acids, the compositions and structures of the five bases also contribute to the structures and properties of the nucleic acids. The base pair compositions and structures cause the secondary and tertiary structures of the nucleic acids. It is important to note that the p+ orbitals extending from the bases interact with the pentosephosphate backbone p+ orbitals magnetically and ferrochemically to modulate the secondary and primary structures and reactivities of the nucleic acids. During the structural changes in the nucleic acids with the assistance of complexing proteins, the magnetic p+ currents between the biomolecules accelerate the different dimensionalities in both the nucleic acids and proteins. The ring nitrogens and oxygens give stronger coupling of the bases and the bases with surrounding proteins. Such stronger coupling allows the coherent magnetic, chemical dynamics of the aromatic ring to couple thru the lone e- pairs of multiple oxygens and nitrogens to p+ currents for synchronizing, stimulating, and organizing p+ currents magnetically between the groups and between the macromolecules. The magnetic, aromatic ring dynamics push and pull correlated magnetic p+ currents into and out of the surrounding pentose sugars, phosphates and proteins. Such strong, correlated, magnetic p+ currents within and from the nucleic acids are how the nucleic acids code the amino acids into proteins.

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E. p+ Orbital Induced Structural Dynamics of Nucleic Acid – Protein Complexes All these aspects cause the native structures by internal, magnetic p+ orbital currents within and between the nucleic acids and proteins. On the basis of structures emerging from the dynamics of magnetic p+ currents of acid - base reactions, the nucleic acid structures can change by changing the patterns of weak acid – weak base reactions. Also the proteins can change the structures of nucleic acids and the nucleic acids can change the structures of the proteins by intermixing and changing their coupled magnetic p+ currents. Disrupting magnetic p+ orbitals of changing internal currents cause changes in the structures, foldings, conformations and natures of the nucleic acids. A protein ferrochemically coupled to the nucleic acid can magnetically introduce characteristic p+ currents for stimulating such particular structural changes ferrochemically. Also the nucleic acids can ferrochemically template the structures of proteins by such characteristic magnetic orbital currents for stimulating and organizing particular changes. Just as in proteins, in nucleic acids the breakage of p+ orbitals of the native structures excites the nucleic acids (proteins) so that energy in the excited magnetic p+ bonds can be ferrochemically organized, synchronized, accumulated, and focused/dissipated for various replicative, transcriptive and translative activities of the nucleic acids. Nucleic acids are not as dynamic as proteins but they are not static. In these magnetically coupled p+ currents the chemical bonds of many bodies get compressed, rarefied for various ferrochemically induced unwinding, uncoiling, coiling, winding and supercoiling activities of the nucleic acid.

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F. Magnetic Cyclic Chemical Dynamics of Nucleic Acids Just as in proteins, the many weak acid-weak base reactions within the nucleic acids and between the nucleic acids and other surrounding molecules determine many interactions for ferrochemical cycles. These ferrochemical cycles can involve many bases of the nucleic acids and externally involve these bases with side chains of polypeptides and amino acids, within these interacting ferrochemical cycles the p+ currents ferrochemically drive cycles, organize the structures and the energy self-interactingly to reversibly focus and dissipate the energy, causing extended resonance and tautomeric processes of the macromolecules involved. Within these nucleic acid - protein complexes the ferrochemical dynamics assume a wave nature with extension over many atoms in space-time. The quantum wave mechanical nature of such complexes and their activities of replication, transcription and translation provide a reason why few errors occur during these critical processes of life. Only 10-10 errors per base per generation occur during replication [46]. Errors during these chemical dynamics can be detrimental and deadly. The low error is a quantum effect. The magnetic p+ orbitals extension over space-time of these many body, chemical processes even give a beauty to how these systems emerge with a feed back to correct for error during translation. Quantum mechanically the protein nucleic acid complex can exist ahead in time to recognize error and go back to the space to correct it. It was Henry Taube who intuited a quantum mechanical basis for consciousness. Here a frame is presented for filling in the details of such quantum consciousness.

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XI. CONCLUSIONS In July 2000, the unknown mechanism of carbon nanotube (CNT) nucleation and growth was formulated on the basis of transient magnetic stimulation, orientation, organization and synchronization of many simultaneous carbon, hydrogen and/or metal (bonds (electron currents) and many chemical reactions (accelerating electron currents) involving catalytic hydrocarbon adsorptions, decompositions, absorptions, diffusions, desorptions and rebondings on and within ferrocatalysts for forming the CNT. On the basis of this formulated ferromagnetic mechanism of CNT formation, the ferromagnetic basis for carbon was first properly conceived on the basis of the magnetic field of the catalyst stabilizing by antisymmetry of the high spin, unsaturated carbonaceous, magnetic, intermediates as they incompletely bond (changing current) during the nucleation and growth. Under such conditions of the synthesis, the changing magnetic field, spin waves and currents of the catalyst were determined to torque, accelerate, stimulate, orient and synchronize many atomic, molecular and metallic orbital rehybridizations and rebondings (the Little Effect) for forming sp2 carbon, π conjugated carbon chains, cyclization and aromatization of carbon chains, and nonplanar aromatic rings about the nanotube circumference as the catalytic exchange and correlational fields vary in magnetic field strength (earth field to 1000 Tesla) and electronic spatial (from 2.5 to 250 Angstroms) and temporal (from femtosecond – nanosecond) influences about the catalyst’s Curie temperature. The discovery of such collective magneto-chemistry opened a new door of ferrochemistry to chemical reaction dynamics. Ferrochemistry fits well within the history of magnetism, electricity and matter. On

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the basis of this ferrochemistry, the magnetic nature of covalent bonding was first determined and the ability of a magnetic field to alter catalyses and chemical covalence dynamics were first demonstrated. On the basis of this discovered ferromagnetism in carbon and this invention of ferrochemistry, static magnetic environments in excess of 1000 Tesla (iron lattice plus external magnetic field) with smaller spatial electronic influence (< 2 Angstroms) were realized for novel diamond synthesis under thermal activation. Currently, there is a lack of understanding the dynamics of biochemical reactions. Biochemical dynamics differ from conventional organic and inorganic chemical dynamics. Here these new aspects of ferromagnetic carbon and the new ferrochemistry of CNT and diamond are extended into biological systems for better understanding the biochemistry of living macromolecules of nucleic acids and proteins. Although differing conditions of pressure and temperature are involved in diamond, CNT and aqueous biomolecular chemistry, the chemistry of all these chemical systems involves many carbon atoms and network carbon bonding dynamics wherein the transient ferromagnetism of carbon allows ferrochemistry of the many carbon bond dynamics and the response of carbon network bonds to surrounding spins and magnetic environments. The carbonaceous structures of both diamond and graphite are resonating and tautomerically manifested in the protein and nucleic acid backbones. In the case of biomolecules, ferromagnetism of C, N, O, H, P, and S functional structures form various transient and persisting fermionic intermediates that organize the many body chemistry of the many functional groups. The lone electron pairs of these many varied functional groups and their associated p+ orbitals play crucial roles in the structures and properties of biomolecules. The reversible chemical nature of thousands of side-chain functional groups of the resulting various weak acidic type (alcohol, thiol, phenol, carboxylic acid, and amide) and of the various weak basic types (alkyl amine, aryl amines and sulfides) in proteins lead to multiple competing proton transfer chemical equilibriums among the many possible acid-base combinations with alkyl and aromatic side chains perturbing the solvent polarity and multiple chemical equilibriums for continuous chemical dynamics and associated magnetic fields in extended space-time for both wave mechanical and relativistic like chemistry of the many chemical rearrangements on and between aqueous proteins, insitu. Such non-equilibrating, multiply coupled weak acid- weak base dynamics involve p+ current modulation of π and aromatic bonds; and aromatic modulation of p+ currents within and between proteins and nucleic acids for π bond conjugative resonances and p+ tautomerisms of and between side chains and along the polypeptide backbone. Such bond dynamics result in electric current flow between side chains thru backbone and thru aqueous surroundings, and the magnetic moments of these dynamical side chain reaction centers are coupled through chemical bonds of both e- orbitals of the chains and backbone and p+ orbitals in surrounding water. Such p+ currents and magnetism cause emerging structural and dynamical effects on chemical bonds for compression rarefaction, bending and distortion beyond conventional steric influences of organic chemistry. The emerging magnetism allows torsional and rotational effects to complement the Coulombic stretch and rarefying effects during the chemical dynamics. Changing π currents and p+ orbitals of hydrogen bonding of and between many varied nucleophilic and electrophilic centers emanate magnetic fields, self-interactions and cooperatively for physiological processes of biomolecules and surrounding water. The quantized p+ transfer reactions and flux (proton orbitals) between the side chains thru the water are stimulated, organized, oriented and synchronized by the magnetism of the many, varied weak acid- weak base reactions. Thereby the peptides of the proteins organize

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themselves by the changing hydrogen bonds (p+ orbitals), resulting magnetism of p+ motions and the magnetic organization of the proton fluxes (p+ orbitals) and changing hydrogen bondings with modulation by backbone. These many coupled reversible chemical reactions form interdependent cycles of chemical patterns. The diamond-graphene backbone crushes side chains for side chain dynamics and the side chains dynamics modulate the backbone. However, unlike the CNT and diamond, the protein and nucleic acid chemical cycles involve dynamical proton (p+) transfer. The carbon nanotubes involve cycles of e- transfer. The more massive p+ manifest larger spatial torques (proton orbitals) by the weaker magnetic fields of proteins and nucleic acids for larger magnetic patterns of the proteins and nucleic acids on the micron and bulk scales relative to nanoscale magnetic patterns during catalyzed carbon nanotube formation. Furthermore, new mechanisms for aqueous nucleic acid structural, energetic, replicative, transcriptive and translative dynamics are developed on the basis of magnetic patterns and cycles of their continuous many, varied weak acid-weak base reactions and proton transfer reactions between water, phosphate, pentose and amine bases and the coupling of these various magnetic patterns and chemical cycles and chemical cycles in nucleic acids and nucleic acid-protein complexes. Such many, varied weak acid – weak base reactions and multi-proton transfers cause perturbation of various resonances and tautomers of various amine bases, pentose sugar, and phosphate linkages and cause consequent magnetism and magnetic order and changing magnetism for structural dynamics about the nucleic acids. By π bond conjugative resonances of these many dynamical amine basic, phosphate and pentose tautomers and resonances, the magnetic moments of such reversible reaction centers are coupled through p+ and e- chemical bonds. The changing resonances and tautaumerisms of the amine bases, phosphates and pentose units and the resulting generated magnetic fields organize, orient and synchronize proton fluxes (p+ orbitals) between the reaction centers with the consequent organization and dynamics of the nucleotides and nucleic acids. The changing ferromagnetism as a result of changing p+ currents within and about proteins and nucleic acids causes the diamagnetic rotation of different portions of macromolecules. On this basis, the magnetic feedback is determined for the collective synergistic of life’s chemical dynamics. Just as magnetism organizes CNT and diamond, magnetism organizes the processes of these biomacromolecules. Eternal Gratitude to GOD. For Reggie Jr and Ryan Arthur for they took you away but with every lift of the pen and every thought my soul cries for you. Someone please tell you how much I love you. In memory of Anderson Mathis Clay II, my best friend.

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Little R. B. Carbon Chemical Vapor Deposition in Intense External Magnetic Field. National High Magnetic Field Laboratory, Annual Research Reviews (2003), p. 107; In Aug 2000 written communication with Dr. Jack Crow, director of NHMFL. Little R.B. and Goddard R. Magnetization for Lower Temperature, Selective Diamond and Carbon Nanotube Formation: A Milestone in Carbon Physicochemical Condensation. Journal of Applied Physics (2004); 95: 2702. Li Z., Dervishi E., Xu Y., Ma X., Saini V., Biris A. S., Little R.B., Biris A,R., and Lupu D. Effects of the Fe-Co Interaction on the Growth of Multiwall Carbon Nanotubes. Journal of Chemical Physics (2008); 129: 074712. Little, R. B. Magnetic Orchestrated Formation of Diamond at Lower Temperatures and Pressures. Physica Scripta (2005); 71(4): 419-422. Little, R. B. On the Dynamical Ferromagnetic, Quantum Hall, and Relativistic Effects on the Carbon Nanotubes Nucleation and Growth Mechanism. Journal of Magnetism and Magnetic Materials (2008); 320(3-4): 540-547. Little R.B. and Roache J. Treatise on the Resolution of the Diamond Problem. Progress in Solid State Chemistry (2008). In Press. Shimizu K., Amaya K., Suzuki N., and Onuki Y. Superconductivity from Magnetic Elements under High Pressure. Physica B: Condensed Matter (2006); 378-380: 632635. Kroto H.W., Heath J.R., O’Brien S.C., Curl R.F., and Smalley R.E. Buckministerfullerene. Nature (1985); 318: 162. Iijima S. Helical Microtubules of Graphtic Carbon. Nature (1991); 354: 56. Dai H., Rinzler A.G., Nikolaev P., Thess A., Colbert D.T., and Smalley R.E. Singlewall Nanotubes Produced by Metal Catalyzed Disproportionation of Carbon Monoxide. Chem. Phys. Lett .(1996); 260: 471. Gilch P., Pollinger-Dammer F., Musewald C., Michel-Beyerle M.E., and Steiner U.E. Magnetic field effect on picosecond electron transfer. Science (1998); 281: 982. Wang G.M., Sevick E.M., Mittag E., Searles D.J., and Evans D.J. Violation of the Second Law of Thermodynamics for Small Systems and Short Time Scales. Phys. Rev. Lett. (2002); 89: 050601. Esquinazi P., Spemann D., Hohne R., Setzer A., Han K.H., and Butz T. Induced Magnetic Ordering by Proton Irradiation in Graphite. Phys. Rev. Lett. (2003); 91: 227201. Rode A.V., Gamaly E.G., Christy A.G., Fitzgerald J.G., Hyde S.T., Elliman R.G., Luther-Davies B., Veinger A.I., Androulakis J., and Giapintzakis J. Unconventional Magnetism in all Carbon Nanofoam. Phys. Rev. B (2004); 70(5): 054507. Makarova T.L. and Sundqvist B. Pressure Induced Ferromagnetism of Fullerenes. High Pressure Research (2003);23 (1-1): 135-41. Mombru A.W., Pardo H., Faccio R., de Lima O.F., Leite E.R., Zanelatto G., Lanfredi A.J.C., Cardoso C.A., and Araujo F.M. Multilevel Ferromagnetic Behavior of Room Temperature Bulk Magnetic Graphite. Phys. Rev. B (2005); 71:100404. Novoselov K.S., Geim A.K., Morozov S.V., Jiang D., Katsnelson M.I., Grigorieva I.V., Dubonos S.V. and Firsov A.A., Two-dimensional Gas of Massless Dirac Fermions in Graphene. Nature (2005); 438: 197. Salzmann D. and Hass M. Deuterium-Deuterium Cross-sections in Insulator and Metallic Environments. ArXiv 0806.0281v1.

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[21] Berger C., Song Z., Li X., Wu X., Brown N., Naud C., Mayou D., Li T.,Hass J., Marchenkov A.N., Conrad E. H., Edward H., First P. N., and de Heer W. A. Electronic Confinement and Coherence in Patterned Epitaxial Graphene. Science (2006); 312(5777): 1191-1196. [22] Rawat N., Gudyaka R., Kumar M., Joshi B., and Santhanam K.S. Thermogravimetric Analysis of the Interaction of Ferromagnetic Metal Atom and MultiWalled Carbon Nanotube. J Nanosci Nanotechnol. (2008);8(4):2044-8. [23] Little R.B. US Patent (2006). [24] Little R. B. Magnetocatalytic Adiabatic Spin Torque Orbital Transformations for Novel Chemical and Catalytic Reaction Dynamics: The Little Effect. International Journal of Physical Sciences (2006); 1 (4): 175. [25] Little R. B. On the Enhanced Reverse Beta Processes in Graphene-Iron Composite Nanostructures at High Temperatures in Strong Magnetic Field. The Open Inorganic Chemistry Journal. (2008); 2: 90-93. [26] Arata, Y. and Zhang Y. The Establishment of Solid Nuclear Fusion Reactor. J. High Temp. Soc. (2008); 34(2): p. 85. [27] Wendt G.L. And Irion C.E. Experimental Attempts to Decompose Tungsten at High Temperatures. American Chemical Society (1922) ; : 1887 [28] Rutherford E. Disintegration of Elements. Science (1922); LV(1425): 422. [29] Stephanakis S.L., Levine L.S., Mosher D., Vitkovitsky M., and Young F. Neutron Production in Exploding-Wire Discharges, Phys Review Letters (1972); 29(9): 568. [30] Winterberg F. Fast Thermonuclear Ignition with Two Nested High Current Low Voltage-high Voltage Low Current Magnetically Insulated Transmission Lines. Phys Letters A (2003); 318 (6): 570. [31] Rahman H.U., Ney P., Wessel F.J., and Rostoker N. Staged Pinch for Controlled Thermonuclear Fusion. Journal of Plasma Physics (1997); 58: 367. [32] Widom A. and Larsen L. Ultra Low Momentum Neutron Catalyzed Nuclear Reactions on Metallic Hydride Surface. Eur. Phys. J. C (2006); 46: 107. [33] Uman M. Scientists Close in On Source of X-rays in Lightning. University of Florida Press Release July 16, 2008. [34] Greenfield M.B., Sukuma K., Ikeda Y., and Kubo K. Delayed Gamma Radiation from Lightning Induced Nuclear Reactions. APS Meeting, (2004); Montreal, Quebec Canada. [35] Limata B., Raiola F., Wang B., Yan S., Becker H.W., D'Onofrio A., Gialanella L., Roca V., Rolfs C., Romano M., Schuermann D., Strieder F., and Terrasi F. First Hint on a Change of the 22Na β +/-Decay Half-life in the Metal Pd. European Physical Journal A: Hadrons and Nuclei (2006), 28(2), 251-252. [36] Gabiano P. Magnetic Rotary Power of Some Gases and Vapors. Ann. Phys. (1933); 20: 68. [37] Vignale G. and Rasolt M. Density Functional Theory in Strong Magnetic Field. Phys. Rev. Lett. (1987); 59(20): 2360. [38] Larbalestier D., Bird M., and Swenson C. New Resistive and Superconducting Magnet Technology (2007) CMMP-2010. [39] Scott H.P., Hemley R.L., Mao H., Herschbach D.R., Fried L.E., Howard W.M. and Bastea S. Generation of Methane in the Earth’s Mantle: Insitu High Pressure-

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In: Carbon Nanotubes: New Research Editor: Avery P. Ottenhouse

ISBN 978-1-60692-236-1 © 2009 Nova Science Publishers, Inc.

Chapter 9

BIOCOMPATIBILITY DIFFERENCES BETWEEN DISPERSED AND VERTICALLY-ALIGNED CARBON NANOTUBES: AN IN VITRO ASSAYS REVIEW A.O. Lobo1,2 , E.F. Antunes1,2; M.B.S. Palma1,3; C. Pacheco-Soares3, M.A.F. Corat4, V.J. Trava-Airoldi1,2and E.J. Corat1,2 1

Laboratório Associado de Sensores e Materiais, Instituto Nacional de Pesquisas Espaciais, CP 515, São José dos Campos/SP, CEP: 12.245-970, Brazil. 2 Instituto Tecnológico de Aeronáutica/CTA, São José dos Campos/SP, CEP: 12228-900, Brazil 3 Laboratório de Dinâmica de Compartimentos Celulares, Instituto de Pesquisa e Desenvolvimento, Universidade do Vale do Paraíba, São José dos Campos/SP, CEP: 12227-010, Brazil 4 Centro Multidisciplinar para Investigação Biológica na Área da Ciência em Animais de Laboratório – CEMIB, Universidade Estadual de Campinas (UNICAMP), Campinas/SP, CEP:13083-877, CP 6095, Brazil

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ABSTRACT An overview about carbon nanotube (CNT) production and quality parameters will be presented, as well a review of current literature about “in vitro” assays commonly used to evaluate the biocompatibility of CNT. The limits of colorimetric assays for CNTs evaluation will be discussed, using comparisons between dispersed CNT and CNT arrays. The influence of nanotopography and wettability of CNT scaffolds for cell adhesion will be shown. Studies carried out in our laboratories with vertically-aligned carbon nanotubes (VACNT) will also be presented. We have shown the interaction among CNT (VACNT) and four cell lines: mouse fibroblasts (L-929), mouse embryo fibroblast (C57/BL6) with or without green fluorescent protein (GFP) and human osteoblast (SaOS-2). The biocompatibility tests were performed with in vitro tests on raw-VACNT and after superficial modification by O2 plasma, which changes its hydrophobic character. The non-toxicity, cell viability, proliferation and cell adhesion were evaluated by: (i) 2-(4,5dimethyl-2-thioazoly)-3,5-diphenyl-2H-tetrazolium bromide (MTT) assay; (ii) Lactate dehydrogenase (LDH) assay; (iii) neutral red (NR) assay; (iv) Scanning electron

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A.O. Lobo , E.F. Antunes; M.B.S. Palma et al. microscopy (SEM); and fluorescence microscopy. The influence of catalyst type, VACNT density and superficial modification were evaluated by morphological, structural and superficial techniques: SEM, Transmission electron microscopy (TEM), Raman spectroscopy, contact angle (CA) and X-Ray Photoelectron Spectroscopy (XPS). High cell viability, exceptional cell adhesion and preference were achieved.

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INTRODUCTION The development of nanostructured biomaterials is very promising because they present good similarity with natural nanostructures components of the extra-cellular matrix (ECM), present in all body tissues. The ECM consists predominantly of interwoven protein fibers such as collagen or elastin that have 10-300nm diameter [1] Cell adhesion to ECM is central to the organization, maintenance, and repair of numerous tissues. Adhesive interactions provide tissue structure and generate anchorage forces that mediate cell spreading and migration, neurite extension, muscle cell contraction, and cytokinesis. Moreover, cell adhesion triggers signal regulating survival, cell cycle progression, and expression of differentiated phenotypes in multiple cell systems. Among other nanomaterials, carbon nanotubes (CNT) promise a great role for the study of tissues regeneration [2,3,4,5,6,7]. The electronic structure, the surface morphology, and exceptional mechanical properties of CNT are typical of graphite-like structures, but they can be distinguished by their tubular construction with nanometric diameters and high aspect ratio, i.e., they are considered a fibrous material [8,9,10] CNT, hence, present physical dimensions similar to ECM components and are appropriated to mimic their features [11] For binding interactions between cells and biomaterial surfaces, it has become increasingly evident that cells are influenced by spatial domains, structural composition and mechanical forces at the micro and nanoscale [12]. Cellular adhesion is generally dependent on time, adhesive forces between one or more cells, and surface topography/wettability [13] Understanding the sensory and regulatory mechanisms that are involved in cellular adhesion will provide key advances in development of biomaterials. Study of cellular adhesion to CNT or CNT composites may give further knowledge about the interaction with biomaterials and the importance of ECM biomimetic. Recent studies focusing on the development of porous materials, called scaffold, made of composites CNT/polymer, for sustained three dimensional growth of cell, are of particular interest in regenerative medicine and tissue engineering [14,15,16,17]. Besides the great importance of cellular adhesion, the evaluation of CNT biocompatibility and cytotoxicity is also fundamental. Cellular adhesion is not even possible if the material is not biocompatible. Evaluation of the CNT biocompatibility consists of numerous tests and includes in vitro (using cells and tissues) tests, ex vivo (whenever applicable) tests, animal models, and clinical trials [18]. Basically two types of in vitro tests are found in the literature: one with CNTs dispersed in the cell culture [19,20,21,22,23,24,25,26] and the other with CNTs held in some structure in contact with the cell culture [27,28,29,30,31] For cells in vitro culture with dispersed CNTs, many studies suggest a low biocompatibility, while others give the opposite conclusion [32,33,34,35]. Other studies show an obvious preference of cell growth on a CNT surface . Several studies highlighted the interference of CNT and other carbon based materials with cytotoxicity dyes,

Biocompatibility Differences between Dispersed and Vertically-Aligned Carbon… 283 commonly used to study integrity, viability and proliferation of cell [35,36,37,38,39,40,41] Besides that, remains the question if the cytotoxicity is due to CNT itself, or due to its contaminants, as metallic particles or amorphous carbon structures, generated simultaneously to CNT production process. Clearly, the studies that obtained good cell viability present some kind of purification or functionalization of the CNT. Some authors suggest that functionalization is necessary to increase cell viability [42] Others, on the contrary, show that functionalization increases cytotoxicity [43] In summary, it is still early to establish a general toxicological profile for CNT material and more systematic in vitro and in vivo investigations are necessary. For that, efforts are arising to explain and clarify their bio-properties and usefulness.

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1. CARBON NANOTUBES: AN OVERVIEW The carbon element, in sp2 hybridization, can form a variety of structures, from high ordered pyrolytic graphite to nanocrystalline structures, such as fullerenes (or buckyballs), nanographite, carbon whiskers, carbon black, carbon nanofiber and CNT [44,45,46,47,48,49,50,51]. Specially, CNT have been the focus of considerable study because of their excellent mechanical [52] electrical [53,54], thermal [55,56], magnetic [57,58] and biomimmetic properties [59]. This unusual set of qualities is due to their graphitic structure combined with their high aspect ratio: nanosized diameter with length of even tens of millimeters. Research in nanotechnology has been recently supported by governmental and private investments in several countries around the world, mainly in USA and Japan [60]. Potential practical applications have been reported in many areas of knowledge with important contribution to the society, such as chemical sensors [61], field emission materials [62], electronic devices [55], anode for lithium ion in batteries [63], supercapacitors [47][47] and hydrogen storage [64]. Special attention has been developed for polymeric composites based in CNTs, where they can be used as reinforcements in structural materials, for aerospace and aeronautical purposes. Tissue engineering is another field in which CNTs probably will have success as composite due also their dimension, which are similar to extra cellular matrix [65,66,67]. Generally CNT are classified by the manufacturers in: single-walled (SWCNT) and multi-walled carbon nanotubes (MWCNT), according to the number of concentric graphene sheets present in each tube and diameter. A CNT can be visualized as a sheet of graphite that has been rolled into a tube with end caps containing pentagonal rings. In general, the nanotubes can be specified in terms of tube diameter and the chiral angle [68.69] In laboratory scale, SWCNT with defined chirality are already achieved, which is very important to control electrical properties of the tubes (metallic and semiconductor) [70,71]. Currently, several companies have already produced CNTs in industrial scale [72]]. Global demand for nanotubes will expand rapidly from a small base to over $200 million in 2009 [73]. The CNTs can be commercialized in powder form [74] or supported by a substrate [75,76,77] or even dispersed in liquids [78,79], ready to be mixed in specific polymers, which is called “masterbatches”. When the CNTs are supported by a substrate, they are called films. Films

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can be built patterned in arrays with different geometries, by conventional and innovative lithography techniques. The price can vary if CNTs are raw, purified or functionalized, and still by both length and diameter distributions of the tubes. High degree of purity is required for some applications, hence all residues of chemicals used during the production process and amorphous carbon contents should be removed. Purification is usually carried out in a multistep process, involving the controlled oxidation of amorphous carbon, followed by removal of catalyst particles with mineral acids and thermal annealing [80,81]. Functionalization can be equally important to obtain homogeneous powder dispersion in polymers [82], or even to help in recognizing certain substances [83], if used as sensor electrodes, for example. Wettability is also greatly affected by functional groups presents in material surface [84,85]. CNT surfaces can change from superhydrophobic to superhydrophilic with simple chemical or physical oxidative treatment [86,87,88]. The structure and properties of CNT are highly sensitive to the production method and synthesis parameters. There are three techniques commonly used for industrial production of CNTs: arc discharge [89,90,91], laser ablation [92,93] , and chemical vapor deposition (CVD) [94] . Particularly, CVD based methods are more used for mass production due to their versatility and low cost [95,96,97], although CNTs produced by laser ablation and arc discharge have a advantage of better crystalline quality. A comparison of these techniques is given in Table 1. Arc Discharge method creates CNT through arc-vaporization of two carbon electrodes placed end to end, separated by approximately 1mm, in an enclosure that is usually filled with inert gas (helium, argon) at low pressure (between 50 and 700 mbar). A direct current (between 50 and 120 A) carried by a driving potential of 30 V creates a high-temperature plasma (>3000 °C) between the two electrodes [98]. Both SWCNT [99] and MWCNT [99] can be produced by this process. The laser-ablation technique operates at similar conditions to arc discharge, since the optimum background gas and catalyst mix [100]. A pulsed (100KW/cm2) [101,102], or continuous (12kW/cm2) [103,104] laser is used to vaporize a graphite target in an oven at 1200 °C, in a chamber filled with helium or argon gas at 500 Torr. The CVD synthesis is achieved by insertion of a hydrocarbon in the gas or vapor phase and using an energy source (plasma, resistively heated coil) for a dehydrogenation reactions, with presence of transition metal catalyst (Fe, Ni, or Co), at temperatures ranges of 5001000oC [105]. Therefore, CVD technique consists in two steps: catalyst preparation and the actual reaction. Catalysts are usually prepared on a substrate using one of four techniques: (i) sol-gel [106], (ii) impregnation [107], (iii) metallo-organic CVD [108] or (iv) co-precipitation methods [109]. More common CVD variants reported in the literature are: thermal CVD [110], plasma CVD[111,112], High pressure CO disproportionation (HipCO) [113] and fluidized beds [114]. The last one is the more effective scale-up process. Other published methods include plastic pyrolysis [115], flame synthesis [116], liquid hydrocarbon synthesis [117], a solar furnace [118], electrolysis [119]] ball milling of graphite [120,121] and plasma torch [122].

Biocompatibility Differences between Dispersed and Vertically-Aligned Carbon… 285 Table 2. More common production methods of CNT

Laser Ablation

Arc Discharge

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Thermal CVD

Plasma CVD

CNT Type: MWCNT, SWCNT high purity. Carbon source: a graphite target vaporized by laser (continuous or pulsed). Temperature: ~3000oC. Catalyst: Fe, Ni, Co,Y, Mo mixed to graphite target (or without catalyst). Vacuum Parameters: 500 Torr. Auxiliary Gases: inert atmosphere (He, Ar).

CNT Type: MWCNT, SWCNT. Carbon source: arc-vaporization of two carbon rods placed end to end, separated by ~ 1mm.. Temperature: ~3000oC. Catalyst insertion way: without or with catalyst, doping of anode with metals (Ni, Fe, Co,Y,Mo). Vacuum Parameters: 50-700 mbar. Auxiliary Gases: inert atmosphere (He, Ar).

CNT Type: MWCNT, SWCNT. Carbon source: hydrocarbons gas or vapor (methane, ethylene, camphor, xylene, toluene, etc.). Temperature: 600-1100oC (heating by furnace). Catalyst insertion way: thin film or continuous insertion. For the first one deposited by spin or dip coating, sputtering or evaporation methods (e-beam) on substrates or continuous insertion for vaporization of organo-mettalic (ferrocene) or colloidal solution from salts. Vacuum Parameters: low and atmospheric pressure. Auxiliary Gases: Ar, N2, H2.

CNT Type: MWCNT, SWCNT. Carbon source: similar to thermal CVD. Plasma: commonly excited by direct current (DC), radiofrequency (RF), microwave (MW). Temperature: similar to thermal CVD. Catalyst insertion way: similar to thermal CVD. Vacuum Parameters: low pressure. Auxiliary Gases: NH3, H2, Ar, He.

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A.O. Lobo , E.F. Antunes; M.B.S. Palma et al. Table 2. (Continued)

Fluidized-bed CVD “High yield production”

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HiPCO – CVD “High yield production”

CNT Type: MWCNT. Carbon source: ethylene, acetylene, propylene, methane. Temperature: 500-850oC. Catalyst insertion way: Fe, Ni, Co-Mo, Ni-Cu in porous substrates (powder form) suspense in a fluidizing medium gas. Since the catalyst is highly porous, the process happens not only at the catalyst particles surface but also inside them, promoting their rupture and disintegration and continues to grow (“expanding universe mechanism”). Vacuum Parameters: ambient pressure, similar to thermal CVD. Auxiliary Gases: H2, N2 and Ar.

CNT Type: SWCNT. Carbon source: CO. Temperature: 800-1200 oC. Catalyst insertion way: catalyst is formed in situ by thermal decomposition of Fe(CO)5, which is delivered intact within a cold CO flow and then rapidly mixed with hot CO in the reaction zone. Vacuum Parameters: high pressure (>10 atm).

The concept of CNT quality is not well-defined in the literature. Consequently, to determine the degree of purity of CNTs, some companies and researchers have defined a set of scientific techniques to evaluate the material produced. For morphological analyses, high resolution scanning electron microscopy (SEM) are used to evaluate density, length and external diameter of tubes; and transmission electron microscopy (TEM) for analyses of internal structures, numbers of graphitic sheets and catalyst nanoparticles. However, to be considered pure it is necessary that the powder or the thin films have graphitic characteristic and to be free of amorphous carbon and residuals of catalysts. Raman spectroscopy and X-ray diffraction are main techniques to analyze graphitic crystallinity. The content of amorphous carbon and other impurities can be estimated by thermogravimetric analyses. For functionalized or doped CNT, infrared spectroscopy and X-ray photoelectron spectroscopy (XPS) can identify functional groups attached to the surface or to the structure of the tubes. In table 2, there is a summary of key characterization techniques for evaluation of CNT morphology and crystalline structure [123] Table 2. Characterization techniques of CNTs

High resolution transmission electron microscopy (HRSEM) [124]

Powder and films analyses Visualization: CNT type, tips, films homogeneity, alignment. Measurement: density, length and external diameter of

Biocompatibility Differences between Dispersed and Vertically-Aligned Carbon… 287 CNTs. SWCNT: 1-10 nm of external diameter. MWCNT: 10-100nm of external diameter. High resolution transmission electron microscopy (HRTEM) [125]

Raman spectroscopy

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[126,127,128,129,130,131,132,133]

X-ray diffraction [134,135]

Powder analyses Visualization: CNT type, internal structures, defects on tube walls. Measurement: outer and inner diameter, number of concentric and intershell spacing of graphene sheets and helicity. Impurity detection: visual verification of nanosized metallic catalyst both outside and inside of the tubes, presence of amorphous carbon and other structures.

Graphitization degree: in general, the narrower bandwidths, the more graphitic the material is. Intensities ratio between D and G band near zero, high intensity G’ are other important indicators. D and G’ position are highly sensitive to laser wavelength, with left shift for lower laser energy. SWCNT: RBM mode (100-500cm-1)*, Asymmetric G band (1583 cm-1)*, chirality information (Kataura Graph). MWCNT: similar to microcrystalline graphite , with G, D, D´ and high intensity G´(2450 cm-1)* band. Vertically -aligned MWCNT films: intensitiy ratio between D and G band can be higher than 1 , if laser were irradiated on the nanotubes tip. Amorphous carbon detection: D and G band are convoluted and G’ band is of very low intensity *laser wavelength: 514,5 nm.

Graphitization degree: presence of peak (002), larger than in HOPG and close to the value determined in turbostratic graphite, shifted to lower 2θ. Evaluation of interlayer spacing and structural strain of graphene sheets for MWCNT. Impurity detection: crystalline residuals of production process (metallic catalyst).

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Thermogravimetric analysis (TGA) [136,137,138]

Infrared spectroscopy (IR) [132,139,140]

X-ray photoelectron spectroscopy (XPS)

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[141,142,140]

Evaluation of thermal decomposition of CNT in air ( 30 – 1000oC), or in inert atmosphere. MWCNT: ~ 600oC in air. SWCNT: -450oC (HipCO). Amorphous carbon detection: material decomposed with temperatures below 400oC. Impurities detection : residues of the burning can be analyzed by atomic absorption or energy- dispersive xray spectroscopy (EDS).

CNT active modes: A2u (850 cm-1) and E1u (1575 cm-1), shifted 5 and 8 cm-1, respectively. Functionalization detection: functional groups (-C-O, COOH, -C=O, -C-H, -NH, -NO, etc.) Generally transmission method, using KBr pellets are preferred with just very small quantities, for that transparency to be maintained. Impurities detection: impurities remaining from synthesis or molecules capped on the CNT.

Information about the chemical structure of CNT. But the most widely used for data refers to the structure modifications of the CNT walls due to the chemical interaction organic compounds or gases adsorption. CNT Peak: C1s (284.6 eV), with negative shifted and larger than HOPG. Functionalization detection: Functional groups (-C-O, COOH, -C=O, -C-H, -NH, -NO, etc.)

Some initiatives to establish protocols for nanometrology has been implanted in several countries, by mean of their metrology institutes, including Instituto Nacional de Metrologia (INMETRO) in Brazil [143]. In particular, the American National Institute of Standards and Technology (NIST) has recently published detailed guidelines for making essentials measurements on samples of SWCNT[144,145]. Obviously, depending on application, additional data can be required, as measurements of electrical resistivity, mechanical strength or thermal conductivity, for example. It is recommended to know deeply the characteristics of the samples studied, mainly for biological tests. The CNT types (MWCNT or SWCNT), presentation form (films, powdered, or in masterbatches), method of production and its catalysts, and purification techniques or presence of functionalization, can deeply influence the results. For any future biomedical application, the warranty of quality is primordial, since human lives are involved.

Biocompatibility Differences between Dispersed and Vertically-Aligned Carbon… 289

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2. CYTOTOXICITY ASSAYS IN VITRO The evaluation of the biocompatibility consists of a sequence of tests and includes in vitro (using cells and tissues) tests, ex vivo (whenever applicable) tests, animal models, and clinical trials. Several guidelines and procedures have been standardized for these purposes (such as the American Society for Testing and Materials, or ASTM, and the International Organization for Standardization, or ISO)[146] In vitro tests in cell culture have been used successfully to evaluate the cytotoxicity of biomaterials. Cellular in vitro models have provided an exceptionally versatile test for evaluating aspects of the biocompatibility of materials. Certainly, these models are very good for studying functions (and pertinent mechanisms) of one cell line at a time. Such approach, however, provides a limited perspective of the complex milieu of the body. The preferred cells used for permanent culture are from established cell lines purchased from biological suppliers or cell banks (L-929, SaOS-2, CHO-K1, HeLa, Vero, etc.). Primary cells (that are freshly harvested from live organism) are also used, despite they have less assay repeatability, reproducibility, efficiency, and, in some cases, availability. Primary cells have more fidelity to original organism, without alteration caused by selective aspect of continuous passages in culture, as observed in the cell lines [18]. L-929 mouse fibroblast cell line has most extensively been used for testing biomaterials, because they are easy to maintain in culture and produce results that have a high correlation with specific animal bioassay [147]. Cell lines from others tissues or species may also be used. Selections of a cell line are based upon the application of the biomaterial, type of assays, and measurement endpoints (viability, enzymatic activity, species specific receptors, etc.). The most common cell culture assays used for evaluating biocompatibility are: direct contact, agar diffusion and extract elution [147]. The three assays differ in the manner in which the test material is exposed to the cells. Commonly, to standardize the methods and compare to the results of these assays, the variables (number of cells, growth phase of the cells, cell type, duration of exposure, test sample size and surface area of test sample) must be carefully controlled. The potential with which CNTs can be applied in biomedical engineering and medicinal chemistry is highly dependent upon biocompatibility. The cytotoxicity of CNTs has been investigated in vitro with dispersed CNT in culture medium [19,20,21,22,23,26] some structure for cell growth [27,28,29,30,31] and on CNT scaffolds [14,15,16]. Therefore, investigating effect of CNTs on human cells and their interaction mechanism is of very importance [148]. In next section, the main in vitro tests used to evaluate CNT cytotoxicity are explained, showing their limits and applications.

3. COLORIMETRIC ASSAYS AND CNT Most of in vitro viability assays are used to evaluate acute cytotoxicity: such as 2-(4,5dimethyl-2-thioazoly)-3,5-diphenyl-2H-tetrazolium bromide (MTT), Neutral Red (NR), Commassie Blue (CB), Alamar Blue (AB) and enzyme lactate dehydrogenase (LDH) assays. These assays are based in optical absorption and evaluate the cellular function by a reduction

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of a detectable product by specific enzymes (ELISA – Enzyme-Linked Immunoabsorbent Assay), thereby determining vital physiological activity. In MTT assays, tetrazolium salts are widely used for measuring the metabolic activity of cells, because of the simplicity of the test set-up. These salts are known to be reduced by various dehydrogenases enzymes [149]. The specificity of their reactivity is defined by positively charged quaternary tetrazole ring core containing four nitrogen atoms. In the case of the positively charged MTT one of the atomic groups is replaced by a thiazolyl ring [150]. The net positive charge of MTT supports the cellular uptake via the plasma membrane. MTT is thought to be nearly exclusively reduced, intracellularly, into its formazan, by a variety of cytoplasmic substrates, including NAD(P)H-oxireductases, but also by the mitocondrial enzyme succinate dehydrogenase. The amount of formazan formed is directly proportional to the number of metabolically active cells in the culture, which can be quantified spectrophotometrically after dissolving the formazan in an organic solvent [151] After removal of the medium, generally an ethanol-dymethyl sulfoxide (DMSO) solution (1:1) is added. After complete solubilization of the dark blue crystal of MTT formazan, the absorbance is measured at 570 nm. Variations of the MTT tests are: (i) the 3-(4,5dimethylthiazol-2-yl)-5-(3-carboxymethoxyphenyl)-2-(4-sulfophenyl)-2H-tetrazolium (MTS) tests described by Barltrop [152], and (ii) 2-(4-iodophenyl)-3-(4-nitrophenyl)-5-(2,4disulfophenyl)-2H-tetrazolium (WST-1) [37]. The NR cytotoxicity assay is based on the ability of viable cells to incorporate and bind neutral red, a weak cationic dye that readily penetrates cell membranes by non-ionic diffusion [153]. It accumulates in the lysosomes of cells where it binds to the sensitive lysosomal membrane. Cells damaged by xenobiotic action have decreased ability of taking up and binding NR, so that viable cells can be distinguished from damaged or dead cells. The dye can be extracted from intact cells using a solution of 1% [v/v] acetic acid and 50% [v/v] ethanol and the absorbance or fluorescence of dissolved dye can be determined [153] The test is very sensitive, specific, and readily quantifiable. Recent literature has highlighted absorptive interferences between carbon black and cellular viability markers such as NR resulting in false readings [39] as in the absence of human epidermal keratinocytes, a false negative signal was generated, inaccurately indicting the presence of viable cells. The enzyme lactate dehydrogenase (LDH) is a marker for membrane integrity in cells and therefore for cell viability and proliferation. The enzyme LDH is freely located in the cytoplasm and upon membrane damage it releases into the surrounding media [154]. This assay detects the presence of LDH in the medium indirectly because the tetrazolium salt INT is reduced in a LDH-dependent reaction with this assay. This enzyme can be detected by measuring its catalytic activity and indirectly the conversion of 2-(4-Iodophenyl)-3-(4nitrophenyl)-5-phenyl-2H-tetrazolium chloride (INT) to another water-soluble formazan dye [154]. The AB assay is designed to quantify the proliferation of various cell lines and is widely utilized to measure cytotoxicity. Viable proliferating cells cause a reduction of the dye causing a color change from a non-fluorescing indigo blue (oxidized) to a fluorescent pink species (reduced). One main advantage of this dye lies in its water solubility. It therefore requires no solvent extraction step and hence cellular viability is unaffected allowing multiple tests to be carried out on the cells. Measurements may be made by absorbance monitoring of AB supplemented cell culture medium or, alternatively, fluorescent measurements can be made [155,156]. The absorbance spectra of the oxidized and the reduced forms overlap.

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Biocompatibility Differences between Dispersed and Vertically-Aligned Carbon… 291 Therefore the absorbance measurements must be made at the absorbance maxima of each form, namely 570 and 600 nm. Fluorescent measurements can be made by exciting from 530 to 560 nm and recording emission at 590 nm [155,156] Other spectroscopic methods are routinely available, including measurement of protein’s intrinsic UV absorbance, and methods generating a protein-dependent color change, namely the Lowry assay and the Smith copper/bicinchoninic assay are well established. The simplest and most sensitive test is the Bradford assay, introduced in the mid 1970s, and based on the equilibrium between three forms of Commassie Brilliant Blue-G250 dye, which binds specifically to tyrosine side chains of protein molecules but not to other cellular constituents. Within the linear range of the assay (approximately 5-25 μg/mL), the more protein present, the more Commassie binds due to hydrophobic and ionic interactions [157,158]. The colorimetric assays also have largely been used to evaluate cell viability of CNT dispersed (various concentrations) or on structures, using several cell lines. De Nicola et al. evaluated the cell viability using MWCNT dispersed in cell culture, produced by electric arc discharge and CVD process. Independently of the CNT type, apoptosis is not induced over the basal level up to 48h of exposition [159]. Mwenifumbo et al. showed that osteoblastic cell cultures have a high metabolic activity on MWCNT constructs produced by CVD method, using MTT and LDH assays [160]. Kalbacova et al. showed a decrease of about 15% in osteoblastic metabolic activity by MTS assay for SWCNT dispersed in culture, compared to the control, but inferior to the Ti6Al4V (20%). This decrease was associated to the impurities of CNT synthesis [161]. Zhang et al. have shown a reduction of the primary osteoblast cell viability (60%) using MTT assays with CNT dispersed in culture (concentration of 00100µg/ml) [162]. However, several studies highlighted the interference of CNTs, and other carbon based materials, with cytotoxicity dyes, including MTT, NR, WST-1, CB and AB [35,36,37,39,41]. These observations indicate that CNT agglomerates, interfering with reaction products (specifically enzymes) or cell culture medium, which give erroneous reading of these colorimetric assays. Woörle-Knirsch et al. used three assays to evaluate the cytotoxicity of dispersed SWCNTs (MTT, WST-1 and LDH) with A549, ECV and NR-8383 cells. The MTT assay produced a false positive to toxicity, while WST-1 and LDH provided high viability. The problem with MTT assay is that SWCNTs bind to the MTT formazan crystal and stabilize their chemical structure and, as consequence, these crystals cannot be solubilized [35]. Casey et al. checked the interference of dispersed SWCNT with CB, AB, NR, MTT and WST-1 dyes with A549 cells. For checking of CB interference with SWCNTs, a two set of experiment varying the concentration of the dyes were performed. The absorbance was observed (1) only with the dye (control) and (2) with the dye and SWCNTs in a 1:1 mass ratio, and expressed as percent of control. CB, AB, MTT, and WST-1 assays presented reduction in the associated absorbance at all concentration for set 2, with significant toxicity at different SWCNT concentrations: above 0.25mg/ml for CB, 0.4 mg/ml for AB, 0.003mg/ml for MTT, and 0.4mg/ml for WST-1. However, an increase of absorbance was verified with NR dyes, with SWCNT concentration above 0.08 mg/ml [37]. This is an indicative that, beside the CNTs interacts with each dyes, they produce different responses. These observed interferences between CNT and the colorimetric dyes indicate that colorimetric assay must be used cautiously to analyze CNT cytotoxicity. Always that it is possible CNT sample should be removed from the cultured cells before applying the colorimetric assay. This is the normal recommendation of all assays. However, if CNT are

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dispersed in the culture and its filtration is not possible, only assays in which CNT do not interfere should be used.

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4. INTERACTION CELL-TO-CNT Properties of CNTs in in vitro biological studies about interaction cell-to-CNT have been provided mainly with the cells involved into the ECM stability and anchorage-dependent cells as fibroblasts, osteoblasts, epithelial cells, among others. Carbon nanoparticles containing materials gave good support to adhesion and growth of bone-derived cells, and they can be considered as promising for construction of bone implants and bone tissue engineering. Adhesion of anchorage-dependent cells (like osteoblast) is a crucial prerequisite to subsequent cell functions such as proliferation, synthesis of proteins (e.g. ECM, morphogenic factors and osteoinductive molecules) and formation of mineral deposits. The cell adhesion is primarily mediated by integrins, a widely expressed family of trans-membrane adhesion receptors [163]. Upon ligand binding, integrins rapidly associate with the actin cytoskeleton and cluster together to form focal adhesions, discrete complexes that contain structural and signaling molecules [164]. The use of cell cultures (osteoblasts, fibroblasts, endothelial cells, mesenchymal stem cells derived from bone marrow) allows a quantitative analysis of cell adhesion necessary to understand cell-material surface interaction. Thus measurement of cell adhesion of cell cultures grown in presence or absence of CNTs will provide additional information about cell physiology. Homeostasis is maintained in multi-cellular organisms by a balance between cell proliferation and cell death. Several types of cell death have been described: apoptosis (type I), cell death associated with autophagy (type II), necrosis or oncosis ( type III) [165]. Cells undergoing apoptosis show typical, well-defined morphological changes, including plasma membrane blebbing, chromatin condensation with margination of chromatin to the nuclear membrane, karyorhecis (nuclear fragmentation), and formation of apoptotic bodies. Apoptosis has been characterized by several biochemical criteria, including different kinetics of phosphatidylserine (PS) exposure on the outer leaflet of plasma membrane [166,167], changes in mitochondrial membrane permeability [168], release of intramembrane space mitochondrial proteins [169], and caspase-dependent activation and nuclear translocation of a caspase-activated DNase resulting in internucleosomal DNA cleavage [170]. Identification of these morphological and biochemical markers of apoptosis makes it possible to distinguish it from other forms of cell death. Necrosis is characterized by rapid cytoplasmic swelling and is therefore also often referred to as oncosis. Necrosis has long been described as a consequence of extreme physicochemical stress, such as heat, osmotic shock, mechanical stress, freeze thawing and high concentration of hydrogen peroxide [171]. However, many different cellular stimuli (TNF on certain lines, ds RNA, IFN-γ, ATP depletion, ischemia ) have shown to induce a necrotic process that follows defined steps and signaling events reminiscent of a true cell death program [171]. The literature about the health effects of CNTs suggests a potential toxicity of this new material [172]. In particular, the first studies, focused mainly on inhalation and dermal

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Biocompatibility Differences between Dispersed and Vertically-Aligned Carbon… 293 exposure, revealed a pulmonary [39,173,174] and dermal [39,175] toxicity. The surprising developments of cell toxicology in recent years led to the recognition of two different type of cell death: apoptosis is a cell-intrinsic mechanism that leads cells with mild damage to choose self-elimination [176,177] whereas severe damage leads cells to passively die by necrosis [178,179]. Recents studies have been reported about cell behavior considering analysis of proteins involved with adhesion, proliferation, cell activity, cell spreading, even apoptotic signaling proteins to clarify the relationship of cell with CNTs components. Cell behavior such as proliferation, cell activity, cell spreading, cytoskeleton architecture and cell adhesion are correlated [180]. Cell spreading and cell morphology have been correlated with changes in cell survival, cell proliferation and cellular differentiation [13]. It seems that the number of focal adhesion is proportional to cell spreading [181] Cell adhesion to biomaterial involves ECM proteins, cell membrane proteins, and cytoskeleton proteins, which interact inducing signal transduction, regulating the activity of transcription factors and consequently modulating gene expression. Knowledge about interaction of cells with the biomaterial will influence the understanding of the cell capacity to proliferate as well as to differentiate on the biomaterial. Focusing mainly the applicability of CNTs to biomaterials, cellular proteins and their expression have been studied. The interest in biological response of signaling proteins is increasing each day. For checking how the proteins are involved at the interaction process of cell to CNTs, diverse assays have been used including Western blot analysis, immunocytochemical, immunofluorescence imaging, flow cytometry analysis and even molecular analysis of DNA integrity and mRNA transcripts. The most common assay for the analysis of proteins that has been done is the immunofluorescence, due the reliable detection of the target protein by specific immune reaction and possibility of localization of the protein inside of the cell. This methodology is based on reaction recognizing epitope of protein by specific antibody. That has been used mainly for visualization of morphology of the cell and localization of determined target proteins involved with adhesion, apoptosis and cytoskeleton organization. Adhesive proteins like vinculin, actin, cadherin, fibronectin were usually used for cytoskeleton and adhesion studies [6,16,160,161]. In general, considering the use of SWCNTs studies have shown an altered organization and decreased amount of those adhesive proteins inside the cells grown with CNTs. The actin stress fiber was observed thinner and diffused when the SaOS-2 cells were grown with SWCNTs, furthermore vinculin formed small patches all around the cells and actin filaments did not convincingly end in these spots, differently to what happened when those cells were cultured on glass as well as on titanium alloy [161]. On the other hand, human cervical carcinoma HeLa cells showed altered in their morphology when they grew on SWCNTs, but their morphology were similar to the cells on the glass when they grew on MWCNTs slide. The focal adhesion kinase (FAK) distribution inside the cells also showed different on SWCNTs (peripheral) and on MWCNTs (homogenously and distributed in whole cell body) [160]. This suggested a variation of the cell behavior according with the type of CNTs where it has grown on. Moreover, other fluorescence technologies were used to stain DNA for cell death analysis by terminal deoxynucleotidyl transferase nick and labeling (TUNEL) [187] and another methodology from Sigma system for checking apoptosis/necrosis [16]. The first technology is a tool to estimate apoptosis/necrosis after cell had lost membrane integrity and DNA cleavage

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had occurred. The results from TUNEL showed the epithelial and mesothelioma cells exposure to SWCNTs bundles (30 μg/mL) for 5 days had no notable effect on programmed cell death. Instead, when those cells were cultivated on raw material SWCNTs the epithelial cells were also not affected, but in contrast, the mesothelioma cells formed agglomerates [187]. It had showed that different cells may have different behaviors with CNTs. The second technology were used for morphological detection of necrotic and apoptotic cells. After 24h of culture, the HeLa cells on amylase-wrapped SWCNTs and acid-treated MWCNTs were healthy and similar with the healthy control cultivated on a glass slide, while only few cells cultured on MWCNTs were in programmed death phase. On the other hand, most cells cultured on SWCNTs and acid-treated SWCNTs were in a late stage of apoptosis [16]. Different treatments in CNTs structure presented different response on interaction of cell to CNTs. Propidium iodide fluorescent was also used for apoptosis analysis and for checking the different phases of cell cycle using a complementary technology of flow cytometry using FACScan Flow cytometer with Cell-Fit software (Becton Dicknson Instruments). In this assay the cell suspension was passed through a 19-gauge needle and the number of cells in different phases of the cell cycle was analyzed (G1; S; G2/M and apoptosis phases). These results confirmed that SWCNTs could cause cell cycle arrest in G1 and induce HEK293 cells apoptosis in a dose- and time- dependent manner [6]. Which were also in accordance with relatively low cell viability of cells cultured with SWCNTs. Immunocytochemistry reaction is a simple and powerful technology and it is generally used to measure protein expression. The protein expression indicates the presence and the quantity of protein are being produced by the cell in determined environment. The technology used to get that was assessed by few groups so far. It is a promising field to better understand the processes triggered into the cells when they had been interacting with CNTs. Western blot was a simple and potent methodology used to check the expression of the adhesive proteins such as laminin, fibronectin, FAK, cadherin and a cycle protein cyclin D3 in HEK-293 cells. All the proteins analyzed dropped their expression gradually as the culture days and the amount of SWCNTs increased [6]. Furthermore, ELISA was applied to quantify proteins involved with cellular adhesion such as vinculin and talin, with osteoblast differentiation as osteocalcin and with immune activation as I-CAM. Human osteoblast-like MG 63 cells were seeded on different substrates such as pure terpolymer of polytetrafluoroethylene, polyvinyldifluoride and polypropylene (Ter), terpolymer mixed with 4 wt.% of single-wall carbon nanohorns (SWNH), or 4wt.% of highly crystalline electric arc multi-wall carbon nanotubes (MWCNT) and tissue culture polystyrene (TCPS). ELISA assay revealed that the cells on the material with SWNH contained a higher concentration of vinculin and talin (by 56±21% and 35±6%, respectively) in comparison with the values in cells on the pure terpolymer. The concentration of osteocalcin was similar in cells on both the NH-SWCNT and the pure terpolymer, and also TCPS. However, in cells on samples with A-MWCNT, the concentration of osteocalcin was significantly lower (by 14±2% and 10±1%) than the concentration in cells on the pure terpolymers and TCPS. The authors had suggested that it could be explained by a higher proliferation activity of these cells, which might delay the process of cell differentiation. In addition, the concentration of I-CAM was not increased in cell samples from both nanotube-modified terpolymer [182]. Continuing the protein analysis and highlighting the importance of those kinds of studies, Cui and Partners in 2005, using molecular biology, applied a sophisticated and modern

Biocompatibility Differences between Dispersed and Vertically-Aligned Carbon… 295 technique for gene expression analysis. Expression levels of genes associated with cell cycle, cell apoptosis and signal transduction in HEK293 cells cultured with 25 μg/ml of or without SWCNTs for two days were analyzed by oligonucleotide microarrays. That report showed alteration at 60 genes, which indicated that HEK293 cells were arrested in the G1 phase, with Rb/P53 as the main apoptosis pathway induced by SWCNTs. Apoptosis-associated genes and cell cycle genes exhibited up-regulation expression. Genes involved in G1/S; S; G2; M phases and associated with signal transduction showed down-regulation expression. These results fully corroborated that SWCNTs prevented the cells to go on continuation from G1 phase toward S, G2 and M phases. Deepen the protein analysis it will be possible to confirm or to check some hypothesis or yet to make a hypothesis based on universe of protein expression when cells are cultured with CNTs. Despite the studies with SWCNTs, in general, show troubles to cell proliferation and survival, studies using different types of CNTs, with different treatments look to be promising and need to be performed to increase the clarification about bioproperties of CNTs.

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5. CARBON NANOTUBES AS SCAFFOLD FOR CELL GROWTH: Cell seeding and growth studies have been performed on scaffolds made of CNT in recent years. The use of MWCNTs supported by a substrate or mixed to a polymeric matrix has revealed very promising for this subject. Some studies have shown that cells tend to migrate and adhere preferentially on CNT arrays [27,28,29,183]. Zanello et al. have demonstrated that CNTs can sustain osteoblast proliferation and bone-formation functions [25]. Giannona et al. have produced CNT arrays with intertube spacing of 1 micron, where the osteosarcoma cells attached only in nanotubes tips [27]. Correa-Duarte et al. obtained considerable adhesion and growth of mouse fibroblast cells on 3D network based on an array of interconnected MWCNTs, functionalized by acid solutions [31]. Abarrategi et al. showed the formation of myoblastic mouse cell layer using MWCNT/chitosan scaffolds [15]. Mwenifumbo et al. demonstrated that osteoblastic cell cultures attach and survive on MWCNT constructs, using SEM (cell morphology) and immunefluorescence (actin and vinculin proteins) [184]. Biggs et al. observed that the primary osteoblast-like cells respond to physical contact with nanotopography, demonstrating that attachment and growth of cells is dramatically influenced by the spacing of individual nanoarrays [185]. The cell preference by a high number of attachment-sites provided by CNT facilitates cell growth and spreading, and encourages the monolayer formation. Thus, in our studies we have highlighted the use of vertically-aligned MWCNT (VACNT) scaffolds.

6. CYTOCOMPATIBILITY AND CELL ADHESION ON VACNT SCAFFOLDS PRODUCED BY MWCVD PROCESS We have produced VACNT supported by a substrate and have submitted them to preliminary in- vitro cytotoxicity tests, which demonstrated high cell viability and exceptional cell adhesion with a cell monolayer formation after 7 days.

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6.1. VACNT Synthesis

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The VACNTs were produced as thin film, using a microwave plasma chamber at 2,45GHz (MWCVD) [16,17]. The substrates were 10mm titanium (Ti) squares, covered by a thin Ni or Fe layers. Ni and Fe catalyst layers of 7nm were deposited by an e-beam evaporator. In some experiments the Fe catalyst (Fe2) was obtained by dip coating technique in Fe (NO3).9H2O solution in ethanol at a concentration of 37 mmol/l. The Ni and Fe layers were pre-treated to promote nanocluster formation, which forms the catalyst for VACNTs growth. The pre-treatment was carried out during 5 min in plasma of N2/H2 (10/90sccm), at a substrate temperature around 760oC. After pre-treatment, CH4 (14 sccm) was inserted in the chamber at a substrate temperature of 800oC for 2 min. The reactor was kept at a pressure of 30 Torr during the whole process. SEM and transmission electron microscopy (TEM) were used to observe the structure of the VACNTs. Figures 1 (a1-c1) show the SEM images of Ni (a1), Fe (b1) and Fe2 (c1) nanoclusters with diameters between 30and 70 nm. Figures 1(a2-c2) show SEM images of the high density of the VACNT obtained for each catalyst. The VACNTs grew perpendicular to the substrate, with average diameter proportional to the diameters of the metallic nanoclusters with lengths of 6-8μm. VACNT produced on Fe nanoclusters are denser than those produced on Ni. Figure 1 (a3-c3) show TEM images of typical internal structures of the VACNT. No contaminants from either metallic particles or amorphous carbon were observed outside the tubes. Virtually all metallic particles are enclosed by the VACNTs produced. The high atomic hydrogen concentration in the gas mixture efficiently removes amorphous carbon residues.

Figure 1. Images of catalyst nanoparticles and VACNT for : (a) Ni catalyst; (b) Fe catalyst; (c) Fe2 catalyst. The numbers indicate (1) SEM images of the catalyst nanoparticles formed in pre-treatment; (2) SEM images of the VACNT films; and (3) TEM images of the VACNT internal structures.

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6.2. Cell Cultures Mouse fibroblast (L-929) and human osteoblast (SaOS-2) cells were provided by Cell Line Bank of Rio de Janeiro/Brazil. The cells were maintained as sub-confluent monolayer’s in minimum essential medium (MEM) for L-929 and McCoy’s5a (SIGMA) for SaOS-2. They were modified with 1.5mM L-glutamine adjusted to contain 2.2 g/L sodium bicarbonate (85%), fetal bovine serum (Gibco, BRL) (15%), 100 units/ml penicillin-streptomycin (Sigma), and 25 µg/ml l-ascorbic acid (Sigma). The incubation occurred within a CO2 (5%) atmosphere at 37º C in different times (24, 48, 72 and 96 h ). Mouse embryo fibroblast (MEF) cells from C57/BL6 or C57/BL6 green fluorescence protein (GFP) mice were extracted between 12.5-14.5 days. After this procedure, were dissected and removed limbs, upper part of the head and scooped out the internal organs. The carcasses were rinsed with sterile medium DMEM without serum. The embryos were minced up to reaching consistency of sludge. Further, this material were digested with trypsin/EDTA for 10 min. at 37º C shaking. This step was repeated three times and each time a aliquot of buffer solution was removed to 50 mL tube and added equal volume of DMEM plus 10% fetal bovine serum. The contents of 50 mL tube was centrifuged at 1500rpm per 7 min. and so, ressuspended in 50 mL of DMEM plus 10% fetal bovine serum. The cells were seeded into approximately seven 9 cm sterile dishes and grew at 37º C with 5% CO2. After they reached confluence they were transferred by trypsin digestion. They were used for the experiment after second transference at the 5x104or 1x105 cells per well of 24 well culture dish.

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6.3. Colorimetric Assays on VACNT Scaffold The cell viability and proliferation on raw-VACNT films were evaluated by three different colorimetric assays: (i) MTT, (ii) LDH, and (iii) NR. Latex fragments were used as positive control. Filter paper was used as negative control for cytotoxicity. All the samples were sterilized for 24 h under UV irradiation and placed in individual wells of 24-well culture plates. Only the cells adhered to the well walls were incubated with: (i) MTT solution (Sigma, Saint Louis, Missouri, USA); (ii) LDH from SIGMA® TOX 7 Kit; and (iii) NR solution (SIGMA) for 4 h at 37°C. The absorbance of the content of each well was measured at 570 nm (MTT), 490 nm (LDH), 405 nm (NR) with a microplate reader on a spectrophotometer Spectra Count (Packard). The background was taken from wells without cells. The optical densities (OD) were normalized by the negative control (MTT and LDH), and expressed in percentage: [ODsample - ODbackground/ODnegative control - ODbackground]*100. For acute cytotoxicity tests, the OD was normalized by the cell culture. To avoid doubts about interference of VACNT with colorimetric assays, the samples and controls were removed from the cell culture before the addition of the colorimetric dye. Data were collected from five different experiments and expressed as the average ± the standard deviation (SD). Figure 2 shows the results of colorimetric assays with L-929 cells for the raw-VACNT grown with Ni and Fe. All of the tests show that the cell viability of positive control decreases rapidly, which characterize cell death. Compared to the positive control, raw-VACNT (obtained with Ni and Fe catalysts) are evidently non-toxic.

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Figure 2. Cell viability study with L-929 cells by (a) MTT and (b) LDH up to 96 h; (c) acute cytotoxicity evaluation using three different colorimetric assays.

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In Figure 2a, a different cell viability result is observed with Fe2 catalyst, showing a decreasing behavior after 24 h. The result of lower cell viability in this case is most probably related to an excess of iron particles present around, due the dip coating process. Figure 2c show the verification of the acute cytotoxicity (24h) of raw-VACNT by three colorimetric assays (LDH, MTT and NR). All tests demonstrated non-toxic effects, but each dye had a different response related to positive control, because each test is due to a different biological processes. The NR was the most efficient colorimetric assay for acute toxicity check of rawVACNT scaffold.

6.4. SEM and Fluorescence Microscopy for Cell Adhesion Study Figure 3 shows the cell morphology of (a) L-929 and (b) SAOS-2 on raw-VACNTs films after (1)48h and (2) 7days of incubation. The attached cells on the substrate were fixed with a 3% glutaraldehyde/0.1M sodium cacodylate buffer for 1 h and dehydrated in a graded ethanol solution series (30, 50, 70, 95 and 100%) for 10 min each. The drying stage used a 1:1 solution of ethanol with hexamethyldisilazane (HMDS) and the samples were dried with pure HMDS at room temperature. A thin gold layer was deposited on the samples to improve the electrical conduction for SEM analysis.

Biocompatibility Differences between Dispersed and Vertically-Aligned Carbon… 299

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Figure 3. SEM images of cell morphology for (a) L929 and (b) SaOs, after (1) 48h and (2) 7 days on raw-VACNT.

The raw-VACNT arrays as obtained in this work exhibit super-hydrophobic behavior [186]. However, in figure 3a1-b1, we show that this effect is controlled after 48 h in cell culture. The cells spread with no preferential direction, acquiring a flat roughly circular form over the surface. It appears that cell spread out after coming in contact with the neighboring cells but they did not effectively attach among themselves, preferring to attach to the rawVACNTs film. After 7 days, the cells already occupy almost the whole raw-VACNT surfaces. Figure 4 shows high resolution SEM images of the cells on raw-VACNT films. In Figure 4a, the initial phase of cell spreading is shown, with the cytoplasmatic projections in all directions. The figure 4b is a higher magnification of figure 4a, showing details of the membrane projection attached to VACNT tips. Figures 4c and 4d are very illustrative, because they show two events: monolayer formation with cells totally spread on rawVACNTs, and cells in multiplication on the first layer.

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b

c

d

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Figure 4. High resolution of SEM images of cell adhered on raw-VACNT at (a-b) initial stages of spreading, and (c-d) after monolayer formation.

Figure 5. Fluorescence images of (a) C57/BL6 MEF-GFP cells and (b) actin filaments marked with phaloidin-rhodamine, after 6 days of incubation on VACNT.

To emphasize the monolayer formation after 6 days, fluorescence microscopy were used to evaluate C57/BL6 cells with or without GFP on raw-VACNT. Figure 5a shows the interaction between “living cells” and raw-VACNT. A monolayer formation of C57/BL6GFP cell is visualized. Figure 5b shows C57/BL6 actin marked with phaloidin-rhodamine. The actin filaments in red show evidence of healthy look of the cells grew on raw-VACNT.

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7. CELL ADHESION ON SUPERHYDROPHILIC VACNT SCAFFOLD The cell adhesion force is defined by cell internal factors (the functional state of the cell) and cell external factors such as the substrate and medium composition [187]. Surface characteristics like topography, chemistry or surface energy, play an important role in the cell’s adhesion. It has been recognized that hydrophilic surfaces are generally favorable for adhesion and proliferation for various cell types [188,189,190,191,192]. Generally, the wettability of a solid surface depends on both its chemical composition (surface energy) and its geometrical structure (related to surface roughness). The contact angle (CA) of a liquid droplet in thermal equilibrium on a horizontal surface is the most common way of judge the wettability of a solid surface. If the liquid used is water, the contact angle can define wettability degree, classifying the surface as: hydrophobic (CA > 90o), hydrophilic (CA< 90o), superhydrophobic (CA>150o) and superhydrophilic (CA< 5o). Controlling surface energy of biomaterials is of significant interest in biomedical applications involving cell-biomaterials interactions. Surface wetting phenomena significantly affect various biological events at the sub-cellular and cellular level (protein adsorption, cell attachment and spreading, etc.). Several chemical and physical treatments have been suggested for functional groups attachment [193,194] on MWCNT coatings, including treatments to change hydrophobic behavior. Compared to other chemical modifications methods, the plasma treatment method is of great importance because of its nonpolluting property and shorter reaction time. The use of radio-frequency (RF) and microwave (MW) oxygen plasma treatment on CNT surface has been recently reported in literature [195,196,197]. Chirila et al. have studied the effects of plasma power chamber pressure and plasma frequency (RF or MW) as well as the effects of the treatment time on the quantity of functional groups (carboxylic, carbonyl, hydroxyl, phenol) introduced onto the CNT. The plasma treatment showed that the wettability increase up to 68% after the treatment with MW-plasma, and 20% with RF-plasma, compared to the untreated CNT [198]. Brandl et al. showed that treatment introduced oxygen containing functional groups (hydroxyl, carbonyl and carboxylic groups) onto the fiber surfaces and also enhanced fiber surface porosity (by etching) as well as the surface energy. After the plasma treatment, the CA with water decreased from 88o to 58o, hence wettability of their fiberpolypropylene composite has been improved [197]. In summary, the oxygen plasma treatment is great and rapid method to introduce both functional groups and roughness, and to improve the wettability on CNT. From a DC-pulsed oxygen plasma treatment, we achieved a very significant CA change (~180º to ~0o) on VACNT films. The superhydrophilicity facilitated the osteoblast (SaOs-2) and fibroblast (L-929 and MEF-GFP) cells attachment and spreading. Figure 6 shows the CA with water and MEF-GFP cell adhesion. Figures 6a.1 and 6b.1 show the CA before (~180º) and after (~0º) DC-pulsed oxygen plasma treatment, respectively. Figures 6a2 and 6b2 show fluorescence images of the interaction between MEFGFP cells on untreated (b.1) and treated (b.2) VACNT scaffolds after 24h of incubation. With the O2 plasma treatment, an increase of cytoplasmatic projections cell (polygonal shape) are observed. These effects can be caused by superhydrophilic properties, which offer different surface energy.

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Figure 6. (a) Optical microscopy (200x) images of contact angle with DI water and (b)fluorescence microscopy images of GFP cell spreading and proliferation on VACNT, after incubation by 24 h, without (1) and with (2) O2 plasma treatment. The parameters of this plasma treatment were: 2 min, 400 V and 80 mTorr.

Similar results are also observed by other authors for development of nanostructured biomaterials [189,190,191,192] The incubation time of 24h is an initial stage, but this interaction will influence the cellular capacity to proliferate and differentiate. The superhydrophilicity is related to the mild corrosion of MWCNT tips and oxygen attachment to their structure. Figure 7 shows Raman spectroscopy (renishaw 2000, laser excitation of 514 nm) and XPS (Microtech, model XR 705) of raw-VACNT and VACNT treated by O2 plasma. In figure 6a, the first- and second-order Raman spectra were collected on VACNT tips, presenting the usual peaks of graphite-like material typical to high quality MWCNT [128,129]. Raw-VACNT presented a narrow bandwidth and no presence of amorphous carbon. After the O2 plasma treatment, an enlargement of bandwith was observed. In figure 7b, typical XPS analyses are exhibited. The C1s peak, related to graphitic structure, and O1s peak were observed for both untreated and treated VACNT. Notice that after the O2 plasma treatment, O1s peak is significantly higher than in untreated films. For treated VACNT, the Fe2p peak also appears, related to exposure of nanoparticles on MWCNT tips, due corrosive process. The influence of plasma conditions (power, type of gas, treatment time, pressure, position of CNT sample inside the chamber) on XPS analysis has been evaluated by other authors [193,194]. The O2 plasma treatment of MWCNT introduces both free radical defects and oxidized carbon groups (C-OH, C=O and COOH) whose concentration increased upon subsequent atmospheric exposure, as the free radicals react with O2 and H2O [195].

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Figure 7. Characterization of VACNT surfaces by (a) Raman spectroscopy and (b) XPS for untreated and treated by O2 plasma.

Figure 8. SEM images of (a) L-929 after 6 h; and (b) SaOs-2 cells after 48 h of incubation on superhydrophilic VACNT treated by O2 plasma.

The high degree of wettability accelerates the cell adhesion and proliferation process. Figure 8 highlighted the efficiency of L-929 and SaOs-2 cells growth on VACNT superhydrophilic surfaces in initial phases. Figure 8a shows L-929 cell totally spread after only 6 h of incubation. Figures 8b1-b2 is very illustrative, because they show SaOs-2 monolayer formation with only 48 h of incubation for VACNT treated by O2 plasma, while it takes 7 days for raw-VACNT, as show in figures 3b1-b2.

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CONCLUSION Nowadays the mass production of CNTs is already a fact. Applications can be discerned and can become real. Knowing the production process and post-treatments of CNTs as well their basic morphological characterizations is extremely important for any further use. Particularly, biomedical applications are very promising, but the crystalline quality, purity and hydrophilicity of CNT should be guaranteed. A great effort of using multiple “in vitro” cytotoxicity assays with several cell lines and different CNT types or forms has been shown in current literature. Colorimetric assays with dispersed CNTs should be cautiously performed, because interferences with dyes commonly happen, although their use is totally recommended for CNT scaffolds. The possibility of using of high purity and superhydrophilic VACNT scaffolds for “in vitro” cell seeding and growth is practically established. The VACNT scaffolds have revealed that an intimate contact between cell structures and nanotopography is decisive to guarantee bioactivity and efficient cell growth and spreading. Primary cells, that generally are more sensitive than permanent lines, also can efficiently proliferate on VACNT scaffolds. The superhydrophilicity is fundamental to accelerate the cell attachment, and consequently, cell monolayers can be formed faster than on hydrophobic ones. Next steps are to figure out the structure of cytoskeleton, observing focal adhesion complexes structures and location to realize tension that might be applied on cells when they are on MWCNT substrate. Other approach is to analyze all the protein expression as a response by cells involved with this interaction. Among them, signaling proteins as cytokines, which involve important signaling of cause-effect, which have an influence with metabolic response in the cell's activity. Those enforces objective to improve the understanding about relationship of cell and CNTs.

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In: Carbon Nanotubes: New Research Editor: Avery P. Ottenhouse

ISBN 978-1-60692-236-1 © 2009 Nova Science Publishers, Inc.

Chapter 10

ENGINEERED ELECTRICAL AND MECHANICAL PROPERTIES OF CARBON NANOTUBE ADDED SI3N4 NANOCOMPOSITES Csaba Balázsi1∗, Orsolya Koszor1, Balázs Fényi1 and Katalin Balázsi2 1

Ceramics and Nanocomposites Department, Research Institute for Technical Physics and Materials Science, Hungarian Academy of Sciences, H-1121 Konkoly-Thege M. út 29-33, Budapest, Hungary 2 Thin Film Physics Department, Research Institute for Technical Physics and Materials Science, Hungarian Academy of Sciences, H-1121 Konkoly-Thege M. út 29-33, Budapest, Hungary

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ABSTRACT This research explores the use of a variety of nanoparticles to impart conductivity to ceramic matrices. We have chosen some highly promising families of carbon materials: multiwall carbon nanotubes (MWCNTs), singlewall carbon nanotubes (SWCNTs), carbon black nanograins and graphite micrograins for use as fillers. In this book chapter, we report the results about two types of carbon nanotubes. The MWCNTs and SWCNTs were dispersed in silicon nitride matrix in different percentages high as 1-5wt%. A high efficient attritor mill has also been applied for proper dispersion of MWCNTs in the matrix. In order to get the full use of the benefits provided by carbon nanotubes (CNT) it is crucial to retain CNT un-attacked in the composites and to optimize the interfacial bonding between CNT and matrix. By conventional sintering techniques, which are characterized by the requirement of extended holding at very high temperatures, the destruction of CNT has been reported. In the present work the development of sintering processes have been performed to consolidate and tailor the microstructure of MWCNTs reinforced silicon nitride-based ceramic composites. The silicon nitride nanocomposites ∗

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Csaba Balázsi, Orsolya Koszor, Balázs Fényi et al. systems retained the mechanical robustness of the original systems. Bending strength high as 700 MPa was maintained and an electrical conductivity of 10 S/m was achieved in the case of 3 wt% MWCNT addition. Electrically conductive silicon nitride ceramics have also been realized by carbon black (in order of 1000 S/m) and graphite additions in comparison. Examples of these systems, methods of fabrications, electrical percolation, mechanical properties and potential uses will be discussed.

INTRODUCTION

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Carbon nanotubes (CNT) are the most popular reinforcing materials in building composite structures because they show advantageous mechanical, electrical, and thermal properties [1-4]. Therefore, the application of CNTs was the main line of building up of the ceramic composites. From electrical point of view ceramic materials are usually applied typically as insulator products. During our research a Si3N4 ceramic was developed that had extreme mechanical and thermal properties [5-7], but from electrical point of view it was insulator. Our aim was to develop a hi-tech ceramic that has excellent electrically conductive property as well. To reach this aim, small amount of electrically conductive additives were mixed into insulator silicon nitride ceramic. Retaining the CNTs un-attacked in the composites and to optimizing the interfacial bonding between CNTs and matrix are the further requirements. In this way the toughening effects characteristic to nano-scale fibre composites could be explored: crack bridging by CNTs, CNT pullout on the fracture surfaces and crack deflection at the CNT/matrix interface [8]. This study is focusing on the preparation processes that allow the tailoring of the microstructure of carbon nanotube reinforced silicon nitride-based ceramic composites. Experimental procedure has been conducted to effectively disperse the CNTs in the matrix. Importance was given to temperature-pressure-holding time relation to preserve the carbon nanotubes in composites and to avoid damaging during high temperature processing. In the case of appropriate mixing of CNTs the fibrillated second phase interlaces the material so the electrical current can flow through of it freely in a percolative way. For comparison effect of the other carbon additives was also examined. To ensure the appropriate construction two types of sintering method were tried out. Furthermore, a matrix base material that contains electrically conductive part (aluminum nitride) was applied to improve electrical conductivity. Carbon-ceramic composites with electrical conductivity in a wide range have been successfully produced.

PRODUCTION OF CARBON NANOTUBE – SI3N4 NANOCOMPOSITES The nanocomposites were prepared from the starting powder mixtures consisted of 90wt% α-Si3N4 (Ube, SN-ESP), 4wt% Al2O3 (Alcoa, A16) and 6wt% Y2O3 (H. C. Starck, grade C) mixing ratios. Different amount of CNTs (multiwall carbon nanotubes MWCNTs, produced as described elsewhere [9], single wall carbon nanotubes - SWCNTs) were added to batches (1, 3 and 5 wt%). The process of carbon nanotube - Si3N4 based nanocomposites is shown in Figure 1.

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Figure 1. Schematic view of carbon nanotube - Si3N4 based nanocomposites preparation.

The powder mixtures together with the added CNTs were milled in distilled water in a highly efficient attritor mill (Union Process Inc.) for five hours. As resulted from weight measurements each batch contained approximately 1-3 wt% zirconia as contamination from balls and discs. After milling surfactants (polyethylenglycol, PEG) were added to the powder mixture. The batches were dried and sieved. Green samples were obtained by dry pressing at 220 MPa. Before sintering an oxidation was carried out at very low heating rates up to 400°C, to eliminate the PEG from samples. Hot isostatic pressing was performed at 1700°C in high purity nitrogen by a two-step sinter-HIP method using BN embedding powder. The heating rate was not exceeding 25°C/min. The gas pressure (2 and 20 MPa) and holding time (0 to 3 hours) were also varied. The dimensions of the as-sintered specimens were 3.5 x 5 x 50 mm. After sintering, the weight change of the samples was determined. All surfaces of the samples were finely ground on a diamond wheel, and the edges were chamfered.

STRUCTURE OF CARBON NANOTUBE – SI3N4 NANOCOMPOSITES

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The density of the sintered materials was measured by the Archimedes method. Phase compositions were determined by Philips PW 1050 diffractometer and by EDS analysis attached on Philips CM-20 transmission electron microscope (TEM). Morphology and structure of the nanocomposites were studied by field emission scanning electron microscope LEO 1540 XB, TEM Philips CM-20 and high resolution transmission electron microscope (HREM) JEOL 3010. Results about the morphology of powder mixture and SWCNT samples processed with attritor milling are presented in Figure 2.

Figure 2. SEM image of Si3N4 based nanocomposite with SWCNTs addition.

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As it is shown in Figure 2 at higher magnification single carbon nanotubes are efficiently dispersed in α-Si3N4, and sintering additives Al2O3 and Y2O3. In Figure 3a the scanning electron image of MWCNTs sample is shown. Starting powder mixtures consisted of crystalline Si3N4, Al2O3, Y2O3 grains and 3 wt% CNTs addition investigated by TEM is shown in Figure 3b. The CNTs are located mainly in the inter-granular places and they are well attached to the silicon nitride grains. The proper separation and dispersion of carbon nanotubes proved to be a difficult task of the composite preparation. For a better homogeneity, we applied the high efficient attritor milling at 4000 rpm rotation speed for 5 hours. By applying this technique advances have been made, but the general tendency of nanotubes (derived from the high specific surface area), the strong adherence and linking behavior to each other could not be totally suppressed. As can be observed, the CNTs in most of the cases are in groups, they can be found as nano- or micrometer sized islands in the matrix after sintering (Figure 4a).

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Figure 3. Structural investigation of a) MWCNTs addition, SEM image and b) Si3N4 based nanocomposite with MWCNTs addition, plan view TEM image.

Figure 4. a) Cross section TEM image of sintered carbon nanotube – Si3N4 nanocomposites, b) HREM image of Si3N4 grain and carbon nanotubes.

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After milling by high efficient attritor mill, as revealed by TEM analysis (Figure 3b), ceramic powder comprised of ~ 200 nm crystallites and dispersed CNTs. The EDS measurements approved a primary composition (not shown). The nanotubes are dispersed in the ceramix matrix. The nanotube radius is ~ 25 nm. The structure of sintered silicon nitride based ceramic at 1700°C and at 20 MPa is shown in Figure 4. The sample consisted of ~ 300 ÷ 400 nm nanocrystalline grains. The porosities were occured between some grains. The CNTs were located in these porosities. The HREM investigation of β-Si3N4 / CNTs interface showed that the nanotubes are oriented quite uniformly (Figure 4b). X-ray diffractograms of sintered samples are presented in Figures 5. The main lines of αSi3N4 (JCPDS-PDF 41-360), β-Si3N4 (JCPDS-PDF 33-160) and ZrO1.96 (JCPDS-PDF 811546) lines can be recognized in the case of samples sintered at 2 MPa. The α-Si3N4 to β-Si3N4 phase transformation was completed at 20 MPa (Figure 5). The X-ray diffractions of sintered samples are showing the main lines of β-Si3N4 and one zirconia phase (Figure 5).

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Figure 5. XRD image of sintered Si3N4 based nanocomposite at 2MPa and 20 MPa.

MECHANICAL AND THERMOPHYSICAL PROPERTIES CARBON NANOTUBE – SI3N4 NANOCOMPOSITES Mechanical properties, the elastic modulus and four point bending strength for sintered samples were determined by a bending test with spans of 40 and 20 mm. Thermophysical properties of samples were tested with the LFA 457 from room temperature to 900°C. The measured samples were disks with a diameter of approx. 10 mm and thickness between 1.3 and 2.0 mm. The samples were coated with graphite on the front and back surfaces in order to increase the absorption of flash light on the samples’ front surface and to increase the emissivity on the samples’ back surface. The samples were

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measured five times at each temperature. The specific heat was measured using the comparative method. For this the system was calibrated with a ceramic standard (Pyroceram). The mechanical observations are presented in Figure 6 and Figure 7. By increasing the gas pressure to 20 MPa the similar level of densification and higher strength values can be achieved for composites with MWCNT.

Figure 6. Modulus of elasticity as a function of the apparent density. a) 2MPa, b) 20MPa sintering pressure.

For measurement of the thermal diffusivity, specific heat and bulk density at room temperature were used to compute the thermal conductivity ( l ) by the following equation: l = r × cp × a

(1)

where r is the bulk density, cp is the specific heat and a is the thermal diffusivity of nanocomposite.

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Figure 7. Four point bending strength of composites as a function of the apparent density. a) 2MPa, b) 20MPa sintering pressure.

Figure 8 and Table 1 depict the thermophysical properties of nanocomposite sample with 3 wt% MWCNT (with 3,239g/cm3 density, 233GPa modulus of elasticity and 678MPa four point bending strength) and a reference sample without carbon nanotube addition (with 3,392g/cm3 density, 254GPa modulus of elasticity and 732MPa four point bending strength). The unit used in this work was equipped with a high temperature furnace capable of operation from room temperature to 1100°C. Using th e sample changer three samples can be measured at the same time. The sample holder for large samples allows sample diameters up to 25.4 mm. The sample chamber is isolated from the heating element by a protective tube allowing samples to be tested under vacuum or in an oxidizing, reducing or inert atmosphere. The temperature rise on the back face of the sample is measured using an InSb detector.

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Table 1. Summarized data of thermophysical properties. a) Carbon nanotubes – Si3N4 nanocomposite and b) Carbon nanotubes – Si3N4 without carbon nanotubes

T(°C)

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26 100 200 300 400 500 600 700 800 900

Carbon nanotubes – Si3N4 nanocomposite Density 3.239 g/cm³, Thickness 1.490 mm Thermal Specific Heat Thermal Diffusivity Conductivity J/(g*K) mm²/s W/(m*K) 9.142 0.650 19.247 7.588 0.804 19.766 6.289 0.899 18.308 5.443 0.949 16.725 4.881 0.975 15.417 4.434 0.998 14.339 4.082 1.019 13.474 3.796 1.037 12.752 3.547 1.050 12.067 3.337 1.060 11.457

Si3N4 nanocomposite without CNTs Density 3.392 g/cm³, Thickness 1.350 mm Thermal Specific Heat Thermal Diffusivity J/(g*K) Conductivity mm²/s W/(m*K) 8.605 0.632 18.465 7.154 0.772 18.749 5.978 0.868 17.611 5.233 0.922 16.376 4.671 0.953 15.104 4.265 0.980 14.176 3.936 1.001 13.363 3.654 1.014 12.566 3.421 1.025 11.894 3.230 1.026 11.246

Figure 8. Thermophysical properties of silicon nitride based nanocomposites. a) carbon nanotubes – Si3N4 nanocomposite (up) and b) reference sample (silicon nitride nanocomposite without carbon nanotubes) (down).

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Data acquisition and evaluation are accomplished using a comprehensive PC software package. The data evaluation software allows 2- and 3-layer calculations as well as the evaluation of the contact resistance. The data can also be corrected for finite pulse and heat loss effects using any number of models. The instrument can be operated in the fullyautomatic or manual mode. The specific heat increased with temperature as expected from the Debye theory. The thermal diffusivity decreased over the entire temperature range. Typical for phonon conductors is a maximum value in the thermal conductivity nearly at room temperature. This trend can clearly be seen at both of samples. The thermal conductivity values in the case of the sample with 3 wt% MWCNT are slightly higher than the values of the reference sample. The standard deviation of 5 shots at each temperature is less than 1 %.

TRIBOLOGICAL PROPERTIES CARBON NANOTUBE – SI3N4 NANOCOMPOSITES

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The tribological test has been performed on each sample using the CSM Tribometer (TRB), which principle and specifications are shown in Figure 9. The test was prepared in air atmosphere at 23°C and the humidity was 30%. The linear test mode with 6 mm amplitude and 5 N normal load, 10 000 laps stop conditions, 5 Hz acquisition rate parameters were used for all samples. The TRB is suited to study the friction and wear behaviour of almost every solid state material combination, with varying time, contact pressure, velocity, lubrication, temperature. A flat or a sphere shaped static partner is loaded on to the test sample with a precisely known force. The static partner, (a pin or a ball), is mounted on a stiff lever, designed as a frictionless force transducer. As the disk is rotating, resulting frictional forces acting between the pin and the disk are measured by very small deflections of the lever using an LVDT sensor.

Figure 9. Schematic view of CSM Tribometer.

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Wear coefficients for both the pin and sample are calculated from the volume of material lost during a specific friction run. The results of wear study is shown in Table 2. It was observed that the Si3N4 ball was more damaged with 3 wt% MWCNTs addition nanocomposite than with pure Si3N4 ceramic. As was observed from tribological measurements, nanocomposite Si3N4 without carbon nanotubes shows a higher friction coefficient than carbon nanotube - Si3N4 sample (Figure 10-12). The very big difference that could be shown in this test concerns the sample wear rate: there was a much higher wear for carbon nanotube - Si3N4 than for Si3N4 without MWCNTs; factor 10 between the both. Table 2. Summarized data of the wear study for a) Si3N4 and b) carbon nanotube - Si3N4 nanocomposite Sample Si3N4 CNTs - Si3N4

Worn cap diameter (μm) 726 899

Worn track section (μm2) 302 3345

Ball wear rate (mm3/N/m) 7.61E-06 1.79E-05

Sample wear rate (mm3/N/m) 3.02E-06 3.34E-05

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Figure 10. Friction coefficient measurements of Si3N4 and carbon nanotube - Si3N4 nanocomposites.

Figure 11. Friction wear test images of reference Si3N4. a) low resolution image, b) high resolution image.

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Figure 12. Friction wear test images of carbon nanotube - Si3N4 nanocomposite. a) low resolution image, b) high resolution image.

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Figure 13 shows the calculation of the worn track section, which was done with a profilometer Taylor Hobson.

Figure 13. Calculation of the worn track section by profilometer. a) Si3N4, b) carbon nanotube - Si3N4 nanocomposite.

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ELECTRICAL PROPERTIES CARBON NANOTUBE – SI3N4 NANOCOMPOSITES For the electrical measurements electrical contacts (4 on each sample) had to be created on the surface of the composites. Multilayer contact was developed that consists of 4 layers and can be seen in Figure 14. The first thin gold layer was vapored on the appropriate part of surface of the sample. The gold layer was covered by conductive glue as second layer that contains silver grains. After drying the current feeds (third layer) were fixed on this layer by ordinary soldering technique (fourth layer). The created contacts should have low resistance in order to not to overload the measurement system and have good adhesion for fix the current feeders during the tests.

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Figure 14. Four layer multilayer contacts for electrical experiments.

Figure 15. Schematic four wire measurements technique to determine the specific conductivity of the composites.

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After the contacting the DC resistivity measurements was started. To determine the pure resistivity of the ceramic composites during the test four wires resistance measurement had to be applied (Figure 15). Our samples with current feeders have many resistivity but with four wire technique the pure resistivity of the ceramic between the two inner contacts can be determined without the resistivity of the contacts. The basis of the 4 wire resistance measurement is that composite was excited through the two outside contacts by stable DC current. During the exciting the voltage drop between the two inner contacts was detected. The resistivity of the section between the two inner contacts was calculated on the basis of Ohm's law from the DC current and voltage drop and the device (Agilent 34411A) was done automatically. For choosing the measurement range of the equipment resistance of the contacts has to be considered. This resistance was determined on the basis of a simply two points method. Specific conductivity of the samples was calculated from the geometry of the samples (the part of the samples between the two inner contacts) and the resistivity. In the case of some composites impedance spectroscopy measurements were fulfilled (see Figure 16).

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Figure 16. Schematic draw of the lock in technique for AC impedance measurements.

DC CONDUCTIVITY OF CARBON NANOTUBE – SI3N4 NANOCOMPOSITES During the impedance spectroscopy the absolute impedance of the composites was determined in a scanned frequency range. For this phase sensitive Lock in measurement system was adopted. As answer to voltage bias of the signal generator current signal was detected separated in two components as in-phase and quadrature (respect to excitation phase). After measuring the two components of the current the sample complex impedance was evaluated according to Ohm’s law. The measuring frequency range was from 100 Hz to 100 kHz limited by the Lock-in detector upper limit.

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The examined composites can be grouped into insulator and conductor types as resulted from four points DC resistance measurements. Samples that overloaded our measurement system (10MΩ measurement limit) can be considered as insulator because their resistance was not measurable. These samples were: basic ceramics without any type of additives, samples that contains 1wt% and 5 wt% MWCNTs (Figure 17).

Figure 17. SEM images of insulator ceramics (a) base ceramic and (b) Si3N4 with 5wt% MWCNT.

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The other group of composites is considering as conductor (Figure 18.) because of the contact and grouping of the additives. As the electrical conduction takes place through the paths that are made by linked conductive phases these materials behave like percolative conductors. The percolation threshold is observed in composites with 3wt% for MWCNT.

Figure 18. Specific conductivity of the composites as a function of MWCNT addition and sintering techniques.

MWCNT addition a larger conductivity range and higher conductivity were detected in the case of 3wt% addition. In the case of GPS sintering higher conductivity was obtained than in the case of HIP. The reason of the differences (in electrical aspects) between the two types of sintering technique is the different grain structure after the heat treatment process. In case

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of HIP technique the higher sintering pressure and the holding time performed the β-Si3N4 grains (Figure 19.) opposite of GPS structure that contains α-Si3N4 grains (Figure 20.).

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Figure 19. X-ray diffractogram of well conductive composites (Si3N4 with 5wt% MWCNT) and insulator base material (reference) prepared by HIP sintering.

Figure 20. X-ray diffractogram of well conductive composites and insulator base material prepared by GPS sintering.

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The bigger grain sized β-Si3N4 decreases the spaces for the percolation network (Figure 21). Furthermore, it can generate the crumbling and decomposing of the conductive clusters, so further decreasing can take place in the conductivity.

Figure 21. SEM images of 5 wt% MWCNT conductor composites produced by (a) GPS sintering, (b) HIP sintering techniques.

AC IMPEDANCE OF CARBON NANOTUBE – SI3N4 NANOCOMPOSITES

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On the insulator sample – that overloaded the DC measurements system – AC impedance spectroscopy measurements were done. This sample is the nanocomposite with 1 wt% MWCNT additions. In this nanocomposite, the conductor particles could not form percolation tracks for current paths. The AC impedance plots of high DC resistance samples are displayed in Figure 22. It shows the imaginary parts of complex impedance versus real parts. The imaginary part that represents capacitive character is more dominant over the frequency range. It means that the conductor parts that do not have connecting segments form capacitor and this results that the sample works as dielectric insulator material.

Figure 22. Impedance curves of different carbon added Si3N4 ceramics up to 100 kHz frequency.

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In Figure 23 absolute impedance versus frequency is displayed. All the curves run with -1 slope in a log-log plot. The impedance has 1 / ω dependence on frequency. This is a typical capacitive impedance feature (Rc = - i / C ω).

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Figure 23. Absolute impedance versus frequency in case of composites that are under the percolation network.

Figure 24. Specific conductivity range of conductive nanocomposites.

The insulator samples changed their high DC impedance due to frequency variation of capacitive impedance (Rc) which is characteristic to dielectric materials. Increasing of the MWCNT additives does not mean higher electrical conductivity because of the nodulation of

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MWCNT (Figure 24). Furthermore increasing the MWCNTs additives the well-grown βSi3N4 derogates the connection between the MWCNT nodules so the conductivity of the main composite material decreases. The reason of it is that β-Si3N4 grain grows during the sintering. Adding the conductor AlN did not cause the improvement of percolation limit in the examined compositions, but increased the electrical conductivity of the originally conductor composites forming more electrical connections between the conductive parts.

INFRARED EXAMINATION OF CARBON NANOTUBE – SI3N4 NANOCOMPOSITES

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To do the infrared measurements voltage was connected (Figure 25) on the composite and the electrical current could flow through the material by percolation way. The material was heated with the Joule heat of the current. 1 kHz frequency sine signal was used for the excitation of the composites. The signal was amplified step by step for the sake of the heat starting up in the sample increases step by step. The stepping of the voltage was continued till the temperature on the sample became ideal 100 °C for the infrared camera till the maximum excitation voltage 80 V was reached. During heating of the samples the rate of the applied excitation was different on the samples because of their different electrical conductivity. The CEDIP infrared measurement system that can be found in the University of Leoben, Institute of Structure- and Function Ceramic was used.

Figure 25. Shematic draw of infrared measurement system.

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EMISSIVITY OF CARBON NANOTUBE – SI3N4 NANOCOMPOSITES

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During the infrared investigations at first the emissivity of the surface of the samples had to be determined. The emissivity of the surface is needed to know the real temperature of the surface that can be evaluated during the calibration on each measurement. The emissivity of the composites was determined by a comparing method. Half of one side of the brick-shaped sample was covered with a layer that had known emissivity in the examination temperature range. This emissivity of the layer was 0.95. The result of the exiting samples were heated and the surface with and without layer showed the same temperature on its equal area (Figure 26). Through the comparison temperatures of the two areas were approximated to each other and the CEDIP program determined the emissivity of the real surface of the composite. The emissivity of the surface was determined on more surface points (at the same points of the lengthwise temperature gradient). The calculated emissivities can be seen in the Table 3. According to the results the Si3N4 carbon-ceramic composites have approximately similar emissivity in the examination temperature (0.95 – 0.99).

Figure 26. Methods of the emissivity determination, area 1.) covered with layer, area 2.) real surface.

The differences of the carbon additions could not be detected. As the determination of the emissivity in case of all the samples happened with the same temperature as the temperature profiles were detected the temperature dependence of the emissivity was not considered in the following.

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Table 3. Surface emissivities of the composites that contain different carbon additions Sample sintering

Carbon addition [wt%]

Specific conductivity Exciting voltage [V] Emissivitiy [S/m]

Si3N4 (GPS)

3 MWCNT

26.6

40

0.96

Si3N4 (HIP)

3 MWCNT

15.9

40

0.97

Si3N4 (HIP)

5 MWCNT

3.56

80

0.98

HEAT CONDUCTIVITY OF CARBON NANOTUBE – SI3N4 NANOCOMPOSITES

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A heat conductivity model was adopted for the determination of the heat conductivity of the composites. This model is a one-dimension heat conductivity model with boundary condition of two parallel infinitesimal planes with heat source inside [10]. For the evaluations the temperature gradients of the surface that were detected by the infrared method were used.

Figure 27. One-dimension heat conductivity model by plane walls with heat source.

In the volume of the plane walls the heat source is distributed steadily. The dimensions of directions deviated from the x direction are so large or the heat gradient is so small in this direction that he heat conductivity can be considered as one-dimension. During the examination it was considered that the heat conductivity does not change in the small temperature range that can be observed on the detected heat profile. This model can be applied well in the case of electrical conductive materials when some current flow through producing Joule heat heats the material. The heat conductivity of the model is described by the following differential equation on the geometry is drafted in the Figure 27: d2T / dx2 + q / k = 0

(2)

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where T is temperature, q is heat flux, k is heat conductivity. For the evaluation of the heat conductivity the resolution of differential equation of the reviewed model Eq. (2) was applied. In our case: ΔT = q · L2 / 2 · k

(3)

where L is the length of the examined profile. The heat flux was generated by the Joule heat emitted in the sample can be determined by Eq. 4 and Eq. 5 calculation: q = U2 / ρ · L2

(4)

q = I2 · ρ / A2

(5)

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where ρ is specific impedance, U is voltage, I is current, A iscross-section of the sample. The dimensions and the specific impedance of the samples were given from former measurements and the generated voltage and later the current through were measured. The model was solved on a symmetrically arranged parabolic heat profile. The heat profile of our samples did not symmetrical because of the current leads had different contact resistance and they insured different heat transfer (Figure 28). In stationer state the border conditions are stable, on the temperature profile of the section using for the evaluation can be chosen anywhere on our asymmetrical profile. On this section two segments were found with same temperature (TW) on the two sides of the maximum (T0). During the determination of the heat conductivities it was observed that in case of using the voltage generator excitation the heat conductivity that was determined with the consideration of the sample resistance in certain cases differs from the exceptions according to the literacy [11]. The reason of this is that our calculation does not consider the contact resistance between the sample and the sample holder.

Figure 28. Temperature profile along the sample.

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In the case of good insulator samples (graphite or MWCNT additives), where the contact resistance could be higher than the impedance of the sample the evaluation of the measurement is not possible (Table 4). Table 4. Heat conductivity determined by infrared thermography Excition

Carbon phase

Specific Conductivity Voltage

Current

Heat conductivity

[wt%]

[S/m]

[V]

[A]

[W/m·K]

Voltage

10 graphite

0.41

80

-

32.5

Voltage

10 graphite

0.52

80

-

37.85

Current

5 carbon black

139

-

0.27

59.68

In the case of current generator drive of small impedance sample the contact resistance is not in the Eq. 5, its effect has no part in the evaluation so that can be applied on any kind of electrically conductive sample. For checking a measurement was done using current generator excitation to determine the heat conductivity of a low resistance sample that can not be evaluated in the case of voltage generator excitation. Considering the data from literature [11] the heat conductivity of our material moves between wide borders. It will be even wider because different porosity material structure become during the sintering. On the basis of the calculation the obtained heat conductivity values are in the range of the reference data.

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CONCLUSIONS Optimisation of the manufacturing processes has been performed in order to thoroughly disperse the carbon nanotube in matrix, to assure a good nanotube-silicon nitride contact and to keep intact the nanotubes during high temperature processing. The grouping of the strength and modulus values as a function of apparent density was observed in the case of samples, sintered at higher pressure, as compared to the lower pressure sintered samples. At 20MPa, the highest densification grade, modulus and strength values were found. The addition of carbon parts in the ceramics drastically changes the electrical properties of composites. Using different type and concentration of carbon additives excellent conductive materials can be produced from the insulators. In our composites the electrical conduction intervenes in percolative way. MWCNT additives electrical conduction appeared at 3wt%. Increasing of the MWCNT additives does not mean higher electrical conductivity because of the nodulation of MWCNT fibers. Furthermore increasing the MWCNTs additives the well-grown β-Si3N4 derogates the connection between the MWCNT nodules so the conductivity of the main composite material decreases. The reason of it is that β-Si3N4 grain grows during the sintering. Composites that are prepared on low pressure by GPS sintering have better conductivity than the high pressured HIP sintering because of the more β-Si3N4 formation. The grain size

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of β-Si3N4 is effectively bigger than the grain size of α-Si3N4 therefore blocks the conductive network formation. Adding the conductor AlN did not cause the improvement of percolation limit in the examined compositions, but increased the electrical conductivity of the originally conductor composites forming more electrical connections between the conductive parts. The results of the infrared analysis showed approximately same emissivity values in the range of examination temperatures. The emissivities did not depend on the mixing ratio and the type of carbon additions or the sintering methods. During the processing of the infra images an evaluation method that can be traced back to a one-dimension heat conductivity problem was worked out. With this method the heat conductivity of the stationer state samples was determined. The heat conductivity values are in agreement with reference data. It can also be observed that the heat conductivity changes according to the quality and the type of the carbon additives just as the electrical conductivity. The growth rate is different from the case of electrical conductivity increase. The electrical conductivity changes with order of magnitudes because of the percolation mechanism during the insulator-conductor transition, while the heat conductivity changes according to mixing rule.

ACKNOWLEDGEMENTS We would like to thank the University of Leoben, Institute of Structure- and Function Ceramic, the ADMATIS Ltd. for their help with the infrared measurements, A. Lindemann from Netzsch-Geratebau GmbH, Applications laboratory for thermophysical measurements, François Davin from CSM Instruments Peseux, Switzerland for tribological measurements and the OTKA T63609 competition for the support. Authors would like to thank Z. Kónya and I. Kiricsi, L. P. Biró, P. Arató for helpful discussions, F. Wéber help in composite preparation, Z. Vértesy for SEM investigation.

REFERENCES

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[1] [2] [3]

[4]

A. K.-T. Lau and D. Hui: The revolutionary creation of new advanced materials-carbon nanotube composites, Composites Part B: Engineering, Vol. 33, (2002), pp. 263-277. S. Roche: Carbon nanotubes: Exceptional mechanical and electronic properties, Annales de Chimie Science des Matériaux, Vol. 25, (2000), pp. 529-532. B. G. Demczyk, Y. M. Wang, J. Cumings, M. Hetman, W. Han, A. Zettl and R. O. Ritchie: Direct mechanical measurement of the tensile strength and elastic modulus of multiwalled carbon nanotubes, Materials Science and Engineering A, Vol. 334, (2002), pp. 173-178. Z. Konya, I. Vesselenyi, K. Niesz, A. Kukovecz, A. Demortier, A. Fonseca, J. Delhalle, Z. Mekhalif, J. B.Nagy, A. A. Koos, Z. Osvath, A. Kocsonya, L. P. Biro and I. Kiricsi: Large scale production of short functionalized carbon nanotubes, Chemical Physics Letters, Vol. 360, (2002), pp. 429-435.

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Cs. Balázsi, Z. Kónya, F. Wéber, L. P. Biró and P. Arató: Preparation and characterization of carbon nanotube reinforced silicon nitride composites, Materials Science and Engineering: C, Vol. 23, (2003), pp. 1133-1137. [6] Cs. Balázsi, F. Wéber, Zs. Köver, Z. Kónya, I. Kiricsi, L. P. Biró and P. Arató: Development of Preparation Processes for CNT/Si3N4 Composites, Key Engineering Materials, Vol. 290, (2005), pp. 135-141. [7] E. T. Thostenson, C. Li and T.-W. Chou: Nanocomposites in context, Composites Science and Technology, Vol. 65, (2005), pp. 491-516. [8] J. D. Kuntz, G.-D. Zhan, A. K. Mukherjee, Nanocrystalline-Matrix Ceramic Composites for Improved Fracture Toughness, MRS Bulletin, January 2004, Vol. 29, Nr. 1, pp. 22-27. [9] Z. Kónya, I. Vesselényi, K. Niesz, A. Kukovecz, A. Demortier, A. Fonseca, J. Delhalle, Z. Mekhalif, J. B. Nagy, A. A. Koós, Z. Osváth, A. Kocsonya, L. P. Biró, I. Kiricsi, Large scale production of short functionalized carbon nanotubes, Chem. Phys. Lett. 360 (2002) 429-435. [10] J. P. Holman, Heat transfer, McGraw-Hill Book Company 26. [11] G. W. C. Kaye, T. H. Laby, Tables of Physical and Chemical Constants and some Mathematical Functions, Longman. [12] B. Fényi, N. Hegman, F. Wéber, P. Arató, Cs. Balázsi, DC conductivity of silicon nitride based carbon-ceramic composites, Processing and Application of Ceramics, Volume 1. Iss. 1-2, 2007 pp. 57-61.

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[5]

Csaba Balázsi, Orsolya Koszor, Balázs Fényi et al.

In: Carbon Nanotubes: New Research Editor: Avery P. Ottenhouse

ISBN 978-1-60692-236-1 © 2009 Nova Science Publishers, Inc.

Chapter 11

FLUORINATED CARBON NANOTUBES: STATE OF THE ART, TRENDS AND ADVANCED CONCEPTS Daniel Claves Laboratoire des Matériaux Inorganiques – UMR CNRS 6002, Université Blaise Pascal 24 Av. des Landais, 63177 Aubière Cedex, France

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ABSTRACT The present contribution details, in an as exhaustive as possible way, the fundamental knowledge acquired on fluorinated carbon nanotubes (CNT), also termed fluorotubes. Since the discrete pioneering articles published in the field a bit more than 10 years ago, around 70 additional references have now appeared which bear witness to the dynamism of this emergent part of the chemistry of nanotubes. As a matter of fact, fluorination stands as the starting point for a great part of the modifications performed on CNT, rendering fluorotubes fundamental intermediates for the integration of CNT in the nanotechnology processes. Many synthesis routes use fluorotubes as precursors in view of the subsequent chemical derivatization of CNT, for instance. In parallel, several attempts of practical developments based on fluorotubes have also lately appeared throughout the literature, covering the tribology, nanocomposites, or electrochemistry sectors, which outline the potential interest of such fluorinated nanostructures. The first part of this chapter compiles the main knowledge reported to date on the subject throughout a still reasonable but increasingly abundant body of literature. The physicochemical properties and special characteristics of the C-F chemical bond in fluorotubes are critically analyzed in a second part, and the last section is devoted to some recent tentative applications and future concepts relating to the fluorination of carbon nanotubes. The present review is essentially depicted from the chemistry of materials standpoint. Some of the concepts illustrated throughout the text are enriched by a few works of unpublished data from our group.

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I. FLUOROTUBES - GENERAL ASPECTS 1. Introduction The covalent addition derivatives of carbon nanotubes are much less diversified than those issuing from the parent fullerenes molecules. Owing to the macromolecular topology of the carbon edifice, a “rough” chemistry consisting of the random fixation of functionalities to the carbon substrate, in a more or less efficient and controlled way and often inducing defects in the continuity of the carbon frame, has succeeded to the fine methodologies employed to functionalize fullerenes. Nanotubes functionalization, most of the time, results from an oxidation of the carbon substrate in harsh conditions, from methods tested and validated decades ago on graphite, carbon fibers, or amorphous to semi-crystalline forms of carbon. Hence, the creation of the basic carbonyl, carboxyl, lactone or hydroxyl functions can be obtained upon treatment of carbon nanotubes with hot nitric acid or with hot aqueous solutions containing the permanganate, peroxodisulfate or perchlorate anions, or still with hydrogen peroxide. If oxygenation turns out to be rather easy, the halogenation of carbon nanotubes is more difficult to obtain, in spite of the strongly oxidizing character of halogen atoms, and only fluorine is known to directly and stably fix to such a carbon matrix. The fluorinated derivatives of carbon nanotubes, the so-called “fluorotubes”, have since proven to be of fundamental importance from both the chemistry of nanotubes and materials standpoints. The present synthetic approach describes and analyzes the widely diversified classes of materials that arise upon fluorine addition to the different tubular carbon allotropes. The first part reviews the main results reported hitherto concerning the synthesis, structural aspects and physico-chemical properties of both single-walled and multiwalled fluorotubes. The characteristics of the C-F chemical bond in fluorotubes will be analyzed in a second part and the last section of this chapter will be devoted to a prospective overview of the potential valorization of fluorotubes. Further research in the present field would preliminary require a perfect knowledge of the unexpectedly complex nature of the fluorinated derivatives of carbon nanotubes, which is far from being acquired hitherto, as will be shown from a critical analysis of some previously published data.

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2. Synthesis of Fluorotubes Single wall nanotubes: The fluorination of single wall carbon nanotubes (SWNTs) is usually carried out by direct reaction with an atmosphere of gaseous fluorine, over temperatures ranging from 50 to around 300 °C [1-12]. The latter value is often recognized as the critical threshold before significant degradation of the tubes begins to manifest. Thus, beyond this limit, the introduction of surface defects [1,3] and even combustion may become important, in which case gaseous fluorocarbons will form. The whole set of results reported converge in the sense that, at constant reaction time, the F/C stoichiometric ratio increases in parallel with the synthesis temperature, and the maximum functionalization rate seems to be around 50 to 60%, i.e. C≈2F.

Fluorinated Carbon Nanotubes

343

Extremely efficient plasma fluorination techniques have been recently developed [13-16], allowing access within a few minutes to important fluorination levels. The most common fluorinating agents are CF4 or SF6. Hence, such processes remain soft, limiting destruction of the tubular macromolecular edifices, and avoid the use of molecular fluorine, which is expensive and dangerous. Multiwall nanotubes: Morphological differences between SWNTs and multiwall carbon nanotubes (MWNTs) are at the origin of a specific reactivity of each one in regard to fluorine. Hence, MWNTs appear more resistant than SWNTs regarding fluorination at high temperature, owing to their higher outer diameters which reduce the strain associated with the local curvature of the network. Their complete fluorination with an F/C ratio close to 1 has been obtained near 500 °C [17-19], at the expense of the creation of many defects and of a more or less pronounced structural disorder. Note that, in the present case, an insufficient fluorination time will yield surface fluorinated tubes only [19-21]. The use of powerful fluorinating agents such as XeF2 has been attempted [22], but similarly results in a partial fluorination, restricted to the outer surface. In parallel, the fluorination of MWNTs can also be performed at low temperature [17,18], following the catalytic process developed several decades ago for graphite [23] and based on the use of gaseous HF. Experimental details in the matter remain scarce, however, since only a few papers on the subject have been published so far [17-22].

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3. Structure and Fluorination Mechanism Single wall nanotubes: SWNTs represent the macromolecular form of fullerenes molecules. In spite of this direct filiation, the fluorination at high temperature of SWNTs yields covalent addition derivatives resulting from independent and nonhomogeneous addition patterns, in contrast to fullerenes molecules in which case regioselectivity is excellent [24]. The direct observation by scanning tunneling microscopy (STM) [2] of the surface of single-walled fluorotubes (F-SWNTs) indeed showed alternating fluorinated and non-fluorinated sections along the tube axis. The nanotexture is thus seemingly made of individual circular ribbons of F addends wrapping the circumference of each tube. XPS is a major technique for surface analysis and consequently happens to be suited perfectly to the study of the surface composition of functionalized SWNTs, providing fine details about fluorine addition to SWNTs. Thus, whatever the final stoichiometry of the product and the synthesis route used, the C1s XPS spectrum corresponding to F-SWNTs [6,7,10,11,15] typically consists of a first feature centred near 284.5 eV (see Figure 1). The latter is similar to the one present in the C1s spectra of raw SWNTs and is therefore, related to bare “graphitic” carbon atoms. It is common knowledge that the C1s core level energy undergoes a substantial primary shift in the presence of a strong electron-withdrawing element. Accordingly, the C1s signal related to carbon atoms attached to one fluorine atom usually appears in the 287-289 eV binding energy range, with reference to standard tables. A second feature is then observed for fluorotubes in the corresponding region. It is also well established that the existence of carbon atoms not directly linked to a fluorine atom but having fluorinated nearest neighbors gives birth to a secondary shift of the C1s energy, which, in the case of fluorotubes, splits the first “graphitic” signal into a second component lying at a

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slightly higher binding energy (≈ 286 eV). Complementarily, weak shoulders over the 291293 eV energy range are always present and arise from >CF2 and –CF3 groups that forms on edges or at local defect sites. At last, XPS almost systematically detects a low atomic percentage of oxygen in both pristine and fluorinated carbon materials.

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Figure 1. Typical C1s XPS spectrum of F-SWNTs (here: CF0.5, obtained after 2 hours under a molecular fluorine gas flow at 300 °C).

The invariable nature of the XPS spectra of F-SWNTs also reflects their texture at the nanometer scale and provides a compelling evidence of an inhomogeneous fluorine addition pattern, besides the direct view of this phenomenon by scanning tunnelling microscopy previously mentioned. Indeed, a uniform halogenation pattern with an F/C ratio close to ½ would constrain each carbon atom to have at least one fluorinated neighbor in its immediate surrounding, suppressing the photoelectron peak assigned to bare carbon atoms. The systematic persistence of the latter then necessarily implies a non homogeneous distribution of fluorine atoms along the longitudinal axis of a tube and the presence of fluorine depleted zones alternating with fluorinated sections. The former experimental STM observation has seemingly provided support for a circumferential exo-addition pattern being the most probable architecture. Different regular exo-addition pathways may allow to reach the apparently optimal experimental C2F composition, but the conclusions of theoretical approaches on the subject [2,25-29], performed most of the time on virtual fragments of fluorotubes, exhibit too much divergence to shed light on the point here addressed. The results of computations are indeed highly dependent on the spatial extension of the system, its initial helicity/diameter parameters, the fluorination rate introduced and on the level of approximation. Somehow, at constant

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parametrization except fluorine location, the modest variations in energy from one model to another probaly reveal the thermodynamical origin of the random addition of fluorine to SWNTs. Lately, some experimental evidence in favor of 1-2 addition instead of a more exotic 1-4 pattern have been seemingly obtained throughout measurement of the 13C NMR chemical shift of F-SWNTs [30]. From the crystal chemistry standpoint, a high temperature fluorination process does not necessarily imply destruction of the bundle configuration, provided the latter was initially present within the pristine tubes sample, as shown on the following micrograph. The bidimensional cell parameter characterizing the compact triangular arrangement of the tubes becomes then notably expanded upon fluorine addition [7], independently confirming the location of some fluorine addends on the outer side of each tube.

Figure 2. TEM observation of SWNTs bundles fluorinated at 300 °C for 2h.

Double-walled carbon nanotubes consist of two nested carbon cylinders. They represent the first step toward MWNTs. Their fluorination has been successfully achieved at room temperature via the use of a fluorinating agent [31,32], which represents much milder conditions than heating under molecular fluorine, but some authors reported that direct fluorination at 200 °C does not break the double-layered morphology [33]. Overall, their apparent fluorination pattern somewhat recalls the one of SWNTs, consisting of surface addends grafted to the outermost sidewall, but interestingly, the core carbon shell remains preserved. Indeed, the radial breathing mode characterizing the Raman signature of the inner shell is kept unchanged upon fluorination, indicating that addition is effective at the level of

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the outermost framework only. The evolution of optical absorption spectra upon fluorination reinforces the former conclusion. These findings offer a soft transition toward the MWNTs case. Multiwall nanotubes: In comparison to SWNTs, the reduced curvature within MWNTs diminishes reactivity, and the conditions required for fluorinating the latter approach those required to fluorinate their flat homologue, graphite. Hence, the formation of covalent fluoroderivatives of MWNTs (F-MWNTs) necessitates significant thermal activation and fluorine atoms tend to graft to the sidewalls of multiwalled nanotubes from 300 °C, near the surface first. Higher temperatures (500-550 °C) can lead to the bulk fluorination of MWNTs [17-19]. The resulting fluorocarbon compounds still exhibit wiry imprints after undergoing such harsh conditions and their overall structure consists of a superposition of more or less fragmented fluorinated shells, some examples of which are displayed on figures 3 and 4. XRD usually shows still reasonably resolved (00l)-type Bragg peaks (see example, Figure 3) which reflect some degree of coherence in the stacking of the fluorinated shells. Their average separation becomes close to that characterizing the interlayer distance in the graphite fluoride (CF)n, obtained at 600 °C. Note that the final morphology turns out to strongly depend on the nature of the precursor MWNTs (Figure 3 and 4): the higher the rate of sidewall discontinuities in the pristine material is, the higher the disorder in the final fluorinated compound is. Accordingly, a well-ordered succession of fluorinated domains along both axial and radial directions can be obtained only by starting from a well organized MWNT. This has been tentatively explained through the “zipper” model [19], in which the fluorination mechanism is chronologically decomposed according to the following steps: i) Fluorination of the outermost sidewall, accompanied by radial inflation of the latter following change in the C/C bond order ii) Diffusion of F in the increased interlayer space with the underlying sidewall made possible, resulting in the attack of the latter by fluorine, on edge first iii) Radial inflation of the second outermost sidewall upon fluorination, inducing progressive cracking of the above fluorinated shell… and so on. Some authors consequently mentioned [21] that delamination of the outer fluorinated shells could occur in the course of progression of the fluorinated front. Globally, essential divergences arise when comparing the high temperature fluorination of MWNTs and SWNTs. The maximum stoichiometry that is usually reported for F-SWNTs is close to F/C ≈ 0.5, whereas fluorination to saturation of the carbon shells occurs in the case of F-MWNTs, without degradation of the substrate. In the latter case, according to XRD, the microstructure locally looks like that of the graphite-derived phase poly-monocarbon monofluoride (CF)n, indicating that more or less ordered rolled perfluorographene sheets form. This consequently implies that both sides of the carbon shells must be fluorinated according to a regularly alternating inner/outer addition pattern. Note that partial fluorination rates, i.e. x500 °C) pyrolysis results in short fragments of SWNTs [9], following gasification of the surface fluorinated sections. In compliance with their synthesis temperature higher than that of F-SWNTs, F-MWNTs appear more resistant to thermal decomposition and show almost no degradation when annealed at reasonably high temperatures under inert atmosphere (see Figure 5). TEM observations on SWNTs fluorinated at 300 °C showed the starting coexistence of some multiwalled fluorinated phases [36], seemingly arising from the transformation of the single-walled phase, that further confirms that the multilayered state constitutes a better intermediate level of stability. Alternatively, F-SWNTs have even been observed to evolve toward multi-walled structures under simple extensive electron-beam irradiation in a TEM [36]. Electronic structure: Contrarily to fullerene molecules, the random addition that takes place on SWNTs renders the concept of an “electronic structure” somewhat meaningless. Indeed, anticipating any individual behavior implies to consider a unique residual conjugation scheme at the surface of an “addended” tube, which requires a regular isomeric structure of the carbon substrate plus a periodical distribution of motifs at its surface. Some theoretical investigations [38-40] have shown that in such conditions, the fluorination of SWNTs can open or close gaps in the band structure of the final material. This kind of approach suffers less from the level of approximation used than from its unrealistic confrontation with actual experimental results, since in practice, the former requirements can not be gathered. So far, the only practically useful data then lies in the prediction of a global lowering of the Fermi level [39] induced by the presence of fluorine. Hence, each fluorinated carbon nanotube individually constitutes a potentially oxidizing species. This draws a direct link with the electronic properties of the parent fluorofullerene molecules, well-know to be able to yield stable fluorofulleride anions [24].

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Given the structural divergences previously evoked between F-SWNTs and F-MWNTs, differences in their respective electronic structures emerge. Thus, multiwalled fluorotubes should not exhibit electronic and macroscopic properties too different from those characterizing the analogous graphite-derived phase (CF)n. However, this will only hold true for tubes saturated with fluorine and yet unexplored hitherto, the expected mixed properties of surface fluorinated MWNTs should be described on the basis of a two-phases model including the core and outermost levels of the structure.

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Figure 5. TGA curves (constant temperatures) illustrating the stability of the C-F chemical bond within a sample of F- MWNTs, bulk-fluorinated at high temperature (520 °C, here).

Chemical bonding: At this stage, we have to first point out that the forthcoming approach considers an average C-F bond, convenient for the purpose of generalization, but that, in practice, non-energetically equivalent C-F moieties should sometimes be distinguished, as detailed in a further section. Globally speaking, a weakening of the C-F bond strength occurs in curved fluorocarbon networks in comparison to conventional fluorochemicals, but the amplitude of variation will strongly depend on the characteristics of the carbon substrate. Thus, if the stability of different fluorinated carbon structures is compared, one essential factor strongly influencing the C-F bond strength intrinsically lies in the respective topologies of the carbon lattices considered. For instance, as clearly illustrated from figure 6, the evolution of the C-F stretching frequency in the IR region shows a concomitant decrease in the averaged bond strength with the radius of curvature of the carbon network. Admitting that bond strength also reflects absolute bond energy, the former phenomenon can be basically explained by a softened covalence between carbon and fluorine. Indeed, bending, when present, imposes valence angles that prevents the realization of a purely sp3 state at the level of “addended” carbon atoms in the final fluorinated structure, which would be associated with too important local strain. Some sp2 character is then partly retained in such a case,

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necessarily implying that the overlap between the hybridized lobes pointing outward the carbon frame and the fluorine atomic orbitals becomes less efficient.

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Figure 6. Experimental IR spectra showing a progressive shift of the approximate intermediate position of the C-F stretching band toward lower wave numbers, following an increase in the carbon substrate curvature - a) Bulk-fluorinated MWNTs (520 °C, composition CF1) b) SWNTs fluorinated at 300 °C (composition CF0.5) c) 80% fluorinated [70]-fullerene.

If curvature presently plays a significant role in diminishing the thermochemical stability of fluorotubes, some additional factors may potentially contribute to further weaken the C-F bond. Thus, an accumulation of adjacent fluorine atoms on one side of a carbon sidewall should create steric hindrance. Yet, this can not hold for F-MWNTs, in which case nearest neighbors fluorine alternatively stand on both sides of a carbon sheet, as seen before. According to theoretical calculations [27], when a given exo- fluorine addition pattern is envisaged, steric repulsion would tend to stabilize those F-SWNTs endowed with the smallest diameters (i.e. the most curved). A pronounced curvature indeed lengthens the separation between nearest neighboring addends. At last, one may also legitimately wonder whether the initial helicity of the tubular substrate can play a role on the thermochemical stability of the C-F moiety within fluorotubes. Computational investigations [27,37] showed that the latter factor has a minor influence compared to that exerted by diameter. Alternatively, it has often been inferred that bond weakening within fluorotubes arises from a polarization of the C-F bond, an opinion issued from the several decades long earlier background dedicated to fluorographites. However, in spite of the ability of fullerenic carbon frames to undergo charge withdrawal [34], such a bonding concept happens definitely obsolete, as discussed later on. To close this paragraph, we then have to point out that a more reasoned overview on chemical bonding in fluorotubes must be provided but appears so unexpectedly complex that a whole detailed part will be devoted to it in the following. The present short section aims only at being a useful preliminary guide to account for some of the properties described below.

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Reactivity: Standard fluorocarbons are known for their chemical inertness, a property inherent to the generally extreme intrinsic robustness of their C-F bonds. One may then expect the less energetically stable C-F bond present in fluorotubes to confer the latest an enhanced chemical reactivity. This naïve picture is at the origin of a frequently committed mistake in the interpretation of the physicochemical properties of fluorotubes, described below. The notion of reactivity will be essentially restricted to single-walled fluorocarbon matrices only, since as seen previously, F-MWNTs consist of rather stable perfluorographene-like shells, resembling their chemically inert flat homologue, graphite fluoride (CF)n. In contrast, F-SWNTs can undergo defluorination upon simple prolonged annealing [8,11,12] at moderate temperature or upon chemical reduction with hydrazine [1,10,43,47] or with some solid halides and sulfides [43], turning back to their initial SWNTs state. More importantly, the latter fluorocarbon matrices are prone to nucleophilic attack, as well. Important pioneering works [41,42] had similarly led to the grafting of functionalities to the [60]-fullerene cage by starting from a fluorinated precursor, whereas some of these reactions may otherwise be more difficult to obtain from the C60 molecule, especially when a high functionalization rate is desired. The interested reader may refer to wider review articles on the subject [24]. Originally initiated within the framework of the study of the chemical reactivity of fluorofullerenes, investigations on this latter aspect have since been intensively extended to fluorine atoms grafted to the surface of a SWNT and have shown the ability of the halogen atom to be readily displaced. Hence, the attachment of alkyl chains and various oxygen or nitrogen-based functional groups [1,43-47] to the sidewall of SWNTs has been reported, by starting from F-SWNTs. So far, simple substitution of mobile fluorine species, which are initially easy to fix to the carbon substrate, turns out to be the best means to enhance the rates of derivatization of fullerenic carbon networks (= fullerenes and tubes). One should be careful to a common confusion when interpreting the above properties. Indeed, the ability of some fluorotubes to undergo defluorination does not arise from the previously illustrated diminution of the absolute average C-F bond energy, but instead likely possesses a kinetic origin [48]. Indeed, absolute bond energies stand with respect to the free atoms and provide information on thermochemical stability, once the energy offset corresponding to the constitutive elements in their more conventional thermodynamic standard state is introduced. Thus, in comparison with “normal” bonds in common fluorochemicals, especially poly-monocarbon fluoride (CF)n, C-F moieties in fluorotubes happen to be destabilized, i.e. the creation of C-F bonds according to Cgraphite + x/2 F2 → CFx is less energetic when the final CFx network is bent. But interpreting the formerly described physicochemical properties of fluorotubes from an energetic standpoint implies to rather consider the bond dissociation energy (BDE), which itself contains an enthalpy contribution relating to the formation of the pristine carbon network. It turns out that the latter term exerts the major influence on the BDE value, as shown from the following example. In the absence of direct thermochemical measurements on fluorotubes, a parent fluorofullerenic framework is compared to the fluorinated derivative of graphite. Hence, direct defluorination of a gaseous fluoro[60]-fullerene molecule according to Cfull.Fx → Cfull. + x F· necessitates on good average 291 kJ/mol C-F [49,50], while the equivalent complete defluorination of one polymonocarbon fluoride (CF)n sheet necessitates only 254 kJ/mol C-F [51] (cohesive energies in the fluorinated and non-fluorinated condensed states of graphite are of nearly the same order, due to only weak van der Waals interaction between layers, so that the corrective terms

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involved in the transition to isolated layers can be safely neglected). Overall, the C-F bond cleavage happens then to be +37 kJ/mol more endothermic for an isolated C60Fx molecule than for a perfluorographene sheet. This energy amount compares very favorably with the +42 kJ/mol C representing the enthalpy of formation of a gaseous C60 molecule from graphite. Consequently, it can be extrapolated that fluctuations in the average BDE of any fluorocarbon lattice turn out to be almost entirely contained in the sole enthalpy of formation of the pristine carbon frame. It follows that the average BDE of a fluorocarbon matrix will increase concomitantly with the radius of curvature of the bare carbon precursor. Consequently, great care should then be taken when evoking poorly bound fluorine atoms, while referring to the physicochemical properties of fluorotubes previously recalled. In fact, regarding the above mentioned energetic considerations, fluorine atoms within fluorotubes turn out to be tightly bound to their carbon substrate since defluorination of a tubular network will require more energy than that of graphite fluoride. Yet, it turns out that this energetic statement appears in strong contradiction with all experimentally established trends, since, as seen before, F-SWNTs can readily release fluorine throughout different processes, whereas graphite fluoride (CF)n is an extremely stable compound until around 500 °C under inert atmosphere, decomposes beyond into gaseous fluorocarbons instead of undergoing defluorination, and is chemically inert. Such a paradox, opposing thermodynamics, clearly means that the easy fluorine departure from F-SWNTs compounds has a pure kinetic origin, so that a terminology like “labile fluorine” should be rigorously preferred. The underlying kinetics can be reasonably understood by referring to hybridization states in conjunction with activation energies. In pristine SWNTs, the sp2 character of the carbon atom is limited by the pyramidalization angle imposed by curvature, while the sp3 character of the carbon atom in the fluorinated derivatives is in turn limited for similar valence angle reasons. Consequently, in the course of either a fluorination or defluorination process, part of the hybrid character initially present is retained, which should then lower the energy barrier over which to pass to reach the transition state involved in the transformation. This makes an initially bent carbon skeleton easier to fluorinate and in parallel, its fluorinated homologue also easier to defluorinate. In contrast, the fluorination/defluorination of graphite is a total sp2↔sp3 transformation involving complete conversion of the hybridization state of carbon. This introduces kinetic limitation which can be overcome only under harsher experimental conditions. Though fundamentally correct and laying the foundation stone of the physico-chemistry of F-SWNTs, we have to here again emphasize that the present approach implicitly stands for an averaging of the chemical bonding properties and that, in practice, partial distinction should be introduced between the C-F moieties, as described later on.

b) Solid State Solubility/dispersion: Bulk samples of F-SWNTs prepared at 250 °C exhibit excellent dispersion properties upon sonication in alcohols [47], whereas perfluorinated solvents happen surprisingly quite inefficient in this purpose, in spite of the “like dissolves like” tendency. This was tentatively attributed to an enhanced dipolar moment of the C-F chemical bond that may facilitate the formation of hydrogen bonds from the partly charged fluorine atoms, but this initial explanation can clearly not be retained anymore.

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Conductivity: It can be readily foreseen that the functionalization of carbon nanotubes should generate insulating materials, following random breaking of conjugation. Thus, not surprisingly, the resistivity of an initially conducting film of SWNTs was found to increase by six orders of magnitude after fluorination [1]. In another study [5], the resistivity was also found to increase in parallel with the level of fluorination. Let’s note that such phenomena, though intimately correlated with the evolution of the “overall” electronic structure, reflect a sum of individual behaviors within a sample rather than a true collective behavior. In regard to the resemblance that F-MWNTs bear to poly-monocarbon fluoride, it can be taken for granted that the latter similarly exhibit strong insulating properties. Nevertheless, when not bulk-fluorinated, it is expected that they can also exhibit a mixed behavior combining the insulating properties of their outer fluorinated shells with those of their conducting to semi-conducting inner pure carbon core.

II. CHARACTERISTICS OF THE C-F CHEMICAL BOND IN FLUOROTUBES 1. A Weakened Plus Versatile C-F Bond

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As for summary of the essential points established in the former part I, one may first basically recall that the high affinity of carbon for fluorine usually makes this combination one of the most energetic simple bonds. Thus, in thermodynamic equilibrium conditions, the simple pairing of one fluorine atom and one carbon atom yields a stable .:CF(g) radical fragment, called fluoromethylidyne, whose bond dissociation energy is 540 kJ/mol [52,53]. We then evoked, independently of any local structural aspect, how the global stability of the latter atomic association in the solid state is made dependent on the carbon frame. The present part II aims at providing a final description of the fluorine addition pattern to carbon nanotubes. Focus will be made on the variability of the C-F binding energy that can appear in fluorotubes, which arises from its ability to be frozen in local minima. MW Fluorotubes: The tendency toward metastability of the C-F bond in fluorotubes is clearly exemplified throughout the low and high temperature forms of multiwall fluorotubes, which clearly denote the opportunity of formation of kinetic products. We have depicted in the first part how the multi-walled tubular carbon allotrope mimics by several ways the chemistry of graphite, especially from the point of view of its reactivity with fluorine. Thus, the high temperature fluorination of MWNTs yields products that compare well with the graphite fluoride form (CF)n prepared at high temperature, whereas low temperature catalytic conditions yields a surface phase analogous to the so-called intercalation compounds of graphite with fluorine. It can be intuitively guessed that the varied addition modes of fluorine to a MWNT, under the form of either intercalation or addition final compounds, are intrinsically associated with changes in the nature of the C-F chemical bond. The experimentally checked quenching of the intercalation process upon increase of the synthesis temperature is the signature of rapid thermal decomposition, providing evidence for the instability of the C-F bond involved in it. The increase in the synthesis temperature alleviates

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kinetic limitations and then turns the fluorination process toward the formation of a true addition compound involving the thermodynamically stable covalent C-F moiety. SWNTs: Though manifesting in a different way, the versatile character of the C-F bond in F-SWNTs has also asserted itself and several authors have explicitly mentioned the coexistence of mixed bonding properties in their samples of single-walled fluorotubes [5,9,12-14,61]. These have been evidenced most of the time by an apparent splitting of the associated F1s XPS signal [5,13,14], or through the wide wave number range associated to the stretching of the C-F bond [9,12,61]. Simple gravimetric techniques exploiting controlled thermolysis have recently provided a quantitative determination of the different bonding modes present in F-SWNTs [12]. As illustrated below, three different modes of fluorine chemisorption can be unambiguously evidenced within single-walled fluorotubes prepared at 100 °C, for instance. The TGA curves of such samples exhibit distinct steps of fluorine desorption, tentatively interpreted as the successive rupture of weak to stronger C-F bonds over the respective ranges 50 °C