Graphene and Graphite Materials [1 ed.] 9781613249659, 9781606926666

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Copyright © 2009. Nova Science Publishers, Incorporated. All rights reserved. Graphene and Graphite Materials, Nova Science Publishers, Incorporated, 2009. ProQuest Ebook Central,

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GRAPHENE AND GRAPHITE MATERIALS

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MATERIALS SCIENCE AND TECHNOLOGIES SERIES Dielectric Materials: Introduction, Research and Applications Ram Naresh Prasad Choudhary and Sunanda Kumari Patri 2009. ISBN 978-1-60741-039-3 Handbook of Zeolites: Structure, Properties and Applications T. W. Wong 2009. ISBN 978-1-60741-046-1 Building Materials: Properties, Performance and Applications Donald N. Cornejo and Jason L. Haro (Editors) 2009. ISBN: 978-1-60741-082-9 Concrete Materials: Properties, Performance and Applications Jeffrey Thomas Sentowski (Editors) 2009. ISBN: 978-1-60741-250-2 Physical Aging of Glasses: The VFT Approach Jacques Rault 2009. ISBN: 978-1-60741-316-5

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MATERIALS SCIENCE AND TECHNOLOGIES SERIES

GRAPHENE AND GRAPHITE MATERIALS

H.E. CHAN

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

EDITOR

Nova Science Publishers, Inc. New York

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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.

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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. 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 Graphene and graphite materials / [edited by] H.E. Chan. p. cm. Includes index. ISBN 978-1-61324-965-9 (e-Book) 1. Graphitization. 2. Graphene. 3. Graphite composites. I. Chan, H. E., 1964TP261.G7G73 2009 662'.92--dc22 2009017717

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CONTENTS Preface

vii

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Research and Review Studies

1

Chapter 1

Electroanalysis of Some Bio–Molecules at the Electrode Modified by Carbon Nanotubes Chenxin Cai

Chapter 2

Serendipity in the Study of the Graphene Carbon-Lithium Reaction Systems Tsutomu Takamura

57

Chapter 3

Molecule-Surface Binding Energies from Molecular Mechanics: Nucleobases on Graphene Thomas R. Rybolt and Christina E. Wells

95

Chapter 4

Lubricity of Graphite Additives in Polyimide Composites at Variable Humidity Pieter Samyn, Gustaaf Schoukens and Patrick De Baets

113

Chapter 5

Advances in Superconducting Intercalated Graphite Nicolas Emery, Claire Hérold and Philippe Lagrange

143

Chapter 6

Composites on the Basis of Polyhydroxiethers and Graphites D.A. Beeva, A.K. Mikitaev, G.E. Zaikov, R.Z. Oshroeva, V.K. Koumykov and A.A. Beev

193

Chapter 7

A Comparative Study of Al, Ge and Sb Self-assembled Nanostructures on Graphite X.-S. Wang, W. Xiao, S.S. Kushvaha, Z. Yan and M. Xu

197

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vi

Contents

Short Communications

231

Self-assembled Fibrillar Carbon Nanotube Heat Transfer Gels with Enhanced Thermal Conductivities Betty Catalina Rostro, Scott Selinger, Nancy Rosenberg, Valery N. Khabashesku and Enrique V. Barrera

233

Von Neumann Algebras Generated by Automata Ilwoo Cho

245

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Index

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PREFACE Graphene is a nanomaterial combining very simple atomic structure with intriguingly complex and largely unexplored physics. Since its first isolation about four years ago researchers suggested a large number of applications for this material in anticipation of future technological revolutions. In particular, graphene is considered as a potential candidate for replacing silicon in future electronic devices. Graphene is a perfect example of the wonders of nanotechnology, in which common substances are scaled down to an atomic level to uncover new and exciting possibilities.The mineral graphite is one of the allotropes of carbon. Unlike diamond (another carbon allotrope), graphite is an electrical conductor, a semimetal, and can be used, for instance, in the electrodes of an arc lamp. This new book presents the latest research in the field from around the world. Chapter 1 describes the electrochemical behavior of some important biological molecules on the electrode modified by carbonaceous materials: carbon nanotubes, and their applications in electroanalysis and some other related fields. The fabrication methods and characterization of the carbon nanotubes–modified electrodes are presented in the chapter. The electrocatalytic activities of the modified electrodes toward the electrochemical reactions of several small molecules with biological importance including ascorbic acid, dopamine, hydronicotinamide adenine dinucleotide (phosphate) (β– NAD(P)H), etc are discussed and compared with those of conventional carbon materials, such as glassy carbon. In addition, the investigation results are given on the electrocatalytic activities (or promotional effects) of carbon nanotubes to the direct electron–transfer reaction of important large biological molecules of proteins and enzymes: heme-containing proteins/enzymes (cytochrome c, myoglobin, hemoglobin, horseradish peroxidase), flavin– containing enzyme (glucose oxidase), and ferredoxin (from Spinacia Oleracea). We mainly depict the immobilization of proteins/enzymes on the surface of carbon nanotubes, mechanism of the direct electrochemistry, the formal potentials and the apparent rate constant (ks) of direct electron–transfer reactions of these proteins/enzymes at the surface of carbon nanotubes, and the bioelectrocatlytic activities to the substrates based on the direct electron–transfer reaction of proteins/enzymes. The application of the direct electron– transfer reaction of enzymes catalyzed by carbon nanotubes in biosensors and biofuel cells are introduced as well. During the course of electrochemical investigation of Li insertion/extraction reaction in graphite and the related substances the author has obtained new findings or methods for

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improving the reactivity. In Chapter 2 the author intends to show the interesting phenomena with explanation and application. The chapters consist of the following eight chapters. 1) Introduction 2) Under-potential deposition (UPD) of Li on the carbon surface.UPD phenomenon is popular on the foreign metal atom deposition on the metal electrode surface and studied extensively by many researchers including the present author, but it has been unfamiliar on the nonmetal electrode. When we examined the cyclic voltammograms of graphite fiber or active carbon fiber in non-aqueous solvent containing LiClO4 we found a sharp peak at a slightly positive to the Li metal deposition potential. This was found to be sensitive to the surface condition, and the peak height was proportional to the carbon surface area, and to the Li+ concentration. We attributed it to the UPD of Li on the carbon surface. Later on this phenomenon was found to be applied as a charge accumulator like double layer capacitor, the charge amount being far larger than that of the capacitor. 3) Mass transfer of Li in metal at room temperature. In an attempt to modify the graphite surface to obtain high reaction rate of Li insertion/extraction, we deposited a metal film on the graphite fiber surface in a vacuum chamber. We found that the Li insertion/extraction rates were much more improved by the deposition of Pd. In addition, we examined Cu, Ag, Au, In, Ni, and many other metals. We found most of the metals examined revealed the reaction enhancing effect. This phenomenon implies that prior to the insertion in the carbon fiber Li has to moves through the deposited metal film. This is our novel finding. By the use of a bipolar cell where the sample metal foil was sandwiched between the two facing cylindrical cell compartmens, we could verify the evidence of Li mass transfer in metal at room temperature. The diffusion coefficient of Li in metal could be determined, i.e., in Cu and Ni the value was 10-7 cm2 s-1, and 10-6 in Ag, the value being in the same order of magnitude as that of ions in liquid electrolyte, and larger than that of hydrogen atom in Pd. 4) Diffusion coefficient of Li in graphitized carbon. A number of studies have so far been conducted for the determination of the diffusion coefficient of Li in graphitized carbon but the values are scattered in the range between 10-11 to 10-6 cm2 s-1. The reason why it is so much scattered is ascribed to the different situation of the carbon sample in the electrode. Usually the sample carbon powders were coated on a Cu foil with some binder, resulting in inhomogeneous electrical contact. Instead of powder sample we used graphitized carbon single fiber potential step chrono-ammperometry was performed. The resulting obtained value was as high as 10-6 cm2 s-1. 5) Postulate and verification of the presence of nano-holes at the graphene layer. It is said that Li cannot pass across a basal plane of graphite crystal since the six members carbon ring of the graphene layer is too narrow. Although the rounded graphite particles are covered by graphene layers sheet over the surface, they are used in the anode of Li-ion battery; implying Li can get into the interior of the particles. The author paid attention to such an apparently contradicting phenomenon and postulated that there are a number of nano-size holes at the graphene layer. We attempted to detect such holes by analyzing the TEM images of graphite, and finally detected a number of images of hole-like structure. Through such holes Li can penetrate into the interior of the carbon very easily. 6) Characterization of the decomposition reaction of propylene carbonate on a graphite anode. It is well-known that propylene carbonate, which is a good solvent for obtaining electrolyte for Li-ion battery, cannot be used for the graphite-like

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anode since it decomposes violently at the surface of the anode during Li insertion. The decomposition has been attributed to the solvent-co-intercalation into the space between the graphene sheets. But we found that when we use a single fiber electrode no decomposition occurred even with a graphitized fiber. After an extensive examination we concluded that such a decomposition phenomenon occurs on the surface where the electrical potential distribution over the surface is inhomogeneous. As far as the distribution is homogeneous, no decomposition was observed. 7) Thus, the solvent co-intercalation mechanism has become no longer valid 8) Propose of a novel activation method for improving the Li insertion/extraction reaction. In an attempt to obtain an active surface for insertion/extraction of Li in non-aqueous electrolyte the author challenged to obtain a simple way to realize it. Finally we have found finally an effective method which is now called “mild oxidation”. Heating the carbon samples at an appropriate amount oxygen content atmosphere was found very effective for the activation. This method was found effective for the activation of active carbon surface. 9) Electrochemical properties of SEI for Li insertion/extraction. The term of “SEI” (Solid/electrolyte interphase) is now very popular on the surface of carbon samples. But it was difficult for characterizing the SEI on the metal surface. Since SEI has been paid attention on the Li insertion/extraction reaction the author proposed a method to characterize the SEI on a metal surface by making a sample where the sample metal is vacuum-deposited on a graphitized carbon fiber. While Molecular Mechanics provides no electronic details, it can be used for estimations of selected molecular properties. Augmented MM2 parameters with no modification have been found to provide useful estimates for the interaction energy of various organic molecules with model graphene surfaces and these prior results are reviewed in Chapter 3. The MM2 binding energies of the five DNA/RNA nucleobases on graphene are determined and compared to reported quantum mechanical calculations. The speed of molecular mechanical computations and its demonstrated correlation with experimental binding energies for carbon surfaces justify its use in selected situations. Molecule-graphitic carbon binding energies (E*) reported from thermal programmed desorption (TPD) and gas-solid chromatography (GSC) experiments are compared to calculated binding energy values (Ecal*). Experimental binding energies from GSC are for isolated molecules in the Henry’s law region of adsorption, while binding energies from TPD are for molecules at monolayer coverage. A comparison of the energetic differences between isolated molecules and monolayer coverage shows that monolayer coverage calculations must include adsorbate molecule-molecule interactions. For a number of applications, MM2 molecular mechanics calculations have been shown to provide Ecal* estimates that are in good agreement with GSC and TPD experimental E* binding energies. For the nucleobase calculations, the model graphene surface used consisted of 702 interconnected benzene rings and 1,510 carbon atoms. Graphitic surfaces were constructed by stacking these graphene layers to, for example, create a Bernal graphite with every other layer aligned. The nucleobases are each treated as an isolated molecule from the gas phase adsorbed on a graphene surface. The nucleobase binding energies for a single graphene layer using MM2 parameters were found to be 0.704, 0.639, 0.579, 0.579, and 0.509 eV for guanine, adenine, thymine, cytosine, and uracil, respectively. Following the procedure of others, the nucleobase molecules each have an attached methyl group in the place where

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the nucleobase would join the sugar ring to form the corresponding nucleoside. This methyl group contributes about 0.06 eV to the overall attractive energy. As explained in Chapter 4, polymers are known as self-lubricating materials that may function under dry sliding conditions, excluding the need of external lubricating systems. In particular, polyimides are a class of high-performance polymers with extremely good thermal and chemical resistance, supposed to operate under severe sliding conditions with high normal loads and sliding velocities. However, polyimides often show high coefficients of friction and high wear rates that highly depend on the environmental humidity. Graphite is known as a material with potentially lubricating properties due to its lamellar structure, and it is therefore often added as flake-like additives into polymer composites, functioning as an internal lubricant for controlling the tribological properties. For a given composition of sintered graphite-polyimide composites, the effect of humidity on its sliding properties cannot be clearly predicted. The tribological properties of the polyimide matrix and the graphite additives seem to depend on the moisture content in an opposite way. Theoretically, graphite provides high friction under dry sliding conditions and adsorption of water molecules is needed for easy shear of the lamellar structure. On the other hand, the water molecules have detrimental effects on the sliding properties of the polyimide surface as they restrict molecular relaxation mechanisms. The friction and wear performance of unfilled and graphite-filled sintered polyimides will therefore be experimentally investigated at three humidity levels during unlubricated sliding against steel. A relationship between the sliding properties of graphite internal lubricants at high humidity versus high temperatures, normal loads and sliding velocities will be further discussed. The discovery in 2005 of superconductivity in YbC6 and CaC6, with substantially higher critical temperatures than the previously observed among the family of the graphite intercalation compounds, has largely renewed the interest for these well known lamellar compounds. Indeed, these critical temperatures reach 6.5 and 11.5 K respectively for ytterbium- and calcium-graphite phases. It was consequently interesting to collect all the informations concerning the superconductivity of these compounds from the discovery of this phenomenon observed in the heavy alkali metals graphite intercalation compounds in 1965, insisting particularly on the recent advances in this research field. After a general introduction, that describes all the carbon materials, which are extremely various with dimensionalities varying from 3 to 0, leading to their large aptitude for the insertion/intercalation reactions, we develop widely the case of graphite : chemical bonds, crystal and electronic structures, anisotropy and ability to become a host structure. We insist on its strong anisotropy of chemical reactivity, that allows the synthesis of very numerous intercalation compounds. The distinctive features of the intercalation reaction into graphite are reviewed (systematic charge transfer, staging, etc…) and are particularly developed in the case of the donor-type intercalation compounds, among which is precisely observed the superconductivity. For the latter, the various synthesis methods are successively described, showing the best route to use in order to obtain each type of compound. Then we review with detail the binary compounds, emphasizing their distinctive crystal and electronic structures and also their transport properties. In a second time, we describe the superconductivity of all the compounds belonging to this family and showing this property. In a last part of Chapter 5, we compare these superconducting binary intercalated graphite compounds with an other lamellar superconductor : magnesium diboride.

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Preface

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The ternary compounds are then studied, and the poly-layered nature of their intercalated sheets is especially underlined. Their distinctive electronic structure is presented and their superconducting properties are described. Lastly, we give a rather short overview concerning the superconductivity observed in the other intercalated carbon materials: diamond, fullerenes and nanotubes. As presented in Chapter 6, by settle polycondensation the polymeric compositions were created, in which high crystalline graphite of the scaly form, using as filler was entered into polymer during synthesis of polyhydroxiethers. The results of experiment showed, that in the presence of synthetic graphite the viscosity of polymer increases; this proves our earlier assumption, that selective adsorption leads to the increase of the local concentration of monomers on the surface of fillers and to the increase of polycondensation reaction speed. In situ scanning tunneling microscopy (STM) investigations of the nucleation, growth, aggregation and coarsening of nanoparticles on an inert substrate, such as graphite, reveal many intrinsic thermodynamic and kinetic properties of nanoparticles important to nanostructural self-assembly and applications. We performed systematic in situ STM studies of Al, Ge and Sb growth on highly oriented pyrolytic graphite (HOPG). At room temperature (RT), three dimensional (3D) clusters of all three elements nucleate and grow at step edges and defect sites of HOPG. The clusters of Al and Ge form chains, while Sb islands are mostly isolated. With increasing deposition at RT, Al clusters grow and coarsen into crystallites with (111) facets on top, which coalesce further into flat islands with craters on the top. In contrast, due to a low sticking probability of Ge atoms on graphite and little coarsening among Ge clusters, single- and double-layer cluster chains as well as ramified islands are observed. When deposited or annealed at T ≥ 450 K, Ge forms crystallites but with randomly oriented high-index facets. As spherical Sb islands grow beyond certain size, (111) facets appear on the top. In addition to 3D islands, 2D crystalline Sb films and 1D nanorods are observed. At T ≈ 375 K and a high flux, only 2D and 1D Sb islands are formed, whereas only 3D islands are formed initially when Sb is deposited with a low flux at RT. This selectivity of different dimensional Sb nano-assembly is explained in terms of Sb4 diffusion and dissociation kinetics. The Sb nanorods start with a simple cubic lattice structure, which is observed under high pressure for bulk Sb crystal. These different growth behaviors reflect the unique nature of interaction among the atoms (molecules), clusters and crystallites of each element, as well as with HOPG substrate, as presented in Chapter 7. There are an increasing number of industrial applications that require energy-efficient heat transfer fluids. As such, fluids with high thermal conductivities are highly sought after. Increased thermal conductivities have been reported in fluids containing suspended nanoparticles – smaller than 100 nanometers (nm) – these were termed nanofluids. Nanofluids made with metal, ceramic, metal oxide, and carbon nanotube particles have shown thermal conductivities that are remarkably higher than the base liquid. The aim of the first Short Communication was to increase the thermal conductivity (TC) of biodegradable synthetic and vegetable oil heat transfer fluids (HTFs). The TC of these base oils was increased by up to 96% using additives of graphene type, Single-Walled Carbon Nanotube (SWNTs), thereby leading to the formation of SWNT nanofluid-HTFs (n-HTFs). The Decagon KD2 was used to measure the TC, and Raman spectroscopy was used to study the TC mechanism. The resulting SWNT nanofluid-HTFs (n-HTFs) are proposed to be defined as a self-assembled fibrillar networked gels.

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The main purpose of the second Short Communication is to introduce how to construct a von Neumann algebra generated by an automaton, containing the full information of the given automaton. We show that the von Neumann algebras generated by automata are characterized by the graph von Neumann algebras in the sense of [10] and [11]. This shows that the von Neumann algebras generated by automata have the same basic properties with graph von Neumann algebras.

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RESEARCH AND REVIEW STUDIES

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Chapter 1

ELECTROANALYSIS OF SOME BIO–MOLECULES AT THE ELECTRODE MODIFIED BY CARBON NANOTUBES Chenxin Cai* Jiangsu Key Laboratory of Biofunctional Materials, College of Chemistry and Environmental Science, Nanjing Normal University, Nanjing 210097, P. R. China

Abstract

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This chapter describes the electrochemical behavior of some important biological molecules on the electrode modified by carbonaceous materials: carbon nanotubes, and their applications in electroanalysis and some other related fields. The fabrication methods and characterization of the carbon nanotubes–modified electrodes are presented in the chapter. The electrocatalytic activities of the modified electrodes toward the electrochemical reactions of several small molecules with biological importance including ascorbic acid, dopamine, hydronicotinamide adenine dinucleotide (phosphate) (β–NAD(P)H), etc are discussed and compared with those of conventional carbon materials, such as glassy carbon. In addition, the investigation results are given on the electrocatalytic activities (or promotional effects) of carbon nanotubes to the direct electron–transfer reaction of important large biological molecules of proteins and enzymes: heme-containing proteins/enzymes (cytochrome c, myoglobin, hemoglobin, horseradish peroxidase), flavin–containing enzyme (glucose oxidase), and ferredoxin (from Spinacia Oleracea). We mainly depict the immobilization of proteins/enzymes on the surface of carbon nanotubes, mechanism of the direct electrochemistry, the formal potentials and the apparent rate constant (ks) of direct electron–transfer reactions of these proteins/enzymes at the surface of carbon nanotubes, and the bioelectrocatlytic activities to the substrates based on the direct electron–transfer reaction of proteins/enzymes. The application of the direct electron–transfer reaction of enzymes catalyzed by carbon nanotubes in biosensors and biofuel cells are introduced as well.

*

E-mail address:[email protected], [email protected].

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1. Introduction It is the chemical genius of carbon that it can bond in different ways to create structures with entirely different properties. The mystery lies in the different hybridization that carbon atoms can assume. The four valence electrons in carbon, when shared equally, sp3 hybridized, create isotropically strong diamond. But when only three are shared covalently between neighbors in a plane and the fourth is allowed to be delocalized among all atoms, the resulting material is graphite. The latter (sp2 hybridized) type of bonding builds a layered structure with strong in-plane bonds and weak out–of–plane bonding of the van der Walls type. Hence, graphite, which is the thermodynamically stable bulk phase of carbon up to very high temperatures under normal ranges of pressure (diamond is only kinetically stable), is weak normal to its planes and is considered as a soft material due to its ability to slide along the planes. A new form of carbon, buckministerfullerence C60, was discovered in 1985 by a team headed by Samlley, Kroto and coworkers [1], and led to the Nobel Prize in chemistry in 1997. C60 is a soccer ball–like molecule made of pure carbon atoms bonded in hexagon and pentagon configurations, and also belongs to the architecture of sp2 bonded carbon. Besides diamond, graphite and C60, quasi one–dimensional nanotube is another form of carbon first reported by Iijima in 1991 when he discovered multi–walled carbon nanotubes (MWNTs) in carbon–soot made by arc-discharge method [2]. About two years later, he made the observation of single–walled nanotubes (SWNTs) [3]. Since then, carbon nanotubes have captured the attention of researchers worldwide. A significant amount of work has been done to reveal the unique structural, electrical, mechanical, electro–mechanical and chemical properties of carbon nanotubes and to explore what might be the key applications of these novel materials. Carbon nanotubes are sheets of graphite that has been rolled into a seamless tube (the structures of diamond, graphite, C60, and carbon nanotubes are displayed in Figure1). Most important structures of carbon nanotubes are SWNTs and MWNTs. A SWNT is considered as a graphene sheet rolled–over into a cylinder with typical diameter on the order of 1.4 nm, similar to that of a C60 buckyball. A MWNT consists of concentric cylinders with an interlayer spacing of 3.4 Å and a diameter typically on the order of 10–20 nm. The lengths of the two types of tubes can be up to hundreds of microns or even centimeters. Carbon nanotubes have been made by chemical vapor deposition, carbon arc methods, or laser evaporation.

Figure 1. Structure illustration of diamond, graphite, C60 and SWNT.

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→

Figure 2. Chiral vector C and chiral angle θ definition for a (2,4) nanotube on graphene sheet. →

→

a1 and a2 are the unit cell vectors of the two-dimensional hexagonal graphene sheet. The circumference of nanotube is given by the length of chiral vector. The chiral angle θ is defined as the angle between →

chiral vector C and the zigzag axis (adapted from [4]).

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→

SWNTs are completely described, except for their length, by a single vector C (called chiral vector) [4–7]. Two atoms in a planar graphene sheet are chosen and one is used as →

origin. The chiral vector C is pointed from the first atom toward the second one (Figure 2) and is defined by the relation: →

→

→

C = n a1 + m a2 →

→

where n and m are integers. a1 and a2 the unit cell vectors of the two–dimensional lattice formed by the graphene sheets. The direction of the nanotube axis is perpendicular to this chiral vector. By folding a graphene sheet into a cylinder so that the beginning and end of a (n, m) lattice vector in the grapheme plane join together, one obtains an (n, m) nanotube. The (n, m) indices determine the diameter of the nanotube, and also the so–called “chirality”. (n, n) tubes are “arm–chair” tubes, since the atoms around the circumference are in an arm–chair patter (Figure 3a). (n, 0) nanotubes are termed “zigzag” in view of the atomic configuration along the circumference (Figure 3b and c). The other types of nanotubes are chiral, with the rows of hexagons spiraling along the nanotubes axes (Figure 3d).

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(a)

(b)

(c)

(d)

Figure 3. Schematic structures of SWNTs and how they determine the electronic properties of the nanotubes. (a) A (10, 10) arm–chair nanotube. Bottom panel: the hexagon represents the first Broulloin zone of a grapheme sheet in reciprocal space. The vertical lines represent the electronic state of the nanotube. The center–line crosses two corners of the hexagon, resulting in a metallic nanotube. (b) A (12, 0) zigzag nanotube. The electronic states cross the hexagon corners, but a small band gap can develop due to the curvature of the nanotube. (c) The (14, 0) zigzag tube is semiconducting because the states on the vertical lines miss the corner points of the hexagon. (d) A (7, 16) tube is semiconducting. This figure illustrates the extreme sensitivity of nanotube electronic structures to the diameter and chirality of nanotubes (adapted from [7]).

(a)

(b)

(c)

Figure 4. Various models of carbon nanotubes taking into account the experimental measurements: (a) coaxial cylindrically curved, (b) coaxial polygonized or (c) scroll graphene sheets (adapted from [8]).

MWNTs are described by different models which are in good agreement with experiments and in particular with the electron microscopic images. MWNTs may be formed from coaxial cylindrically curved, coaxial polygonized or scrolls graphene sheets [4,8] (Figure 4). The coaxial cylindrical model is widely accepted for MWNTs, however polygonized tubes are also observed. These are generally restricted to large tubes sizes which

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Electroanalysis of Some Bio–Molecules...

7

allow three–dimensionally correlated regions: low-angle title and well–aligned boundaries are then observed [9]. Carbons nanotubes are among the strongest and most resilient materials know to exist in nature. A carbon nanotube has a Young’s modulus of 1.2 TPa and tensile strength about a hundred times higher than steel and can tolerate large strains before mechanical failure [10]. The electrical properties of carbon nanotubes depend sensitively on the (n, m) indices and therefore on the diameter and chirality. A SWNT can be either a metal, semiconductor or small–gap semiconductor depending in the (n, m) structural parameters [11]. For example, the (n, n) arm–chair nanotubes are always metallic; the (n, m) nanotubes with n – m ≠ 3 × integer are semiconducting and the energy gap scales is on the order of 0.5 eV (for a SWNT with typical diameter 1.4 nm); the (n, m) nanotubes with n – m = 3 × integer would be semimetals but become small–gap semiconductors (band gap scales is ca. 10 meV for typical diameter 1.4 nm) due to a curvature induced orbital rehybridization effect [12]. The extreme sensitivity of electric property on structural parameters is unique for carbon nanotubes. This uniqueness leads to rich physical phenomena in nanotube systems, and process a significant challenge to chemical synthesis in terms of controlling the nanotube diameter and chirality. The intriguing properties of carbon nanotubes have led to an explosion of research efforts worldwide. Understanding these properties and exploring their potential applications have been a main driving force in this area. Theoretical and experimental work has been focusing on the relationship between nanotube atomic structures, electronic structures, transport properties, electron-electron and electron–phonon interaction effects. Extensive effort has been made to investigate the mechanical properties of carbon nanotubes. Thus far, carbon nanotubes have been utilized individually or as an ensemble to build functional device prototypes, used for field emission based flat–panel displays, composite materials with improved mechanical properties and electromechanical actuators. Bulk quantities of carbon nanotubes have also been suggested as high-capacity hydrogen storage media. Individual nanotube has been used for field emission sources, tips for scanning probe microscopy, nanotweezers, and chemical sensors. Carbon nanotubes are also promising as the central elements for future miniaturized electronic devices. Carbon nanotubes can also be used in the field of biomedical and the related devices [5,13]. Many applications for carbon nanotubes have been proposed including biosensors, drug and vaccine delivery vehicles and novel biomaterials [14]. For example, carbon nanotubes can be used as nano–fillers in existing polymeric materials to both dramatically improve mechanical properties and create highly anisotropic nanocomposites [15,16]. They can also be used to create electrically conductive polymers and tissue engineering constructs with the capacity to provide controlled electrical stimulation [17–19]. Recent studies demonstrated that carbon nanotubes have the ability to promote electron transfer reactions when used as electrode materials in electrochemical reactions [20–23]. As electrode materials, carbon nanotubes–modified electrodes have shown superior performances as compared to other carbon electrodes, including good conducting ability and high chemical stability. It had been reported that the resistivities of a single carbon nanotube could be as low as 5.1 × 10–6 Ω cm [24], while the resistivities of pyrolytic graphite, glassy carbon, and carbon fiber were 2.5 × 10–4 (in a axis direction), 4 × 10–3, and 7.5 × 10–4 Ω cm [25], respectively. Electrodes modified with carbon nanotubes have been used to improve the electrochemical behaviors of many biologically importance molecules, including several small molecules with biological importance and the proteins/enzymes [26–51]. In addition to

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enhanced electrochemical reactivity, carbon nanotubes–modified electrodes have been shown useful to accumulate important biomolecules (e.g., nucleic acids) [52] and to alleviate surface fouling effects (such as those involving in the NADH oxidation process) [26,28]. Those unique properties make carbon nanotubes very promising in electrochemical applications, especially in electrochemical biosensors and other electrochemical devices from amperometric enzyme electrodes to DNA hybrization biosensors. For example, Rusling and coworkers [53–55] fabricated the sensitive immunosensors by attaching antibodies to SWNTs forests, which were prepared by self–assembling 20–30 nm long terminally carboxylated SWNTs into forests standing in upright bundles on Nafion–iron oxide decorated conductive surfaces [44,56]. Those highly sensitive immunosensors were used to detect biotin [54], human serum albumin [53] in buffer solution, and a cancer biomarker in serum and tissue lysates [55]. Wang and coworkers [57–59] used CNTs–based enzyme electrodes to amperometrically detect the V–type nerve agents (O–ethyl–S–2–diisopropylaminoethyl methylphosphonothioate and O–isobuthyl–S–2–diethylaminoethyl methyphosphonothioate) [57], the RuOx/CNTs–modified electrode to detect insulin [58], and the nano–Fe3O4/CNTs composite electrode to detect glucose [59] etc. To take advantages of the remarkable properties of these unique nanomaterials in such electrochemical sensing applications, the carbon nanotubes need to be properly functionalized and immobilized. The aim of this chapter is to report main results of the recent studies in our group in use of carbon nanotubes for electrochemical sensing. Specifically, we will report the fabrication methods and characterization of the carbon nanotubes–modified electrodes; the electrocatalytic activities of the modified electrodes toward the electrochemical reactions of several small molecules with biological importance including ascorbic acid, dopamine, adrenaline, hydronicotinamide adenine dinucleotide (phosphate) (β–NAD(P)H), etc.; the electrocatalytic activities (or promotional effects) of carbon nanotubes to the direct electron– transfer reaction of important large biological molecules of proteins and enzymes: heme– containing proteins/enzymes (cytochrome c, myoglobin, hemoglobin, horseradish peroxidase), flavin-containing enzyme (glucose oxidase), and ferredoxin (from Spinacia Oleracea). We mainly depict the immobilization of proteins/enzymes on the surface of carbon nanotubes, the direct electrochemistry, the formal potentials and the apparent rate constant (ks) of direct electron–transfer reactions of these proteins/enzymes at the surface of carbon nanotubes, and the bioelectrocatalytic activities to the substrates based on the direct electron–transfer reaction of proteins/enzymes. The work presented in this chapter would promote the developments of electrochemical research for enzymes (proteins), biosensors, biofuel cells and other bioelectrochemical devices.

2. Fabrication of the Carbon Nanotubes–Modified Electrodes Electronic and mechanical properties of carbon nanotubes are unique. However, to achieve these properties, the carbon nanotubes usually need to be chemically processed in order to purify (the aim of purification is to remove the amorphous carbon and the metal particles) and bring appropriate functionalizations. Typical treatment involves the use of oxidative methods with nitric acids. The caps at both ends of the carbon nanotubes are removed and defects such as carboxylic acid groups on the surface are revealed by these

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% transmittance

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purification techniques [60]. The properties of the carbon nanotubes are influenced by these defects sites on the walls and the ends. We employed the SWNTs to fabricate the modified electrodes and study their electrochemical characteristics since the SWNTs are, compared with MWNTs, the well– defined system in terms of electronic properties and individual SWNT can be regarded as quantum wires [61]. We employed two methods to treat the SWNTs. The one is the SWNTs (< 2–nm in diameter with the purity of > 90%) were purified by refluxing in 3 M HNO3 for at least 24 h, filtered with a minipore membrane (the pore size is 0.22–μm in diameter, Anpel), then thoroughly washed with water, and finally dried under vacuum at 60 ºC overnight to obtain purified SWNTs. The other is following the method reported by Tohij et al. [62]. 1 g of pristine SWNTs was put in a 3–neck flask containing ca. 500 ml of double–distilled water and sonicated for ca. 30 min. After that, this flask was placed in an oil bath at 130 ºC with a reflux attachment for 10 h. This hydrothermal treatment is known to assist water molecules in breaking the physical entanglements among carbon nanotube, amorphous carbon, and metal particles [62]. The SWNTs, after being treated hydrothermally, were dried in a convection oven at 60 ºC for 12 h and then heated to ca. 470 ºC in a furnace and kept at this temperature for 30 min to burn out the amorphous carbon. The metal particles were completely removed by refluxing in 3 M HNO3 for ca. 3 h. The sample was filtered with a minipore membrane (the pore size is 0.22–μm in diameter, Anpel), then thoroughly washed with double–distilled water, and finally dried under vacuum at 60 ºC overnight to obtain purified SWNTs. After treatment, the carboxylic acids and other oxygen–containing groups are formed on the surface of SWNTs as indicated by the FTIR spectroscopy (Figure 5). The Raman spectroscopic results indicated that the amount of residual ill–organized graphite (amorphous carbon) in the sample of purified SWNTs was very less and reached the extent of negligible since the disorder–induced D–band, which was resulted from the residual ill–organized graphite [63], was very small and almost disappears.

88 86 84 1715

82 80 78

3426

1574 1166

76

4000 3500 3000 2500 2000 1500 1000

500

-1

Wavenumber / cm

Figure 5. FTIR spectrum of purified SWNTs. The FTIR spectra were recorded on KBr disk containing about ~1% sample by weight using a Nexus 670 FT–IR spectrophotometer (Nicolet Instruments, USA). For each sample, a total of 64 scans at a resolution of 4–cm–1 were used. Graphene and Graphite Materials, Nova Science Publishers, Incorporated, 2009. ProQuest Ebook Central,

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The peaks at 1715 cm–1 and 1574 cm–1 correspond to the carboxylic group and the carboxylate group, respectively. The peaks at 3426 cm–1 and 1166 cm–1 are due to stretching vibration of –OH and C–OH, respectively. The FTIR spectra were recorded on KBr disk containing about ~1% sample by weight using a Nexus 670 FT–IR spectrophotometer (Nicolet Instruments, USA). For each sample, a total of 64 scans at a resolution of 4–cm–1 were used. Carbon nanotubes are insoluble in most solvents [64,65] and especially in water. To prepare the modified electrode, SWNTs (1 mg) was dispersed in 1 ml CTAB (in water, 0.1% by weight, concentration greater than the critical micellar concentration, the critical micellar concentration of CTAB is 0.034% [66], CTAB is cetyltrimethylammonium bromide, which is a surfactant) with aid of ultrasonication to give a 1 mg/ml stable black SWNTs suspension. Alternatively, 1 mg of SWNTs was directly dispersed in 1 ml of DMF (N,N– dimethylformamide) to give the 1 mg/ml stable black SWNTs suspension. Then 2 μl of the suspension was cast onto the surface of a GC (glassy carbon) electrode with a microsyringe and allowed to dry at ambient temperature. Sometimes, 1 μl of Nafion (5%) was used as a binder to hold the SWNTs on the electrode surface stably. The final electrode is taken as SWNTs/GC (or Nafion-SWNTs/GC) electrode. The typical morphology of the SWNTs on the surface of GC electrode (Figure 6) shows that small bundles of SWNTs entangle each other and distribute almost homogeneously exhibiting a special three–dimensional structure. Such small bundles of SWNTs homogeneously distribute on GC electrode surface are expected to be very attractive for detection of substrates, because each of the SWNTs is fully and easily accessible to the substrates, and consequently can be readily and totally used as electrochemical sensing unit, yielding a high ratio of signal–to–noise for electrochemical determination.

Figure 6. A typical SEM image of SWNTs on the surface of GC electrode. The SEM image was recorded using a LEO 1530 VP field–emitting scanning electron microscope (Germany).

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The cyclic voltammogram of SWNTs/GC electrode in 0.1 M PBS (pH 7.0) shows a pair of broad redox peaks at a potential of about –50 mV (Figure 7a), which can be ascribed to the electrochemical reaction of oxygen–containing groups on the surface of CNT [67], while no any electrochemical reactions can be observed from cyclic voltammogram of bare GC electrode (Figure 7b). The background currents of Figure 7a is much larger than those of Figure 7b, which might be attributed to the reason that the apparent surface area of a SWNTs/GC electrode is larger than that of a bare GC electrode. The SWNTs on the surface of GC electrode is fairly stable since the electrochemical response of SWNTs/GC electrode stored in a desiccator for several days does not almost change comparing with that of the electrode prepared immediately.

10

a

i / μA

5

b

0 -5 -10

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-15 -0.4 -0.3 -0.2 -0.1 0.0

0.1

0.2

0.3

0.4

0.5

E / V (vs. SCE) Figure 7. The cyclic voltammograms of SWNTs/GC (a) and bare GC (b) electrode in 0.1 M PBS (pH 7.0) at a scan rate of 10 mV/s. The cyclic voltammetric experiments were carried out with a CHI660B electrochemical workstation (CH Instruments) with a conventional three–electrode cell. The coiled Pt wire and the saturated calomel electrode (SCE) were used as the counter electrode and the reference electrode, respectively. Buffers were purged with high–purity nitrogen for at least 30 min prior to experiments and a nitrogen environment was then kept over solutions in the cell to protect the solution from oxygen.

To further characterize the electrochemical characteristics of the prepared SWNTs/GC electrode, the electrochemical performance of K3Fe(CN)6 at the electrode was carried out. Figure 8 is the cyclic voltammograms of 4 mM of K3Fe(CN)6 in 0.1 M KCl solution at a bare GC electrode (curve a) and a SWNTs/GC electrode (curve b) at a scan rate of 50 mV/s. The anodic and cathodic peak potentials (Epa and Epc), the peak potential separation (ΔEp) and the formal potential (Eo´) are presented in Table 1.

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Chenxin Cai Table 1. Electrochemical parameters of K3Fe(CN)6 at a bare GC electrode and a CNT/GC electrode Epc (mV)

Epa ( mV)

Eo´ (mV)

ΔEp (mV)

SWNTs/GC

150

207

178.5

57

Bare GC

138

225

181.5

87

Electrode

80

b

60

a

40

i / μA

20 0 -20 -40 -60 -80 -100 -0.3 -0.2 -0.1

0.0

0.1

0.2

0.3

0.4

0.5

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E / V (vs. SCE) Figure 8. Cyclic voltammograms of 4 mM of K3Fe(CN)6 in 0.1 M KCl solution on a bare GC electrode (curve a) and a SWNTs/GC electrode (curve b) at a scan rate of 50 mV/ s.

From Table 1, it can be seen that the anodic and cathodic peak potentials of K3Fe(CN)6 at a SWNTs/GC electrode shift toward the negative and positive direction, respectively, compared with those at a bare GC electrode. The peak separation (ΔEp) of 87 mV indicates that K3Fe(CN)6 undergoes a one–electron quasi–reversible reaction at a bare GC electrode, while the ΔEp of 57 mV at SWNTs/GC electrode shows that the K3Fe(CN)6 undergoes a oneelectron ideal reversible reaction, because it is almost the same as the theoretical value which is 59 mV for one–electron ideal reversible reaction. These results show that SWNTs has catalytic activity toward electrochemical reaction. The reason for the superior performance of SWNTs/GC in comparison with the bareGC electrode may originate from the SWNTs dimensions (of the tubes, the channels that are inherently present in the tubes), the electronic structure and the topological defects present on the tube surfaces [68].

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3. Electrocatalytic Oxidation of Dopamine, Ascorbic Acid, and Nadph at the Swnts/Gc Electrode Electroanalyitcal methods have been used during the last three decades to investigate the role of neurotransmitters in the brain due to their electroactive natures [69–71]. This area of analytical chemistry, so–called “brain chemistry”, was introduced originally by Ralph Adams in the 1970s [72]. In vivo detection of neurotransmitters mammalian brain has been the subject of considerable interest by using modified electrode and microelectrodes [70,72,73]. Dopamine (DA) is one of the important catecholamine neurotransmitters in the mammalian central vervous system, and is related to several diseases such as schizophrenia and parkinsonism [74]. Therefore, it is of great significance to understand the electrochemical reaction and to quantify the content of DA in human body fluids. It can be detected through electrochemical methods due to its electroactive property, however, the irreversibility of its electrochemistry as well as the fouling of the electrode surface by the oxidation product results in poor performance at the conventional electrodes. Furthermore, the coexisted ascorbic (AA) and uric acid (UA) in the body fluids in high levels can be easily oxidized at a potential rather close to that of DA and always interfere with the determination of DA at the conventional electrodes. Therefore, improvement of the sensitivity and selectivity of the working electrode towards DA has been becoming a long–standing of researches. To meet this need, a variety of modified electrodes have been proposed to determine the content of DA by their selectivity and electrocatalytic activity [75–88]. O

HO NH3

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HO

+

O NH3+

HO

2H

+

+

2e

(1)

HO

N H

+

+

H

(2)

O

N H

O

O O

O

+

HO

O

HO

NH3

+

N H

+

+

2H

+

2e

(3)

HO NH3+

HO

N H

(4)

The electrochemical reaction of cationic DA is a multi–step reaction. The first step is an electrochemical oxidation process involving two–electrons and two–protons; the product of this step can undergo a follow–up ring closure reaction by the loss of one proton leading to a Graphene and Graphite Materials, Nova Science Publishers, Incorporated, 2009. ProQuest Ebook Central,

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Chenxin Cai

product of leuodopaminechrome, which in turn is oxidized to dopaminechrome [77]. When pH is lower than 7, the DA oxidation cannot undergo follow–ring closure reaction (Eq.4). These reaction consequences are responsible for the quasi–reversible electrochemical redox process of DA at the electrodes. 100

c

80 60

i / μA

40

b

20

a

0 -20 -40 -60

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

E / V (vs. SCE)

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Figure 9. Cyclic voltammograms of a SWNTs/GC electrode in 0.1 M PBS (pH 6.8) in the presence (curve c) and the absence (curve a) of 1 mM of DA at a scan rate of 50 mV/s. Curve b is cyclic voltammogram of a bare GC electrode in the same solution and the same scanning rate as curve c.

At the bare GC electrode (Figure 9b), DA showed a quasi–reversible electrochemical reaction with an oxidation at 230 mV and a reduction at 91 mV in 0.1 M phosphate buffer solution (PBS, pH 6.8), at a scan rate of 50 mV/s. From the cyclic voltammogram, it can be concluded that the rate of electrochemical oxidation of DA at a bare GC electrode is slow and irreversibility is high because the anodic and cathodic peaks are board and the peak separation (ΔEp = 139 mV) is relatively large. The cyclic voltammogram of DA on SWNTs/GC electrode in 0.1 M PBS (pH 6.8) at a scan rate of 50 mV/s indicated that the redox peak current increases significantly and the anodic and cathodic peak potentials shift toward negative and positive directions (Figure 9c), respectively, in comparison with curve b. The anodic and cathodic peak potentials are 170 mV and 136 mV, respectively. The peak potential difference is 34 mV, suggesting DA undergoes a two–electron oxidation with high reversibility at the SWNTs/GC electrode since the peak potential difference is very close to the theoretical value, 30 mV, for two–electron ideal reversible electrochemical reaction. Curve a in Figure 9 shows the cyclic voltammogram of SWNTs/GC electrode in 0.1 M PBS (pH 6.8) in the absence of DA, and no any redox reaction can be found. These results indicate that the SWNTs/GC electrode has an excellent electrocatalytic activity toward DA electrochemical reaction. Table 2 summaries the dependence of the peak potential and current on the scan rate.

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Table 2. Dependence of peak potential and current on the scan rate for DA at a SWNTs/GC electrode v (mV/s)

Epc (mV)

Epa (mV)

ΔEp (mV)

ipa · v–1/2 (μA·s1/2/mV1/2)

20

138

168

30

7.0

40

137

169

32

8.1

60

133

170

37

8.4

80

130

177

47

8.8

100

127

182

55

9.2

150

120

188

68

10.3

200

111

193

82

10.4

From Table 2, it can be seen that the anodic and cathodic peak potential shift to positive and negative direction, respectively, and the peak potential difference increases with the increase of the scan rate. The important results concluded from Table 2 shows that DA undergoes an ideal reversible electrochemical reaction on SWNTs/GC electrode at low scan rates, for example, 20 mV/s, since the ΔEp at the scan rate is 30 mV, which is the same as the theoretical value. This result suggests that intramolecular cyclization of dopaminequinone, which is the product of DA oxidation, is absent on SWNTs/GC electrode surface [89,90]. Perhaps the oxidation occurring on the SWNTs/GC electrode surface is stabilized in comparison with the product formed elsewhere in the sample. From the Table 2, it can be also noted that the current function, ip·v–1/2, is not a constant with increase of the scan rate, but it has an increasing tendency. This may be because the inner surface of SWNTs is also electrochemically accessible. The current function increases with the increase of the scan rate, the more DA can enter the inside of SWNTs. It was reported that the electrode surface is easy to be contaminated owing to the electrochemical polymerization of DA in the electrochemical process and the malanie–like compounds will be produced on the surface of the electrode [91]. But the cyclic voltammetric response of the SWNTs/GC electrode is almost unchanged after the electrode has been cycled several times in one DA solution and one SWNTs/GC electrode in five DA solutions (same concentration) produces the same voltammetric response. The fact suggests that the SWNTs/GC electrode has an excellent reproducibility and stability. These results also indicate that DA is not adsorbed or polymerized on the surface of the SWNTs/GC electrode. The oxidation of ascorbic acid (AA) has also been documented to undergo two steps, the first of which involves one–electron and one–proton oxidation followed by a second step of one-electron oxidation. The product, dehydroascorbic acid, produced in the electrochemical process can further undergo a hydration reaction [92]. These reaction consequences are responsible for the irreversible electrochemical process of AA oxidation at the electrodes, as shown in Figure 10. The irreversible anodic peak for oxidation of AA at the SWNTs/GC electrode occurs at ~265 mV (Figure 10c), which is ~150 mV more negative than that at the bare GC electrode (414 mV, Figure 10b). This might be due to the electrocatalytic activity of SWNTs and also to the subtle electronic properties of SWNTs because it had been proved that carbon nanotubes have higher electrical conductivity than other forms of carbon.

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100

c

80

b

i / μA

60 40 20

a

0 -20

-0.2

0.0

0.2

0.4

0.6

E / V (vs. SCE)

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Figure 10. Cyclic voltammograms of the bare GC (b), and SWNTs/GC (c) electrode in 0.1 M of PBS (pH 7.0) in the presence of 1 mM ascorbic acid. The curve (a) shows the cyclic voltammogram of the SWNTs/GC electrode in 0.1 M of PBS (pH 7.0) in the absence of 1 mM ascorbic acid. The scan rate is 50 mV/s.

NAD(P)H and its oxidized form, NAD(P)+, are the key central charge carriers in living cells since the NAD(P)H/NAD(P)+ couple is the cofactor taking part in more than 300 dehydrogenase enzymatic reactions [93]. Thus, the electrochemical oxidation of NAD(P)H at the electrode surface has received considerable interest due to its significance both as a cofactor for dehydrogenase enzymes and its role in the electron–transfer chain in biological system, and also due to the need to develop amperometric biosensors based on the NAD(P)+– dependent dehydrogenase for use in the fields of environmental, and clinical analysis [26,28,29,63,94–100], etc. Many compounds, such as phenoxazine dyes [63,95], conducting polymers [100] and their composites, such as polyaniline/poly(acrylic acid) composite [101], and/or CNTs–polymer hybrid thin film [102], carbon nanofiber [99], and nanoparticles, such as gold nanoparticles self–assembled on three–dimensional sol–gel network [103,104] etc., have been immobilized on the electrode surface as electron–transfer mediators to catalyze the oxidation of NADH at a low potential since the direct oxidation of NADH at a conventional solid electrode surface is highly irreversible and takes place at considerable potentials, and usually involves the formation of radical intermediates that cause electrode fouling and the loss of analytical sensitivity reproducibility and operational lifetime [105,106]. We studied the electrocatalytic oxidation of NADPH at the SWNTs/GC electrode to check electrocatalytic activity of SWNTs. In Figure 11, curve a and b are cyclic voltammograms of a bare GC and a SWNTs/GC electrode, respectively, in 0.1 M PBS (pH 6.0) at a scan rate of 10 mV/s. No any electrochemical reactions can be observed from curve a, while a pair of broad redox peaks appears on the curve b at a potential of about –50 mV, which can be ascribed to the electrochemical reaction of oxygen–containing groups on the surface of CNT [67]. Curve c is a cyclic voltammogram of a SWNTs/GC electrode in 0.1 M PBS (pH 6.0) containing 1 mM of NADPH at a scan rate of 10 mV/s. A large and sharp anodic peak, which corresponds to the potential of direct electrochemical oxidation of

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NADPH, appears at about –4 mV. From the results, one can conclude that NADPH can be directly oxidized on the SWNTs/GC electrode at a very low potential. The oxidation process starts at ca. –150 mV with an anodic peak locating at about –4 mV (at a scan rate of 10 mV/s). There occurs an irreversible electrochemical reaction for NADPH with an anodic peak at 719 mV on a bare GC electrode in 0.1 M PBS (pH 6.0, see curve d, the inset of Figure 11), hence, a decrease in overpotential of more than 720 mV is achieved on a SWNTs/GC electrode. The decrease of the overpotential is much larger than that obtained on an electrode modified with copolymerization of pyrrole and methylene blue (400 mV [107]). The anodic peak current of the oxidation of NADPH at bare GC electrode is much lower than that obtained on a SWNTs/GC electrode, suggesting that CNT is very effective in promoting the electrochemical oxidation of NADPH. The cyclic voltammetric results at various scan rates indicate that the anodic peak potentials of the electrochemical oxidation of NADPH on the SWNTs/GC electrode move to positive direction with the increase of the scan rates. For example, the anodic peak potential is –4 mV at a scan rate of 10 mV/s, however, this value changes to be 89 mV at a scan rate of 80 mV/s. Moreover, the peak currents increase linearly with the increase of square root of the scan rates at least up to 100 mV/s, indicating that the currents are limited by the diffusion of NADPH in solution.

20

6

i / μA

30

4 2

d

0 -0.3 0.0 0.3 0.6 0.9

i / μA

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E / V (vs. SCE)

10

a

0

c b

-10 -20 -0.4 -0.3 -0.2 -0.1 0.0

0.1

0.2

0.3

0.4

0.5

E / V (vs. SCE) Figure 11. Cyclic voltammogramms of the bare GC (curve a and d) and the SWNTs/GC (curve b and c) electrode in 0.1 M PBS (pH 6.0) in the absence (curve a and b) and presence (curve c and d) of 1 mM of NADPH. The scan rate is 10 mV/s.

The electrochemical oxidation of NADPH is a pH–dependent reaction and can be expressed as follows: NADPH → NADP+ + H+ + 2e

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(5)

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Chenxin Cai

the effect of solution pH on the performance of the SWNTs/GC electrode in electrochemical oxidation of NADPH was studied by cyclic voltammetry in 0.1 M PBS in pH range of 4.5 to 9.3. The anodic peak potential shifted linearly to negative direction with the increase of solution pH. The slope was found to be –34.2 mV/pH unit within the studied pH range and is very close to the theoretical value of –29.3 mV/pH unit (at 22 ˚C) since the oxidation of NADPH is a two–electron, one–proton reaction (equation 5). The largest anodic current appears at pH value of about 6.0. The anodic current increases with the increase of the solution pH when the solution pH is lower than 6.0, however, it decreases drastically when the solution pH is higher than 6.0. Hence, the solution pH of 6.0 is used in the following experiments. The cyclic voltammetric responses of the SWNTs/GC electrode in 0.1 M PBS (pH 6.0) containing various concentration of NADPH indicated that both the anodic currents and the anodic potentials depended on the concentration of NADPH. The anodic peak potential shifts to positive direction with the increase of the concentration of NADPH. The anodic peak currents increase with the increase of the concentration of NADPH (Figure 12A). In the range of 5×10–7 M to 1×10–3 M, the anodic peak currents increase linearly with the increase of concentration of NADPH (Figure 12B) with r = 0.99966 (11 points), and the detection limit is about 1×10–7 M. This linear range can be used as a calibration to determine the concentration of NADPH in sample.

80

16

A

12

ipa / μA

ipa / μA

60 40 20 Copyright © 2009. Nova Science Publishers, Incorporated. All rights reserved.

B

14

10 8 6 4 2

0 0

5

10

15

20

0 0.0

cNADPH / mM

0.2

0.4

0.6

0.8

1.0

cNADPH / mM

Figure 12. Dependence of the anodic currents of the SWNTs/GC electrode on the concentration of NADPH (A) and the linear relationship between them (B).

The stability of the SWNTs/GC electrode was studied by repetitive cycling the electrode in a solution of NADPH. Although the cyclic voltammetric response of NADPH decreases rapidly in the initial several cycles (about 6 to 7 cycles), the electrode can still remain about 72% of the response of the first cycle after 40 repetitive scanning cycles (Figure 13). These results indicate that the SWNTs/GC electrode has a good stability toward the electrochemical oxidation of NADPH. The decrease of response upon continuous cycling is not due to the NADPH depletion near the surface of electrode since the similar phenomenon is also found when the solution is stirred. It may be due to the decrease of the concentration of oxygen– containing groups on the surface of SWNTs/GC in the continuous cycling [26]. The dependence of the anodic current of the SWNTs/GC electrode to the electrochemical

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Electroanalysis of Some Bio–Molecules...

19

oxidation of NADPH on the storage time was also investigated by keeping one electrode in a desiccator, and each day the cyclic voltammogram was recorded and the peak current was measured using the same one. In the first several days (about 6 to 8 days), the peak current decreases rapidly, then, the peak current decreases slowly. For example, the response of the electrode remains only 84% of the initial one at the second day, however, it can still remain more than 60% of the initial at the 22nd day (the inset of Figure 13).

0.8 Normalized peak current

Normalized peak current

1.0

0.6 0.4 0.2

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25

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0.0

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Figure 13. Dependence of the normalized anodic peak current of the SWNTs/GC electrode towards the electrochemical oxidation of NADPH on the continuously scanning (the main) and the storage time (the inset).

The reproducibility of the SWNTs/GC electrode toward the electrochemical oxidation of NADPH was also studied. The cyclic voltammetric response of oxidation of 1 mM of NADPH was recorded at six SWNTs/GC electrodes. The results indicated that the responses of six SWNTs/GC electrodes are similar and the average anodic current is 15.84 ± 0.41 μA for oxidation of 1 mM NADPH, suggesting that the SWNTs/GC electrode has a good reproducibility toward the electrochemical oxidation of NADPH.

4. Direct Electron–Transfer Reaction of Proteins/Enzymes at Swnts/Gc Electrode Direct (mediatorless) electron exchanges between a redox group of protein/enzyme and the electrode surface has been studied for a number of proteins/enzymes such as cytochrome c, peroxidase, ferredoxin, plastocyanin, azurin, azotoflavin, glucose oxidase, etc. [108–115]. These studies developed an electrochemical basis for the investigation of proteins/enzymes structure, mechanism of redox transformations of protein/enzyme molecules, and metabolic process involving redox transformation.

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Meanwhile, the ability of a number of oxidoreductase to catalyze an electron–transfer from the electrode surface to the substrate molecule (or vice versa) has been demonstrated [114–122]. In this case, the electrochemical transformation of the substrate is a catalytic process. An important fact is that the electron–exchange is associated with, or occurs during, the catalytic transformation of the enzyme substrate into the product of the reaction. The redox enzyme (oxidoreductase) acts as an electrocatalyst, facilitating the electron transfer between the electrode and substrate molecule with no mediator involved in the process [114]. The enzyme–catalyzed electrochemical transformation of the substrate (biomolecular electrochemical: bioelectrocatalysis) is not only completed by an electrochemical interaction between the protein/enzyme and electrode, but it further involves a catalytic decrease of energetic barrier for electrochemical transformation of the substrate molecule. This is essentially a catalytic process. The analytical applications of these phenomena are based on the ability of several oxidoreductases to interact with the electrode surface forming a “molecular transducer”. The sensing principle of such an electroanalytical device is based on the ability of the enzyme to catalyze a selective transformation of a specific substrate (enzyme selectivity). The principle of direct electron–transfer allows construction of “reagentless” electrochemical biosensors. The bioelectrocatalytic process allows electrochemical detection of both the generated catalytic current and the catalytic reduction of the electrode overvoltage. Electrode probes and assay technique based on amperometric or potentiometric detection can be designed. Thus, direct electron transfer of enzymes and proteins is being one of the leading areas of research in the fields of biochemical and biophysical sciences, and therefore has received considerable attention. Recently, our groups devoted to employ the SWNTs–modified electrode to promote the direct electron–transfer of some important proteins/enzymes. In this section, we would like to present the main results we obtained.

4.1. Direct Electron–Transfer of Heme–Containing Proteins/Enzymes Heme is a molecule which forms a number of reduced and oxidized states. Moreover, its electrochemical characteristics, e.g., formal potential (E0’) for its redox conversion between Fe2+ and Fe3+, can be varied over a wide range of potentials by the proteins/enzymes environments, e.g., from –0.27 V (versus SHE, standard hydrogen electrode) for horseradish peroxidase [123] to +0.26 V for cytochrome c [124]. By itself, heme exhibits various catalytic properties, which drastically change when incorporated into a protein environment. This creates wonderful opportunities for the heme-proteins and heme–enzymes in terms of their bioelectrochemical applications, e.g., in biosensors based on the direct electron–transfer. For this, it is essential to establish high heterogeneous electron transfer rates between the heme and the electrode [125]. In heme, the heme active site is surrounded by polypetides, which makes the direct electron transfer distance longer. We take the myoglobin as a model to study the immobilization and direct electron–transfer reaction of heme–enyzmes and heme-proteins on the surface of SWNTs. Myoglobin (Mb), which is a small heme–containing protein found in muscle cells with a molecular weight ranging from 16,900 to 17,800 and composed of one polypeptide chain, functions physiologically in the storage and transport of molecular oxygen in cell, and is an

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ideal model molecule for the study of the direct electron–transfer reactions of heme– containing proteins (enzymes) because it is commercially available and is also a known and documented structure. The structure of Mb is shown in Figure 14. Electron–transfer between Mb in solution and bare solid electrode is usually very slow, and the electrochemical behavior is unstable and very sensitive to the sample purity and the nature of the electrode surface [126]. Numerous efforts have been made to improve the electron–transfer characteristics of Mb by using mediators, promoters, or other special materials to modify the surface of electrode [127−131]. Among these, surfactant micelles have been shown to be efficient in promoting the direct electron transfer of Mb. However, it is reported that the surfactant has drastic effects on the structure of heme–containing proteins and thereby leads to denaturation of the protein [132,133]. The immobilization of Mb on the surface of SWNTs is as following. Two microliters of SWNTs suspensions (typically, SWNTs suspensions were formed by dispersing 1 mg of SWNTs into 1 ml aqueous solution of 0.1% (by weight) CTAB with aid of ultrasonication) were thoroughly mixed with 2 μl Mb solution (5 mg/ml in PBS, pH 7.0). Two microliter of the mixture was then cast onto the surface of a GC electrode with a microsyringe and allowed to dry at ambient temperature. Thus, the total amount of Mb on the surface of electrode was about 5.92 × 10−10 mol, when a molecular weight of 16,900 g/mol is adopted. Finally, 1 μl of Nafion was cast and used as a binder to stably hold the Mb–SWNTs on the electrode surface. The solvent was allowed to evaporate before use. Nafion-Mb-SWNTs-CTAB/GC electrode was chosen as the final electrode. The electrode was stored at 4 ˚C when it was not used. The Nafion-SWNTs-CTAB/GC electrode was prepared in a similar manner but without Mb.

Figure 14. The structure of Mb (adapted from protein data bank).

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400.4

N1s

a b 390

395

400

405

410

415

Binding energy / eV

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Figure 15. XPS spectra Mb–SWNTs (a) and SWNTs (b). XPS experiments were carried out on ESCALab MK2 using monochromatic Mg Kα line at 1253.6 eV. The values of binding energy were calibrated with those of C1s (284.6 eV).

The XPS data confirm the adsorption of Mb on SWNTs surface (Figure 15). As shown in Figure 15a, the peak at 400.4 eV was a characteristic peak of N 1s, whereas no peak was observed in Figure 15b, indicating the existence of Mb on the SWNTs surface. However, the XPS adsorption of Fe 2p of Mb on SWNTs surface could not be detected. The reason might be that the Fe atom was deeply buried in the center of the Mb molecule. The results of the FTIR spectra (Figure 16) indicated that the Mb retained its original structure even after adsorption. In proteins (enzymes), although the peptide bonds −CO−NH− had several distinct vibrational modes, amide I (1700−1600 cm−1), which was caused by C=O stretching vibrations of peptide linkages, and amide II (1620−1500 cm−1), which resulted from a combination of N−H in–plane bending and C−N stretching vibrations of the peptide groups, were the most useful modes for obtaining detailed information on the secondary structure (i.e., α–helix and β–sheet) of polypeptide backbone chain [134]. The amide I and II bands in the FTIR spectrum of Mb on the surface of SWNTs (Figure 16a) had shapes similar to that of the free Mb (not adsorbed on the surface of CNT, Figure 16b), except that the bands had a slight shift (1645 to 1660 cm−1 and 1542 to 1541 cm−1 for amides I and II, respectively), which indicated the existence of interaction between Mb and SWNTs. Figure 16c shows the FTIR spectrum of SWNTs. The appearance of the peaks (1726, 1578, and 1165 cm−1) indicated that carboxylic and carboxylate groups were present on the surface of the SWNTs. The oxygen–containing group might be introduced during purification using HNO3. The peaks of oxygen–containing groups also appeared in the FTIR spectrum of Mb–SWNTs (Figure 16a). The above results further verified that Mb was adsorbed on the surface of SWNTs and also indicated that Mb retained its original structure after adsorption.

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1165 621

1106

619

500

23

c

1578 1726

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1542 1645

a 1105

1541 1660 1165

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2000

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-1

σ / cm

Figure 16. FTIR spectra of Mb–SWNTs (a, 5 times of original signals), free Mb (b), and SWCNTs (c). 1.25 1.00

c

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A

0.75 0.50

b

0.25

a

0.00

250

300

350

400

450

500

550

600

λ / nm Figure 17. UV–Vis spectra of SWNTs (a), Mb (b), and Mb–SWNTs (c). The UV–Vis spectroscopy, which was performed using a Cary 5000 UV–VIS–NIR spectrophotometer (Varian, USA).

The UV–Vis spectroscopic results also indicated that Mb was adsorbed on SWNTs surface and retained its original structure. The position of the Soret adsorption band of heme iron provided structural information about the heme pocket [135]. Figure 17b and Figure 17c presented the UV–Vis spectra of Mb and Mb–SWNTs, respectively. Both the Mb-SWNTs (Figure 17c) and Mb (Figure 17b) showed the Soret band at 409 nm, whereas the UV–Vis spectrum of SWNTs (Figure 17a) just showed a smooth curve, suggesting the microenvironment of heme pocket in adsorbed Mb remained almost the same as that in free Mb. Figure 18 showed the cyclic voltammograms of the Nafion-SWNTs-CTAB/GC (curve a) and Nafion-Mb-SWNTs-CTAB/GC electrode (curve b) in 0.1 M PBS (pH 7.0) at a scan rate of 60 mV/s. No redox peaks were observed at the Nafion-SWNTs-CTAB/GC electrode in the potential range of interest, but a pair of well–defined and nearly symmetrical redox peaks was

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obtained at the Nafion-Mb-SWNTs-CTAB/GC electrode. This suggested that the redox peaks in curve b were ascribed to the electrochemical reaction of Mb immobilized on the surface of SWNTs. The anodic (Epa) and cathodic (Epc) peak potential were detected at –0.310 and −0.383 V, respectively, at a scan rate of 60 mV/s. The separation of peak potentials, ΔEp, was 73 mV, indicating that Mb immobilized on the surface of SWNTs displayed a quasi– reversible electrochemical reaction despite its large molecular structure. Its formal potential, E0’, which was defined as average of anodic and cathodic peak potentials, was –0.347 V (at 60 mV/s). According to those previous reports, the electrochemical reaction shown in Figure 18, curve b could be ascribed to the conversion of Mb–Fe(III) and Mb–Fe(II).

9

b

6

a

i / μA

3 0

c

-3 -6 -9 -0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

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E / V (vs. SCE) Figure 18. Cyclic voltammograms of the Nafion-SWNTs-CTAB/GC (curve a), Nafion-Mb-SWNTsCTAB/GC (curve b) and Nafion-Mb-CTAB/GC (curve c) electrode in 0.1 M PBS (pH 7.0). The scan rate is 60 mV/s.

To verify that the direct electron–transfer of Mb was facilitated by SWNTs and not by the surfactant (CTAB) that was covered on the surface of SWNTs, the following control experiments were performed. Two microliters of Mb solution was mixed with 2 μl of CTAB solution (without SWNTs) and 2 μl of the mixture was cast on the surface of GC electrode, after which 1 μl of Nafion was applied (the electrode chosen was Nafion-Mb-CTAB/GC electrode). The resultant electrode did not show any observable electrochemical responses (curve c in Figure 18), which indicated that the possibility that the electrochemical reaction of Mb promoted by CTAB contributed to the observed redox waves in curve b of Figure 18 should be excluded. The result also indicated that only Mb adsorbed on the surface of SWNTs could undergo the direct electron–transfer and that the physically entrapped Mb (not adsorbed on the surface of SWNTs) could not undergo direct electron–transfer. To further study the effect of CTAB on the direct electron–transfer of Mb, Mb was directly immobilized on SWNTs (SWNTs was not covered with CTAB, but SWNTs was dispersed in N,N– dimethylformamide (DMF), because the dispersion ability of SWNTs in water solution was very poor in the absence of CTAB). The resultant electrode was chosen as the Nafion-MbSWNTs/GC electrode. The voltammetric result shows one pair of redox peaks with the anodic and cathodic peak potentials of –330 and –392 mV, respectively, in the voltammogram of

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Nafion-Mb-SWNTs/GC electrode. The peak potentials were very close to those shown in Figure 18b. The result further indicated that CTAB did not promote the direct electrontransfer of Mb but just improved the dispersion ability of SWNTs in water. It was reported previously that some surfactants (such as CTAB) could promote the direct electron-transfer of enzymes and proteins [129]. The results of this study, however, indicated that CTAB could not facilitate the direct electron–transfer of Mb. The reason might be that the method that was used to immobilize protein was different from that used previously [129]. The cyclic voltammograms of the Nafion-Mb-SWNTs-CTAB/GC electrode in 0.1 M PBS (pH 7.0) at various scan rates indicate that the values of E0’ (the average value was – 0.346 ± 0.001 V in the scan rate range of 20 to 160 mV/s) and ΔEp (48.2 ± 7.3 mV) were almost independent on the scan rates because the values of Epa and Epc remained almost unchangeable with the scan rates. And also, the reduction and oxidation peak heights at all scan rates are almost equal, indicating that all electroactive ferrous Mb (Mb–Fe(II)), which was produced by reduction of ferric Mb (Mb–Fe(III)) on the forward scan, could be oxidized to M–Fe(III) on the reverse scan. The anodic and cathodic peak currents were linearly proportional to scan rate up to more than 200 mV/s, indicating that the reaction was not a diffusion–controlled process but a surface–controlled one, as expected for immobilized systems. From the dependence of ΔEp on the various scan rates, the apparent heterogeneous electron transfer rate constant, ks, could be calculated to be 3.11 ± 0.98 s−1, using the method developed by Laviron [136] for a surface–controlled electrochemical system. The amount of the electroactive Mb (expressed as ΓA, in mol) on electrode surface could be estimated using the following equation:

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ΓA = Q / nF

(6)

where Q was the charge consumed in coulombs, which was obtained by integrating the anodic (or cathodic) peak area in cyclic voltammograms under the background correction and A the apparent area of electrode, which was estimated using Ru(NH3)63+ as a probe based on equation (2) by adopting the diffusion coefficient of 2.3×10−9 cm2/s for Ru(NH3)63+ in Nafion film [137] ip = 2.69 × 105n2/3AD1/2v1/2c*

(7)

The average ΓA value of (1.12 ± 0.08) × 10−10 mol was obtained at a scan rate of 20 to 200 mV/s. Compared with the total amount of Mb deposited on the electrode (5.92 × 10−10 mol), the electroactive amount obtained here accounts for about 18.9%, suggesting that only a part of Mb present on the electrode surface underwent the direct electron–transfer reaction, because only those adsorbed on the surface of SWNTs can undergo direct electron–transfer reaction (described above). The fractions of electroactive Mb obtained here was slightly larger than those of immobilized Mb in surfactant or polymer films (about 5 to 12%) [138], indicating that SWNTs was much effective in promoting the direct electron–transfer of Mb. The stability of the direct electron–transfer of Mb was tested by two methods. When the Nafion-Mb-SWNTs-CTAB/GC electrode was continuously scanned in 0.1 M PBS (pH 7.0), the voltammetric response decreased very slowly with the increase in the number of cycles. The electrode could still retain about 86% of the initial response after 100 continuous cycles. The storage stability of the Nafion-Mb-SWNTs-CTAB/GC electrode was investigated by

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keeping one electrode in pH 7.0 blank buffers, and the cyclic voltammeric tests were periodically carried out. The peak current decreased with the increasing of the storage time to about two weeks, after which the peak current almost remained constant. The electrode could still retain about 75% of the initial response after four weeks of storage. These results indicated that the direct electron–transfer of Mb immobilized on the surface of SWNTs showed good stability with the two tested methods. It was known that solution pH modulated the accessibility of water to the heme pocket of heme–containing proteins, such as Mb and hemoglobin, and the protonation of the heme iron–bound proximal histidine and/or the distal histidine in the heme pocket accordingly influenced their redox potential [139]. Cyclic voltammetric characteristics of Nafion-MbSWNTs-CTAB/GC electrode showed considerable dependence on the external buffers. An increase of pH in solution led to a negative shift in potential of both the anodic and cathodic peaks. The changes of cyclic voltammetric peak potentials with pH were reversible in the range of pH 5.0 to 9.0. For example, a Nafion-Mb-SWNT-CTAB/GC electrode was first placed in pH 5.0 buffers and tested by cyclic voltammetry. It was then transferred to pH 7.0 buffers and its cyclic voltammetric characteristics were examined. When the electrode was placed in the pH 5.0 solution again, the cyclic voltammogram was quite reproducible and demonstrated almost the same peak potentials and heights as before. All the Epa, Epc, and E0’ had a linear relationship with solution pH with a slope of –46.4, –40.9, and –43.7 mV/pH unit, respectively, in the range of 5.0 to 9.0. Those values were quite different from the theoretical value of –58.6 mV/pH at 22 ºC for a reversible electron transfer coupled with an equal number of transported protons. The reason for this was probably due to the more complex reactions mechanism involving in the electron transfer process between the electrode and proteins, in which the ratio of the number of protons to the number of electrons was more complicated. The microenvironment of Mb at the surface of the electrode might significantly influence the detailed mechanism of its direct electron–transfer. The overall reaction of direct electron-transfer of Mb at SWNTs might include several fundamental steps, and some steps might correspond to the transfer of one or more protons. Thus, it was not surprising that the total number of electrons and protons involved in the overall reaction was not equal. Nevertheless, the pH–dependent peak potentials indicated that the electron transfer between the protein and the electrode was indeed accompanied by proton transfer. It was reported that proteins (enzymes) containing the heme, such as cytochrome c, hemoglobin, horseradish peroxidase and Mb et al., usually has good electrocatalytic activities toward the reduction of oxygen (O2), trichloroacetic acid (TCA), and hydrogen peroxide (H2O2) et al. [140,141]. Having demonstrated the direct electron–transfer of Mb on the surface of SWNTs, we next studied the bioelectrocatalytic activities of Nafion-Mb-SWNTsCTAB/GC electrode toward the reduction of H2O2, and O2. Figure 19 shows the cyclic voltammograms of the Nafion-Mb-SWNTs-CTAB/GC electrode in 0.1 M PBS (pH 7.0) in the absence (curve a) and presence (curve b) of 5 mM H2O2 at a scan rate of 100 mV/s. In the absence of H2O2, a pair of the redox peaks of Mb was observed (curve a), which was the same as curve b in Figure 18. However, in the presence of H2O2, the voltammetric behavior drastically changed. A large cathodic current for the reduction of H2O2 appeared, and the anodic peak completely disappeared. Controlled experimental results indicated that no catalytic current was observed at the Nafion-SWNTs-CTAB/GC electrode in the presence of H2O2 (curve c in Figure 19). The ratio of cathodic current in the presence and absence of substrate (H2O2) can be defined as catalytic efficiency. It was found that the catalytic

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efficiency decreased with increasing of scan rate, and the cathodic current increased with increasing concentration of H2O2 in solution, which were all characteristics of electrochemical catalysis. These results indicated that Mb retained its bioelectrocatalytic activity after immobilization on the surface of the electrode.

10

a

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E / V (vs. SCE) Figure 19. Cyclic voltammograms of the Nafion-Mb-SWNTs-CTAB/GC (a and b) and Nafion-SWNTsCTAB/GC (c) electrode in 0.1 M PBS (pH 7.0) in the absence (a) and presence (b and c) of 5 mM H2O2. Scan rate is 100 mV/s.

a

10

d

0 -10

i / μA

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20

-20

b

-30 -40

c

-50 -60 -0.6

-0.5

-0.4

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-0.2

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0.0

E / V (vs. SCE) Figure 20. Cyclic voltammograms of the Nafion-Mb-SWNTs-CTAB/GC (a, b, and c) and NafionSWNTs-CTAB/GC (d) electrode in anaerobic (a), air–saturated (b, dashed lines) and O2–saturated (c and d, dotted lines) 0.1 M PBS (pH 7.0). Scan rate is 100 mV/s.

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Table 3. The values of E0’ and ks of some heme–containing proteins/enzymes obtained at SWNTs–modified electrode Proteins/enzymes Mb Hb Cyto c HRP

E0’ / V (vs. SCE) −0.346 −0.343 0.078 −0.319

ks / s–1 3.11 ± 0.98 1.25 ± 0.25 2.64 ± 0.86 2.07 ± 0.56

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Electrocatalytic behavior was also observed for the reduction of O2 at Nafion-MbSWNTs-CTAB/GC electrode. Figure 20a and 20b show that the cathodic peak of Nafion-MbSWNTs-CTAB/GC electrode had a significant increase when the cyclic voltammogram was obtained in air–saturated PBS (curve b) compared with that obtained in anaerobic buffer (curve a). When cyclic voltammetric experiment was performed in a PBS saturated with O2, the cyclic voltammogram of the Nafion-Mb-SWNTs-CTAB/GC electrode was characterized by a large cathodic peak, and the anodic peak completely disappeared (Figure 20c). The controlled experimental results showed that the Nafion-SWNTs-CTAB/GC electrode had no electrocatalytic activity toward the reduction of O2 (Figure 20d). All these features were characteristics of electrochemical catalytic reduction of O2 by Nafion-Mb-SWNTs-CTAB/GC electrode. The direct electron–transfer of other heme–containing proteins/enzymes, such as horseradish peroxidase (HRP), cytochrome c (Cyto c), and hemoglobin (Hb), was also studied using the SWNTs–modified electrode with the similar procedures as the case of Mb. The formal potential and the heterogeneous electron transfer rate constant, ks, are expressed in Table 3.

4.2. Direct Electron–Transfer of Glucose Oxidase Glucose oxidase (GOx), from Aspergillus or Penicillium, is a homodimer with molecular weight of about 150 to 180 kDa containing two tightly bound flavine adenine dinucleotide (FAD) cofactors [142] (the structure of GOx is presented in Figure 21), catalyzes the electron transfer from glucose to oxygen accompanying the production of gluconic acid and hydrogen peroxide. Industrially, it has been used in the production of gluconic acid. The most important application is in biosensors for the quantitative determination of glucose in body fluids, foodstuffs, beverages and fermentation liquor. GOx has been immobilized on various kinds of matrices and carries, for example entrapping into sol–gel matrix [143,144], incorporating into polymer film [145–147], and covalently linking to the electrode surface or immobilizing onto self–assembled monolayer [148–150]. Although there are so many investigations on the GOx, only a few examples of quasi–reversible voltammograms for direct electron transfer between GOx active site and electrode surface were reported. Ianniello et al. [151] studied the direct electron–transfer of adsorbed GOx at a graphite electrode and a cyanuric chloride modified graphite electrode using differential pulse voltammetry. The direct electrochemistry of GOx, immobilized at a self–assembled monolayer of 3,3’–dithiobis–sulfosuccinimidyl propionate (DTSSP), was reported by Jiang et al. [149]. Savitri et al. [150] covalently immobilized FAD onto carbon matrix using a 13–carbon atom long spacer arm firstly, and then the GOx

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apoenzyme was coupled to the FAD modified matrix. They studied the electrochemical characteristics of the reconstituted GOx electrode and obtained the direct electron–transfer of GOx, but the cyclic voltammograms is not well–defined.

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Figure 21. The structure of GOx (adapted from protein data bank).

To study the direct electron–transfer of GOx, the negatively charged (at pH 8.2) GOx (pI ~ 4.2) was assembled onto the surface of single–walled carbon nanotubes (SWNT), which was covered (or wrapped) by a layer of positively charged polyelectrolyte poly(dimethyl– diallylammonium chloride) (PDDA), via the electrostatic interaction forming GOx–PDDA– SWNT nanocomposites. The illustration of the process for assembling PDDA and GOx on SWNT and the electrode fabrication was schematically showed in Figure 22.

Figure 22. Illustration of the process for assembling of PDDA and GOx on SWNT. A layer of Nafion, which was covered on the outside of GOx–PDDA–SWNT, was omitted for clarity.

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Cyclic voltammtric results indicated that a pair of well–defined and nearly symmetric redox peaks was obtained at the Nafion-GOx-PDDA-SWNT/GC electrode (Figure 23). After incubated the Nafion-GOx-PDDA-SWNT/GC electrode in 3 M guanidine hydrochloride solution overnight, the redox peak disappeared (Figure 23). Treatment of the Nafion-GOxPDDA-SWNT/GC electrode with concentrated salt solution can easily strip FAD active center from GOx molecule and/or remove the adsorbed GOx from electrode surface [150– 152], it is relatively ineffective in removing adsorbed free FAD from the electrode surface [151,152]. These results suggest that the redox peaks in curve b of Figure 23 can be ascribed to the redox reaction of the prosthetic group (FAD) bound to the GOx [150,152] and not to free FAD, which may have dissociated away from GOx due to conformational changes during immobilization. Controlled experimental results indicated that the voltammetric responses of the Nafion-FAD-PDDA-SWNTs/GC electrode remained a 68% of the initial one after the electrode was incubated 2 days in 3 M guanidine hydrochloride solution and still remained 24% even incubated 12 days. The anodic and cathodic peak potential of curve b in Figure 23 is –0.445 V and –0.483 V (at 40 mV/s), respectively. The separation of peak potentials is small (ΔEp = 38 mV), although not zero. The E0’ is –0.464 V at a scan rate of 40 mV/s. The cathodic and anodic peak currents are of similar magnitude, with an ipa/ipc ratio about unity. The anodic and cathodic peak currents are linearly proportional to scan rate up to more than 100 mV/s, suggesting the reaction is not a diffusion–controlled process but a surface–controlled one, as expected for immobilized systems.

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2 μA

a

b

5μA

c

-0 .7

-0 .6

-0 .5

-0 .4

-0 .3

-0 .2

E / V (v s. S C E ) Figure 23. Cyclic voltammograms in 0.1 M of PBS (pH 6.9) at a scan rate of 60 mV/s for the NafionPDDA-SWNT/GC (a), Nafion-GOx-PDDA-SWNT/GC (b), and Nafion-GOx-PDDA-SWNT/GC electrode after incubated in 3 M guanidine hydrochloride solution for 24 h (c).

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10

c

8 6

i / μA

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direction, respectively, and consequently, the ΔEp increases with increasing of the scan rate. However, the value of E0’ is independent on the scan rates (E1/2 = –0.466 ± 0.001 V in the scan rate range of 20 to 140 mV/s). From the dependence of ΔEp on the scan rates, the apparent heterogeneous electron transfer rate constant, ks, can be calculated to be 1.53 ± 0.45 s–1. This value of ks is much larger than that obtained by Jiang et al. (0.026 s–1) [150] using the same method at a DTSSP modified gold electrode, suggesting SWNTs are more effective in facilitating the direct electron transfer of GOx than DTSSP. In order to clarify whether GOx still retained its bioelectrocatalytic activity to the oxidation of glucose after it was immobilized on PDDA–SWNT, a series of cyclic voltammetric experiments were carried out in the solution with and without glucose, respectively, under the presence of ferrocene monocarboxylic acid (FcM) as the electroactive mediator. A couple of well–defined redox peaks (curve b), which corresponded to the redox reaction of FcM/FcM+, with the anodic and cathodic potential of 0.342 and 0.256 V, respectively, appeared when FcM was presented in solution. The redox peaks exhibited diffusion-controlled character since both anodic and cathodic peak currents increased linearly with the square root of scan rates. No electrochemical response was observed in the absence of FcM (Figure 24a). Upon addition of glucose (12 mM), the anodic currents increased greatly and a steady-state electrocatalytic plateau was observed (Figure 24c) accompanying by the disappearance of the reduction peak. The further addition of glucose caused the further increase of the electrocatalytic currents, the electrocatalytic current was, however, almost independent of the scan rate. All these results were characteristic of electrocatalytic oxidation of glucose by GOx via electron–transfer mediator of FcM (the electrocatalytic process was illustrated in Figure 25). Controlled experimental results showed that electrocatalytic oxidation of glucose did not occur on Nafion-FAD-PDDA-SWNT/GC or Nafion-PDDASWNT/GC (without GOx) electrode whether the FcM was present or absent in solution. These results indicated that the GOx immobilized on PDDA–SWNT remained bioelectrocatalytically active and could catalyze the oxidation of glucose.

4

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E / V (vs. SCE) Figure 24. Voltammetric responses of the Nafion-GOx-PDDA-SWNT/GC electrode in 0.1 M PBS (pH 8.2) in the absence (a) and presence (b) of 0.5 M FcM. Curves c and d are bioelectrocatalytic responses of the Nafion-GOx-PDDA-SWNT/GC (c) and the Nafion-GOx-PDDA/GC (d) electrodes, respectively, to the oxidation of 12 mM glucose in 0.1 M PBS (pH 8.2). The scan rate is 1 mV/s.

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Figure 25. Illustration of the electrocatalytic process of Nafion-GOx-PDDA-SWNT/GC electrode to the oxidation of glucose using FcM as the electron-transfer mediator. A layer of Nafion, which was covered on the outside of GOx–PDDA–SWNT, was omitted for clarity.

To further demonstrate the function of SWNT, GOx and PDDA were immobilized on the surface of bare GC electrode using Nafion resulting in the Nafion-GOx-PDDA/GC electrode (without SWNT). The voltammetric results indicated that the electrocatalytic activity of Nafion-GOx-PDDA/GC electrode to the oxidation of glucose was low (Figure 24d) compared with that of Nafion-GOx-PDDA-SWNT/GC electrode, suggesting that SWNT should have promotion effect on the electrocatalytic activity of GOx to the oxidation of glucose. At an optimal condition, the electrocatalytic currents increase linearly with the concentration of glucose from 0.5 to 5.5 mM with correlation coefficient of 0.999. The detection limit was estimated to be ~83 μM at a signal–to–noise ratio of 3. The linear range was considered to be useful since the normal glucose concentration in blood serum was around 4.6 mM [153], suggesting that Nafion-GOx-PDDA-SWNT/GC electrode should be used as a sensor to sensing the glucose concentration in serum. And the response deviated from linearity at higher concentration represented a typical characteristic of Michaelis– Menten kinetics. The apparent Michaelis–Menten constant, KMapp , was evaluated to be 4.5 mM.

4.3. Direct Electron–Transfer of Ferredoxin Ferredoxins (Fds), constitute a large family of redox proteins with iron–sulfur clusters as the redox center [154], participate in on–way electron–transfer through the oxidation and reduction of iron atoms [155]. Fd, extracted from plants, exhibits comparatively low negative redox potentials and acts as an electron carrier (acceptor) in photosynthetic processes [156,157]. Electron–transfer patterns of Fds are, however, not straightforward due to their multi-step nature. Electrochemistry has offered effective means to study electron–transfer features of Fds. Electrochemical measurements of spinach ferredoxin (sFd) were investigated on a viologen (an electron–transfer mediator)–coated glassy carbon electrode [158]. Nassar et

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al. [156] and Tominaga et al. [159] independently reported the electrochemical properties of chlorella Fd on cast layer of lipid on the basal plane of a pyrolytic graphite (BPG) electrode. Recently, Nam et al. [160] reported electrochemical behavior of sFd immobilized on lipid membrane film of dimyristoylphosphatidylcholine. Although there are several investigations on the direct electrochemistry of plant Fd, only a few examples of well–defined voltammetric peaks were reported. Our purpose is to immobilize sFd on the surface of carbon nanotube and then to study its direct electron–transfer by cyclic voltammetry. The immobilization of sFd (the structure is presented in Figure 26) on the surface of SWNTs is made via electrostatic interaction since the negative charged sFd (the isoelectric point is about 4.0 [161]) was adsorbed on the surface of SWNTs, which was covered with a layer of positive charged CTAB (Figure 27).

Figure 26. The structure of spinach ferredoxin (adapted from protein data bank).

Figure 27. Scheme for sFd immobilization on the surface of SWNTs (sFd–SWNTs).

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Voltammetric results showed that a pair of well–defined and nearly symmetrical redox peaks was obtained at the Nafion-sFd-SWNTs-CTAB/GC electrode (Figure 28b) in oxygen– free buffers (0.1 M PBS, pH 7.2). This suggested that the redox peaks in curve b were ascribed to the electron–transfer reaction of sFd immobilized on the surface of SWNTs. The anodic (Epa) and cathodic (Epc) peak potential located at –550 and –588 mV, respectively, at a scan rate of 20 mV/s. The separation of peak potentials, ΔEp, is 38 mV, indicating that sFd immobilized on the surface of SWNTs displayed a quasi–reversible electrochemical reaction in spite of its large molecule structure. These peaks were almost invariable after the electrode was continuously scanned for a long time (more than 30 min) and showed litter change over 14 days storage in buffer in 4 ºC (only 13% decrease), indicating that the responses of Nafion-sFd-SWNTs-CTAB/GC electrode was fairly stable. The redox couple had a formal potential, E0’, of –569 mV (vs. SCE, at 20 mV/s), estimated as the average midpoint potential between the oxidation and the reduction peak. The value of E0’ was close to that previously reported for sFd dissolved in a solution obtained at didodecyldimethylammonium bromide multilayer films modified pyrolytic graphite electrode (–535 mV, vs. Ag/AgCl/Sat. KCl, pH 7.2) [162] and γ–aminopropyltriethoxysilane or N–(2–aminoethyl)–γ–aminopropyl– trimethoxysilane modified In2O3 electrode (–600 mV, vs. Ag/AgCl/Sat. KCl, pH 7.2) [163]. It was also similar to that for chlorella ferredoxin entrapping into dioctadecyldimethylammonium bromide lipid films (–510 mV, vs. Ag/AgCl/Sat. KCl, pH 7.2) [159]. 2

b

i / μA

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1

a

0

c

-1 -2 -0.8

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E / V (vs. SCE) Figure 28. Cyclic voltammograms of the Nafion-SWNTs-CTAB/GC (a), Nafion-sFd-SWNTsCTAB/GC (b) and Nafion-sFd-CTAB/GC (c) electrode in 0.1 M PBS (pH 7.2) at a scan rate of 20 mV/s.

By measuring peak potential at various scan rates, the apparent heterogeneous electron– transfer rate constant, ks, could be calculated to be 0.73 ± 0.04 s–1, which was 3–18 times higher than that obtained by Zhang et al. [164] at thiolate-modified Au (111) surface, suggesting that SWNTs could promote the direct electron–transfer of sFd more effectively.

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5. Rtils/Swnts Nanocomposites and their Application to the Direct Electrochemicstry of Heme–Containing Proteins/Enzymes Room temperature ionic liquid (RTILs), which are ionic media resulting from the combination of organic cations and various anions, are liquids at ambient temperatures or even far below ambient temperatures, and have emerged as novel nonaqueous, polar, environmentally benign solvents that hold great promise in the development of green chemical applications and processes because of their unique chemical and physical properties, such as high chemical and thermal stability, negligible vapor pressure, high conductivity, and the ability to dissolve a wide range of organic and inorganic compounds [165–168]. So far, RTILs have been used as alternatives to classical molecular solvents in various fields of fundamental researches and applications, including organic and inorganic synthesis [169], catalysis [170–172], separation [173], etc. Particularly in electrochemistry, RTILs are advantageous over other kinds of solvents since they display a wide electrochemical potential window and high ionic conductivity (for example, [bmim]PF6 has a conductivity of 2.1 ×10–3 S/cm and has been shown to be electrochemically stable in a potential window over 4.5 V [174]) and allow electrochemical studies to be undertaken without an additional supporting electrolyte, which can simplify the electrochemical measurements [175]. They have been widely used in capacitors [176], metal deposition [177], electropolymerization [178], batteries [179], biosensors, and biocatalysis [170,171], etc. Recently, direct electrochemistry of proteins/enzymes in RTILs and at RTILs or RTILs– related composites (for example, RTILs–CNTs composites [180], RTILs–chitosan composites [181], RTILs–sol–gel–based silica matrixes composites [182], etc.) modified electrodes has attracted considerable attention because the results of the direct electrochemistry of proteins/enzymes can provide a basis for constructing biosensors, biomedical devices, enzymatic bioreactors, and biofuel cells, etc. Those studies are usually conducted using RTILs of [bmim]BF4 (1–butyl–3–methylimidazolium tetrafluoroborate), [bmim]PF6 (1–butyl–3–methylimidazolium hexafluorophosphate) or [bmin]Ntf2 (1–butyl–3– methylimidazolium bis(trifluoromrthlsulfonyl imide), and taking the heme–containing proteins/enzymes (cytochrome c, horseradish peroxidase, myoglobin, and hemoglobin, etc.) as models. Although there are several papers published in this field [173,183–187], a systematic study on the effect of RTILs on the direct electrochemistry of heme–containing proteins/enzymes is still unavailable. The published results usually cannot be compared to each other because those studies were performed in different ways. Moreover, some contradicting results even exist. For example, Compton et al. [188] reported that RTILs had a deleterious effect on the redox behavior of the cytochrome c and the cytochrome c would lose its redox activities due to denaturing caused by contact with RTILs; several other authors [183,184,186,189] reported, however, that the RTILs could promote the direct electron– transfer reaction between the proteins/enzymes and the matrix electrode, and the proteins/enzymes were very stable when they were incorporated into RTIL–based composites or could directly be adsorbed on the RTILs’ modified electrode surface (in this case, denaturation did not occur). Even among the papers in which the RTILs had promotion effects on the direct electron–transfer reaction of proteins/enzymes, big differences exist. Zhao et al. [180] calculated the apparent rate constant (ks) for direct electron–transfer of hemoglobin at [bmim]PF6 modified MWNTs to be 2.3 s–1, which was in accordance with that

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obtained with other electrode materials. Using the same method as Zhao’s, Ding et al. [185] reported the value of ks of myoglobin (a similar heme protein to hemoglobin, the difference is that myoglobin contains only one polypeptide subunit whereas hemoglobin contains four polypeptide subunits) to be as high as 18.4 ± 0.2 s–1. To merge these differences, a systematic study on the effects RTILs on the direct electrochemistry of proteins/enzymes is highly desirable. We choose the heme-containing proteins/enzymes as a model to conduct a systematic study of the direct electrochemistry of them at the [bmim]BF4–SWNTs–modified glassy carbon electrode, and compare the results obtained with different proteins/enzymes. The reason to choose the heme–containing proteins/enzymes as models is that they contain several proteins/enzymes with different isoelectric points and, thus, the net electric charge of the proteins is different at the same solution pH, and can be adjusted by changing the solution pH; also, they are commercially available and have a known and documented structure. Not all RTILs are suitable for biocatalysis, proteins (enzymes) are usually active in RTILs containing BF4–, PF6–, and Ntf2– anions. [bmim]BF4, which is soluble in water, has been chosen to prepare the RTILs–SWNTs composites (namely, [bmim]BF4–SWNTs composites) Typically, 2 mg of purified SWNTs were dispersed in 1 ml of [bmim]BF4 by grinding them in an agate mortar for about 1 h. The positively charged imidazolium ion would wrap (or adsorb) on the surface of SWNTs in the course of grinding, and a resultant [bmim]BF4–SWNTs composite would be formed. Afterward, the suspensions were centrifuged at 18,000 rpm for 30 min. The separation of a transparent liquid phase (pure RTILs) and a black gel phase ([bmim]BF4–SWNTs composite) would be identified. The [bmim]BF4–SWNTs was finally collected by removing the supernatant with a pipet. For the fabrication of the protein (enzymes) –RTILs–SWNTs modified electrode, ca. 2 mg of [bmim]BF4–SWNTs composite was dispersed in 1 ml of double–distilled water forming 2 mg/ml of a [bmim]BF4–SWNTs aqueous suspension. The solution of 10 mg/ml of Mb, 20 mg/ml of HRP, and 8 mg/ml of Cyto c was prepared by dissolving 10 mg of Mb, 20 mg of HRP, and 8 mg of Cyto c in 1 ml of 0.1 M PBS (pH 7.0). For comparison, the solution of 10 mg/ml of Mb was also prepared using 0.1 M PBS with the pH of 8.2, and 5.4, respectively. 2 μl of the [bmim]BF4–SWNTs suspension was then thoroughly mixed with 2 μl of Mb, HRP, or Cyto c solution, respectively. Finally, 2 μl of the mixture was cast on the surface of a pretreated GC electrode with a microsyringe and the solvent (water) was allowed to evaporate at ambient temperatures. The electrode was denoted as Mb-[bmim]BF4-SWNTs/GC electrode (or HRP-[bmim]BF4-SWNTs/GC, Cyto c-[bmim]BF4-SWNTs/GC electrode). Thus, the total amount of Mb, HRP, and Cyto c on the surface of electrode was 5.92 × 10–10, 4.55 × 10–10, and 1.29 × 10–9 mol, respectively. The modified electrodes were stored at 4 ˚C when they were not in use. The adsorption of [bmim]BF4 on the surface of SWNTs is characterized and verified by XPS measurements. The [bmim]BF4-SWNTs composite exhibits a well–defined peak at 399.5 eV (Figure 29b), which was not recorded for SWNTs (Figure 29a). Such a peak is due to the presence of nitrogen atoms (N1s) on the surface of SWNTs, and is indicative of the effective adsorption of the imidazolium ion on SWNTs. By a further careful analysis using a nonlinear regression, the main peak at 399.5 eV included the models of 399.4 and 401.0 eV (the dash lines in Figure 29b), implying that two different types of nitrogen atoms may be involved in the imidazolium ion adsorbed on the SWNTs surface. Because the two nitrogen atoms in the free imidazolium ion may essentially have the same binding energy, the two observed types of nitrogen atoms on the [bmim]BF4–SWNTs composite may consequently

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result from the interactions between the imidazolium ion and the SWNTs. As was demonstrated previously [180,190], the imidazolium ion could interact with the SWNTs through π–π or/and π–cationic, hydrophobic, or electrostatic interactions. These possible interactions could be mainly responsible for the formation of the [bmim]BF4–SWNTs composite and the presence of different types of nitrogen atoms in the adsorbed imidazolium ion. N1s

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Binding energy / eV Figure 29. XPS spectra of the SWNTs (a), and [bmim]BF4–SWNTs composite (b) in the N1s region. The dash lines in curve b is the nonlinear regression results of N1s spectrum of [bmim]BF4–SWNTs composite.

It has been reported [188,191] that some kinds of RTILs can inactivate proteins (enzymes) and lead to their denaturation. To clarify whether the [bmim]BF4 could seriously distort the structure of the Mb, HRP, and Cyto c and thus lead to the loss of their bioactivities, circular dichroic (CD) spectroscopy is used to characterize the structural integrity of Mb in aqueous and entrapped in [bmim]BF4–SWNTs composites since CD spectroscopy is able to give an insight into the structure and the conformation of the proteins/enzymes [192]. The far–UV CD spectrum of Mb in aqueous solution exhibits two negative peaks at ca. 208 and 223 nm (Figure 30a), respectively, which is similar to that of the other heme–containing proteins [193,194]. The CD spectrum of Mb–[bmim]BF4–SWNTs (Figure 30b) in this region is also characterized by two negative peaks, whose positions are almost the same as that in Figure 30a. The clear similarities between the CD spectra of Figure 30a and b indicate that the structure and the conformation of Mb after being confined in [bmim]BF4–SWNTs composites are essentially the same as the native ones because the CD spectrum in the far– UV region is dominated by contributions from peptide bonds [193]. Moreover, the similarities in the CD spectra in the Soret bands region (340 to 450 nm) for Mb in aqueous (Figure 30c) and Mb–[bmim]BF4–SWNTs (Figure 30d) verify that the microenvironment of a heme pocket in Mb entrapped in [bmim]BF4–SWNTs composites also remains the same as

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-1

that of the native one since the Soret CD spectrum directly relates to the structure of the heme pocket in proteins [193]. The above results demonstrate that Mb entrapped in the [bmim]BF4– SWNTs composites doesn’t undergo the structural change and remains its native integrity.

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-10 -20 -30

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Figure 30. Far–UV CD spectra of Mb in aqueous (a) and Mb–[bmim]BF4–SWNTs composite (b), and the Soret CD spectra of Mb in aqueous (c) and Mb–[bmim]BF4–SWNTs composite (d).

CD measurements were made on JASCO Model J–810 dichrograph (Japan Spectroscopic Co. Ltd., Tokyo, Japan) at room temperature in a 1–cm quartz cuvette. The final spectra were the mean of ten accumulated scans at a bandwidth of 2 nm, and were corrected for the unspecific dichroic absorbance of the medium by computer manipulation. The data were expressed in term of molar ellipticity, [θ], in deg.cm–2.dmol–1. The spectra were collected over wavelength range of 195 to 250 nm (far–UV region), and of 350 to 450 nm (Soret band), respectively. The electrochemical methods can also be used to characterize the [bmim]BF4–SWNTs composite. The [bmim]BF4–SWNTs composite was cast on the GC electrode surface forming a [bmim]BF4-SWNTs/GC electrode, and this electrode was then used to study the electrochemical impedance of two different kinds of redox couples, namely, Fe(CN)63– /Fe(CN)64– and Ru(NH3)63+/Ru(NH3)62+. It has been documented that the redox process of the Fe(CN)63–/Fe(CN)64– is a typical negatively charged inner–sphere reaction [195], whereas Ru(NH3)63+/Ru(NH3)62+ is a typical positively charged outer–sphere reaction [195]. The electron-transfer kinetics of both redox couples is electrode surface–dependent, and is generally determined by several factors including tunneling, electrostatic, and electrocatalytic effects et al. Electrochemical impedance spectroscopy (EIS) is a powerful tool for studying the interface properties of the modified electrode and can provide information on the impedance changes of the interface of the electrode surface/electrolyte solution. The value of the electron-transfer resistance (Rct) depends on the dielectric and insulating features at the electrode/electrolyte interface. The typical results of the impedance spectra (Nyquist plot) of

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the redox couple of Fe(CN)63–/Fe(CN)64– (Figure 31a and b), and of Ru(NH3)63+/Ru(NH3)62+ (Figure 31c and d) at the SWNTs/GC (Figure 31a and c), and at the [bmim]BF4-SWNTs/GC (Figure 31b and d) electrode are obtained. Here, Z’ and Z’’ are the real variable and the negative value of the imaginary variable of impedance, respectively. The profiles show a semicircular part at high frequencies corresponding to the electron–transfer limited process and a linear part at low frequencies corresponding to the diffusion process. To obtain detailed information about the electrode/solution interface, the Randles circuit (the inset) is chosen to fit the impedance data obtained. The value of Rct for the redox couple of Fe(CN)63–/Fe(CN)64– at [bmim]BF4-SWNTs/GC electrode (~120 Ω, Figure 31b) decreases drastically compared with that obtained at the SWNTs/GC electrode (~230 Ω, Figure 31a). On the contrary, the value of Rct for Ru(NH3)63+/Ru(NH3)62+ at the [bmim]BF4-SWNTs/GC electrode (~35 Ω, Figure 31d) is larger than that at the SWNTs/GC electrode (~15 Ω, Figure 31c). These results suggest that the adsorption of [bmim]BF4 on the surface of SWNTs can accelerate the electron transfer of the couple of Fe(CN)63–/Fe(CN)64– and impede that of the couple of Ru(NH3)63+/Ru(NH3)62+. The difference in the electrochemical behavior obtained for the two different redox couples can be explained by considering the electrostatic interaction between the [bmim]BF4–SWNTs and the different charged species. After the [bmim]BF4 is adsorbed on the surface of SWNTs, the formed [bmim]BF4–SWNTs composite is positively charged due to the imidazolium cationic ion. The surface positively charged composite can attract the negatively charged species of Fe(CN)63–/Fe(CN)64– and repel the positively charged species of Ru(NH3)63+/Ru(NH3)62+. This electrostatic interaction certainly favors the electron transfer of Fe(CN)63–/Fe(CN)64–, and is unfavorable for the electron transfer of Ru(NH3)63+/Ru(NH3)62+. The above results further indicate the formation of the [bmim]BF4–SWNTs composite.

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Figure 31. Nyquist plots for the SWNTs/GC (a, c), [bmim]BF4-SWNTs/GC (b, d) in presence of 5– mM Fe(CN)63–/5–mM Fe(CN)64– (a, b) or 2–mM Ru(NH3)63+/2–mM Ru(NH3)62+ (c, d) in 0.1 M of KCl solution in the frequency range of 0.01 to 100 kHz with a perturbation signal of 5 mV. The electrode potential was biased at 0.21 and –0.22 V (vs. SCE) for the redox pair of Fe(CN)63–/Fe(CN)64–, and Ru(NH3)63+/Ru(NH3)62+, respectively. The electrochemical impedance measurements were performed on a PAR M273 Potentiostat/Galvanostat equipped with a 5208 Lock–in (EGandG, PARC, USA).

[bmim]BF4-SWNTs/GC electrode was also used to study the direct electron transfer reaction of heme-containing proteins/enzymes with cyclic voltammertry. As expected, there is no electrochemical reaction occurrence at the electrodes of SWNTs/GC and [bmim]BF4SWNTs/GC in the potential range of interest. The shape of the cyclic voltammograms of both electrodes is similar except that the baseline of the [bmim]BF4-SWNTs/GC electrode is lower than that of the SWNTs/GC electrode. This phenomenon may result from the adsorption of [bmim]BF4 on the surface of SWNTs, which may lead to changes of the double layer of the modified electrode. The cyclic voltammogram of the Mb/GC electrode shows a small irreversible anodic peak at ca. –370 mV, suggesting that Mb at the bare GC electrode surface cannot undergo the effective quasi–reversible direct electron–transfer reaction. Both the Mb-[bmim]BF4-SWNTs/GC and Mb-SWNTs/GC electrodes have a pair of the well-defined redox peaks with the similar anodic (Epa) and cathodic peak (Epc) potential and, consequently, the value of formal potentials (E0’), and ΔEp are also similar (Table 4). The peak currents obtained at the two electrodes are almost identical as can be seen by considering the different background between the two electrodes. The value of E0’ was close to those obtained previously for the heme FeIII/FeII redox couple, suggesting that the obtained redox peaks at the Mb-[bmim]BF4-SWNTs/GC and Mb-SWNTs/GC electrode could be ascribed to the redox process of the heme FeIII/FeII redox couple in Mb molecules. Such a redox process is unable at the Mb-[bmim]BF4/GC electrode, which is prepared by immobilization of Mb directly on the [bmim]BF4/GC electrode. Those results suggest that [bmim]BF4 cannot promote or facilitate the direct electron–transfer of Mb, whose results are not consistent with that reported previously [185]. Moreover, the [bmim]BF4 after being

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adsorbed on the surface of SWNTs doesn’t affect the promotional effects of SWNTs on the direct electron–transfer reaction of Mb. To further study the effects of [bmim]BF4 on other heme–containing proteins (enzymes), the Cyto c are immobilized on the electrode of [bmim]BF4-SWNTs/GC and the SWNTs/GC electrode, respectively, resulting in electrodes of Cyto c-[bmim]BF4-SWNTs/GC and Cyto cSWNTs/GC, and the cyclic voltammetric experiments of the two electrodes are performed in 0.1 M of PBS (pH 7.0). The results indicate that the value of E0’ of Cyto c obtained at Cyto c[bmim]BF4-SWNTs/GC electrode (–10 mV) is ~90 mV more negative than that obtained at the Cyto c-SWNTs/GC electrode (~78 mV), and the value of ΔEp for the Cyto c-[bmim]BF4SWNTs/GC electrode (132 mV) is much larger than that for the Cyto c-SWNTs/GC electrode (55 mV), which is indicative of the reversibility of the direct electron–transfer reaction of Cyto c at the [bmim]BF4-SWNTs/GC electrode decrease compared with that at the SWNTs/GC electrode. The results for the direct electron–transfer of HRP obtained from the HRP-[bmim]BF4-SWNTs/GC and HRP-SWNTs/GC electrodes in PBS (pH 7.0) are similar to that of Cyto c (Table 4), the value of E0’ of HRP-[bmim]BF4-SWNTs/GC electrode shifts in negative direction by more than 40 mV and the value of the ΔEp increases compared with that for the HRP-SWNTs/GC electrode (Table 4). The reason for the different changes in the value of E0’ and ΔEp of Cyto c (and HRP) and those of Mb obtained at the [bmim]BF4SWNTs/GC and SWNTs/GC electrode may due to the different charge possessed by the Mb, Cyto c, and HRP at pH 7.0. The isoelectric point of Mb, Cyto c, and HRP is 7.2 [196], 10.1 [197], and 9.0 [198], respectively, and thus Cyto c and HRP are positively charged, and Mb is, however, almost neutral at a pH of 7.0. The redox peak potentials of the direct electron– transfer of neutral Mb are essentially not affected by the surface charge of the electrode, namely, the SWNTs/GC (the surface is essentially negatively charged because of the SWNTs) and the [bmim]BF4-SWNTs/GC (the surface is made to be positively charged after [bmim]BF4 is adsorbed) electrodes. Compared with the SWNTs/GC electrode, whose negatively charged surface favors the direct electron–transfer of opposite charged species, the positively charged [bmim]BF4-SWNTs/GC electrode repels the positively charged Cyto c and HRP, and led to the negative shift in value of E0’ and the enhancement of the ΔEp and, consequently, a decrease in the reversibility of the direct electron–transfer of Cyto c and HRP at the [bmim]BF4-SWNTs/GC electrode. To clarify the importance of the surface charge effects of [bmim]BF4–SWNTs upon the direct electron–transfer of proteins, two controlled experiments are conducted for Mb. One is that Mb is prepared using 0.1 M of PBS with the pH value of 8.2 and the cyclic voltammograms of the Mb-[bmim]BF4-SWNTs/GC and Mb-SWNTs/GC electrode are also performed in a pH 8.2 buffer solution. In this pH solution, Mb is negatively charged. In the other experiment, Mb is prepared with the PBS of pH 5.4, and the MB is positively charged under this pH value. The cyclic voltammograms of the Mb-[bmim]BF4-SWNTs/GC and MbSWNTs/GC electrodes are then conducted in this pH buffer again. In a solution of pH 8.2, the values of E0’ for the Mb-[bmim]BF4-SWNTs/GC and Mb-SWNTs/GC electrode are –312 and –374 mV, respectively and, as expected, the E0’ at the Mb-[bmim]BF4-SWNTs/GC electrode shifts toward the positive direction (by more than 60 mV). The values of ΔEp are 67 (at Mb[bmim]BF4-SWNTs/GC electrode) and 80 mV (at Mb-SWNTs/GC electrode), respectively. Moreover, the redox currents for the direct electron–transfer of Mb at Mb-[bmim]BF4SWNTs/GC electrode are enhanced significantly compared with that at the Mb-SWNTs/GC electrode. These results show that the reversibility of the electron–transfer reaction of the

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negatively charged Mb (at pH 8.2) increase at the Mb-[bmim]BF4-SWNTs/GC electrode, whose positively charged surface attracts the negatively charged Mb via the electrostatic interaction and favors its electron–transfer reaction. Table 4. The parameters of heme–containing proteins (enzymes) at various electrodes Electrodes

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Mb-SWNTs/GC (pH 7.0) Mb-[bmim]BF4-SWNTs/GC (pH 7.0) Mb-SWNTs/GC (pH 8.2) Mb-[bmim]BF4-SWNTs/GC (pH 8.2) Mb-SWNTs/GC (pH 5.4) Mb-[bmim]BF4-SWNTs/GC (pH 5.4) Cyto c-SWNTs/GC (pH 7.0) Cyto c-[bmim]BF4-SWNTs/GC (pH 7.0) HRP-SWNTs/GC (pH 7.0) HRP-[bmim]BF4-SWNTs/GC (pH 7.0)

Epc / mV −383 −381 −414 −345 −246 −380 50 −76 −339 −394

Epa / mV −310 −311 −334 −278 −176 −280 105 56 −300 −330

E0’ / mV −346.5 −346 −374 −311.5 −211 −330 77.5 −10 −319.5 −362

ΔEp / mV 73 70 80 67 70 100 55 132 39 64

1010 ΓA / mol 2.25 ± 0.16 2.34 ± 0.11 1.94 ± 0.21 3.86 ± 0.18 2.58 ± 0.25 1.89 ± 0.32 5.67 ± 0.37 4.75 ± 0.38 2.84 ± 0.30 1.97 ± 0.24

When the Mb is prepared using the PBS with a pH of 5.4 and the cyclic voltammetric experiments are also performed in a solution of pH 5.4, the E0’ for Mb-[bmim]BF4SWNTs/GC electrode (–330 mV) shifts negatively by ca. 120 mV compared with that for the Mb-SWNTs/GC electrode (E0’ is –211 mV), and the value of ΔEp is 70 and 100 mV for MbSWNTs/GC and Mb-[bmim]BF4-SWNTs/GC electrode, respectively, suggesting a decrease in the reversibility of the electron–transfer of Mb due to the electrostatic repellence between the positively charged Mb (at pH 5.4) and the [bmim]BF4-SWNTs. The cyclic voltammetric results of Cyto c, HRP and Mb at various pH levels indicate that [bmim]BF4 itself cannot promote the direct electron–transfer reaction of heme–containing proteins (enzymes); however, the positively charged imidazolium ion, after being adsorbed on the electrode surface, has the important effects on the electrochemical parameters of the electron-transfer reaction of non–neutral species. When the heme proteins are positively charged (HRP, Cyto c at pH 7.0, and Mb at pH 5.4), the positively charged electrode surface ([bmim]BF4-SWNTs/GC) leads to the negative shifts in the value E0’ of those proteins and the decrease in reversibility (compared with the results at SWNTs/GC electrode), and when the protein is negatively charged (Mb at pH 8.2), the positively charged [bmim]BF4SWNTs/GC leads to positive shifts in the value E0’ of the protein and the increase in reversibility. These differences may be explained by considering that the direct electron– transfer reaction of heme proteins usually starts from the reduction of those proteins since the resting state of heme proteins is usually at ferric state (Fe(III) state). The repellent interaction between the positive charged proteins and positive electrode surface ([bmim]BF4SWNTs/GC) will lead to an increase in the difficulty for the reduction reaction and thus E0’ shifts in the negative direction, while the attractive interaction between the negative charged protein and positive electrode surface leads to a decrease in the difficulty for the reduction reaction and, correspondingly, the E0’ shifts toward the positive direction. The cyclic voltammograms of heme–containing proteins (enzymes) at the [bmim]BF4SWNTs/GC electrode are scan rate (v) dependent. It is observed that the anodic and cathodic peak potentials remain almost unchangeable when the scan rate is lower than 100 mV/s, and

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they shift linearly in positive and negative directions, respectively, with the scan rates when v is higher than 500 mV/s. From the slopes of plots of the peak potential versus lnv, the chargetransfer coefficient (α) can be calculated to be ~0.48. The values of E0’ are, however, almost independent on the scan rates and the average value of E0’ is –315 ± 5 mV in the scan rate range of 5 to 2000 mV/s. From the dependence of ΔEp on the various scan rates, the apparent heterogeneous electron transfer rate constant, ks, could be calculated to be 4.6 ± 0.4 s−1 (at pH 8.2). The value of ks is slightly higher than that obtained at the Mb-SWNTs/GC electrode (3.11 ± 0.98 s−1) [45]. The amount of the electroactive Mb, HRP, and Cyto c (expressed as ΓA, in mol) on the electrode surface could be estimated using equation (6) by integrating the anodic (or cathodic) peak area in cyclic voltammograms under the background correction. The values of ΓA for the Mb, HRP, and Cyto c at the electrode of SWNTs/GC and [bmim]BF4-SWNTs/GC were listed in Table 4. From those values, it can be concluded that the values of ΓA for the negatively charged proteins/enzymes (Mb at pH 8.2) on the [bmim]BF4-SWNTs/GC electrode were higher than that on the SWNTs/GC electrode; the values of ΓA for the positively charged proteins/enzymes (Mb at pH 5.4, HRP and Cyto c at pH 7.0) on the [bmim]BF4-SWNTs/GC electrode were lower than that on the SWNTs/GC electrode. This phenomenon was consistent with the reversibility of the proteins/enzymes in different pH solutions and electrodes, and could be explained by considering the electrostatic interaction between the proteins/enzymes and the electrode surface.

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6. Conclusion Carbon nanotubes present significant opportunities to basic science and nanotechnology, and pose significant challenge for future work in this field. The key advantages of carbon nanotube modified electrodes are their small diameter but long length which has allowed them to be plugged into proteins [20], their electroactivity which appears to be as good as or better than any of the other carbon based electrodes and the high surface area that nanotube modified electrodes posses. However, there are a number of challenges related to the preparation and use of carbon nanotube modified electrodes. Many of these challenges relate to the processing of the nanotubes so the electrodes can be modified in a more controlled way. For example, the separation of the semi–conducting from conducting tubes, the separation the nanotubes into uniform lengths and prevention the non–specific adsorption of the proteins to the walls of nanotubes are still not fully solved [20]. The next stage of research into carbon nanotube modified electrodes is expected to conduct in the following directions: (1) the fundamental research into understanding the mechanisms by which carbon nanotubes give such excellent electrochemical performance, (2) improvement our understanding on how to nanostructure surfaces with carbon nanotubes in a highly controlled and robust manner, and (3) improvement our understanding of how to integrate these exciting nanomaterials with biological systems. The use of carbon nanotubes as nanocircuitry elements is particularly interesting [5]. Biomaterials linked to carbon nanotubes may be used as binding elements for the specific linkage of the carbon nanotubes to surface in the form of addressable structures. The rapid developments in using biomaterials as templates for the preparation of metallic or

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semiconductive nanowires suggest that the integration of such template biomolecules with carbon nanotubes may lead to new functional devices. The application of carbon nanotubes in the biomedical field is another important research area. However, before such materials can be successfully incorporated into biomedical implants, drug/vaccine delivery vehicles or biosensors, there is a need to establish their biocompatibility [13]. Despite the importance of determining if carbon nanotubes have associated toxicity in vivo, relatively few studies have been devoted to this topic. Other caron-based biomaterials have demonstrated excellent long–term biocompatibility and biological performance in medical device applications. Early biocompatibility data for carbon nanotubes suggest that unrefined carbon nanotubes possess some degree of toxicity (in vivo and in vitro), predominately due to the presence of transition metal catalysis. Exposure to pristine carbon nanotubes has been shown to cause minimal cytotoxicity at higher concentration [13]. The success of carbon nanotubes technology is dependent upon the continuation of research into the toxicology of carbon nanotubes and the related materials.

Acknowledgments The work presented in this chapter is supported by the National Natural Science Foundation of China (20373027, 20673057, 20773067, 20833006), the Program for New Century Excellent Talents in University (NCET–06–0508) of MOE, the Natural Science Foundation of Jiangsu Province (BK2005138), and the Foundation of the Jiangsu Key Laboratory for Molecular and Medical Biotechnology, China (MMBKF05001).

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In: Graphene and Graphite Materials Editor: H.E. Chan, pp. 57-94

ISBN: 978-1-60692-666-6 © 2009 Nova Science Publishers, Inc.

Chapter 2

SERENDIPITY IN THE STUDY OF THE GRAPHENE CARBON-LITHIUM REACTION SYSTEMS Tsutomu Takamura Invited Guest Professor of Harbin Institute of Technology, Harbin, China

Abstract

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During the course of electrochemical investigation of Li insertion/extraction reaction in graphite and the related substances the author has obtained new findings or methods for improving the reactivity. In this article the author intends to show the interesting phenomena with explanation and application. The chapter consists of the following eight sections:

1) 2)

3)

Introduction Under-potential deposition (UPD) of Li on the carbon surface.UPD phenomenon is popular on the foreign metal atom deposition on the metal electrode surface and studied extensively by many researchers including the present author, but it has been unfamiliar on the nonmetal electrode. When we examined the cyclic voltammograms of graphite fiber or active carbon fiber in non-aqueous solvent containing LiClO4 we found a sharp peak at a slightly positive to the Li metal deposition potential. This was found to be sensitive to the surface condition, and the peak height was proportional to the carbon surface area, and to the Li+ concentration. We attributed it to the UPD of Li on the carbon surface. Later on this phenomenon was found to be applied as a charge accumulator like double layer capacitor, the charge amount being far larger than that of the capacitor. Mass transfer of Li in metal at room temperature. In an attempt to modify the graphite surface to obtain high reaction rate of Li insertion/extraction, we deposited a metal film on the graphite fiber surface in a vacuum chamber. We found that the Li insertion/extraction rates were much more improved by the deposition of Pd. In addition, we examined Cu, Ag, Au, In, Ni, and many other metals. We found most of the metals examined revealed the reaction enhancing effect. This phenomenon implies that prior to the insertion in the carbon fiber Li has to moves through the deposited metal film. This is our novel finding. By the use of a bipolar cell where the sample metal foil was sandwiched between the two facing cylindrical cell compartmens, we could verify the evidence of Li mass transfer in metal at room temperature. The diffusion coefficient of Li in metal could be determined, i.e., in Cu and Ni the value was 10-7 cm2 s-1, and 10-6 in

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4)

5)

6)

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7) 8)

9)

Ag, the value being in the same order of magnitude as that of ions in liquid electrolyte, and larger than that of hydrogen atom in Pd. Diffusion coefficient of Li in graphitized carbon. A number of studies have so far been conducted for the determination of the diffusion coefficient of Li in graphitized carbon but the values are scattered in the range between 10-11 to 10-6 cm2 s-1. The reason why it is so much scattered is ascribed to the different situation of the carbon sample in the electrode. Usually the sample carbon powders were coated on a Cu foil with some binder, resulting in　inhomogeneous electrical contact. Instead of powder sample we used graphitized carbon single fiber potential step chrono-ammperometry was performed. The resulting obtained value was as high as 10-6 cm2 s-1. Postulate and verification of the presence of nano-holes at the graphene layer. It is said that Li cannot pass across a basal plane of graphite crystal since the six members carbon ring of the graphene layer is too narrow. Although the rounded graphite particles are covered by graphene layers sheet over the surface, they are used in the anode of Li-ion battery; implying Li can get into the interior of the particles. The author paid attention to such an apparently contradicting phenomenon and postulated that there are a number of nano-size holes at the graphene layer. We attempted to detect such holes by analyzing the TEM images of graphite, and finally detected a number of images of hole-like structure. Through such holes Li can penetrate into the interior of the carbon very easily. Characterization of the decomposition reaction of propylene carbonate on a graphite anode. It is well-known that propylene carbonate, which is a good solvent for obtaining electrolyte for Li-ion battery, cannot be used for the graphite-like anode since it decomposes violently at the surface of the anode during Li insertion. The decomposition has been attributed to the solvent-co-intercalation into the space between the graphene sheets. But we found that when we use a single fiber electrode no decomposition occurred even with a graphitized fiber. After an extensive examination we concluded that such a decomposition phenomenon occurs on the surface where the electrical potential distribution over the surface is inhomogeneous. As far as the distribution is homogeneous, no decomposition was observed. Thus, the solvent co-intercalation mechanism has become no longer valid Propose of a novel activation method for improving the Li insertion/extraction reaction. In an attempt to obtain an active surface for insertion/extraction of Li in non-aqueous electrolyte the author challenged to obtain a simple way to realize it. Finally we have found finally an effective method which is now called “mild oxidation”. Heating the carbon samples at an appropriate amount oxygen content atmosphere was found very effective for the activation. This method was found effective for the activation of active carbon surface. Electrochemical properties of SEI for Li insertion/extraction. The term of “SEI” (Solid/electrolyte interphase) is now very popular on the surface of carbon samples. But it was difficult for characterizing the SEI on the metal surface. Since SEI has been paid attention on the Li insertion/extraction reaction the author proposed a method to characterize the SEI on a metal surface by making a sample where the sample metal is vacuum-deposited on a graphitized carbon fiber.

1. Introduction Carbon is a very interesting material in view of not only material science but also practical application. This may be due to the ease of atomic orbital hybridization of 1s, 2px, 2py, and 2pz to form sp1, sp2 and sp3 types. After the discoveries of both of the fullerenes and carbon nanotubes the number of papers published in the scientific periodical of “Nature” until April in 2007 were 177 papers on fullerenes, and 178 papers on carbon nanotubes, respectively. This indicates that the number of papers appearing in all the scientific

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periodicals may be so huge that we cannot infer them. Since the naming of “graphene” was proposed by Bowman at the 1st and 2nd Conference on Carbon at University of Buffalo (1956), graphene has become popular to be used. There are some ambiguity on the meaning of “graphene” since it does not define the size and the number of plane, and accordingly, Inagaki proposes that it is better to use “carbon hexagonal layers” in stead of “graphene” [1]. But now the name of “graphene” is so popular that the author prefers to use “graphene”. Graphene layer consists of carbon sp2 hybridization orbital alone, which means that it should keep rigidly flat plane. On the other hand, carbon nano-tubes (CNT) consist of the same orbitals as well, but it is not flat but bending to form tubes. This means that the sp2 hybridized orbital is rather flexible. Such flexibility causes to provide wide variety of properties in material science. On the other hand, lithium has special unique properties in view of material science. Lithium is the smallest atom belonging to the alkali metal group (Group I) in Periodic Chart of Elements, and accordingly, Li has unique properties, viz., the diffusion coefficient of Li in solid materials is the highest among the alkali metal group. Therefore, the combined system of graphene and lithium is expected to provide many unique stories in science. The author has been engaged in the research of the anode materials of “Lithium-ion Batteries” where a unique property of “Insertion of Li in the anode materials” is utilized for realizing a highly negative potential with safety. In this article the author would like to show several unique phenomena found in this system by the author’s research with curiosity and “Serendipity” mind.

2. Under-Potential Deposition (UPD) of Li on the Carbon Surface

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2.1. Introduction The under-potential deposition phenomenon was found at first by Haїssinsky in 1935. It is very natural that the electrochemical plating of any metal (M(a)) on the surface of a substrate metal electrode (M(b)) proceeds with ease at some more negative potential to the reversible potential of reaction (1), this means that the reaction proceeds with ease at some over-potential.

⎯⎯ → 　M(a) M(a)n+ + ne- ←⎯ ⎯

(1)

However, if the affinity of M(a) and M(b) is higher than the affinity among M(a) in the ordinarily plated M(a) metal, the reversible potential of the formation of adsorbed atom of M(a) on M(b) will be more positive, and accordingly, the reaction (2) takes place at more positive potential than that of (1), corresponding to under-potential region.

⎯⎯ → 　M(b)-M(a) M(b) + M(a)n+ + ne- ←⎯ ⎯

(2)

This mechanism is called as “under-potential deposition” (UPD). Afterwards, a number of studies on UPD have so far been carried out until now. Now the UPD phenomena been

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investigated precisely not only based on electrochemical method but also on spectroscopic and STM-AFM methods [2][3]. We found such a phenomenon to take place not only in the metal-metal system but also in the system of Li-carbon. The initiation of this study, however, was not started for the purpose of investigating the “under-potential deposition” phenomenon, but on investigating the surface modification of graphite materials in view of Li intercalation/deintercalation reaction at the carbon anode (negative electrode) of Li-ion battery. For the purpose of advancing the improvement of the materials research of carbon anode, use of a appropriate form of the corresponding sample is very convenient. Carbon fiber was just the appropriate one, since being different from the other form of the carbon sample such as powder it is not necessary to use another additional materials to fabricate the test electrode. In case of powder material it is necessary to use binder, conductive additives, and current collector for preparing the test electrode, where it is difficult to obtain the performance of the sample material in question without disturbance of the other materials. In case of carbon fiber an integrated fiber felt it can be the test electrode by itself.

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2.2. Newly Found Phenomenon By using such a fiber electrode introduced in the above section we have obtained very interesting results. Phenomenon of under-potential deposition of Li on carbon was found by the use of such a fiber electrode. The aim of our study was to improve the Li insertion/extraction rate on a carbonaceous material. In order to activate the surface of carbonaceous material we adopted “mild oxidation treatment”. The method is to cover the sample with sufficient amount of acetylene black powder and heat at 300°~ 750°C for a few minutes-one hour, the variation of temperature and time being dependent on the nature of sample species. The method was effective to remove (burning off) the contaminant adsorbed on the surface of the sample. By this method the Li deintercalation peak on the cyclic voltammogram of the sample was successfully enhanced as shown in Figure 1. The cyclic voltammogram (CV) was much more enhanced in peak height by mild oxidation treatment as shown in Figure 1 (B) although the height becomes reduced upon repetition of cycling. In addition, a new sharp peak appeared at about 0.1 V [4]. In case of active carbon fiber the peak at around 0.1 V appeared very much enhanced like the main peak. Figure 2 shows such a feature. In Figure 2 (A) the peak at about 0.1 V was too high in the initial cycles to reveal a shift to the more anode side due to the kinetic effect. This showed that the peak was sensitive to the activity of the reaction site and liable to be degenerated during cycling. After the repetition of many cycles the feature tended to the stable situation as shown in Figure 2 (B). At first the author thought that the new sharp peak is due to the electrochemical dissolution of metallic Li deposited on the anode surface by an inhomogeneous distribution of the potential over the test electrode. Therefore, the author reprimanded the graduate students (Mr. Awano and Mr. Takasu), being in charge of carrying out the measurement, with such saying as “Never do such a rough experiment to make appearing an unexpected peak like this”. But as written in the paper [4] it was proved not due to the deposited metallic Li but due to the Li atom formed by UPD on the carbon surface. The finding was a piece of good luck by the use of CV for evaluation, but the students might feel unhappy when they were reprimanded by their professor.

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Figure 1. CVs of graphite fiber felt (Melblon, Petoca, Ltd. Prepared at 2320°C) obtained in EC+DMC (1:1,v/v) containing 1 M LiClO4 at 25°C. (A) Pristine (B) Heated at 700°C covered with a sufficient amount of acetylene black for 1min. in air. Potential sweep rate: 1 mV s-1.

Figure 2. CVs of active carbon fiber (Toho Rayon Co. FW#510) in EC+DMC (1:1. v/v) containing 1 M LiClO4. Potential sweep rate: 1 mV s-1. The fiber felt was activated by heating at 500°C with a sufficient amount of acetylene black for 5 min. in air. (A) Fresh sample; (B) After the CV repetition of 50 cycles.

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Tsutomu Takamura The mechanism of UPD of Li on a carbon surface is shown in (3).

⎯⎯ → C-Li C(s) + Li+ + e- ←⎯ ⎯

(3),

where C(s) denotes the surface carbon atom and C-Li, the UPD bond formed between C(s) and Li atoms. In case of the arrangement of carbon atoms is regular like in graphite crystal, each carbon atom on the surface should have the same energy state, and accordingly, the bond energy formed in (3) should be the same as each other, resulting in a very sharp peak on the CV as shown in Fig 1 (B).

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2.3. In Case of Activated Carbon In case of activated carbon the surface bond situation is supposed to differ site by site, forming the variation of C-Li bond energies, and accordingly, the peak on the CV is expected to be broad as shown in Figure 2. The extreme case is on the internal pore surface of the porous activated carbon, where kinetics of ion transfer in the narrow pore will strongly affect the shape of CV. The CV shows a negative sharp peak followed by a very broad diagram whose width becomes narrower in the positive potential region. On the anodic sweep branch the sharp peak at about 0.1 V can be attributed to the UPD occurring on the outer surface of the carbon, and the broad diagram is supposed to correspond to the UPD of Li on the surface of internal narrow pore where the ion transfer of solvated Li+ is presumably controlled by transfer kinetics. Accordingly, all the features in Figure 2 can be attributed to the UPD of Li on the carbon surface. The broad diagram after the sharp peak can be ascribed to the UPD of Li on the internal pore surface of the carbon even though the current due to the double layer capacity charging is involved. The amount of charge due to UPD of Li is large enough not to be ignored as compared to that of intercalated Li. In case of graphite the theoretical capacity due to the intercalated Li is 372 mAh g-1 for LiC6 compound, which is the highest amount for the graphite anode of Li-ion battery. If the capacity of UPD-Li is comparable to that value it is very attractive for putting use of super capacitor since the capacity of the conventional capacitor is far lower than that of Li-ion battery. Now HEV (hybrid type of electric vehicle powered by battery or capacitor) attracts attention due to the fossil fuel saving and the reduction of exhausting CO2. In case of battery powering for HEV there is an issue that the power capability is not enough to be required. In contrast the capacitor-powered case the power is sufficient enough but the capacity is very low. To solve the problem the capacitor-powered HEV should be equipped with a large size capacitor having heavy weight, which reduces the energy efficiency. If the capacity of the capacitor is increased to that of battery level, then the energy efficiency will be much enhanced as compared to that of conventional one. The estimated capacity for the case of active carbon corresponding to Figure 2 is about 200 mAh g-1, which is not so lower than that of Li-ion battery. Since the energy density of the power source is proportional to the working voltage, UPD capacitor working at 3 V with Li system is very attractive. There are wide varieties of carbonaceous materials available. An example is a partially graphitized activated carbon having a high specific surface area. Such a material is expected to have a larger anode specific capacity with sufficient power capability, since this has three

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types of charge capacities such as Li intercalation capacity, Li UPD capacity and the double layer capacity. The overall charge capacity is expected to surpass over that of the anode of Liion battery. Future material design of such a compound is very attractive for providing a surpassing HEV. Further idea of increasing the UPD capacity is to utilize the contribution of a vacuum deposited metal film on the surface of activated carbon fiber [5]. Figure 3 shows a huge UPD peak due to the vacuum deposited Ag (several hundreds-Å-thick). When an activated carbon fiber is coated with a 500 Å-thick vacuum-deposited Ag film and treated with a mild oxidation, then, a UPD capacity over 250 mAh g-1 was obtained. A small sharp peak after the huge UPD peak is attributed to the extraction of Li from the Li-Ag alloy in the Ag film.

Figure 3. CV of active carbon fiber felt (Kuractive 2000 Kuraray Co.) in PC containing 1 M LiClO4. The curve was obtained with the fiber sample mildly oxidized followed by a vaccum deposition of a 500 Å thick Ag film. The scan rate: 1 mV s-1.

3. Mass Transfer of Li in Metal at Room Temperature 3.1. Introduction Diffusion of metal atom in liquid Hg is very popular, which has been investigated in the field of polarography as well [6]. Free mass transfer of metal atom in solid metal at room temperature, however, appears to have been believed impossible for conventional metal atom. The reason may be ascribed to the fact that the strong mechanical properties of solid metal is attributed to the stable position keeping of the metal atom at the fixed lattice point. Upon heating the metal at a temperature sufficiently high enough to be softened, the metal atoms

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become to have sufficient energy of motion, allowing to move easily in the metal matrix, which corresponds to melting phenomenon. Any foreign atom other than hydrogen, where the mass is low enough to be allowed to move, appears believed to be fixed in the metal matrix at a definite position. Huggins and coworkers obtained the values of Li diffusion coefficient at 415°C and for the alloy systems of LiAl, Li3Sb (at 360°C), Li3Bi (at 380°C), Li12Si7, Li7Si3, Li22Si5, LiSn, Li7Sn3, Li5Sn2, Li13Sn5, Li7Sn3, Li22Sn5, LiGa, LiIn, and LiCd [7]. The values are in the range of 10-4 to 10-6 cm2 s-1 at these high temperatures. Judging from these values the values at room temperature are estimated to be as slow as 1 x 10-18 cm2 s-1. However, as far as the author knows, there is only one paper that has so far been published on the very high diffusion coefficient of Li in LiGa alloy is on the measurement of self-diffusion of 8Li by the method of using the short-lived radiotracer of 8Li [8]. The apparently common sense mentioned above had been broken during the experiment by us for improving the electrochemical Li insertion/extraction rate at the surface of carbon fiber which is in contact with an organic electrolyte containing molar amount of Li+ cation. We have engaged in the research program for improving the anode performance. In addition to “mild oxidation treatment” we had an idea for improving the reaction rate, that was to modify the surface of a sample of graphitized carbon fiber by covering with a vacuum deposited metal film. In the beginning, the selected candidate of the metal film was Pd film since Pd is well known to occlude hydrogen in the metal matrix. The cathodic polarization of Pd electrode in contact with an aqueous electrolyte solution tends to form hydrogen atom on the surface even though the polarization voltage is more anodic to the reversible hydrogen potential, which corresponds to UPD of H atom on the surface of Pd metal electrode. We expected the same phenomenon to take place for Li as that of H, since Li belongs to the same low with the neighboring position as that of H in periodic table of elements. The experiment was to evaporate Pd by heating in a vacuum chamber where an integrated fiber of the graphtized carbon fiber felt was mounted in the chamber. We could observe the Li insertion/extraction peak on the cyclic voltammogram (CV) at the surface of graphitized carbon fiber covered with a vacuum deposited Pd film [9]. The improvement, however, could not be recognized clearly. But, afterwards, we could succeed to obtain a clear indication of the improvement by depositing a Au film [10]. Succesively, we found that the deposition of many kinds of metal films on the graphitized carbon fiber surface enabled us to enhance the Li insertion/extraction rate [11-13]. Typical example is shown for the case of Ag film deposition in Figures 4 and 5. Figure 4 shows the SEM image of a graphitized single carbon fiber (Melblon 3100, Petoca made) deposited with a 400Å-thick-Ag film. Even after the film deposition the SEM image was very similar to the uncovered carbon so that it was difficult to identify the presence of the film. In order to identify the presence of the covering film the author asked to a graduate student (Dr. Junji Suzuki, now Associate Professor of Matsue College of Technology, Matue, Japan) to scratch the film at a small portion. He was quite skilful to scratch the very thin film, resulting in obtaining the SEM image shown in Figure 4, where a part of the film reveals to be removed to show up the uncovered portion of the fiber surface without damage. This implies that the vacuum deposited film was not tightly bound to the carbon surface but covers simply to leave a gap between them. The CV diagrams of Li insertion/extraction in the carbon fiber are compared for with and without the Ag film in Figure 5. After the deposition of a Ag film the peak

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height was enhanced about two times to the initial state even in the presence of additional film on the surface.

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Figure 4. SEM image of a well-graphitized carbon fiber (Melblon 3100, Petoca, Ltd.) with a 300 Å thick Ag film whose small part was scratched to remove the film.

We analyzed the mechanism of the movement of Li particles during the polarization: Upon cathodic polarization of the fiber sample in contact with an organic electrolyte containing LiClO4, Li+ cations near the surface may be reduced to form Li atoms on the surface of the Ag film covering over the carbon surface. The reaction rate on the Ag surface is presumably much more higher than that on the bare carbon fiber surface. Then the adsorbed Li atoms get into the Ag layer, some of which may form alloy with Ag, the rest may diffuse to the opposite side, move across the metal/carbon contact phase into the carbon matrix. Upon anodic polarization, the process is reversed. During the course of such movement Li particle should move across the Ag film. We hit upon the idea that “Li can move in the Ag metal matrix at room temperature with a considerable rate, and this phenomenon should not be restricted to the case in Ag”. We hurriedly initiated to test for the other metals. As a result, we found that Li can move through in any sample of vacuum-deposited metal on the carbon fiber, even though the rate was different depending on the kind of metal. Even in Cu and Ni which form no alloy with Li at room temperature, we found Li can move very easily. We announced this phenomenon at the electrochemistry academic meeting in Japan, but nobody appeared to agree with our idea positively and showed us suspicious faces. Somebody said, “the metal film you tested would have a number of micro-pores through which the electrolyte can pass”. A professor in the university where the author belonged said to his

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colleagues that “never say such a unacceptable idea to cause the students to loose a proper way of thinking”.

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Figure 5. CV without (A) and with (B) a 400 Å thick Ag film in a mixture of EC/DMC (1:1, v/v) containing 1 M LiClO4.

3.2. Experimental We decided to outsmart them by verifying this phenomenon with a sound experimental method. Use of “bipolar cell system” is very helpful, we noticed. Figure 6 shows the bipolar cell constructed by Mr. Junji Suzuki and our colleague teacher, Prof. Sekine. A 2 m-thick copper foil was used as the sample bipolar electrode which was sandwiched between the two facing Teflon made cylindrical cells of Cell A and Cell B. An electrolyte solution of 1:1 mixture of ethylene carbonate (EC) and dimethyl carbonate (DMC) containing 1 M LiClO4 was filled in Cell A, whereas 1:1 mixture of EC and propylene carbonate (PC) containing 1 M NaClO4 was filled in Cell B. At first the Cu bipolar electrode in Cell B was polarized at a sufficiently positive potential of 500 mV vs. Pt counter electrode and the bipolar electrode in Cell A was let at open circuit potential. Then the Cu bipolar electrode in Cell A was set at a cathodic potential of 125 mV vs. Li|Li+ reference electrode and the concentration of Li+ in Cell B was measured from time to time by pipetting out an aliquot of the solution in Cell B to the measurement cell of the atomic absorption spectrometer for determining Li+ concentration.

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Figure 6. A bipolar cell constructed for verifying Li mass transfer through a centering metal foil (bipolar electrode).

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3.3. Results and Discussion The time dependency of Li+ ion concentration in Cell B is shown in Figure 7 which shows that the concentration of Li+ was about zero level at first but after the polarization it increased linearly. This means that upon cathodic polarization of the Cu bipolar electrode in Cell A Li+ began to move through the Cu foil to the counter side of Cell B. The results were reported in Electrochem. Solid-State Letters, and afterwards our opinion appears to have been accepted hopefully in general [14]. The reader will be interested in the value of diffusion coefficient of Li in the metal sample. In order to determine the diffusion coefficient it is necessary to monitor the Li+ concentration near the surface of the bipolar electrode in Cell B. For the purpose of monitoring the topological concentration of Li+ we developed a needle like Li+-ion-sensing electrode. The idea of the Li+ ion-sensing electrode was come up to the author’s mind by remembering the time of development program of electrochromy device when the author was worked in Toshiba Company long time ago. Tungsten oxide changes the color to deep blue when it is reduced in an aqueous electrolyte containing proton. The electrochemical potential of the oxide varies depending on the amount of absorbed proton. We supposed that the similar phenomenon might be observed in case of Li+ insertion in tungsten oxide. A needle of tungsten metal was oxidized in an aqueous solution of sulfuric acid, washed with clean water, dried and immersed in PC electrolytes containing LiClO4, and polarized negatively for insertion of Li+ in the oxide matrix. The needle electrode thus obtained revealed a reversible potential in a PC solution containing Li+. As expected, the observed potential was dependent on the Li+ concentration of the electrolyte in contact with the electrode.

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Figure 7. Time dependency of the Li ion concentration of the electrolyte in Cell B after the polarization of the bipolar electrode to a definite cathodic potential in Cell A.

Figure 8. Bipolar cell mounted with a Li+ ion-sensing electrode in Cell B for determining Dchem of Li in the electrode metal.

The bipolar cell for the determination of the chemical diffusion coefficient of Li is shown in Figure 8. The W/WOx electrode for sensing Li+ was set near the bipolar electrode surface in Cell B. With a similar method as above the bipolar electrode in Cell B was polarized initially at a sufficient positive potential and the signal of the W/WOx electrode was recorded, then the polarization potential of the bipolar electrode in Cell A was set to a definite cathodic potential. The resulting signal-time curve of the Li+ sensor electrode thus obtained is shown

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in Figure 9. As shown in this figure the Li+ concentration in Cell B began to increase after a delay time (in Figure 9 it is shown as tb, breakthrough time). This means that upon polarization Li get into the bipolar electrode of Cu foil instantaneously at the surface facing to Cell A, and diffused to the opposite face in contact with the electrolyte in Cell B, and get into Cell B after the breakthrough time of tb.

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Figure 9. Time dependency of the output signal of the Li+ sensing electrode mounted near the surface of the Cu bipolar electrode in Cell B. The increase of the signal after the time delay tb (breakthrough time) indicates that the Li+ concentration was increased.

The time, tb, corresponds to the time required for Li to move in Cu from Cell A to Cell B side. Therefore, the chemical diffusion coefficient of Li （Dchem） in the Cu bipolar electrode is obtained by 　　　　　　　　　　　　　 tb = 0.5

l2 π 2 Dchem

(4),

where l denotes the thickness of the metal foil sample [15]. The values were independent on the setting potential in Cell A. The values obtained by our students in Rikkyo Univeristy are listed in Table 1. The values differ from metal to metal but in general larger than 10-10 cm2 s-1, that are quite much larger than those estimated from the values obtained by Huggins and coworkers at high temperatures. On some day in 2005 a mail was sent to the author from a Chinese scholar to notify that he published a paper on the diffusion of Li in copper. We were quite much pleased to recognize a sentence in the beginning of Introduction part, ”Surprisingly Li can move in Cu easily at room temperature, which is reported in the paper published by J. Suzuki, et al in [16]. Professor Chen and coworkers wanted to verify such a phenomenon by ab initio

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calculation. He kindly sent his paper on the verification stating that Li can move easily in Cu [17]. These stories tell us that “Never discard your self-belief on the findings you obtained”. Table 1. Chemical Diffusion Coefficient of Li in Metals at 25°C Measured with a Bipolar Cell Kind of Metals Ag Al Cu as obtained annealed Ni Pb Si single crystal Vacuum-deposited on a Ni sheet Sn Zn

Diffusion Coefficient Dchem (cm2 s-1) 5.0 x 10-7 2.0 x 10-9 8.0 x 10-8 2.0 x 10-7

Literature Thesis, Rikkyo University, Department of Chemistry Junji Suzuki, 2004 Junji Suzuki, 2005 Junji Suzuki, 2004 Junji Suzuki, 2004

1.5 x 10-7 1.7 x 10-11 1.0 x 10-10

Junji Suzuki, 2004 Kazutaka Yoshimura, 2005

1.1 x 10-11

Takahide Ohta, 2004

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4.1. Introduction For the purpose of designing the battery electrode for practical use the data of diffusion coefficient of chemical entities that take part in the charge/discharge reaction in the active materials is very important for realizing a high power battery. In case of Li-ion battery a number of studies have so far been conducted for the determination of Li chemical diffusion coefficient. The reason why so many studies should have to be conducted is that the obtained values were scattered in a wide range especially for the carbon anode materials from 10-11 to 10-6 cm2 s-1 [18],[19]. The cause of the scattering may be ascribed to two reasons: The one is that there are many kinds of carbonaceous materials where the internal structure differ depending on the preparation conditions, and the second is that the materials are produced in general in the form of powder. In case of using powder sample for the determination of diffusion coefficient it is necessary to prepare the test electrode by coating slurry comprised of the powder suspension in a solvent with binder on a current collector sheet. In such aggregate type electrode electron and Li should move among particles to particles and the diffusion process may be disturbed by complicated situation. Accordingly, it is very difficult to measure the rate of the movement of Li particle in the homogeneous solid medium. Use of NMR technique enables us to evaluate the Li diffusion coefficient correctly but there are some issues to overcome for obtaining the reliable data [20-22].

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Once the author belonged Petoca Materials Ltd, where several carbon fiber materials were produced. We noticed that the use of carbon fiber was quite convenient for researching the electrochemical properties of Li insertion since various types of carbonaceous materials including graphite, soft carbon, hard carbon, and active carbon could be produced form the precursor material of mesophase pitch fiber. Usually the practical application of these products was using “milled fiber” prepared by cutting the as obtained long fiber. Once we noticed that the as obtained fiber being available as an integrated fiber felt can be sliced into a thin fiber felt which could be sandwiched between two sheets of Ni expanded metal. By spotwelding the peripherals of the sandwiched sheet we found that it was quite convenient for the electrochemical test electrode. The most favorable point was that it requires no binders, nor electro-conductive additives, which could be used free from the interference of the additive materials. We tried to use the new test electrode and recognized that the rate of Li insertion/extraction was higher than that of the electrode prepared by binding the milled fibers with binder.

4.2. Experimental

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At first the cyclic voltammograms (CV) was measured for the graphitized carbon fiber with the most common sample of an integrated fiber felt which was sliced into a 1 x 1 square thin sheet, sandwiched with a folded Ni expanded metal sheet, and the peripherals were spotwelded for fixing to make the evaluating electrode. The Li insertion/extraction CV obtained in an electrolyte of 1:1 mixture (v/v) of EC/DMC containing 1 M LiClO4 is shown in Figure 10, which shows a distinct cathodic and anodic peaks corresponding to the Li insertion and extraction, respectively. A slight initial irreversible insertion current was found extending to a wide potential range.

4.3. Results and Discussion Long time dream of the author is to get an ideal electrode free from the disturbance of binder, conductive additive, and aggregation of sample particle. The favorable one is not a system under microscope but can be manipulated without the aid of microscope. One day an idea came up to the author why not to use a single fiber. A student, Mr. Keita Yamaguchi, joined with us as a graduate student. He belonged a gymnastic club of “Kyuudo”, (Japanese archery) in our university, and quite much skilful to handle a single fiber as thin as φ = 7 μm. He could pick up a grahitized single fiber, from an integrated fiber felt. I asked him to use the single carbon fiber as the test electrode. After many times trial and struggle he finally could succeed a single fiber electrode system where the very thin fiber was immersed in the electrolyte solution in a small glass beaker cell (Figure 11). How about the CV of a single carbon fiber? Figure 12 shows the resulting CV for the pristine fiber sample. Even though the peak current was microampere level we obtained a clear CV. The peak for Li deinsertion (extraction) was far sharper than that of an integrated fiber felt sample and no initial irreversible cathodic current was identified. This means that the electrochemical reaction is free from the disturbance of some side reactions under the uniform potential distribution on the test electrode.

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Figure 10. Cyclic voltammogram of a graphitized carbon fiber felt electrode in EC/DMC containing 1 M LiClO4 at 25°C. The voltage-scanning rate: 1 mV s-1.

We have paid attention on the activation of the electrode surface. We developed several methods effective to the carbon surface activation. This time we tried to activate the single fiber electrode by depositing a Ag thin film on the fiber surface by vacuum evaporation, followed by oxidation in a reduced oxygen atmosphere at 350°C for 10 min. On the story of finding this activation method please refer to 7-3-2. After the activation treatment we obtained CVs shown in Figure 13, where we see the peak height is enhanced remarkably indicating the Li insertion/extraction reaction rates to be much more improved. We can recognize a very sharp small anodic peak at about 30 mV vs. Li|Li+ on the anodic scan branch, which indicates a formation of Li by UPD. The large main anodic peak shows to be split into two peaks caused by the stage formation indicating the reaction became more reversible. Upon repeating the cycling the peak height becomes to be reduced and the peak position shifted toward positive. This is presumed to be due to the deactivation of the highly activated surface.

4.4. Determination of Chemical Diffusion Coefficient of Li in Carbon As discussed in 4-1 the literature values of the chemical diffusion coefficient of Li (Dchem) in carbon so far reported scatter to a wide range between 10-11 to 10-6 cm2 s-1. One of the main reason of this scattering is ascribed to the difference of the electrode states among the electrodes examined. In contrast our single fiber electrode is a kind of ideal electrode because of uniform single phase and single particle free from extra substances like additives. We utilized a single fiber electrode for the evaluation of Dchem, especially paying attention of

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the effect of surface activation. Dchem should be independent on the surface condition of the electrode since it is the phenomenon in the interior of the carbon sample. Method of the evaluation, however, affects the values in question especially for the case of using electrochemical method.

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Figure 11. Schematic figure of an electrochemical cell for the evaluation of a single carbon fiber electrode as thin as φ = 7 μm.

Figure 12. Cyclic voltammogram obtained with a graphitized single carbon fiber electrode by the use of an electrochemical cell illustrated in Figure 11. The measurement was done in EC/DMC (1:1 v/v) containing 1 M LiClO4 at room temperature with the potential scan rate of 1mV s-1.

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Figure 13. Cyclic voltammogram of an surface activated graphitized single carbon fiber electrode by the use of an electrochemical cell illustrated in Figure 11. The measurement was done in EC/DMC (1:1 v/v) containing 1 M LiClO4 at room temperature with the potential scan rate of 1mV s-1.

We adopted a conventional method of “potential step chrono-ammperometry (PSCA)”, where the potential of the sample electrode in contact with an electrolyte is stepped to a definite value and the resulting current flow is recorded and analyzed. The obtained results are shown as lack filled circles in Figure 14. Dchem was found dependent on the stepping potential region, the lowest value being in the 100-200 mV region. This dependency can be elucidated based on the stage formation potential. Graphite consists of a regular stacking of graphene layers and Li particles are inserted in these graphene layer stacking according to the rule of stage formation [23]. Formation energy of each stage differs each other, resulting in different formation potential, and the formation of each phase of the stage requires activation energy, so that the PSCA process is supposed to be influenced by this kinetic process. This means that the Dchem value obtained by PSCA method may be slower than the true value. Mr. Yamaguchi observed CV for the graphitized single fiber with the slowest scan rate, by which we can identify more precise reaction process, and obtained the corresponding CV shown in Figure 15, where at least 4 peaks are found on the anodic branch. These peaks reveal the separation of each disappearing stage. The potential range wherein two large peaks appear on the CV is 100-200 mV which is just corresponding to the low Dchem region. Therefore, we can conclude that the values of Dchem obtained by PSCA method in these potential region is not necessary show the true value of Dchem but lower than the true one.

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Figure 14. Chemical diffusion coefficient of Li in a graphitized single fiber electrode measured with a PSCA method as a function of stepping potential at 25 °C. ● before the activation; ○ after the activation.

Figure 15. Cyclic voltammogram of a graphitized single fiber electrode with the slowest scan rate of 0.01 mV s-1 in EC/DMC (1:1 v/v) containing 1 M LiClO4 at room temperature.

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Figure 16. Chemical diffusion coefficient of Li in a low temperature fired single fiber electrodes measured with a PSCA method as a function of stepping potential at 25 °C.

On the other hand, the Dchem values shown with open circles in Figure 14 became about 50 times enhanced after the activation treatment of the fiber surface, implying the obtained Dchem approaches the true values. Figure 14 implies that the Dchem values for the graphitized sample are over 1 x 10-6 cm-2 s-1 in the potential region of 0-100 mV vs. Li|Li+, which is the highest value among those ever reported. Not only graphitized carbon but also lower temperature fired carbon can be evaluated on the values of Dchem. Mr. Omae who was my graduate student of Rikkyo University published a paper on the Dchem values of low temperature fired mesophase carbon. The values are depicted in Figure 16 [24]. As shown in the figure the values are nearly the highest level as those appearing in literature [18]. This means that the value of Dchem in literature should be reexamined in view of the surface activity of the sample.

5. Characterization of the Decomposition Reaction of Propylene Carbonate on A Graphite Anode 5.1. Introduction It is well-known that propylene carbonate (PC), which is a good solvent for obtaining electrolyte for Li-ion battery, cannot be used for the graphite-like anode since it decomposes violently at the surface of the anode during Li insertion (Figure 17). The decomposition has been attributed to the solvent-co-intercalation into the space between the graphene sheets [25]. Since PC is a very good solvent because of providing good conductivity even at low temperature and cheap price, trial to use PC on the graphitized anode had been attempted by many workers. It was well-known that PC is stable on the surface of non-graphitized carbonaceous anode materials. We worked on the use of less graphitized carbon fiber since the price was far lower than that of graphitized one. The issues to be solved were how to make a stably working large size anode. Our idea was to bind carbon fibers together with a conductive carbon binder. However conventional glue type binder was not preferable due to

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its dissolution into the electrolyte solution. We noticed that phenol resin is a good precursor for giving rise to no-dissolving binder since after the pyrolysis it changed to be nondissolution type and highly electric conductive.

Figure 17. Cyclic voltammogram of a graphitized fiber felt electrode in propylene carbonate (PC) containing 1 M LiClO4 at room temperature.

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We succeeded to use a kind of phenol resin, resol resin, which gave a good binding covering all over the fiber surface giving high conductivity [26,27].

5.2. Experiment and Results Once an idea came up to mind that complete coating with resol resin over the surface of grahite material may allow to use it even in PC electrolyte. The author ordered to Dr. M. Satio, who is working now actively at Tokyo University of Science, to test it with a thick graphitized carbon fiber. He reported us it may be hopeful. He repeated experiments many times but it was difficult for him to recognize whether the whole surface was covered or not. On day he reported “Now I have succeeded to cover whole surface since no PC decomposition was found on the CV”. But looking precisely the magnified SEM image of the coated carbon fiber did not make believe us the perfect covering. Then we stopped further research. Once Mr. Yamaguchi started to use a single carbon fiber experiment I reminded the results obtained by Mr. Saito and asked Mr. Yamaguchi to reexamine the PC decomposition. After repeating experiment Mr. Yamaguchi reported me that without resol binder the fiber was stable in PC even under cathodic polarization (Figure 18 (right). That was really unbelievable thing. He found that as far as we use a thin single fiber electrode no decomposition took place even with a graphitized fiber.

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Figure 18. Cyclic voltammograms of a graphitized single fiber electrode in EC/DMC (1:1 v/v) containing 1 M LiClO4 (left) and in propylene carbonate containing 1 M LiClO4 (right) at room temperature. The potential scan rate was 1 mV s-1.

Figure 19. Cyclic voltammograms of graphtized carbon fibers electrode where 5 fibers were arranged regularly (top) and irregularly (bottom) in PC containing 1 M LiClO4 at room temperature, the potential scan rate being 1 mV s-1.

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Figure 20. SEM image of the widely used negative electrode material formed by mechanical rounding of natural graphite powder.

The author discussed with him on the reason of preventing the PC decomposition on a single graphitized fiber. How about to use a bundle of the single fiber? He tried to make two five fibers array electrodes, the one having the direction each fiber being well arranged, and the other, having ill-arranged array electrode. The results are shown in Figure 19. We found that the degree of decomposition was dependent on the arrangement and the ill-arranged one causees to decompose more seriously. We published on this phenomenon with our conclusion that the decomposition phenomenon is caused by the non-uniform potential distribution on the electrode surface, which causes non-uniform reaction to take place, triggering the PC decomposition. After an extensive examination we concluded that such a decomposition phenomenon occurs on the surface where the electrical potential distribution over the surface is inhomogeneous. As far as the distribution is homogeneous, no decomposition was observed. Thus, the solvent co-intercalation mechanism has become no longer valid [28].

6. Postulate and Verification of the Presence of Nano-holes at the Graphene Layer 6.1. Introduction The anode active material of conventional Li-ion battery is, in general, graphitized carbon. Example of the SEM image of the widely used graphitized anode material is shown in Figure 20, where the particle appears to be covered by graphene layers sheet over the whole surface. During the charging/discharging of Li-ion battery, Li+ ions in the electrolyte are intercalated into the spacing between the graphene layers, and vise versa. The mechanism

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how Li can get into the graphite crystal interior has so far been discussed, concluding that Li can get into the interior only through the edge pane and not via the basal plane since the basal plane consisting of benzene rings having too narrow holes to allow Li to migrate through. But upon glancing the SEM image of the active material shown in Figure 20 we feel Li cannot get into the interior through the surface hard cover consisting of basal plane. On the other hand, the author has kept a question in mind on the Li stage structure transformation during Li insertion/extraction in the stack of graphene layer spacing. For example, the stage arrangement of stage two is C/C/Li/C/C/Li-----, and stage three is C/C/C/Li/C/C/C/Li-----. How can change smoothly from stage two to stage three without withdrawing all the Li inserted? The author has kept in mind to solve the issues in such an apparently contradicting phenomena. Finally we arrived at the concept that there is no completely perfect thing in nature. Crystal should have imperfection more or less even though it is an artificial one. We postulated that there are a number of nano-size holes at the graphene layer. We attempted to detect such holes by analyzing the TEM images of graphite, and finally detected a number of images of hole-like structure. Through such holes Li can penetrate into the interior of the carbon very easily.

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6.2. Proposed Model on the Nano-hole Finally the author has arrived at the concept that there is no completely perfect thing in nature. Crystal should have imperfection more or less even though it is an artificial one. The illustration of graphite crystal is shown in Figure 21. The basal plane consists of graphene layers having the carbon hexagonal layers composed of benzene ring skeletons. We postulated that there are a number of nano-size holes at the graphene layer. The cross section model is shown in Figure 22. If there are such holes at each graphene layer the issues are easily solved. We attempted to detect such holes by analyzing the TEM images of graphite, and finally detected a number of images of hole-like structure.

6.3. Trying to Find Out the Nano-sized Holes on Graphite Material The High Resolution Transmission Electron Microscope (HRTEM) image is the most dependable for detecting the nano-size holes at the graphene layers. Author began to try for identifying the presence of nano-size holes. The author reminded that Professor Kinoshita of Lawrence Berkeley laboratory, California Institute of Technology, Lawrence Berkeley, USA, with whom the author is acquainted is an expert for obtaining HRTEM image of graphite, and tried to identify the nano-size holes on the HRTEM image of graphite in his papers. The paper contains many HRTEM images of coke carbons graphitized at several graphitization degree [29]. The author tried to find a ring-like image in the HRTEM images in this paper. After many struggling, the author could succeed to identify the hole images. In Figure 23 the readers may hopefully identify the presence of image of hole as ring-like images that are surrounded by white squares with arrows.

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Figure 21. SEM image showing the edge plane of graphite and illustration of graphite structure wherein Li particles are intercalated.

Figure 22. Cross section model of graphite structure having nano-size holes at the graphene layers.

If the above-mentioned identification work is reasonable, such ring-images should be identified generally in any HRTEM image of graphite. The author requested to my Chinese graduate girl student, Miss Lijun Fu, belonging to Professor Yuping Wu of Fudan University, Shanghai, China. She was quite much interested in this work and began to work immediately. After many times trial she succeeded to obtain beautiful HRTEM image of graphite wherein we could identify a number of ring-like images of nano-size holes. Figure 24 is an example she obtained, where a number of white squares with arrows are surrounding the ring-like images. A number of thin stripes running slantingly with the same separation in the HRTEM image indicate that the sample is well crystallized to graphite.

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Figure 23. Pointing out of ring-like image of nano-size holes in HRTEM image of graphitized carbon cited from a literature published by Kinoshita’s group [29].

Figure 24. HRTEM image showing the presence of a number of nano-size holes in the graphite crystal (courtesy of Miss Lijun Fu, [30]).

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We aimed to publish this work in a scientific journal and worked together for publication. The publication was succeeded recently [30]. Upon preparation of paper the author wanted to criticize the Li insertion process based on quantum chemistry discussion. Dr. Takatoshi Matusmoto, Tohoku University, Sendai, Japan, is an expert of “Ab initio calculation. The author requested him to show what size of hole at the graphene layer can allow Li to pass through. He accepted the author’s request and rushed for obtaining the results. In the paper his calculated results are shown, and we can understand how the benzene ring size hole is difficult of allow Li pass through. As shown in Figure 25 the size of pyrene is still not large enough for Li to pass, requiring 23.712 kcal mol-1. The size of coronene is enough to make Li pass through easily.

Figure 25. Potential energy curve calculated for Li to pass through the hole of pyrene-like shape.

7. Propose of a Novel Method of Surface Activation for Improving the Li Insertion/Extraction Reaction 7.1. Introduction At the time of early stage of improving the electrode materials of Li-ion battery the author moved from Toshiba Corporation, Tokyo, Japan, to Rikkyo University as a professor

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of physical chemistry. In Toshiba the author worked as a general manager of Chemical Laboratory for research and development of chemical materials for electric products use, and battery was one of major interest as well. The author had kept in mind on the negative electrode material of new secondary battery, especially zinc electrode for nickel-zinc secondary battery having the highest specific energy density since that was quite much difficult to realize a reliable reversible anode. This background induced me to start a new research program at Rikkyo University for obtaining the reliable reversible anode (negative electrode) of Li-ion system. As stated in section 4, graphitized carbon fiber was chosen as the ideal electrode sample. At first mesophase pitch-based carbon fiber prepared at a temperature lower than 1000°C was selected since the specific capacity is higher than that of graphite. The low temperature fired carbon fiber, however, was proved to have a large initial irreversible capacity which is a great issue for realizing the practical product. The starting program was to find an effective method to reduce the large initial irreversible capacity. In addition, the cycle performance as well as the power capability was not satisfactory as well.

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7.2. Experimental Sample: Pitch-based mesophase carbon fibers were prepared by heat-treating the precursor fiber material at temperature of 650°C, 700°C, 800°C, 1000°C, 1200°C, 1500°C, respectively, in vacuum for 5 hours. Electrochemical evaluation: Test electrode was prepared by slicing the fiber felt to 1 x 1 cm square with a thickness of 3mm, sandwiched with a folded expanded Ni metal and fixed by spot-welding at several points on the peripheral. As the electrolyte 1:1 (v/v) mixture of ethylene carbonate (EC) and dimethyl carbonate (DMC) dissolved with 1 M LiClO4 was used. Sometimes propylene carbonate (PC) was used in place of DMC. Three electrode-beaker type cell was constructed for electrochemical evaluation. Surface evaluation: IR spectra of samples were evaluated with FTIR spectrometer, where the surface treated sample was placed in the sample beam room, and a pristine sample was placed in the reference beam room. Surface treatment: 1. Mild oxidation: An integrated fiber felt was contained in a crucible and covered with a sufficient amount of acetylene-black powder and heated in a reduced air pressure chamber at temperatures of 350°C-1000°C for several min. The temperature was monitored with a thermocouple inserted on the sample position in the crucible. Heating was done in a Tanmmann furnace. 2. Heat-treatment after the vacuum deposition of metal film: Film of Ag or Au was vacuum deposited on the carbon fiber sample by the method described in 7-3-2 then it was heated at about 300-400°C for 1 h in vacuum. The surface of the carbon fiber was quite much activated.

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7.3. Results and Discussion

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7.3.1. Mild Oxidation The CV diagram obtained for the pristine sample of 1000°C fired fiber is shown in Figure 26 where we see a large initial irreversible current peak on the CV of the first cathodic run. This indicates that some reducible entities were present on the surface of pristine sample. The difference FTIR spectra showed the presence of considerable amount of hydorxyl group. In order to remove the surface hydroxyl groups the chemical reduction treatment was recommended. It is said that acetylene black powder contains some reducing chemical entities, so that heating with a large amount of acetylene black powder was expected to be effective remove the irreversible capacity by reduction. After the treatment for appropriate time we took CV for the treated sample. The results are shown in Figure 27, where we see not only the cycle performance but also the initial irreversible capacity was quite much improved. We were pleased very much that our method was favorable, and aimed to present our paper at the international meeting. The author presented our attractive results at the Material Society Symposium held April 17-20, 1995, San Francisco, California, USA. After the presentation the author got questions by many audience. Among them Professor E. Peled of Tel Aviv University, Tel Aviv, Israel, was involved. He contacted us and gave detailed question. “That paper is quite much interesting, especially for finding of a successful tool for removing the large initial irreversible capacity. By the way, is the method based on “reduction” or “oxidation”? This question was really essential. The author should criticize myself deeply. And the final answer was “that is not reduction, but oxidation”. This was reverse of our initial idea! He agreed with the author’s opinion. Later on he published his paper on the effectiveness of surface treatment [31]. In this paper he noticed that a new method of surface activation was proposed by Takamura and coworkers, and he recommend to use a new word “mild oxidation”, the function being to burn-off the surface contaminant entities. Afterwards, the author prefers to use “mild oxidation” as well.

7.3.2. Metal Film Deposition Followed by Heating in Vacuum The author has been kept in mind the audience saying (Please refer to Chapter 3) that the vacuum deposited metal film should be porous to allow the electrolyte to pass through. One day an idea came up to mind that annealing might seal such pores. The author asked Dr. Suzuki to examine the process of annealing of metal film on carbon fibers. He understood the meaning in a moment and started the experiment immediately. He asked what temperature is convenient for annealing? The author said that Tammann Temperature, TT, is a good reference, where TT is about 1/3 of the melting temperature of metal based on absolute temperature. For example, for Ag which melts at 961°C, that is 1234K and 1/3 of that value is 138°C. We were afraid that might be too low to facilitate the annealing so that we decided that to be 350°C in vacuum. Next morning Dr. Suzuki rushed to Professor and said that I was quite much astonished to look the SEM image after annealing. We expected the deposited Ag film became became much more compact and smoother due to sintering. But the result was quite much different

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from expected. He showed the image shown in Figure 28 (b) and said the pattern is just like to that of poisonous snake which terrified me throughout the night. The vacuum deposited film is considered to melt on the carbon and flow on the surface to merge together to form droplets. He was accustomed to measure CV of everything. He again surprised to notice that the CV was quite much enhanced as shown in Figure 29. Hereafter we adopted this method to be a new effective surface activation of carbonaceous fiber.

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Figure 26. CVs (in PC containing 1 M of LiClO4) of a disordered mesophase carbon prepared at 1000 °C measured with a potential scanning rate of 1 mV s-1 (before the heat-treatment).

Figure 27. CVs (in PC containing 1 M of LiClO4) of a disordered mesophase carbon prepared at 1000 °C measured with a potential scanning rate of 1 mV s-1. (after the heat-treatment in vacuum).

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Figure 28. SEM images of graphitized mesophase carbon fibers (Melblon 3100). a carbon fiber covered with a 450-Å-thick Ag film, (b) a carbon fiber covered with a　450-Å-thick Ag film followed by heattreated at 350 °C for 1 hour in vacuum.

Figure 29. Cyclic voltammogram of graphitized mesophase carbon fiber measured in EC/DMC (1:1 v/v) containing 1 M LiClO4 with a potential scanning rate of 1 mV s-1. (a) as obtained sample; (b) as obtained sample was vacuum deposited with a 450 Å-thick Ag film and heated at 350 °C for 1 hour in vacuum.

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Figure 30. Schematic model of SEI depicted by Peled for the case of first charge of the graphite anode [33].

8. Electrochemical Properties of SEI For Li Insertion/Extraction 8.1. Introduction The word of “SEI” was firstly proposed by Professor Peled [32,33]. SEI is the abbreviation of “Solid Electrolyte Interphase” (Do not confuse from “Interface”). This is a layer having thickness but “Interface” has no thickness just like “Surface”. In contrast, interphase is a layer having a thickness covering over the surface of electrode, and acts as a passivation layer, which in some cases may be part of a thicker passivating layer. On the graphite electrode at the time of first intercalation of Li SEI layer is only partially formed as shown in Figure 30, which was proposed by Professor Peled. The SEI layer is comprised of Li2CO3, LiF, and LiCl, and not comprised of organic polymer, ether, or ester. In case of battery during the stabilizing formation period a well-grown SEI layer is supposed to form all over the anode graphite surface.

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The word of SEI is frequently used in many papers without careful consideration. The chemistry of SEI is complicated and cannot be defined simply. In the following we would like to show SEI formed on the metal electrode surface differs depending on the kind of metal. As shown in the preceding sections vacuum deposition of metal film on the fiber surface is a good method of surface modification. Many students of the author’s laboratory took part in the surface modification by varying the depositing metal film for carbonaceous materials. The use of the anodic peak due to deintercalation of Li from graphitized carbon fiber is useful for evaluation of the SEI formed on metal surface. The CV of metal plate gives a mixture of undefined peaks being difficult to attribute it to what electrochemical process. But the peak due to the Li deintercalation from the graphitized anode is very easy to be attributed to the deintercalation process as shown in Figure 5, and Figures 12 to 13.

8.2. Experimental

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Vacuum deposition of a metal film on a graphite fiber felt: A tungsten boat was loaded with pieces of metal sample and placed in a vacuum chamber, and electric cables were connected to the boat. The fiber felt sample having the size of working electrode was fixed over the tungsten boat. After evacuation the boat was heated by powering directly with current. The thickness of the depositing film on the sample fiber was adjusted by monitoring with a quarts crystal vibration balance equipped near the sample. In case of depositing different metal over the film-covered sample, another boat system loaded with different metal was arranged together in advance.

Figure 31. Cyclic voltammograms of a graphitized carbon fiber covered with a vacuum deposited Cu film in EC/DMC containing 1 M LiClO4 with a potential scan rate of 1 mV s-1.The Cu film thickness: (a) 100 Å; (b) 200 Å.

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Figure 32. Cyclic voltammograms of a graphitized carbon fiber covered with a (A) vacuum deposited Cu film, and (B) vacuum deposited Cu film on which over-layered with a Ag film in EC/DMC containing 1 M LiClO4 with a potential scan rate of 1 mV s-1. The thickness: (A) 600 Å thick Cu: (B) 300 Å thick Cu and 300 Å thick Ag.

Figure 33. Cyclic voltammograms of a graphitized carbon fiber covered with four-layered films of Cu/Ag/Cu/Ag in EC/DMC containing 1 M LiClO4 with a potential scan rate of 1 mV s-1. The thickness of each film was 200 Å.

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SEM observation: The surface of the metal film-deposited felt sample was mounted in the SEM chamber and the image was taken. Electrochemical evaluation: The sample felt deposited with the metal film was sandwiched with a folded Ni expanded metal, spot-welded at several points on peripheral for fixing, pretreated in a evacuating oven at 250 °C for two h, and equipped in the electrochemical cell. Evaluation was performed mainly with CV measurement in an electrolyte of EC/DMC mixture containing 1 M LiClO4.

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8.3. Results and Discussion Graduate student Mr. M.Yoshida, now working at Kureha Chemical Co., and the author paid attention on the comparison of Ag loaded felt and Cu loaded felt because these two metals are similar to each other on the very high electric conductance. As shown in Figure 5 Ag film covered grahitized fiber showed a very good improvement effect, we expected Cu to show the similar performance. Especially different from Ag, Cu gives no alloys with Li at room temperature; disturbance due to alloy formation could be avoided. The results on Cu film covered sample are shown in Figure 31, the features being unexpectedly pity even though the peak height enhancement was recognized. We considered the cause of poor cycleability for the case of Cu. The most probable reason is the contact of Cu film on the carbon fiber surface is not enough to deliver good cycleability. But investigation of the situation of the contact between the substrate fiber and the deposited film appeared not easy. Once Mr. Yoshida stroked on a good hint, why not to utilize the good performance of Ag film. He deposited a Ag film over the Cu film-deposited sample. The results are shown in Figure 32. Surprisingly, we obtained very good results showing very good cycle performance even though the under-layering film was Cu which showed unfavorable cycle performance. With this result we could prove that the contact between substrate carbon and covering Cu was not the reason of poor cycle performance. Mr. Yoshida was very persistent for making sure the obtained results. Finally he obtained CV with four-layered films of Cu/Ag/Cu/Ag, the film thickness being 200Å for each. The results are shown in Figure 33. Even though the total film thickness is 800 Å, the cycle performance is far better than that of Cu single layer deposited sample. Summarizing the results we can conclude that as far as the top layer is Ag the cycle performance is very good, while as far as the top layer is Cu the cycle performance is poor irrespective of the kind of under layered metal. How about the ESI on the metal film? We can surely conclude that the SEI on a Ag film is very favorable for delivering good cycle performance. In contrast, the SEI on a Cu film is unfavorable for delivering good cycle performance, and these results indicate that the SEI formed on a metal surface is strongly dependent on the kind of metal. Without any investigation on the chemistry of the SEI we can get sound conclusion for the cycle performance of carbon sample covered with metal films, which is very important for the practical anode of Li-ion battery.

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[5]

[6] [7] [8]

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[9]

[10]

[11]

[12]

[13]

M. Inagaki, “Carbon Families” (Japanese), Agne-shofu, Inc., Tokyo (2001) p.76) (ISBN4-900508-82-9 C3508). T. Takamura and K. Kozawa, ed., “Surface Electrochemistry”, pp. 222-234, Japan Scientific Society Press, 1978, Tokyo, Japan. Dieter M. Kolb “Advances in Electrochemical Science and Engineering (Advances in Electrochemical Science and Engineering)”. Tsutomu Takamura, Hidekazu Awano, Ryoichi Takasu, Koji Sumiya, and Kyoichi Sekine. “Origin of a sharp current peak appearing at a potential slightly more positive than 0 V versus Li/Li+ on the cyclic voltammograms of carbonaceous materials”, J. Electroanal. Chem., 455, 223-227 (1998). Ryoichi Takasu, Kyoichi Sekine, and Tsutomu Takamura, “Faradaic adsorption of Li on carbon. A novel concept for the capacity of the anode of the Li-ion secondary batteries”, J. Power Sources, 81-82, 224-228 (1999).) I. M. Kolthoff and James J. Lingane, “Polarography”, Volume 1, Second Edition, Interscience Publishers, New York, London (1952)) Juergen O. Besenhard (Ed), “Handbook of Battery Materials”, Wiley-VCH. Weinheim (1999) page 367, Table 3. Sun-Chan Jeong, Ichiro Katayama, Hirokane Kawakami, Yutaka Watanabe, Hironobu Ishiyama, Nobuaki Imai, Yoshikazu Hirayama, Hiroari Miyatake, Masao Sataka, Satoru Okayasu, Hiroyuki Sugai, Shin-Ichi Ichikawa, Katsuhisa Nishio, Shinichi Mitsuoka, Takamitsu Nakanoy2, Masahito Yahagi, Takanori Hashimoto, Kazunori Takada4, Mamoru Watanabe, Tomoko Ishikawa and Akihiro Iwase, “Measurement of selfdiffusion coefficients in Li ionic conductors by using the short-lived radiotracer of 8Li”, Journal of Phase Equilibria and Diffusion, 26, Number 5 / pp. 472-476 (2005). Ryosuke Takagi，Takaharu Okubo，Kyoichi Sekine and Tsutomu Takamura, “Charge/discharge behavior of the graphitized mesophase pitch-based carbon fiber covered with palladium thin film as a lithium secondary battery anode”, Denki Kagaku (Presently “Electrochemistry”), 65, 333-334 (1997) (in Japanese). T. Takamura. K. Sumiya, Y. Nishijima, J. Suzuki, and K. Sekine, “A novel method for obtaining a high performance carbon anode for Li-ion secondary batteries”, Mat. Res. Soc. Symp. Proc., Vol. 496, 557-562 (1998). Koji Sumiya, Junji Suzuki, Ryoichi Takasu, Kyoichi Sekine, and Tsutomu Takamura “Enhancement of the electrochemical Li doping/undoping reaction rate of a graphitic material by an evaporated film of Sn, Zn, or Pb”, J. Electroanal. Chem., 462, 150-156 (1999). Tsutomu Takamura, Koji Sumiya, Junji Suzuki, Chikayoshi Yamada, and Kyoichi Sekine “Enhancement of Li doping/undoping reaction rate of carbonaceous materials by coating with an evaporated metal film”, J. Power Sources, 81-82, 368-372 (1999). Junji Suzuki, Masaomi Yoshida, yoichiro Nishijima, Kyoichi Sekine, and Tsutomu Takamura “Effect of a vacuum-deposited metal film on the CV of the Li insertion/extraction reaction at a graphitized carbon fiber electrode”, Electrochim. Acta, 47, 3881-3890 (2002).

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[14] Junji Suzuki, Masaomi Yoshida, Chieko Nakahara, Kyoichi Sekine, Masahiro Kikuchi, and Tsutomu Takamura “Li Mass Transfer through a Metallic Copper Film on a Carbon Fiber during the Electrochemical Insertion/Extraction Reaction”, Electrochem. SolidState Letters, 4, A1-A4 (2001). [15] N. Boes and H. Züchner “Determination of hydrogen diffusion coefficient in metal hydride electrode by cyclic voltammetry”, J. Less-Common Met. 49, 223–240 (1976). [16] Junji Suzuki, Masaomi Yoshida, Chieko Nakahara, Kyoichi Sekine, Masahiro Kikuchi, and Tsutomu Takamura “Li Mass Transfer through a Metallic Copper Film on a Carbon Fiber during the Electrochemical Insertion/Extraction Reaction”, Electrochem. SolidState Letters, 4, A1-A4 (2001). [17] Z. Xiong, S. Shi, C. Ouyang, M. Lei, L. Hu, Y. Ji, Z. Wang, L. Chen “Ab initio investigation of the surface properties of Cu(111) and Li diffusion in Cu thin film”, Physics Letters A, 337 (3), 247-255, (2005). [18] Hui Yang, Hyun Joo Bang, and Jai Prakash, “Evaluation of electrochemical interface area and lithium diffusion coefficient for a composite graphite anode”, J. Electrochem. Soc., 151, A1247-A1250 (2004). [19] Ryosuke Takagi, Miyoko Yashiro, Kyoichi Sekine, and Tsutomu Takamura, “Factors affecting the lithium transport rate in carbon being determined by potential step method”, Denkikagaku (presently Electrochemistry), 65, 420-422 (1997). [20] Hiroshi Kataoka, Yuria Saito, Osamu Omae, Junji Suzuki, Kyoichi Sekine, Toshifumi Kawamura, and Tsutomu Takamura “Lithium Storage Mechanism of Disordered Mesophase Carbon Fibers Studied by 7Li-Nuclear Magnetic Resonance”, Electrochem. Solid-State Letters, 5, A10-A13 (2002). [21] F. Chevallier, M. Letellier, M. Morcrette, J.-M. Tarascon, E. Frackowiak, J.-N. Rouzaud, and F. Béguin, “In Situ 7Li-Nuclear Magnetic Resonance Observation of Reversible Lithium Insertion into Disordered Carbons”, Electrochem. Solid-State Letters., 6, A225-A228 (2003). [22] Yuria Saito, Hiroshi Kataoka, Kazuyuki Nakai,Junji Suzuki, Kyoichi Sekine, and Tsutomu Takamura, “Determination of Diffusion Rate and Accommodation State of Li in Mesophase Carbon for Anode Materials by NMR Spectroscopy”, J. Phys. Chem. B, 108(13), 4008-4012 (2004). [23] Juergen O. Besenhard (Ed), “Handbook of Battery Materials”, Wiley-VCH, Weinheim, (ISBN 3-527-29469-4), (1999), pp.390-392. [24] O. Omae, J. Suzuki, T. Katsuta, K. Yamaguchi, F. Kikuchi, K. Sekine, T. Kawamura, and T. Takamura, “Influence of surface treatment on the Li doping/undoping reaction at a mesophase low temperature carbon fiber”, Solid State Ionics, 152, 105-110, (2002). [25] Juergen O. Besenhard (Ed), “Handbook of Battery Materials”, Wiley-VCH, Weinheim,(1999), pp.396-398.(ISBN 3-527-29469-4). [26] Morihiro Saito, Koji Sumiya, Kyoichi Sekine, and Tsutomu Takamura, “Attaining a Long Cycle Life of Li Charge/Discharge for Less Graphitized Carbon by Forming a C/C Composite”, Electrochemistry, 67, 957-959 (1999). [27] Morihiro Saito, Keita Yamaguchi, Kyoichi Sekine, and Tsutomu Takamura, “On the Improvement of Li Charge/Discharge Cycleability of Carbon Fibers by Making a C/C Composite with Thermosetting Resins”, J. Solid State Ionics, 135, 199 (2000). [28] Keita Yamaguchi, Junji Suzuki, Morihiro Saito, Kyoichi Sekine and Tsutomu Takamura, “Stable Charge/discharge of Li at a Graphitized Carbon Fiber Electrode in a

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[30]

[31]

[32]

Pure PC Electrolyte and the Initial Charging Loss”, J. Power Sources, 97-98, 159-164 (2001). R. Kostecki, T. Tran, X. Song, K. Kinoshita, and F. McLarnon, “Raman Spectroscopy and Electron Microscopy of Heat-Treated Petroleum Cokes for Lithium-Intercalation Electrodes” J. Electrochem. Soc., 144, 3111-3117(1997). Tsutomu Takamura, Koji Endo, Lijun Fu, Yuping Wu, Kyeong Jik Lee, and Takatoshi Matsumoto, “Identification of Nano-sized Holes by TEM in the Graphene Layer of Graphite and the High rate Discharge Capability of Li-ion Battery Anodes”, Electrochimica Acta, 53, 1055-1061 (2007). E. Peled, C. Menachem, D. Bar-Tow, and A. Melman, “Improved Graphite Anode for Lithium-Ion Batteries Chemically Bonded Solid Electrolyte Interface and Nanochannel Formation”, J. Electrochem. Soc., 143, L4-L7 (1996). E. Peled, “The Electrochemical Behavior of Alkali and Alkaline Earth Metals in Nonaqueous Battery Systems—The Solid Electrolyte Interphase Model”, J. Electrochem. Soc., 126, 2047-2051 (1979). E. Peled, “The role of SEI in lithium and lithium-ion batteries”, in Daniel H. Doughty, Brijesh Vyas, Tsutomu Takamura, James R. Huff, (Editors), “Materials for Electrochemical Energy Storage and Conversion--Batteries, Capacitors and Fuel Cells”, Symposium Proceedings, Vol. 393, Material Research Society, (1995) pp.209-221.

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[33]

Tsutomu Takamura

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In: Graphene and Graphite Materials Editor: H.E. Chan, pp. 95-112

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Chapter 3

MOLECULE-SURFACE BINDING ENERGIES FROM MOLECULAR MECHANICS: NUCLEOBASES ON GRAPHENE Thomas R. Rybolt1 and Christina E. Wells Department of Chemistry, University of Tennessee at Chattanooga, Chattanooga, TN 37403, USA

Abstract

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While Molecular Mechanics provides no electronic details, it can be used for estimations of selected molecular properties. Augmented MM2 parameters with no modification have been found to provide useful estimates for the interaction energy of various organic molecules with model graphene surfaces and these prior results are reviewed. The MM2 binding energies of the five DNA/RNA nucleobases on graphene are determined and compared to reported quantum mechanical calculations. The speed of molecular mechanical computations and its demonstrated correlation with experimental binding energies for carbon surfaces justify its use in selected situations. Molecule-graphitic carbon binding energies (E*) reported from thermal programmed desorption (TPD) and gas-solid chromatography (GSC) experiments are compared to calculated binding energy values (Ecal*). Experimental binding energies from GSC are for isolated molecules in the Henry’s law region of adsorption, while binding energies from TPD are for molecules at monolayer coverage. A comparison of the energetic differences between isolated molecules and monolayer coverage shows that monolayer coverage calculations must include adsorbate molecule-molecule interactions. For a number of applications, MM2 molecular mechanics calculations have been shown to provide Ecal* estimates that are in good agreement with GSC and TPD experimental E* binding energies. For the nucleobase calculations, the model graphene surface used consisted of 702 interconnected benzene rings and 1,510 carbon atoms. Graphitic surfaces were constructed by stacking these graphene layers to, for example, create a Bernal graphite with every other layer aligned. The nucleobases are each treated as an isolated molecule from the gas phase adsorbed on a graphene surface. The nucleobase binding energies for a single graphene layer using MM2 parameters were found to be 0.704, 0.639, 0.579, 0.579, and 0.509 eV for guanine, adenine, thymine, cytosine, and uracil, respectively. Following the procedure of others, the nucleobase molecules each have an attached methyl group in the place where the nucleobase 1

E-mail address: [email protected] (Corresponding author: T.R. Rybolt).

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Thomas R. Rybolt and Christina E. Wells would join the sugar ring to form the corresponding nucleoside. This methyl group contributes about 0.06 eV to the overall attractive energy.

Keywords: gas-solid interaction energy, molecular mechanics, binding energy, adsorption energy, graphene, carbon surfaces, nucleobases, guanine, adenine, thymine, cytosine, uracil

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Introduction Molecular mechanics force fields [1-3] are routinely used to determine structural and energetic properties of isolated molecules [4,5] and also have been used to estimate moleculesurface binding energies, on a variety of carbon surfaces [6-9]. Dispersion or van der Waals (vdW) forces dominate the adsorption of neutral molecules on a carbon surface, and in prior work we have shown that existing MM2 parameters are well suited to find calculated molecular binding energies for porous [6], rough [7], and smooth [8, 9] carbon surfaces. Calculated, Ecal*, and experimental, E*, binding energies were found to be in close agreement in these earlier studies. The interactions of molecules with graphene and graphitic surfaces have been investigated in various studies [10-14] including applications such as hydrogen storage [15, 16]. Interactions among adsorbed molecules and between adsorbate and surface are important in self-assembly systems, air and water purification, chemical warfare agent protection, energy gas storage, odorant removal, and the possible use of graphene or carbon nanotubes for electronic-nose (chemical sensor) devices [17-19]. One of the interesting places where material science can interface with biological systems is on the surface of carbonaceous materials. There have been a variety of studies using quantum mechanical and molecular mechanical techniques or experimental methods in idealized gas phase or in solvent to ascertain surface binding energies of the five DNA/RNA nucleobases or (Watson-Crick) nucleobase pairs [20-28]. There have been nucleobasegraphite imaging studies using Atomic Force Microscopy (AFM) and Scanning Tunnel Microscopy (STM) [29]. In this work we wish to use the MM2 and MM3 parameter sets to generate nucleobase binding energy, Eb, values and compare to the results of Gowtham et al. [20]. Prior to the current analysis to find Eb,, it will be helpful to examine our previous studies that utilized a similar approach and to consider the effectiveness of this earlier work in determining binding energies. We wish to illustrate the basis for considering that molecular mechanics and specifically MM2 parameter calculations can provide good estimates of molecular binding energies for both low coverage and monolayer coverage applications on carbon surfaces. Comparisons are made of calculated (Ecal*) and experimental (E*) binding energy values. In prior work, graphene layers were used to create models representing porous surfaces, rough surfaces, and smooth surfaces [6-9]. The porous and rough surface models were applied to low coverage, Henry’s law adsorption experiments. The smooth surface models were used for both low coverage and monolayer coverage data. The use of each of these models to determine the calculated molecule-surface binding energy, Ecal*, is discussed below. Experimental adsorption binding energies, E*, at low coverage were determined by

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the temperature variation of the second gas-solid virial coefficients, B2s, determined from gassolid chromatography (GSC) [9]. B2s = (tF1/m) where m is the mass of powder in a packed column, t is the corrected retention time, and Fl is the flow rate corrected for pressure and temperature changes across the column [30]. The retention time is given by t = ts- tm, where ts is the sample measured retention time and tm is a low interacting marker gas (such as neon) measured retention time and further t must be extrapolated to the limit of zero coverage based on varying sample size. Experimental desorption binding energies, E*, at monolayer coverage were taken from published values determined by thermal programmed desorption (TPD) [31, 32].

Porous-Low Coverage

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Molecular mechanics calculations were used to determine binding energies for a series of 9 alkanes and haloalkanes using a nanoporous parallel plate model to represent Carbosieve SIII [6]. Carbosieve S-III (Supelco), is a carbon powder with uniform, predominately 0.55 nm, slit width pores and a N2 BET surface area of 995 m2/g. MM2 and MM3 molecular mechanics were used to determine Ecal*, for each of the nine molecules on flat and nanoporous model surfaces. The nanoporous model was based on two sets of three graphene layers (127 benzene rings per layer) separated by an internuclei separation corresponding to a slit width pore opening of 0.50nm. The MM2 parameters gave better results than MM3 and the porous model was clearly superior to the flat model [6]. The calculated pore diameter was selected by optimizing the r2 value for linear regression of E* versus Ecal* for a series of different pore widths. The result agreed well with size exclusion data and value from N2 pore analysis giving the Horvath-Kawazoe [33] differential pore volume plot maximum at 0.55 nm [6].

Rough Surface-Low Coverage In another prior study [7], a rough surface model was created to calculate binding energies for 16 molecules (alkanes, haloalkanes, and ethers) on Carbopack B (Supelco, N2 BET area of 90 to 100m2/g). Three parallel graphene layers were used with 127 rings per layer. Two additional nanostructures were placed on the top graphene layer. As these nanostructures were brought together, it represented increasing surface roughness. Although the actual surface is not the same physical shape as the model surface, the model led to calculated energies quite similar to the experimental binding energies [7]. E* can implicitly incorporate information about more complex gas-solid adsorption energy potentials and surface structures. MM2 parameters were used and the binding energy regression for the best rough surface model gave E* = 1.018 Ecal* and r2=0.964. A later study [9] with 18 linear, branched and cyclic alkanes gave a linear regression of E* = 0.9848 Ecal* and r2 = 0.976. While it was necessary to optimize the surface structure, all the experimental and calculated values based on this structure agreed within a few percent.

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Smooth Surface – Low Coverage Experimental binding energy values for 10 molecules (alkanes and halogenated alkanes) on Carbopack C (Supelco, N2 BET area of 10m2/g), a low surface area graphitic carbon, were determined using gas-solid chromatography at varied temperatures, T [34]. The experimental procedure is described in detail elsewhere [30]. These GSC experiments were used to determine second gas-solid virial coefficient values, B2s. B2s is given by an integral that depends on the gas-solid interaction potential, and this potential depends on the gas-solid interaction energy, E*. Plots of the natural logarithm of B2s versus 1/T for each adsorbate molecule yield slopes which are equivalent to E* values [30, 34]. A larger E* indicates a deeper potential well and stronger molecule-surface attraction. Calculated binding energies, Ecal*, were determined for a three layer model with 127 rings per layer and MM2 parameters. Each of the 10 molecules were placed close to and far from the surface and the difference of these values were used to find Ecal* values. Linear regression gave E* = 1.115 Ecal* with r2 = 0.927 [8]. In a similar manner, benzene, toluene, and 9 substituted benzenes with 2, 3 or 4 attached methyl groups in different positions were placed on a model graphite surface, Ecal* was found, and Ecal* and E* compared [8]. Linear regression gave E* = 0.934 Ecal* with r2 = 0.981. E* values were based on GSC Henry’s law constants determined by Kalashnikov et al. [35] and plots of the logarithm of the Henry’s law constants versus 1/T [8]. In the smooth surface cases discussed above, note that the slopes for E* versus Ecal* were slightly above and below one, but both plots scale in such a way that Ecal* remains directly proportional to E* and so an intercept at zero works well.

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Monolayer Coverage of Organic Molecules Thermal programmed desorption (TPD) has been used to determine monolayer coverage binding energies for polyaromatic hydrocarbons (PAH) [31] and for a diverse set of 14 organic molecules including: polyaromatic hydrocarbons, alcohols, benzene, substituted benzenes, methane, chloroalkanes, N,N-dimethylformamide, and C60 Buckyball on a sample of highly oriented pyrolytic graphite (HOPG) [32]. The original published data included estimates of experimental uncertainty for each compound and when averaged for the 14 organics equaled +/- 8.9%. The TPD data provides an interesting comparison to the GSC data since it becomes necessary to include adsorbate-adsorbate interactions as well as adsorbate-surface interactions. It is also possible to explore the role of hydrogen bonding among surface molecules. The thermal desorption spectra at monolayer coverage were converted to binding energy values, E*, in this work by Zacharia et al. [31] and Ulbricht et al. [32]. With a surface model that includes adsorbate-adsorbate interactions (presented in the theory section) and our MM2 mechanics based calculations, an improved correlation between E* and Ecal* [8] relative to that previously reported for the TPD data was obtained [32]. The graphitic surface was represented by three graphene layers with 702 benzene rings and 1,510 carbon atoms per layer. An isolated molecule and a 1+6 simulation with six nearest neighbors around one molecule were made. A vdW default cutoff value of 0.9nm and MM2 parameters were used.

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Six identical molecules with the same surface orientation were placed around a center molecule to achieve a six nearest neighbors packing arrangement. If hydrogen bonding between molecules was possible such as for methanol and ethanol, they were oriented and arranged so hydrogen bonding between the O–H and O on a neighboring molecule was allowed. The nearest atoms of adjacent molecules were placed closer than the optimal distance. When molecular mechanics energy optimization was run, the molecules moved apart to the proper distance. After placing the seven molecules in the described arrangement and 0.2 to 0.25 nm above the top layer of the surface, MM2 mechanics was run to obtain the value for Enear. Then the center molecule was moved to a distance well away from the surface and other molecules. The six remaining molecules were locked in place so that there could be no adjustments between these six molecules after the center molecule was removed. The center molecule that was moved remained unlocked. Mechanics was run to obtain the value for Efar. As discussed in the Theory Section, binding energies for one isolated molecule (∆E1 or Ecal*1 ) and one molecule removed from a group of 6 nearest neighbors (∆E1+6 or Ecal*1+6 ) were used to find the monolayer binding energy per molecule( ∆En or Ecal*ML). Calculated values of Ecal*1, Ecal*1+6, and Ecal*ML are shown in Table 1 along with the reported experimental TPD binding energies, E*. A plot of E* versus Ecal*ML for the 14 molecules used gave E* = 1.119 Ecal* and r2 = 0.967 [8]. Thus our simple model using the average of 1 and 1+6 molecules as described in the Theory section seems to represent the actual monolayer binding energy.

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Table 1. Experimental average binding energies, E*avg, and calculated values for isolated molecule, Ecal* 1, molecule removed from 6 neighbors, Ecal* 1+6, and monolayer model, Ecal*ML Molecule 1,1-Dichloroethane Benzene Buckyball Coronene Ethanol Ethylbenzene Methane Methanol N,N-Dimethylformamide Naphthalene o-Dichlorobenzene Ovalene Toluene Trichloromethane

E*avg (eV) 0.53 0.50 1.69 1.41 0.52 0.82 0.17 0.50 0.55 0.85 0.72 2.18 0.70 0.56

Ecal*1 (eV) 0.33 0.41 0.69 1.31 0.26 0.49 0.15 0.21 0.37 0.62 0.56 1.70 0.50 0.35

Ecal* 1+6 (eV) 0.61 0.63 2.04 1.63 0.69 0.78 0.28 0.63 0.73 0.90 0.86 2.03 0.74 0.56

Ecal*ML (eV) 0.47 0.52 1.36 1.47 0.48 0.64 0.21 0.42 0.55 0.76 0.71 1.86 0.62 0.45

Ulbricht et al.’s [32] experimental error estimates vary from 6 to 17% with the average about 8.9% as reported for E* 2006 TPD data. TPD is a difficult experiment to achieve exact values for E* since desorption peaks are broad. The slope of 1.12 indicates the calculated values on average are lower than experimental ones and must be multiplied by a factor above

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one to increase them, but with the intercept at the origin (0,0) it indicates that correlation scales well as E* and Ecal* values are decreased. Their TPD E* values span a range of from 1918 K up to 25257 K (0.17 up to 2.18 eV)–more than a factor of 10 difference. Given the success of the MM2 mechanics calculations not only for pore and rough surface where positions were adjusted to maximum quality of fit, but also for the flat, smooth surface composed of graphene layers; it is anticipated that similar molecular mechanics determination of the nucleobase binding energies, Eb, should be fairly reliable. Therefore, it will be of interest to compare the reported results from prior quantum methods [20] to the molecular mechanics results obtained in this work.

Theory Binding energy calculations involve placing a molecule or molecules on a model surface in an adsorbed state and calculating the energy of this system (Enear) and also placing a molecule or molecules at a significant distance from the surface and calculating the energy of this system, (Efar). The change in energy, ∆E, is then found from

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∆E = Enear - Efar

(1)

Considering the proper final and initial states, ∆E(adsorption) = Enear – Efar and ∆E(desorption) = Efar – Enear. To avoid having to distinguish between adsorption and desoprtion, Eq. (1) is used for all ∆E calculations; however, these binding energies are always reported as positive values to indicate how strongly a molecule is attracted to the surface and the energy that would be required to remove it from the surface. E* is used to represent experimental values of binding energy and Ecal* is used to represent calculated values. In calculations of energy change due to adsorption, the binding energy for a single gas phase molecule may be further expressed as ∆E1 = Enear(1g-s) - Efar(1g, s)

(2)

where Efar(1g, s) represents the total steric energy of one molecule and a model surface at sufficient separation so there is no measurable interaction between them. Enear (1g-s) represents the energy of this same system where the gas molecule is adsorbed on the surface at a selected position and orientation to give appropriate interaction [8]. To obtain an energy change for n molecules desorbed from the surface, consider a surface that is covered with n molecules, where each molecule has a pairwise attraction to m nearest neighbors, and that n is much greater than m. Let Egs be the gas molecule-surface binding energy, and Egg be the molecule-molecule binding energy for a pair of gas molecules on the surface. Under conditions of monolayer (ML) coverage if all the molecules are desorbed into the gas phase, then the total binding energy of the n molecules on the surface is ∆En(for n molecules) = (n) Egs + (n m /2 ) Egg.

(3)

where the gas molecule-surface energy change is nEgs, and the number of gas-gas interactions is (n m /2). Division by 2 is included since Egg involves a pair of molecules and otherwise Graphene and Graphite Materials, Nova Science Publishers, Incorporated, 2009. ProQuest Ebook Central,

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would be counted twice. The surface is completely covered, and no special effects due to ML edges are included. To place Eq.(3) on a per molecule basis, it is necessary to divide the above by n which gives ∆En (per molecule) = Egs + (m/2) Egg

(4)

Although calculated per molecule, it is common to expresses the above in units of (kJ/mol), (kcal/mol), (eV),or (K). E* may be expressed in units of Kelvin because of division of the binding energy by the Boltzmann constant which is based on the conversion factor of E*(K) = {503.22 K/(kcal/mol)} {E*(kcal/mol)}. For comparison of energy units, a C-H covalent bond is about 100 kcal/mol and 100 kcal/mol is the same as 418.4 kJ/mol, 4.336 eV or 50,322 K. To avoid having to model n number of molecules, our simplified surface ML model [8] uses only m+1 molecules, removes one molecule that has m nearest neighbors from the surface, and then, as shown below, is adjusted to give the value obtained for ∆E in Eq. (4). The change in energy to remove the central molecule from a group of 1+m molecules on the surface, ∆E1+m , is the sum of the direct gas-surface interaction binding energy and the breaking of m gas-gas interactions and is given by ∆E1+m = Egs + m Egg

(5)

The energy to remove a single isolated molecule with no other molecules on the surface may be written as ∆E1 or Egs where ∆E1 = Egs. To obtain a useful method to find ∆En, solve Eq. (5) for Egg Egg = ( ∆E1+m - Egs)/m

(6)

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And then substitute the above into Eq. (4) which gives ∆En (per molecule) = Egs + (m/2) { ( ∆E1+m - Egs)/m}

(7)

Finally, substitute ∆E1 for Egs to give ∆En (per molecule) = ∆E1 + ( ∆E1+m - ∆E1 )/2

(8)

This result shows that ∆En(per molecule) can be determined from a combination of two simpler models: one isolated molecule on the surface to give ∆E1 and 1+m molecules on the surface to give ∆E1+m. If the packing arrangement on the surface is based on six nearest neighbors then m=6. In this case, the simple ML model system requires only 7 molecules be placed on the surface[8]. In this work the symbols Ecal*1, Ecal*1+6, Ecal*ML are used to represent the calculated energies where Ecal*1=∆E1, Ecal*1+6=∆E1+6, and Ecal*ML=∆En. A comparison of the experimental E* and calculated Ecal* is based on a simple linear regression and ideally gives E* = a + b Ecal* with a=0, b=1, and r2=1.

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Analysis and Results Computational calculations were performed using CAChe (Computer Aided Chemistry) computer software (Fujitsu, Version 6.1.12.33) for the five nucleobases (guanine, adenine, thymine, cytosine, and uracil). The following six sets of experiments were performed on each nucleobase: MM2 and MM3 molecular mechanics for an isolated nucleobase on a one layer graphene surface, two layer graphite surface, and three layer graphite surface (3 MM2 and 3 MM3 sets of experiments per nucleobase). Each experiment set consisted of an Enear and Efar calculation. Following the procedure of Gowtham et al. [20], each nucleobase was terminated with a methyl group at the carbon atom that would normally be the attachment point in the sugar ring in the corresponding nucleoside. Each of these nucleobases and surface was optimized in free space using the appropriate molecular mechanics experiment, either MM2 or MM3. For collections of multiple layers of graphene, the layers were arranged in the form of Bernal graphite with the first and third layer directly aligned and the middle layer offset by half a benzene ring. The structure was optimized using MM2 parameters and the results give a layer separation of 0.344 nm in good agreement with the accepted value of 0.34 nm [36]. The optimized surface structure was then locked so there were no allowed rearrangements of the surface atoms during any of the calculations. Surface rearrangement is not necessarily a problem for large multi-layered surfaces, but a single graphene layer which is not locked may curve toward an adjacent adsorbate molecule. The surface used consisted of 702 benzene rings per layer. Specifically this surface has 624 aromatic rings and 78 non-aromatic rings around the edge and 1510 carbon atoms in total. In prior work molecules were placed on the surface with an orientation to maximize the more polarizable atoms. For example, CHCl3 would be placed with all three chlorines oriented toward the surface and a toluene molecule would be placed with its benzene ring parallel to the surface. We are intentionally trying to see how well E* and Ecal* values compare with just one molecule-surface orientation and one placement on the surface. This approach seeks to keep the calculation fairly simple so a large number of molecules could be examined with the same approach. In the current nucleobase work, the molecule orientation is based on an essentially flat molecule but each placed on the surface as done by Gowtham et al. [20] and indicated in Figure 1. Prior to utilizing any adsorbate molecule on the surface, the isolated molecule was placed in an expected conformation and then the geometry optimized using MM2 parameters and standard methods (calculation continued until energy difference less than 0.001 kcal/mol). For the Enear calculation an isolated nucleobase was manually placed approximately 0.20 – 0.25 nm above the center benzene ring of the top layer of the surface according to the orientation displayed in Gowtham et al. [20] and shown in Figure 1. The nucleobase was placed closer than the optimal distance above the surface so that when molecular mechanics was performed, the nucleobase would be pushed out to the optimal distance (0.32 – 0.36 nm).

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Figure 1. Placement of nucleobases on graphene surface for molecular mechanics calculations.

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Table 2. Calculated binding energy Eb (eV) of DNA/RNA nucleobases using MM2 and MM3 molecular mechanics Nucleobase

Formula

Method

Eb 1 Layer

Eb 2 Layer

Eb 3 Layer

Guanine

C6H7N5O

MM2

0.704

0.763

0.756

Adenine

C6H7N5

MM2

0.639

0.698

0.687

Thymine

C6H8N2O2

MM2

0.579

0.600

0.626

Cytosine

C5H7N3O

MM2

0.579

0.619

0.622

Uracil

C5H6N2O2

MM2

0.509

0.550

0.562

Guanine

C6H7N5O

MM3

0.728

0.784

0.787

Adenine

C6H7N5

MM3

0.655

0.700

0.708

Thymine

C6H8N2O2

MM3

0.604

0.650

0.655

Cytosine

C5H7N3O

MM3

0.570

0.615

0.610

Uracil

C5H6N2O2

MM3

0.543

0.581

0.586

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After the Enear calculation, the nucleobase was moved 5.0 nm away from the surface to calculate Efar and molecular mechanics run. The distance of 5.0 nm was used to ensure that no interactions occurred between the nucleobase and the surface in order to calculate Efar. Table 2 gives the results for the MM2 and MM3 calculations on 1, 2 and 3 layers of graphene. A column plot (see Figure 2) of the binding energy (eV) of the five nucleobases on 1, 2, and 3 layer surfaces was generated using data in Table 2. This figure illustrates the change in energy as a layer is added to the surface.

Figure 2. Binding energy of each nucleobase for 1, 2, and 3 graphene layers with error bars representing reproducibility error of repeated calculations.

Reproducibility error bars were calculated for Figure 2 by placing the guanine and adenine independently on the 1 and 2 layer surface four times for repeated calculations of binding energy for the MM2 molecular mechanics calculations. The one layer results for guanine were 0.704, 0.708, 0.692, and 0.712 eV and a standard deviation (SD) of 0.009 eV. The two layer results for guanine were 0.763, 0.769, 0.770, and 0.764 eV and a SD of 0.004 eV. For adenine the one layer results were 0.639, 0.652, 0.653, and 0.653 eV and a SD of 0.007 eV. The two layer results for adenine were 0.698, 0.682, 0.698, and 0.698 eV and a SD of 0.008 eV. The average was taken of the standard deviations and this resulted in the value of the error bars found in Figure 2 of 0.007 eV. Table 3 contains the values for the one layer graphene surface for our calculations and the results obtained by Gowtham et al. using the second-order Møller-Plesset perturbation theory (MP2) and the plane-wave pseudopotential approach within the local density approximation (LDA) of density functional theory (DFT) [20].

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Table 3. Calculated binding energy Eb (eV) of DNA/RNA nucleobase on single graphene layer for molecular mechanics MM2 and MM3, and ab initio Hartree-Fock, second order Møller-Plesset perturbation theory (MP2) and Local density approximation (LDA) of density functional theory (DFT) Nucleobase Guanine Adenine Thymine Cytosine Uracil

LDA (eV) 0.61 0.49 0.49 0.49 0.44

MM2 (eV) 0.704 0.639 0.579 0.579 0.509

MM3 (eV) 0.728 0.655 0.604 0.570 0.543

MP2 (eV) 1.07 0.94 0.83 0.80 0.74

α (e2 ao2 Eh-1) 131.2 123.7 111.4 108.5 97.6

Plots of nucleobase binding energy, Eb(eV), versus polarizability, α, on one layer graphene surface for our MM2 and MM3 calculations and the prior MP2 and LDA methods [20] were generated and resulted in the following equations with the intercept set to zero: MP2:

Eb = 0.007673α

r2 = 0.9143

MM3:

Eb = 0.005417α

r2 = 0.9506

MM2:

Eb = 0.005261α

r2 = 0.9784

LDA:

Eb = 0.004399α

r2 = 0.7307

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and with the intercept allowed to vary from zero to give best fit: MP2:

Eb = 0.009681α – 0.2322

r2 = 0.9558

MM3:

Eb = 0.005437α – 0.0023

r2 = 0.9506

MM2:

Eb = 0.005508α – 0.0285

r2 = 0.9804

LDA:

Eb = 0.004103α + 0.0343

r2 = 0.7346

Plots of Eb versus α where the intercept is zero are shown in Figure 3. As mentioned previously, the nucleobases in our experiment and the Gowtham et al. [20] experiment were terminated with a methyl group at the carbon atom that would normally be part of the sugar ring. The methyl group may not allow the nucleobase to be positioned as close to the surface as would be possible if the methyl group was instead replaced with a hydrogen atom. To determine any difference in binding energy this methyl group on cytosine was removed and replaced with a hydrogen atom. MM2 molecular mechanics calculations were then performed for cytosine on 1, 2, and 3 layers. The binding energies for the cytosine with the methyl group on 1, 2, and 3 layers were 0.579, 0.619, and 0.622 eV respectively whereas the binding energies for the cytosine with a hydrogen atom in place of the methyl group gave 0.517, 0.553, and 0.554 eV on 1, 2, and 3 layers, respectively. So the inclusion of the methyl, slightly increases the overall binding energy of the molecule.

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Figure 3. Plots of nucleobase binding energy, Eb (eV), versus polarizability, α, on one layer graphene surface for our current MM2 and MM3 calculations and the second-order Møller-Plesset perturbation (MP2) and local density approximation (LDA) of density functional theory calculations done previously [20]. Lines from top to bottom are MP2 [20], MM3 [this work], MM2 [this work], and LDA [20] and the correlations were: Eb (MP2) = 0.007673α with r2 = 0.914, Eb (MM3) = 0.005417α with r2 = 0.951, Eb (MM2) = 0.005261α with r2 = 0.978, and Eb (LDA) = 0.004399α with r2 = 0.731.

Discussion Our results for the five DNA/RNA nucleobases coincide with the binding energy trend calculated by Gowtham et al. [20], Sowerby et al. [23] (adsorption isotherms on the surface of crystalline graphite in water) and Das et al. [28] (single-walled nanotubes using ab-initio Hartree-Fock method and force field calculations). All these studies gave an Eb trend of guanine > adenine > thymine > cytosine > uracil. Figure 3 that shows the binding energy vs. polarizability on a single graphene layer illustrates that MM2 and MM3 values fall above the LDA and below the MP2 values of Gowtham et al. [20]. Our MM2 molecular mechanics gave the best and highest r2 value while the Eb (LDA) resulted in the lowest r2 value. Gowtham et al. [20] suggested that since vdW interactions are the primary attractive force that Eb should be proportional to the polarizability values [20] given in Table 3. The importance of polarizability has been demonstrated previously for gas-solid interactions since the retention times for 152 compounds have been correlated based on properties that included the polarizability [37] and polarizability has been used in predicting naphthalene, phenanthrene, and anthracene adsorption on graphite [38]. It is interesting to note that if the intercept is allowed to be nonzero, then the best fit for MP2 gives an intercept of -0.2322 while MM3 is -0.0024, MM2 is -0.0285 and LDA is 0.0343. Therefore the MP2 values do not scale as well as the other three toward zero.

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However, requiring a zero intercept gives r2 values of 0.731, 0.914, 0.951, and 0.978 for LDA, MP2, MM3, and MM2, respectively. MM2 scales best with polarizability in this case and gives the r2 value closest to 1. LDA did not distinguish between adenine, thymine, and cytosine Eb values (see Table 3). According to Zhu et al [21], the binding energies of guanine and adenine were 0.327 eV and 0.333 eV respectively when they adsorbed the two nucleobases onto rough pyrolytic graphite electrodes in solution. They also commented that both had a moderate to strong adsorption on the rough pyrolytic graphite electrode [21]. Sowerby et al. [22] used a van’t Hoff plot to obtain a value of 0.207 eV for the adsorption enthalpy of adenine. They performed frontal analysis using water as the mobile phase on the surface of graphite crystals [22]. Of course, solution and gas phase binding energies will vary due to solvent effects with the adsorbate and with the surface and one might expect binding energies to be reduced in solution. Das et al. reported that by using ab-initio Hartree Fock method and force field calculations for the DNA nucleobases with single-walled carbon nanotubes (CNT) the binding energies for guanine, adenine, thymine, and cytosine were 0.58 eV, 0.54 eV, 0.49 eV, and 0.46 eV respectively [28]. Although these results are similar to the LDA based binding energies, CNT binding energies are known to be less than those for graphene due to the surface curvature of the CNT. As a rough comparison of the per atom binding energies, the hydrogen atoms were ignored and the number of carbons and the number of nitrogen and oxygen atoms (N and O grouped together) were counted for each molecule for the one layer structure. These values were used along with the MM2 binding energies to find that the average contribution per C atom is 58meV and per N or O atom 60meV. The experimental binding energy from GSC as described previously for benzene on graphite was 4474 K or 0.386 eV and this gives (0.386 eV/6 C atoms) or about 64 meV. If the E* was about 8% lower as typical in comparing 1 and 3 layers (see Table 2),then this value would drop to about 59meV so our Eb value per C atom seems reasonable. Zacharia et al. [31] used Allinger’s MM3 C-C and C-H vdW parameters but adjusted the parameters to give best fit for binding energies for benzene and polyaromatic hydrocarbons (PAH): naphthalene, coronene, and ovalene. They used these results to get estimates of exfoliation energy for graphene layers. This approximation may have been successful because the ratios Ecal*1+6/Ecal*1 are quite similar for these four molecules with an average of 1.38 and thus adsorbate-adsorbate interactions could be ignored. As reported by Zacharia [31], theoretical estimates vary for ab initio or semiempirical methods from 8 meV/atom up to 170 meV/atom due to difficulty of calculating longer range dispersion forces. In their own work [31] they found a graphite binding energy per carbon atom in PAH of 52 meV and estimated a cleavage energy of graphite of 61meV/atom. Prior DFT calculations gave 35 meV/atom [39] but may underestimate cohesive energies attraction between layers [31]. Again our binding energy of 58meV per carbon seems reasonable. Ortmann et al [24] found that for the adsorption of adenine on graphite using density functional theory calculations, van der Waals interactions contributed the greatest in binding energy. Also, from our mechanics calculations, we found that the main interaction responsible for the binding energy between each nucleobase and the surface was van der Waals (vdW) forces. Hydrogen bonding was the second most important contributing interaction. For MM2 calculations the overall steric energy is a sum of contributions due to stretch, stretch bend, improper torsion, electrostatics, angle, dihedral, van der Waals, and hydrogen bonding. In the

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specific case of adenine on a single graphene layer, only vdW and hydrogen bonding made significant contribution to ∆E. The vdW contributed about 84% and hydrogen bonding about 16% to the energy lowering when the nucleobase and surface were adjacent instead of far apart and isolated from one another. It has been shown that weak hydrogen bonds can form between O-H and N-H hydrogens and benzene rings or other aromatic systems. [40] In prior work an experimental value for the benzene-graphite interaction of E*= 4474 K was determined and used for comparison to Ecal* values [8]. Table 4 shows the results using MM2 and MM3 molecular mechanics parameters with 1, 2, or 3 layers, and the benzene molecule placed in an atom centered, bond centered, or eclipsed configuration relative to the top surface layer. Notice in Table 4 there is relatively little difference among the three placements, however the MM2 parameters did provide a closer match between Ecal* and E* than MM3.

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Table 4. Comparison of MM2 and MM3 parameters for 1, 2, and 3 layers of graphene and for 3 different benzene surface placements for calculated binding energies, Ecal*, and percent error where E* = 4474 K Mechanics Parameter MM2 MM2 MM2 MM2 MM2 MM2 MM2 MM2 MM2

Graphene Layers 1 1 1 2 2 2 3 3 3

eclipsed C centered bond centered eclipsed C centered bond centered eclipsed C centered bond centered

4395 4460 4474 4740 4768 4784 4739 4817 4793

Percent Error 1.77 0.31 0.01 5.95 6.56 6.92 5.93 7.68 7.13

MM3 MM3 MM3 MM3 MM3 MM3 MM3 MM3 MM3

1 1 1 2 2 2 3 3 3

eclipsed C centered bond centered eclipsed C centered bond centered eclipsed C centered bond centered

4993 5036 5040 5348 5469 5407 5431 5465 5427

11.59 12.55 12.65 19.53 22.25 20.85 21.39 22.15 21.29

Surface Placement

Ecal* (K)

In other prior work [8] the vdW cutoff value was adjusted from 0.70 to 1.80nm while the number of graphene layers were varied from 1 to 8. Benzene Ecal* values were determined under these varied conditions and compared to an experimental binding energy of E*=4474 K [8]. Each graphene layer had 432 interconnected benzene rings. At the extremes 1 layer with a vdW cutoff of 0.70 nm gave Ecal*=4159 K and 8 layers with a vdW cutoff of 1.80 nm gave Ecal*=5089 K. At these extremes Ecal* values are 7.0% below and 13.7% above the benzene-graphite E* value. Thus binding energy values can be increased by including more

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layers and longer range vdW forces or decreased by reducing the cutoff distance and number of layers. However, based on multiple molecules on varied carbonaceous surfaces, the default 0.9 nm vdW cutoff and use of models based on three graphene layers to represent graphite provided good agreement between calculated and experimental binding energies [6-9]. The data in Table 2 shows that going from 1 to 3 layers increases Eb by about 8 to 10%. Based on these several prior studies it is expected that MM2 rather than MM3 parameters would give Ecal* that better agree with E*. In this work a simple approach to calculating Eb was used so that one preferred placement of the molecule on the surface was used. It is expected that the orientation would maximize the polarizability of the atoms placed on the surface. While a more complex statistical averaging of various orientations with respect to the surface would be necessary in some cases, this simple approach works for many organic molecules studied thus far and especially for ring structures that are expected to have a flat orientation to the surface plane. Our nucleobase-graphene binding energy estimates using MM2 parameters are 0.704, 0.639, 0.579, 0.579, and 0.509 eV for guanine, adenine, thymine, cytosine, and uracil, respectively. Recall that these nucleobase models include a methyl group from what would be part of the attached sugar ring in corresponding nucleosides. Without this methyl group, each nucleobase binding energy should each be roughly 0.060 eV lower. Cytosine was shown to decrease from 0.579 to 0.517 eV and the others should be rather similar.

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Conclusion The results of our earlier studies where molecule-carbon surface binding energies were calculated using augmented MM2 parameters with no modification suggest that MM2 binding energies for nucleobases on graphene should provide useful estimates of the experimental values. It was noted that the mechanics results were greater than the LDA DFT values and below the MP2 values. This result makes sense if DFT results may tend to underestimate Ecal* values and the MP2 results tend to overestimate the interaction. DFT calculations have been reported to underestimate vdW interactions [31]. In addition LDA DFT calculations were reported to underbind a system based on dispersive forces [20]. The difficulty of these noncovalent interaction calculations was indicated by the results of forty density functionals that were compared with published noncovalent interaction energies to determine which ones might be best used for this purpose [41]. Ab initio results have found density functional theory (DFT) to be not completely satisfactory for π–stacking [42-44]. MP2 calculations have been reported to overestimate the pair correlation effect and give binding energies that are too large [45]. The basis set used to model the individual molecules and their dimer cluster can dramatically affect the calculated interaction energy in what is known as the basis set superposition error (BSSE) [46]. Ab initio quantum calculations of benzene-coronene interactions were used to model benzene-graphite interactions [45]. The MP2 value was modified by a counterpoise correction for the BSSE and this correction lowers the MP2 calculation. For these benzene-coronene MP2 calculations, this correction factor was about 40% [45]. Tauer and Sherrill [42] have examined π-π interactions for benzene dimers and trimers and observed that Møller-Plesset perturbation theory (MP2) used with small basis sets tend to

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have errors that cancel each other. Small basis sets cause the binding energy computation to be too small while MP2 tends to cause the values to be too large. By combining these two effects, Tauer and Sherrill were able to achieve nonbonding benzene interaction energies within a few tenths kcal/mol of their prior complete basis set couple cluster ( CCSD(T) ) limit [42]. In general the weakness of the interactions in vdW forces presents a challenge for more exact quantum mechanical methods [47]. Molecular mechanics and quantum mechanics techniques can be combined in the QM/MM method where more time consuming QM computations are limited to smaller portion of the full system. Reactions on single wall carbon nanotubes (SWNT) have been studied with QM/MM [48]. Van der Waals and π−π interactions continue to have interesting new applications such as the synthesis by Sygula et al. of a concave hydrocarbon molecule designed to hold a C60 Buckyball by wrapping around a portion the C60 fullerene [49]. In addition to interest in the role of dispersion forces in interlayer graphene attraction and self assembly on graphene surfaces, π-stacking interactions between ligands are important in determining the crystalline structure of some metal complexes [50] and π−π interactions are important in biological applications such as insertion of aromatic structures parallel to nucleobases in DNA intercalation [42]. With no adjustment, the standard MM2 parameters for atom-carbon interactions prove to be surprisingly effective in calculations of molecule-surface binding energies. A flat graphitic surface can be well represented by three parallel graphene structures with a large number of interconnected 6 member aromatic (benzene) rings. Molecular mechanics offers the speed and simplicity to use hundreds of rings per layer and place multiple molecules on the surface. The energy differences between near and far molecule-surface separation with and without nearest neighbor adsorbates can be used to obtain estimates of adsorption or binding energy for smooth carbon surfaces for both isolated molecules and molecules adsorbed in monolayer coverage. MM2 parameters with no modification have been found to be useful to estimate binding energies for organic molecules on porous, rough, and smooth carbon surfaces and in this work for individual nucleobases on graphene. Relatively simple calculations continue to be of interest to correlate binding energies based on weaker dispersive interactions. The molecular mechanics method will not elucidate electronic details, but it does provide some useful applications. Where appropriate, there is value in having a computationally simple and rapid method to estimate gas-solid interaction energies. The same approach used in this work should provide useful estimates of CNT binding energies for isolated nucleobases and should also be useful in examining (Watson-Crick) binding pairs or monolayer coverage of nucleobases on a variety of carbon surface structures.

Acknowledgment We acknowledge the support provided by the Grote Chemistry Fund and the Wheeler Odor Research Center at the University of Tennessee at Chattanooga.

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[28] Das, A.; Sood, A.K.; Maiti, P.K.; Das, M.; Varadarajan, R.; Rao, C.N.R. (2007). Binding of nucleobases with single-walled carbon nanotubes [cond-mat.mtrl-sci]. Los Alamos National Laboratory, Preprint Archive. 1-7, arXiv:0709.3071v1. [29] Hui, O.Y.; Marcus, R.A.; Kellebring, B. J. Chem. Phys. 1994, 100, 7814-13.I. Allen, M.J.; Balooch, M.; Subbiah, S.; Tench, R.J.; Balhorn, R.; Siekhaus, W. Ultramicroscopy 1992, 42-44(Pt. B), 1049-1053. [30] Rybolt, T. R.; Thomas, H. E. In Interfacial Phenomena in Chromatography; Pefferkorn, E.; Marcel Dekker: NY, 1999; pp 1-40. [31] Zacharia, R.; Ulbricht, H.; Hertel, T. Phys. Rev. B 2004, 69, 155406, 155406/1155406/7 (DOI: 10.1103/PhysRevB.69.155406). [32] Ulbricht, H.; Zacharia, R.; Cindir, N.; Hertel, T. Carbon 2006, 44, 2931-2942. [33] Horvath, G.;Kawazoe, K. J. Chem. Eng. Jpn. 1983, 16, 470-475. [34] Rybolt, T. R.; Logan, D. L.; Milburn, M. W.; Thomas, H. E.; Waters, A. B. J. Colloid Interface Sci. 1999, 220, 148-156. [35] Kalashnikova, E. V.; Kiselev, A. V.; Petrova, R. S.; Shcherbakova, K. D.; Poshkus, D. P.; Chromatographia 1979, 12, 799-802. [36] Bondi, A. J. Phys. Chem. 1964, 68, 441-451. [37] Katritzky, A. R.; Ignatchenko, E. S.; Barbock, R. A.; Lobanov, V. S.; Karelson, M. Anal. Chem. 1994, 66, 1799-1807. [38] Vidal-Madjar, C.; Bekassy-Molnar, E. J. Phys. Chem. 1984, 88, 232-238. [39] Rydberg, H.; Jacobson, N.; Hyldgaard, P.; Simak, S. I.; Lundqvist, B. I.; Langreth, D. C. Surf. Sci. 2003, 532, 606-610. [40] Jeffrey, G. A. An Introduction to Hydrogen Bonding; Oxford Press: New York,NY, 1997; pp 92-95. [41] Zhao, Y.; Truhlar, D. G. J. Chem. Theory Comput. 2007, 3, 289. [42] Tauer, T. P.; Sherrill, C. D. J. Phys. Chem. A 2005, 109, 10475. [43] Ye, X. Y.; Li, Z. H.; Wang, W. N.; Fan, K. N.; Xu, W.; Hua, Z. Y. Chem. Phys. Lett 2004, 397, 56. [44] Johnson, E. R.; Wolkow, R. A.; DiLabio, G. A. Chem. Phys. Lett. 2004, 394, 334. [45] Ruuska, H.; Pakkanen, T. A. J. Phys. Chem. B 2001, 105, 9541-9547. [46] Chalasinski, G.; Szczesniak, M. M. Chem. Rev. 2000, 100, 4227-4252. [47] Engkvist, O.; Astrand, P.; Karlstrom, G. Chem. Rev. 2000, 100, 4087-4108. [48] Basiuk, V. A. J. Phys. Chem. B 2003, 107, 8890-8897. [49] Sygula, A.; Fronczek, F. R.; Sygula, R.; Rabideau, P. W.; Olmstead, M. M. J. Am. Chem. Soc. 2007, 129, 3842-3843. [50] Janzen, D. E.; Patel, K.; VanDerveer, D. G.; Grant, G. J. J. Chem. Crystallography 2006, 36, 83-91. Janiak, C. J. Chem. Soc. Dalton Trans. 2000, 3885-3896.

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Chapter 4

LUBRICITY OF GRAPHITE ADDITIVES IN POLYIMIDE COMPOSITES AT VARIABLE HUMIDITY Pieter Samyn1*, Gustaaf Schoukens1 and Patrick De Baets2 1

Ghent University – Department of Textiles, Technologiepark 907, B-9052 Zwijnaarde, Belgium 2 Ghent University – Department of Mechanical Construction and Production, Sint-Pietersnieuwstraat 41, B-9000 Gent, Belgium

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Abstract Polymers are known as self-lubricating materials that may function under dry sliding conditions, excluding the need of external lubricating systems. In particular, polyimides are a class of high-performance polymers with extremely good thermal and chemical resis-tance, supposed to operate under severe sliding conditions with high normal loads and sliding velocities. However, polyimides often show high coefficients of friction and high wear rates that highly depend on the environmental humidity. Graphite is known as a material with potentially lubricating properties due to its lamellar structure, and it is there-fore often added as flake-like additives into polymer composites, functioning as an internal lubricant for controlling the tribological properties. For a given composition of sintered graphite-polyimide composites, the effect of humidity on its sliding properties cannot be clearly predicted. The tribological properties of the polyimide matrix and the graphite additives seem to depend on the moisture content in an opposite way. Theoretically, graphite provides high friction under dry sliding conditions and adsorption of water molecules is needed for easy shear of the lamellar structure. On the other hand, the water molecules have detrimental effects on the sliding properties of the polyimide surface as they restrict molecular relaxation mechanisms. The friction and wear performance of unfilled and graphite-filled sintered polyimides will therefore be experimentally investigated at three humidity levels during unlubricated sliding against steel. A relationship between the sliding properties of graphite internal lubricants at high humidity versus high temperatures, normal loads and sliding velocities will be further discussed.

Keywords: graphite, lubricant, additive, polymer, tribology *E-mail address: [email protected]. (Corresponding author) Pieter Samyn is a Post-doctoral Research Fellow of the Research Fuondation Flanders (F.W.O.), Belgium.

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1. Introduction Polymers often replace metal parts in sliding applications, because they function under dry sliding conditions and can be used when external oil lubrication is impossible or undesirable. Softening and/or melting of the polymer surfaces allow for self-lubricating properties. Polymers posses visco-elastic mechanical properties, which are weaker than metal parts and strongly dependent on the operating and environmental conditions. Besides discussions on the influence of sliding parameters such as sliding motion [1], normal load [2], sliding velocity [3] or temperature [4], some studies on the influences of humidity [5] are available, but less frequently reported. Kawakame et al. [6] reported that variations in the relative air humidity from 50 to 70% can duplicate the lost wear volume of PTFE composites and, consequently, double the wear rate of self-lubricating seals. Under atmospheric conditions, different testing atmospheres can be applied according to ISO-291: (i) 23°C, 50 % RH as recommended for most applications, or (ii) 27°C, 65 % RH as recommended for tropical regions. Also different environmental humidity during winter time (< 20% RH) or summer time (> 80% RH) may cause different friction and wear results. Engineering polymers under sliding have different sensitivities to moisture: water vapours directly affect the mechanical properties, in contrast to metals, and indirectly change the transfer mechanism. The absorption of a water layer may cause boundary lubrication under extreme conditions of 100% humidity [7]. For engineering polymers, the effect of humidity generally depends on whether the polymer has free hydrogen bonds into its structure. Polymers with no or only few of those hydrogen bonds, such as ultra-high-molecular weight polyethylene (UHMWPE), polyacetal (POM), polypropylene (PP), polytetrafluouroethylene (PTFE) or polyethylene terephtalate (PET), are less sensitive to atmospheric conditions because the physical material properties are not strongly altered by humidity. For those polymers repelling water, the presence of humidity eventually may have positive effects due to lubrication. Polyacetals are completely insensitive to any variation in humidity due to low water absorption and insolubility. Vale Antunes et al. [8] also showed that a variation in humidity did not greatly influence the behaviour of polypropylene composites. Hammerschmidt et al. [9] indicated that humidity effects for PET are not as strong as for other more hydrophilic polymers: only 0.4% water content is absorbed under equilibrium conditions at 40% relative humidity, causing a very small shift in relaxation temperature. Da Silva et al. [10] demonstrated for high density polyethylene (HDPE), in contrast, that the coefficient of friction increases at higher humidity for low applied loads, while there was no variation in friction observed for high applied load. McNicol et al. [11] found that humidity influenced the wear of both PTFE and HDPE. For worn PTFE, it is known that a band-like structure develops under dry conditions while it generally changes into a fiber-like aspect at higher humidity due to destruction of the sheetlike molecular planes [12]. Tanaka et al. [13] showed that the friction of PTFE decreased at higher humidity independently of crystalline transitions. Morgan et al. [14] performed indentation-recovery tests on composites of PTFE/glass fibres and found that higher humidity was associated with greater resilience and reduced relaxation. Bearings using this liner material exhibited larger torque at increasing humidity. Polymers with active hydrogen bonds in their structure, such as polyamides (PA) or epoxies, are more sensitive to the effect of water absorption on their sliding properties. Polyamides are extensively studied as

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engineering materials due to easy synthesis and flexibility in composition [15-17]. The coefficient of friction for polyamide may increase from 0.40 to 1.20 at higher humidity, because the polymer becomes tough and the deformation component of friction increases [18]. The wear resistance of polyamide may improve at higher humidity [19]. The formation of additional bonds in between the polymer chains under high humidity generally disfavours the molecular mobility and prevents the formation of an oriented transfer film. The adsorption of moisture causes weakening of the polymer structure and consequently increases the coefficient of friction. Small water molecules can generally permeate into the amorphous regions of semi-crystalline polymers through diffusion. Water is considered to be present in the free volume and becomes active when it is attached to polymer chains by hydrogen bonds. For polyamides, water permeation occurs in a somewhat thicker surface layer compared to polyethylene and this is may be observed as plasticization of the surface [20]. Therefore, polyamides are prone to swelling in moist environment and mechanical properties deteriorate with consequently changing dimensions. For oil-filled polyamide grades, exposure of the clean material to moisture may prevent the absorption of oil into the capillaries [21]. The main modifications in properties of polyamides result from the interaction of the amide groups with polar organic molecules [22]. The degree to which polyamides absorb moisture is related to the number of amide groups per given polymer chain length. At room temperature and 50 % relative humidity (RH), polyamide could absorb up to 2.75 % and every 1 % moisture increase may result in 0.2 to 0.3 % increase in its dimension. The moisture acts as a plasticizer that reduces the entanglement and bonding between molecules, therefore increases their volume and mobility [23]. The moisturized material exhibits lower glass transition temperature (Tg), which makes it easier for further crystallization [24]. Lim et al. [25] studied the water-vapour transmission rates, which were enhanced above 60 to 70 % RH due to a transtion of the polymer from glassy to rubbery states. Based on the frequency shift of FTIR peaks, moisture sorption appeared to reduce the average hydrogen-bond strength of the N - H group, while an increase was seen for the C = O groups. More in general, Garoff et al. [26] studied the influences of humidity on hydrophilic polymer surfaces, such as cellulose, concluding that the magnitude of friction and adhesion and their dependence on humidity decreased with increasing hydrophobicity of the contacting surfaces. In the limit of waterlubricated sliding, one of the two rubbing surfaces should be hydrophilic. It was suggest that friction of hydrophilic polymer surfaces under ambient conditions is greatly influenced by capillary condensation. For high-performance polymers, the tribological properties are improved by the formation of molecular superstructures in the bulk polymer or by copolymerisation. They should withstand sliding systems under severe working conditions with high loads, high sliding velocities and/or high temperature, ensuring longer life-expectance and reliability due to their strength, load-carrying capacity and thermal resistance. The chemical resistance of high-performance polymers, however, still depends strongly on their structure and is different for, e.g., polyphenylenesulphide (PPS), polyether-etherketone (PEEK) or liquid crystalline polymers (LCP). Hoa et al. [27] measured significant moisture absorption into PPS composites and a large reduction in tensile strengths from 25 to 46%. Lhymn et al. [28] reported that absorbed moisture reduces the shear strength and plasticization can be observed for PPS and its composites. Wang et al. [29] showed that the fracture toughness of PEEK was unaffected by crystallinity and moisture content. Also polyimides (PI) are a broad polymer family with extremely high mechanical strength, chemical inertness and thermal stability,

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having a linear or cyclic imide unit connected by aliphatic [30] or aromatic [31] groups. After sintering, they have virtually no melting temperature and behave as semi-thermosetting materials, making them potential candidates for bearing materials at extremely high temperature. Low friction is then desirable, as the conversion of mechanical energy into energy losses should be minimized. The earliest work on polyimide tribology by Buckley [32] and Fusaro [33] was made under vacuum conditions. They concluded that low friction and wear for thermoplastics is caused by a beneficial transfer film developing on the counterface. Transfer was attributed to plastification ability of the polyimide surface in absence of water vapour. It can be predicted that water molecules restrict the formation of a transfer film and cause a transition from low to high friction and/or wear, before achieving a low steady-state friction regime. Water molecules possibly act as anti-plasticizers restricting the molecular mobility (relaxation) and orientation under sliding [34], i.e. they suppress the secondary relaxation processes. The surface then acts brittle and the secondary transition temperature artificially increases. Under full water lubrication, however, Tanaka [35] reported lower friction and higher wear compared to dry sliding of polyimides. The effect of other environments such as cooling liquids was investigated by Sheiretov et al. [36], indicating no chemical degradation and no strong effect of refrigerants on friction and wear behaviour of polyimides, as they are resistant to most common solvents or chemicals. For internally filled polymer composites, mainly the fillers influenced the sliding behaviour at different atmospheric conditions: organics either improved or deteriorated the wear rates compared to dry atmospheric sliding. Shen and Dumbleton [37] reported on galling mechanisms and three-body abrasive wear under moist conditions while good performance under dry sliding was noticed for filled polyimide and polyimide(amide) copolymers. This was attributed to low cohesion of fillers and polymer matrix resulting in stress-cracking. Dislodgements on the wear surface were most likely observed near the fillers, as the matrix may change size in contact with moisture while fillers does not. For glass-filled polymers, Tsenoglu et al. [38] found that water penetration is enhanced through a network of microchannels formed along the imperfectly bonded polymer-fiber interface. For carbon-fibre reinforced composites, the effect of moisture often becomes worse due to different wateruptake of the constituent phases as demonstrated for PEEK [39]. For further considerations about the tribological performance of graphite- and carbon-fiber reinforced polymers, we refer to available literature [40-45]. For polymers with too high friction and/or wear under certain sliding conditions, graphite flakes are often added as internal lubricant for improved wear resistance and load-carrying capacity. Han et al. [46] investigated the nano-scale friction and microhardness for different filler particles and confirmed that the graphitic phase has lower friction than a polymeric phase. Many investigations report on the favourable wear resistance of graphite-composites in, e.g., epoxy matrices [47] or phenolic coatings [48] under dry sliding. Kang et al. [49] described use of graphite additives in polyamides for electrical anti-static sliding. Data on friction behaviour of graphitic composites is less comprehensive with either reducing or increasing coefficients of friction. Chang et al. noticed for polyamides [50] or epoxy [51] that graphite flakes are not most favourable to reduce the coefficient of friction at elevated temperatures and/or high pv-values and further insight in the lubricating action of graphite flakes is needed. Sub-micron particles were more favourable to further reduce the coefficient of friction and wear rate of the composites especially at elevated temperatures. Su et al. [52] showed that graphite as fillers were harmful to the improvement of friction and wear behaviours of fabric composites, depending on variable bonding strength

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between the fabric, the filler and the adhesive resin with the particulate filler type. Also Kawakame et al. [53] stressed the micro-mechanical effects due to micro-cutting and flake delamination in graphitic composites. Samyn et al. [54] illustrated that the lubricating efficiency of graphite flakes into a polymer matrix does not only depend on the environmental operating conditions, but that it is also influenced by intrinsic tribochemical reactions at high sliding temperatures. Graphite is expected to have low shear resistance through its molecular structure with parallel hexagonal sheets (sp2 hybridisation). The basal planes of graphite are dense and the electrons between carbon atoms in these planes are held together by weak covalent Van der Waals forces. The coefficient of friction parallel to these planes is consequently low. According to Spreadborough [55], the first understanding on the lubricating mechanism of graphite consisted of rolling-up of the planes to form small roller bearings. The atomic scale friction between graphite surfaces was studied by Matsushita et al. [56] using molecular dynamics. The simulation reproduces atomic scale stick-slip motion and a low coefficient of friction. It was concluded that the microscopic origin of low friction of graphite does not only rely on the weak interlayer interaction but also on the honeycomb structure of each layer. Dienwiebel et al. [57] observed that the ultra-low friction of graphite is due to a superlubricity effect, illustrated between a small graphite flake attached to the scanning tip of an atomic force microscope and a graphitic surface. However, the lubricating action of pure graphite depends strongly on the test conditions and interaction with the test environment: fillers successfully used in one typical sliding condition may not perform equally in another. Lancaster [58] ascribed some transitions in friction of graphitic and non-graphitic carbons to mechanical and/or thermal effects, which seems most important for carbons with high graphiticity. Since the work of Savage [59], it is known that the shear resistance along the graphitic basal planes becomes low only in presence of moisture or other vapours suitable to adsorb on the surface. In contrast, the shear resistance under dry or vacuum conditions is high and the associated increase in coefficient of friction is often ascribed to the presence of dangling bonds. Dangling bonds exist near edge sites of the sp2 sheets or may be formed by mechanical fracture under sliding outside the basal planes and have high chemical reactivity [60], leading to an increase in adhesive surface interaction. Low friction then results from the desactivation of dangling bonds through chemical reaction with molecules from the environment. In ambient (moist) atmosphere, those bonds are rapidly desactivated by chemisorption of water [61]. According to Yen et al. [62], the desactivation of dangling bonds may also be created from reaction with other gasses: the friction and wear of all carbon materials can be similarly influenced by oxygen [63] or inert gasses [64], favouring the reorientation of the crystallites parallel to the sliding direction. Bryant et al. [65] calculated the interlamellar binding energy of the ideal lamellar structures being influenced by the air environment. The variation in interplane distance under different environments was correlated to the elastic constants and tribological behaviour by Zaidi et al. [66]. Referring to Lancaster [67], low friction for graphitic materials prevails as long as the fraction of the graphitic surface area covered by the adsorbents remains larger than a critical value. Possible transitions from low to high friction often occurs abruptly and have been associated to vapour desorption. However, referring to Gardos [68], the adsorbed vapours do not necessarily play the role of boundary lubricants, but rather modify the electronic orbitals within the graphite and thus the shear resistance. From previous discussion, the desactivation of dangling bonds in graphitic composites may theoretically also be created from the reaction with wear debris

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from the bulk polymer. Hence, the tribochemical mechanisms by which the test environment and test conditions in general influence the dry sliding properties of graphitic composites is dubious. At high temperatures, the main reported wear mechanism of pure graphite was fatigue and groove formation according to Sheng et al. [69], while Rowe [70] observed small influences on strength but lower friction as the temperature increased under high vacuum. According to the available literature, the effect of humidity on sliding properties of sintered graphite-polyimide composites cannot be clearly predicted. The tribological properties of polyimide and graphite lubricant seem to depend on the moisture content in an opposite way. Water molecules are needed for easy shear of the graphitic structure, while they have detrimental effect on the sliding properties of the polyimide surfaces. The friction and wear performance at three humidity levels will therefore experimentally be investigated and compared to microscopic evaluation of the worn surfaces. Test results will be discussed in relation to mechanisms known in literature for polyimide and graphite. The tribological performance of the system graphite powder – polyimide – humidity is dubiously influenced by humidity and has not intensively been described before.

2. Experimentals Details 2.1. Test Materials

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Polyimides were synthesized from a polycondensation between pyromellitic dianhydride (PMDA) and 4,4’ diamino diphenyl ether or oxydianyline (ODA). The reaction scheme is shown in Figure 1. Due to limited solubility of the polyamide acid precursor, it has relatively low molecular weight (Mw = 10000 to 250000 g/mol, Mn = 13000 to 55000) with a polydisper-

Figure 1. Reaction scheme and molecular structure of PMDA-ODA polyimide.

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sity index 2.0 to 5.0. Unfilled sintered polyimide (SP-1) resins with initial grain size diameter of 10 to 20 µm were pre-compacted into 100 µm particles before sintering. Sintering happened under pressures of 500 to 2000 bar at a temperature of about 300°C for 10 minutes. Graphite-filled sintered polyimide (SP-2) contained 15 wt.-% synthetic graphite flakes with density 2.25 g/cm3, surface area 9 m2/g and 5 to 10 µm diameter. The mechanical properties of graphite sheets have been investigated in terms of the density changes and flake sizes by Leng et al. [71]. An optimum concentration of 15 wt.-% graphite flakes depends on the balance between low shear resistance and sufficient strength. According to Xian et al. [72], an increase in graphite content from 15 wt.-% to 20 wt.-% did not further reduce the wear rate of thermoplastic polyimides. The influence of the graphite particle sizes on friction was studied by Bijwe et al. [73] for different composites. The mechanical properties of unfilled polyimide and graphite-polyimide composites are given in Table 1. It is obvious that the graphite additives somewhat lower the mechanical strength and the shear strength, while they increase the stiffness and thermal conductivity of the bulk polyimide.

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Table 1. Mechanical properties of unfilled sintered polyimide (SP-1) and graphite-filled sintered polyimide (SP-2)

The SP-1 and SP-2 bulk structures were characterised by the fracture aspects shown on SEM images in Figure 2. Notched cylindrical samples were cooled in nitrogen to approximately -40°C and fractured according to ASTM E399. The original sintered structure

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of fine powders with diameter of approximately 10 µm is visible on the surfaces. The fine wedge-like particles in between the polymer matrix as seen for SP-2 (Figure 2a) refer to the graphite flake-like fillers. The onset of chevron lines near the notch is slightly observed for sintered polyimides, while the entire fracture aspect is rather brittle.

(a)

(b)

Figure 2. Fracture aspect of sintered polyimide composites, (a) unfilled SP-1, (b) graphite-filled SP-2.

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The used steel counterfaces were 40 CrMnMo864 (DIN 1.2738) high-alloy steel with a hardness HV = 320, yield strength Re = 765 N/mm2 and tensile strength Rm = 900 to 1100 N/mm2. They were ground and polished with GRID 600 Si-C paper to an average roughness Ra = 0.05 µm in order to simulate adhesive sliding conditions.

2.2. Tribological Testing Conditions Polyimide cylinders (diameter 5 mm x width 15 mm) were reciprocatingly slid in a line contact against a steel counterface on a PLINT TE 77 High Frequency sliding tester. The total sliding distance was 15 km, corresponding to 5000 cycles with a single stroke of 15 mm. The effect of normal loads 50, 100, 150 and 200 N was evaluated at a fixed 0.3 m/s sliding velocity. The effect of sliding velocities 0.3, 0.6, 0.9 and 1.2 m/s was evaluated at a fixed 50 N normal load. The test environment was surrounded by a plastic box that is connected to an external climate conditioner. The environmental temperature was fixed at 23 ± 2°C and the relative humidity was varied between 30 ± 2, 40 ± 2 and 60 ± 2 %. Conditioned air was continuously circulated and parameters were PID-controlled with feedback. After mounting the test samples in a mechanical fixation, they were conditioned in the required testing atmosphere at zero load for at least 12 hours before starting the test. The coefficients of friction were recorded on-line with a piezo-electrical force transducer in contact with the stationary steel counterface. Wear was recorded on-line with a contactless displacement transducer as the diameter reduction of the polyimide sample, representing material loss and deformation. Real wear rates or material losses were calculated from weight measurements of the samples before and after testing. The samples underwent a drying

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procedure of 12 hours at 60°C before weight measurements at the beginning and end of the test.

2.3. FurtherAnalysis and Characterisation The chemical changes at the worn polymer surfaces were further studied with Raman spectroscopy, using a Brucker FT spectrometer Equinox 55S (Bruker Optik, Ettlingen, Germany), equipped with a Raman module FRA 106 fitted to a nitrogen cooled (77 K) germanium high sensitivity detector D418-T. The applied laser wavelength during the experiments was the 1.064 µm line from a Diode Laser Pumped Nd:YAG laser. Each spectrum was collected as an average of 250 scans on ten different locations on the sliding surfaces. The transfer films were quantitatively studied under a Leica optical microscope.

3. Tribological Test Results In this paragraph, the experimentally observed friction and wear behaviour of graphitefilled sintered polyimides (SP-2) will be compared to the behaviour of the unfilled sintered polyimides (SP-1). In order to asses the long-time wear resistance and transitions in friction and wear performance of the composite materials, it is important to first evaluate the influence of the sliding distance, and secondly to evaluate the behaviour of the materials under various sliding parameters, such as normal loads and sliding velocities. It is obvious that the sliding performance will depend on the formation of a lubricating transfer film onto the counterface.

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3.1. Influence of Sliding Distance On-line measurements (Figure 3) show the variations in coefficients of friction and diameter reductions of SP-1 and SP-2 as a function of the sliding distance. The effect of 40 or 60 % relative humidity at 50 N, 0.3 m/s is illustrated. Low sliding velocities and low normal loads are represented because variations in sliding and transfer are most pronounced at mild sliding conditions. At higher sliding velocities and normal loads, thermal heating and overload interfere with sliding mechanisms. The environmental atmosphere influences importantly the evolutions in friction and diameter reduction with sliding distance. Friction for SP-1 at high humidity (60 % RH) has a maximum at running-in and stabilises with ongoing sliding distance. This behaviour is typical for polymers sliding under Hertz contact conditions, and is attributed to a change from line contact (running-in) into flat contact (steady-state). It was previously demonstrated that the stabilization in coefficient of friction after 2000 m sliding distance coincides with levelling of the contact pressure from initially 34 MPa (line contact) to 2 MPa (full contact) under steady-state [74]. The friction value under steady-state remains constant and is reasonably high, which indicates a constant interaction between the polyimide and the steel counterface without significant alterations by transfer.

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(a)

(b) Figure 3. On-line measurements of tribological properties for SP-1 (i, ii) and SP-2 (iii, iv) at 50 N, 0.3 m/s under relative humidity of 60 % RH (i, iii) and 40 % RH (ii, iv), (a) friction as a function of sliding distance, (b) wear depth as a function of sliding distance. Friction for SP-1 at low humidity (40 % RH) is more stable at running-in and progressively decreases with higher slope after longer sliding time. The peak-value at running-in disappears at low humidity, which indicates that the interaction between polyimide and steel is altered by transfer from the first meters of sliding on. Friction for SP-2 indicates smooth sliding during running-in and decreasing friction with sliding distance. The initial slope is parallel between unfilled and graphite-filled polyimide, with a transition after 8000 m at 60 % relative humidity and after 2000 m at 40 % relative humidity. The transition into steady-state sliding happens more rapidly at high loads or velocities. The steady-state friction of SP-2 is however less stable compared to SP-1, reflecting larger bulk inhomogeneities with dispersed graphite powder within the matrix. Therefore, the transfer film is supposed to contain graphite layers

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with low shear strength as reported by Langlade [75], while the debris particles consist of both polyimide and graphite. Instabilities in friction are most pronounced at 40 % relative humidity and indicate strong interactions with interfacial transfer particles while relatively smooth sliding at higher relative humidity suggest the removal of transfer particles outside the interface. Diameter reductions for SP-1 linearly increase with sliding distance under steady-state conditions. The change in wear depth evolution between running-in (high slope) and steadystate (moderate slope) relates to the Hertz line contact [74]. The wear evolutions are slightly influenced by the test environment. At 40 % relative humidity, running-in wear is somewhat higher and more scatter in the steady-state wear depth curve is noticed. Both observations are due to the periodical formation of a transfer film and removal of polymer particles from the interface. The smooth wear curve at 60 % relative humidty refers to the permanent interactions between the composite and transfer film with less interfacial debris interactions. Diameter reductions for SP-2 have two different slopes with a clear separation between running-in and steady-state sliding: the transition into constant wear depth coincides with the transition into lower friction. The graphite-filled polyimide cylinders wear until the contact pressure is sustained by the transfer film. Wear at 40 % relative humidity is significantly lower than at 60 % relative humidity, but it shows more instabilities in parallel to friction.

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3.2. Influence of Sliding Parameters The steady-state values for coefficients of friction and wear rates of SP-1 and SP-2 are summarised in Tables 2 to 5, including various normal loads and sliding velocities at 30, 40 and 60 % relative humidities. Test results are averaged from three runs per sliding parameter, showing a statistical variation of 7 % on coefficients of friction and 8 % on wear rates. These are acceptable for tribological data [76] and the trends described below are repeatable under different sliding conditions. For unfilled SP-1 (Table 2 & 3), the coefficients of friction are lowest at low relative humidity and gradually increase at higher relative humidity for every sliding velocity. At 30 % relative humidity, coefficients of friction increase with an increase in sliding velocity. At 40 to 60 % relative humidity, in contrast, coefficients of friction decrease with an increase in sliding velocity. A theoretical model of Matsubara [77] considers the orientation of molecules at the sliding surface in relation to the sliding velocity: it predicts higher friction at high sliding velocities because the polymer chains react stiffer at high shear rates and disfavour a conducive surface texture. This trend applies to SP-1 at 30% relative humidity and indicates that molecular mobility is limited at low relative humidity while improving at higher relative humidity. Also at 50 to 100 N normal loads, the coefficients of friction are lower at low humidity compared to moist air, but this trend may reverse at 150 to 200 N due to overload and brittle fracture. The increase in friction with normal loads does not agree with the sliding performance of thermoplastics, where plastification of the sliding surface contributes to lower friction. For sintered polyimide, there is a tendency of brittle fracture at high load levels, characterised by a monotoneous increase in friction. This behaviour is most pronounced at low compared to high humidity. Due to mechanical overload, some tests were stopped prematurely. The wear rates are highest at low humidity (30 %) and monotoneously decrease at higher relative humidity (40 to 60 %) for all test conditions. The decreasing wear rates at

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higher relative humidity are accompanied with increasing coefficients of friction. A critical normal load of 150 N is due to mechanical overload, in parallel to the transition into brittle fracture noticed for friction. The behaviour of sintered polyimide under variable humidity is clearly different to previous reports on thermoplastic polyimide by Tanaka [78]. Table 2. Coefficients of friction (μ) and wear rates (w, 10-4 mm3/m) for unfilled SP-1 at different normal loads and constant sliding velocity (0.3 m/s)

Table 3. Coefficients of friction (μ) and wear rates (w, 10-4 mm3/m) for unfilled SP-1 at different sliding velocities and constant normal loads (50 N)

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Table 4. Coefficients of friction (μ) and wear rates (w, 10-4 mm3/m) for graphite-filled SP-2 at different normal loads and constant sliding velocity (0.3 m/s)

Table 5. Coefficients of friction (μ) and wear rates (w, 10-4 mm3/m) for graphite-filled SP-2 at different sliding velocities and constant normal loads (50 N)

For graphite-filled SP-2 (Table 4 & 5), the coefficients of friction are lower than SP-1 for most sliding parameters, except at some overload conditions. In contrast to SP-1, graphitefilled SP-2 presents both lower coefficients of friction and lower wear rates at low relative humidity compared to high relative humidity, for all sliding velocities and normal loads. At

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30 % relative humidity, coefficients of friction increase at higher sliding velocties. At 40 to 60 % relative humidity, coefficients of friction decrease at higher sliding velocities. These trends are similar to unfilled SP-1 and indicate that the sliding properties of the graphite-filled composite may be strongly determined by the polyimide matrix. At 50 to 200 N, the coefficients of friction generally increase at higher loads and sometimes become higher than the values of unfilled polyimide, because the graphite fillers somewhat reduce the mechanical strength of the polyimide bulk. It is assumed and visually observed that the sliding behaviour of graphite-filled polyimides is controlled by the formation and the quality of a graphite transfer film. Such films are able to support the load, but have limited strength due to their lamellar structure. From Table 1, it reveals that sintered polyimide with graphite additives has lower mechanical strength and is more brittle. The influence of intrinsic mechanical strength mainly manifests at low sliding velocities with a continuous increase in friction as a function of normal load. This mechanical overload is also reflected in high wear rates and lumpy transfer, being most pronounced at high humidity. It was previously noted that low velocity / high load conditions are sometimes unfavourable, as the lubricating mechanisms through ‘easy shear’ of the graphite structure is not fully exploited [79]. The wear rates for graphitefilled SP-2 are only 10 to 20 % of the values for unfilled SP-1, and gradually increase at higher normal load and/or sliding velocity. A discontinuous increase in wear rates above 150 N refers to the mechanical overload situation for unfilled SP-1. It indicates that the bulk properties of unfilled sintered polyimides – although inferiorly – influence the behaviour of its composites. A transition into brittle fracture does not happen for SP-2 at any humidity condition and all tests have run over the full sliding distance.

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3.3. Transfer Film Formation The sliding behaviour of smooth surfaces depends on adhesion and formation of an interlayer with low shear strength, consisting of a lubricant or transfer film [80]. Early theories state that the formation of a thin film is favourable for reducing the counterface roughness and therefore lowers friction and wear [81]. For polymers, often a reverse trend is observed depending on the morphology of a polymer transfer film. Polymer/steel contact is reversed into (local) polymer/polymer contact with variations in adhesion and/or deformation. For unfilled polyimides SP-1, optical micrographs of the transfer films are shown in Figure 4 after sliding at different normal loads, sliding velocities and variable humidity. Transfer of sintered polyimides occurs mainly at low humidity and develops more difficult at high humidity. At 30 % relative humidity, transfer orients favourably along the sliding direction and becomes smoother at higher normal loads or sliding velocities. This film type is called ‘platelet-like’ transfer. A thin film shown at 50 N, 0.3 m/s is most favourable for low friction and is similar to the transfer type observed after sliding against stainless steel [82]. However, the platelet-like film causes higher wear rates compared to smoooth films because it acts more abrasive. It is concluded that mechanical interaction in the sliding interface is most important above thermal interaction: (i) the contact area is reduced from the entire steel surface to local debris particles, reducing friction and (ii) the platelet particles are brittle and cause deformation and abrasion of the polyimide sliding surface. At 40 % relative humidity, the transfer films look rough with separate flakes at mild sliding conditions and a gradually thicker film at more severe sliding conditions. This film type is called ‘lumpy’ transfer. It

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causes higher friction because of large variations in adhesion and deformation in the sliding interface. At 60 % relative humidity, there is no film formation at mild sliding conditions and only some separate debris particles accumulate at severe sliding conditions. This film type is called ‘island-like’ transfer. It suggests that particles detach from the polyimide bulk and deposit without conglomeration in the interface. The transfer types for sintered polyimide under different atmospheric conditions are different from the continuously thin layers observed in vacuum sliding [83]. A smooth and continuous film is mostly expected at 1.2 m/s due to high shear, but only develops at low humidity.

Figure 4. Overview of unfilled SP-1 transfer films on steel counterfaces after sliding at different humidity, normal loads and sliding velocities (horizontal sliding direction).

Optical micrographs of the graphite-filled SP-2 transfer films are shown in Figure 5. At 30 % relative humidity, transfer consists of a thin and viscous film with mixed polyimide and graphite particles that are smoothened in the direction of sliding. At 40 % relative humidity, the polyimide and graphite transfer particles demix and form two separate phases on the counterface. At 60 % relative humidity, the transfer only contains graphite particles and no polyimide phase. The latter is in agreement with the observations for unfilled SP-1 that did not show transfer at high humidity. The lumpy transfer of graphite at 200 N explains the increase in friction and wear due to limited loading capacity of SP-2 composites.

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Figure 5. Overview of graphite-filled SP-2 transfer films on steel counterfaces after sliding at different humidity, normal loads and sliding velocities (horizontal sliding direction).

4. Discussion High performance composites have good thermal resistance and are supposed to present chemical resistance, but their sliding behaviour is strongly influenced by humidity. The kinetics of water vapour absorption into a porous polyimide structure was studied by Bertrand et al. [84], using an infiltration model. Depending on the sample thickness, it was measured that 90% of the saturation value is attained after 300 min (thickness 0.25 cm) or 60 min (thickness 0.12 cm), while slower absorption into the smallest 10% of the pores took about two days. Mainly in presence of graphite additives, the environmental sliding conditions (humidity) and sliding conditions in general (normal loads, sliding velocities and temperatures) have a much stronger influence on the tribological properties compared than the unfilled polymers. Therefore, the effect of humidity on the lubricity of unfilled and graphite-filled polyimide will be further discussed in relation to the lubrication efficiency under other sliding conditions.

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4.1. Influence of Humidity on the Sliding Mechanisms of Polyimide From previous literature [33-34], the effects of humidity on polyimide are related to absorption of water molecules at the sliding surface and formation of hydrogen bonds between the carbonyl groups in adjacent molecular chains. The effect of humidity on sliding properties, however, strongly depends on the polyimide structure. Kang et al. [85] reported that for thermoplastic polyimides, synthesized from benzophenone tetracarboxylic dianhydride (BTDA) and bisaniline (Bis-P) with glass transition temperature Tg = 285°C, the wear rates increased at higher humidity due to weakening of the polymer bulk through water absorption. The carbonyl linkage in the BTDA molecule is a site where water can directly attach to the chain through hydrogen bonding. It was postulated that the flexibility of a molecule permits it to reorient under stress and fracture rather than to flow plastically when this is restricted. For sintered PMDA polyimides, a different trend is noticed with decreasing wear rates at high humidity suggesting that strengthening effects dominate at high humidity. The absence of clear glass transition temperature and lower concentration of carbonyl groups in the molecular structure makes it less sensitive to weakening in presence of water. For PMDA polyimides, it can be expected that cross-links are formed which give the surface structure better mechanical strength with lower wear rates and lower tendency for overload at high humidity. On the other hand, also the brittleness seems to reduce by hydrolysis as revealed from the smoother surfaces at high humidity, while overload conditions at 150 to 200 N at low humidity cause unstable friction. An increase in wear rates for sintered polyimides at low humidity is in contrast to literature data on thermoplastic polyimides [34], reporting smooth transfer and progressively lower wear as the moisture content in air decreases. Present results on tribological properties of sintered polyimides show some parallel tendencies with adhesion measurements made by Hu et al. [86]. They reported that the peel strength of polyimide films on silicon substrates decreases with increasing relative humidity due to the hydrolysis of polyimide, reaches a minimum, and then increases with increasing relative humidity due to the hydrogen bonding at the weak boundary layer. In a high-humidity environment, peel crack tips are attacked by moisture and result in weak adhesion measurement. Water adsorption by the polyimide films and diffusion into the peel crack tip was the main mode of moisture attack. Sager et al. [87] correlated the humidity absorption to a linear volume exapansion over a wide range of humidity. The observed material behaviour, however, strongly depends on the conditions of the polyimide fabrication process. The transfer film morphology for unfilled SP-1 is clearly affected by relative humidity. At high humidity, therefore, transfer lacks and friction increases. At low humidity, transfer establishes and another reason for high wear rates is found in the abrasive action of the smooth-lumpy transfer film. The lack of transfer at 60 % RH and easy transfer at 40 % RH agrees with findings for thermoplastic polyimides by Jia et al. [88], who tested explicitly in dry and water environments. The worn polyimide surface under dry sliding was characterised by severe plastic deformation and micro cracking, while a large amount of transferred debris particles was observed on the counterpart. The worn polyimide surfaces after sliding at high humidity were smoother and no signs of transfer were noted. In other words, water inhibited the transfer of polyimide to the metal counterface. Lower wear rates of polyimide composites under water-lubricated conditions compared to dry sliding were related to the polar imide radicals which were liable to adsorb water and lead to swelling and decreasing shear strength.

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On the contrary, Kang et al. [85] observed an increase in wear rates of polyimide coatings under fretting conditions at high humidity compared to dry humidity, however more likely attributed to the formation of abrasive iron oxide debris. Earlier investigations by Fusaro [83] on thermoplastic polyimides reveals a friction coefficient µ = 0.60 during a 50 % RH test, dropping to µ = 0.10 in a 0.13 Pa vacuum or µ = 0.05 in a 0.00013 Pa vacuum while wear rates progressively lowered under more severe vacuum conditions. These differences were also ascribed to water vapour concentration. The sensitivity of polyimides to changes in humidity was reported to be lowered for siloxane-modified copolymers, however, they have generally larger wear rates compared to unfilled polyimides. Also the effects of fluorine were favourably exploited to reduce the effect of moisture on tribological behaviour, because of its hydrophobic properties.

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4.2. Influence of Humidity on the Sliding Mechanisms of Graphite From literature, the lubricating action of graphite depends strongly on the test conditions and interaction with the test environment [59]. Fillers successfully used in one typical sliding condition may not perform equally in another. Under dry conditions the shear resistance is high and the associated increase in friction coefficient is often ascribed to the presence of dangling bonds with high chemical reactivity, leading to an increase in adhesive surface interaction [89]. Graphite does therefore not function well under vacuum conditions. Low friction may result from the complete desactivation of dangling bonds, e.g. through chemical reaction with available molecules from the environment. In ambient atmosphere, those bonds are rapidly desactivated by chemisorption of water and result in low friction. Desactivation of dangling bonds may also be created from reaction with wear debris. Hence, the mechanism by which water is influencing the shear resistance of graphite incorporated in polymer composites is still not fully clear. According to the present test results, the general believe of low friction for pure graphite at high humidity atmosphere does not seem to apply generally to graphite-filled polymer composites. The present test results on graphite-filled polyimide SP-2 indicate low friction at 30 % RH and high friction at 60 % RH. So far, very few papers are found in literature focussing on sliding interactions of sintered polyimide filled with graphite flakes. Most polyimide composites studied include graphite fibre reinforcements and/or PTFE and/or MoS2 fillers [90]. For pure graphite, higher friction at high humidity was recently observed in certain sliding conditions of low sliding velocities by Brendlé et al. [9192], modelling the tribo-reactions of moisture at the sliding surface of graphite as a triboreactor. He concluded that the real amount of water entering and consumed in the contact depends not only on the relative humidity but also on the sliding temperature and sliding velocity, responsible for the initiation of chain reactions by, e.g. particle detachment. A hypothesis can be drawn from previous discussion of mechanisms found in literature in relation to present test results. For graphite-filled sintered polyimides the fraction of graphite is only 15 wt% and it can be estimated that the polyimide bulk properties are most important. The interactions between polyimide wear debris and graphite debris seem to play an important role in the formation of a lubricating transfer film inducing low friction and wear. At low humidity, the improved transfer of polyimide is beneficial for the formation of a mixed graphite-polyimide transfer film with good sliding properties. At low humidity, also the theoretical presence of dangling bonds on graphitic surfaces makes them chemically

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reactive and may also stimulate interaction with polyimide debris for more homogeneous transfer.

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4.3. Lubricity of Graphite Additives: Humidity Effects versus Temperature Effects The influence of temperature on friction and wear under the same contact conditions as used in this chapter, was investigated during our previous research for both sintered polyimide [93] and graphite-filled sintered polyimide [54]. For SP-1, high friction occurred at temperatures between 100 to 180°C due to hydrolysis reactions, while low friction was observed at temperatures between 180 to 260°C due to imidisation. In a similar way, it was demonstrated in this chapter that polyimides have high friction at high atmospheric humidity and lower friction at low atmospheric humidity. Concerning coefficients of friction, conditions of low humidity seem to correspond to conditions of high temperatures. In an opposite way, it was observed that wear rates for SP-1 stabilise at high temperatures while wear rates increase at low humidity. Concerning wear, conditions of low humidity does not correspond to conditions of high temperatures. It indicates that chemical reactions manifesting at high temperatures, such as imidisation, additionally improve the strength of the transfer film. As a function of sliding temperatures, no coherent transfer film was observed at low temperatures, while a transfer film only developed above 180°C. In a similar way, most favourable transfer is observed at low humidity. When transfer lacks, separate debris particles collect into the interface and act as third-body abrasive particles that strongly increase the wear rates. Both the counterface and the polymer surface are then characterised by abrasive grooves along the sliding direction. The relation between humidity and temperature can be further explained by studying the variations in structure on the worn surfaces of sintered polyimides. A Raman spectrum of worn polyimide surfaces at different temperatures is shown in Figure 6. The relation between imide structure and hydrolysed carboxylic acid structure is illustrated by comparing the 1612 cm-1 and 1601 cm-1 band, respectively (Figure 7). For a constant 1601 cm-1 position, there is a downward shift in the 1612 cm-1 wavenumber at 100 to 140°C at different normal loads. The lower frequencies represent deterioration of the imide structure, partially changing into polyamic acid that is characterised by the 1601 cm-1 band. Enhancement of the imide structure through ring-closing of carboxylic acid is given by an upward shift of 1612 cm-1 and establishes at 180 to 200°C. Hydrolysis at 100 to 140°C is also reflected in the relative intensity I (1612) / I (1601), with a maximum in hydrolysis and minimum in imidisation reactions at 140°C for each normal load. Dehydration happens most intensively at 180°C irres-pective of the 50 to 150 N normal loads, represented by a maximum 1612 cm-1 band. The 1612 cm-1 band only represents the aromatic imide part, but also characteristic C=O imide groups (1788 cm-1) and C-N-C imide groups (1395 cm-1) show similar trends relatively to the carboxylic acid structure (Figure 8). The 1788 cm-1 position shifts down from 1787.12 cm-1 (60°C) to 1785.19 cm-1 (140°C) and it shifts up from 1789.12 cm-1 (180°C) to 1791.11 cm-1 (260°C) at 50 N normal loads. The minimum intensity of the imide I band through hydrolysis at 140°C is more pronounced for the 1788 cm-1 band than observed for the aromatic imide ring at 1612 cm-1, as mainly the C=O groups with high polarity are affected through hydrolysis. Imidisation starts at 180°C and shows clearer evolutions at 180 to 260°C

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by additional orientation of the functional C=O polyimide groups. The C-N-C imide bonds relatively to the carboxylic acid indicate identical decreasing and increasing tendencies.

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Figure 6. Raman spectrum of polyimide surfaces worn at different temperatures [93].

(a) Figure 7. Continued on next page.

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(b)

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Figure 7. Raman analysis of imide aromatic band (1612 cm-1) and carboxylic acid band (1601 cm-1) for unfilled SP-1, (a) wavenumber position, (b) relative intensity.

The minimum in the curve has shifted, however, from 140 to 180°C as the C-N-C structures are not directly hydrolysed. Hydrolysis is mainly affecting the C=O bonds and aromatic imide rings. At high loads, other reactions happen to the C=O and C-N-C structures with a decreasing intensity of imide-related bonds. According to Li et al. [95], a drop in C=O was also found for PEEK in the high load region and not in the low load region, correlated to bond rupture and radical formation by higher mechanical energy input. According to Cong et al. [96], XPS analysis indicated carbonation on the friction surfaces of thermoplastic polyimides, which was presently not revealed for sintered polyimides. Referring to the molecular structure of sintered polyimide in Figure 1, it is clear that imide ring-opening reactions are explained either by hydrolysis (low temperatures) or by water supply (high humidity). From these reactions, it seems that the water supply in the interface does not only depend on the environmental humidity, but the effective water content in the sliding interface is not constant and depends on tribochemical reactions that are induced by frictional heating. Therefore, sliding conditions of low temperatures (100-180°C) can be related to sliding conditions of high humidity. For SP-2, there was observed high friction at temperatures between 60 to 100°C and lower friction at temperatures between 140 to 260°C, explained by the interaction of graphite lubricant and effective humidity in the sliding interface. In a similar way, it was demonstrated in this chapter that graphite-filled polyimides have high friction at high atmospheric humidity and lower friction at low atmospheric humidity. Concerning coefficients friction, there is a correlation that conditions of low humidity agree to conditions of high temperature in parallel to the observations for unfilled polyimide SP-1. The wear rates for graphite-filled polyimide are lowest at low humidity, while they are also lowest at low temperatures. Concerning wear,

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conditions of low humidity does not seem to correspond to conditions of high temperatures. In parallel to sintered polyimide SP-1, the variations in mophology of the polyimide transfer film mainly control wear rates: transfer films for graphite-filled polyimide are smoother under both low-humidity and high-temperature conditions.

(a)

(b)

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Figure 8. Raman analysis of imide bands (1788, 1395 cm-1) and carboxylic acid band (1601 cm-1) for unfilled SP-1, (a) imide I (C=O) relative intensity, (b) imide II (C-N-C) relative intensity.

The effect of tribochemical reactions on shear stresses in the sliding interface follows from optical microscopy of the wear debris (Figure 9). The graphite particles were separated from the polyimide particles. The role of graphite as third body abrasives was previously discussed by Bouvard et al. [97]. Also Kowandy et al. [98] studied graphite debris after sliding against iron, in order to understand tribochemical reactions. We observed three graphite morphologies, characterising the sliding regimes as a function of temperature: (i) coarse debris at 60 to 100°C corresponds to high shear and wear protection, (ii) fine debris at 140 to 180°C corresponds to decreasing shear and high wear, and (iii) no separate debris at 180 to 260°C corresponds to very low friction with formation of a fully protective transfer film. These transitions are repeatable over the temperature intervals under different normal loads. Further assessment of the crystallite sizes can be made by atomic force microscopy, which we preliminary studied elsewhere [99]. Brendlé et al. [91] found similar variations in debris morphology of pure graphite, depending on the ambient humidity: graphite particles are coarse in humid air, while fine graphite powders form in dry air. Depending on the level of moisture, the mechanical response of graphite was either cleavage along the basal planes or embrittlement into small particles. The cleavage is associated with relatively high humidity and low shear stresses. In contrast, the fragmentation into particles is associated with dry conditions and shear stresses exceeding the tensile strength of the sheets.

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500 µm

(a)

(b)

Figure 9. Graphitic wear debris particles of SP-2 after sliding under different temperature regimes: (a) sheet-like at 60-100°C, and (b) powdery at 100-180°C [54].

From previous discussion, the lubricating efficiency of graphite flakes added into polymer composites is qualitatively explained by considering debris morphology, transfer and effective amount of water in the sliding contact. Transfer film formation basically involves polymerisation or chemical bonding between free radicals formed during sliding [100]. For graphite-filled polyimide composites, the following correlations result from present study:

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•

•

•

At 60 to 100°C, the effective humidity in the sliding interface is controlled by ambient humidity without significant reactivity of the polyimide bulk, causing a relatively ‘wet’ atmosphere (60% RH): coarse graphite debris then forms by cleavage. When graphite particles are broken parallel to their basal planes, weak Van der Waals bonds are disrupted and dangling bonds with low chemical reactivity are created. The graphite debris consequently does not interact with polyimide debris and is deposited as pure graphite particles, weakly adhering to the counterface. At 100 to 180°C, the effective humidity in the sliding interface is lower than ambient humidity due to hydrolysis of polyimide, causing a relatively ‘dry’ atmosphere: powdery graphite debris then forms by brittle fracture. The latter small particles do not allow for easy shear and act as third bodies in the sliding interface. They increase the sliding resistance in the interface by abrasion, while polyimides have poor abrasive resistance [101]. When graphite particles are broken across their basal planes, strong covalent bonds are disrupted and dangling bonds with high chemical reactivity may form. It is likely that the coexistence of distinct pure graphite and pure polyimide transfer is due to the attachment of polyimide debris to the active graphite sites. As unfilled polyimides did not form a transfer film in this temperature interval, bonding between the polyimide particles and steel counterface is unlikely. The graphite thus seems to act as linking agent between the steel on the one side and the polyimide particles on the other side. At 180 to 260°C, the effective humidity in the sliding interface is higher than ambient humidity due to polycondensation of polyamic acid into polyimide. Graphite particles then easily cleave into sheets with low shear strength, although no separate graphite

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particles are observed. The polymerisation of the polyimide wear debris is predominant and the formation of intermediate radicals may improve the reactivity with the graphite particles. The radical formation in polyimide was studied by Ramos et al. [102], mainly showing reactivity around the carbonyl groups. Compared to transfer of unfilled polyimide, a transfer film with incorporated sheet-like graphite particles is more homogeneous and presents lower friction. It is concluded that the morphology of graphite wear debris can be explained in parallel to the morphology pure graphite, considering chemical reactions in the bulk material. The tribological response of graphite additives in polyimide composites may be different from pure graphite, as it also depends on the transfer ability of the bulk material. Present research reveals, e.g., that large graphite particles at low temperatures form under relatively high humidity (in parallel to pure graphite), while they correspond to high shear forces (in contrast to pure graphite) as they not incorporated in a polyimide transfer film.

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4.4. Lubricity of Graphite Additives: Normal Load versus Sliding Velocity Effects The influence of normal loads and sliding velocities on friction and wear under the same contact conditions as used in this chapter was investigated during our previous research for both sintered polyimide [94] and graphite-filled sintered polyimide [79]. For graphite-filled SP-2, the coefficients of friction monotoneously decrease with sliding velocities and this trend becomes more pronounced at higher normal loads. Possibly higher wear rates then contribute to larger exposure of graphite lubricant in the sliding interface and influence friction more favourably. Related to the low friction, temperature rise becomes less important for graphite-filled polyimide compared to unfilled polyimides and cannot be solely responsible for the decrease in friction. On the other hand, formation of a graphite transfer film mainly determines friction. At higher sliding velocities, shear between the graphite layers occurs more readily and they perform lower friction resistance. As a function of normal loads, the coefficients of friction for graphite-filled SP-2 either (i) increase with normal load at low sliding velocities, or (ii) decrease with normal load at 0.6 to 1.2 m/s sliding velocities. These trends are reversed in relation to unfilled SP-1 and relate to the amount of lubricant (additives) in the interface. It is assumed and visually observed that the sliding behaviour of graphite-filled polyimides is controlled by the formation and the quality of a graphite transfer film. From Table 1, it reveals that sintered polyimide with graphite additives have lower strength, which has also consequences for its sliding behaviour. The influence of the intrinsic mechanical strength mainly manifests at low sliding velocities (0.3 m/s) with a continuous increase in friction. This mechanical overload was also reflected in high wear rates and lumpy transfer. The influence of a transfer film prevails at high sliding velocities (0.6 to 0.9 m/s) as it becomes more homogeneous and is favoured by shear. The strong reduction in friction coefficients, mainly at high sliding velocity and high normal loads, can be related to the combination of (i) the brittleness of the polyimide structure resulting in high lubricant supply, and (ii) the shear stresses favouring homogenisation of polyimide and graphite debris. Both actions result in the formation of a mixed graphite/polyimide transfer film. For each of the test parameters, graphite was exposed as fine powder. No large agglomerated particles

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were observed as the friction (and shear stresses in the polyimide bulk) are lower with less stress concentrations at the sintered interfaces. The differences in wear behaviour for unfilled and filled sintered polyimide are importantly reflected in the wear versus sliding distance curve. For unfilled SP-1, volumetric wear ratesremain constant over the entire sliding distance with hardly any difference in running-in and steady-state. For graphite-filled SP-2, the curves of either volumetric wear or wear depth versus sliding distance have two different slopes with a clear separation between running-in and steady-state sliding: a transition results from graphite transfer after certain sliding time, causing a constant wear depth during steady-state. However, there is no stabilisation of the wear curve for the most severe testing parameters (100 N - 1.2 m/s; 150 N - 0.6 to 1.2 m/s and 200 N - 0.6 to 1.2 m/s), reflecting overload conditions. A graphite transfer film builds-up gradually to support the implied load, but strength is limited due to its lamellar structure. The synergistic effect of normal loads (contact pressures) and sliding velocities results in an increase in sliding temperature that further controls the sliding mechanisms. The combined effect of contact pressure p and sliding velocity v is expressed as a pv-value allowing to determine the favourable working range and overload conditions. The effect of pv-conditions on the tribological properties of SP-1 and SP-2 under the present specific sliding configuration (cylinder-on-plate) is summarized in Figure 10. The effect of frictional heating is expressed as the maximum polymer surface temperature T* that was previsously calculated and validated for the present sliding configuration [103]. Unfilled SP-1 (Figure 10a) has an initial regime of decreasing friction due to normal load - sliding velocity effects at 0.5 MPa.m/s < pv < 1.5 MPa.m/s. These sliding conditions are mainly mechanically controlled by shear. The coefficient of friction stabilises at 1.5 MPa.m/s < pv < 3 MPa.m/s independently of any further increase in sliding velocity or normal load, as the poly-mer act as a thermosetting and is not further influenced by chain orientation. Possibilities for polymer chain orientation induced by friction are thermo-chemically controlled, as discussed before. The transition into stable friction happens at T* = 175°C. Overload in friction at severe sliding conditions determines a limiting pv-value = 3 MPa.m/s with temperatures T* > 260°C. The wear rates are mainly determined by the applied normal load, because of brittleness. Graphite-filled sintered polyimides SP-2 (Figure 10b) have no overload in friction or wear, in present pv-range. Lewis [104] noted a pv-limit of 12 MPa.m/s for SP-2 in air from pin-on-disc tests. However, a transition in friction with change in slope and maximum value is presently noted at 3 MPa.m/s, corresponding to the pv-limit causing overload for unfilled SP-1. This transition coincides with a change in transfer morphology that is graphite-based at low pv, while smooth and mixed graphite/polyimide-based at high pv. The transition in friction for SP-2 coincides with stabilisation in maximum polymer surface temperature T* = 115°C. Comparing the transition into stable friction at 1.5 MPa.m/s for SP-1 and at 3 MPa.m/s for SP-2, shows a maximum polymer surface temperature T* = 175°C for SP-1 and T* = 115°C for SP-2. The temperature ratio 175°C / 115°C = 1.52 agrees approximately to the ratio of polyimide heat conductivities 0.46 (W/mK) / 0.30 (W/mK) = 1.53. Therefore, not only the thermal characteristics of the steel counterface are important, but also the polymer composition influences frictional heating at steady-state. This effect is obviously explained by heat conduction through polymer transfer particles in the interface, having lower thermal conductivity. For unfilled polyimides, polyimide films only develop at high loads and high sliding velocities. The stabilisation in friction for SP-1 at pv = 1.5 MPa.m/s corresponds to the formation of a platelet-transfer film, while no film developed at low pv-levels.

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(a)

(b) Figure 10. Influence of the regime pv-value (contact pressure x sliding velocity) on coefficients of friction µ (■), volumetric wear rates w (♦) and maximum polymer surface temperatures T* (○) for sliding in cylinder-on-plate configuration at 23°C bulk temperature, 60 % relative humidity against steel for (a) unfilled polyimde SP-1, and (b) graphite-filled polyimide SP-2 [79].

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The stabilisation in friction for SP-2 at pv = 3 MPa.m/s corresponds to the formation of a mixed graphite-polyimide film , mainly controlled by mechanical shear. The graphite additives do not only lower the coefficient of friction but they also improve the thermal conductivity of the polymer depositions: these two effects lower the maximum polymer surface temperature T* and improve the sliding performance of a polymer component. According to McEttles et al. [105] the transition towards stable friction for thermoplastics was denoted as ‘thermally controlled sliding’. For semi-thermosetting polyimides, the sliding regime with constant friction at high load / high sliding velocity is controlled by mechanical shear and tribochemical reactions such as hydrolysis and imidisation, controlling the interfacial interactions.

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5. Conclusions Graphite flakes have high potential to be used as internal lubricants into sintered polyimides. The tribological properties of graphite-filled polyimides strongly depend on the testing conditions and good knowledge on the influences of environmental humidity, sliding tempera-ture, normal load and sliding velocity is important for adequate use of those composites. For graphite-filled polyimides, both coefficients of friction and wear rates decrease at low humidity by formation of a thin and mixed polyimide/graphite transfer film. The reaction of graphite dangling bonds with wear debris is likely at low humidity. At higher humidity, phase separation of the graphite and polyimide transfer is observed. The sliding behaviour under low humidity corresponds to the sliding behaviour under high temperatures. Overall, the tribochemical reactions in the interface such as imidisation and hydrolysis of the polyimide structure control the actual humidity through presence of water molecules in the interface and highly interfere with the lubricity of graphite additives. The mechanical and thermochemical effects on sliding performance of graphite-filled polyimides is expressed in a pv-model, indicating the the lubricity of graphite flakes is superior at high sliding velocities compared to high normal loads.

Acknowledgements Pieter Samyn acknowledges the Research Foundation Flanders (F.W.O.) for financial support and assignment of a post-doctoral research grant.

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In: Graphene and Graphite Materials Editor: H.E. Chan, pp. 143-191

ISBN: 978-1-60692-666-6 © 2009 Nova Science Publishers, Inc.

Chapter 5

ADVANCES IN SUPERCONDUCTING INTERCALATED GRAPHITE Nicolas Emerya, Claire Hérolda,* and Philippe Lagrangea,b

a

Laboratoire de Chimie du Solide Minéral – UMR 7555, Nancy Université – Université Henri Poincaré, B.P. 239, 54506 - Vandœuvre-lès-Nancy Cedex – France b Ecole Européenne d’Ingénieurs en Génie des Matériaux, Nancy Université - Institut National Polytechnique de Lorraine 6, rue Bastien Lepage, B.P. 630 54010 - Nancy Cedex – France

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The discovery in 2005 of superconductivity in YbC6 and CaC6, with substantially higher critical temperatures than the previously observed among the family of the graphite intercalation compounds, has largely renewed the interest for these well known lamellar compounds. Indeed, these critical temperatures reach 6.5 and 11.5 K respectively for ytterbium- and calcium-graphite phases. It was consequently interesting to collect all the informations concerning the superconductivity of these compounds from the discovery of this phenomenon observed in the heavy alkali metals graphite intercalation compounds in 1965, insisting particularly on the recent advances in this research field. After a general introduction, that describes all the carbon materials, which are extremely various with dimensionalities varying from 3 to 0, leading to their large aptitude for the insertion/intercalation reactions, we develop widely the case of graphite : chemical bonds, crystal and electronic structures, anisotropy and ability to become a host structure. We insist on its strong anisotropy of chemical reactivity, that allows the synthesis of very numerous intercalation compounds. The distinctive features of the intercalation reaction into graphite are reviewed (systematic charge transfer, staging, etc…) and are particularly developed in the case of the donor-type intercalation compounds, among which is precisely observed the superconductivity. For the latter, the various synthesis methods are successively described, showing the best route to use in order to obtain each type of compound. Then we review with detail the binary compounds, emphasizing their distinctive crystal and electronic structures and also their transport properties. In a second time, we describe the superconductivity of all the compounds belonging to this family and showing this property. In *

E-mail address: [email protected]. (Corresponding author).

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Nicolas Emery, Claire Hérold and Philippe Lagrange a last part, we compare these superconducting binary intercalated graphite compounds with an other lamellar superconductor : magnesium diboride. The ternary compounds are then studied, and the poly-layered nature of their intercalated sheets is especially underlined. Their distinctive electronic structure is presented and their superconducting properties are described. Lastly, we give a rather short overview concerning the superconductivity observed in the other intercalated carbon materials : diamond, fullerenes and nanotubes.

I. General Introduction about Carbon Materials

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Carbon possesses a very particular position in the classification of the elements : indeed, it is the head of the central column of the periodic table. And this 14th column appears in fact as the spine of the classification. Its electronegativity is medium, and during the chemical reactions, it can be as well electron donor as electron acceptor, according to the cases. On the other hand, it exhibits a very large ability to create some chains by bonding with itself. It is well known that the organic chemistry is born from this remarkable property. But it exists also some important consequences of this latter in the field of the inorganic chemistry. Indeed, the extreme variety of its allotropy is partly due to this property. It is due also to the ease for the carbon atom to change hybridization : sp3, sp2, sp, and even in some cases spx with x included between 2 and 3 (Figure 1).

Figure 1. Allotropy of carbon materials: fullerene, nanotube, graphite and diamond.

The elemental solids obtained from sp3 carbon atoms are diamond (cubic variety) or more rarely lonsdaleite (hexagonal variety). Both materials are three-dimensional, because they exhibit strong covalent bonds, that grow to infinity in the three directions of the space. But, in the room conditions, the thermodynamically most stable carbon material is graphite, that appears as a lamellar solid. It is built from sp2 carbon atoms and it is twodimensional, because its covalent bonds grow to infinity in two directions of the space only : indeed the graphene planes are of course covalent structures, but they are stacked along the

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third axis by the means of very weak Van der Waals’s bonds. One knows two graphite varieties : the hexagonal one, whose stacking is ABABAB…, and the rhomboedral one with an ABCABC… stacking. The first one is slightly more stable than the second one. With sp hybridization, the carbon atoms lead to several one-dimensional solids called « chaoïtes ». They exhibit a fiber structure, since their covalent bonds grow to infinity in an unique direction of the space only. These linear covalent structures are gathered in beams. All these carbon materials can be observed in the nature, but the chaoïtes are however particularly rare, due to their weaker thermodynamical stability. Several other carbon materials derive from distorted graphene planes. Indeed, a perfect graphene plane is strictly flat, but if several hexagons are replaced by pentagons, it becomes convex and can turn into a closed structure. For this reason, it is admitted that the carbon hybridization in this case is included between 2 and 3. Thus, this phenomenon generates the class of fullerenes, among which the roughly spherical (truncated icosahedron) C60 molecule is the best known. Using Van der Waals’s bonds, the assembly of numerous C60 molecules leads to a cubic solid, that appears as zero-dimensional, because its covalent bonds do not grow in any direction. This material is called fullerite and it is of course rather volatile, because it contains rather small molecules linked by Van der Waals’s bonds. Lastly, it is also possible for a graphene plane to wind around itself, after having suffered a more or less important torsion, leading to a cylindrical structure. These objects constitute the class of carbon nanotubes. They can be single-walled (the cylinder is unique) or multiwalled (several cylinders are fitted together), and they are associated within beams generated by Van der Waals’s bonds. Of course, these carbon nanotubes, whose diameter is nanometric, appear as one-dimensional materials. Save the 3D diamond structure, all these carbon materials are anisotropic and exhibit Van der Waals’s bonds, that appears as weak points concerning the cohesion of these solids. Soft chemical reactions can exist for the latter, because, in these cases, the chemical reagents attack exclusively the areas of weak cohesion of the materials (often called Van der Waals’s gaps), without disrupting their covalent parts. These gaps simply spread apart in order to create the space necessary for setting up the reagent. These specific soft reactions are called insertion or intercalation reactions, according to the cases : insertion preferentially corresponds to reactions without appreciable dilation for the pristine material, while intercalation makes use on the contrary of large dilation. In most cases, these insertion/intercalation reactions are reversible and it is possible to regenerate the pristine carbon material by heating. Because of its medium electronegativity, we have seen that carbon appears as an amphoteric element. Indeed it is able to give or to pull out electrons, when it reacts with an other chemical species. This phenomenon turns up also in the case of the various allotropic carbon materials during these soft insertion/intercalation reactions. The donor or acceptor character is more or less pronounced according to the nature of the carbon material. However, whatever its range, the electron transfer is generally compulsory, otherwise the reaction doesn’t take place at all. With fullerites, the insertion word is more convenient, because the dilation remains often weak, due to the very large size of the tetrahedral and octahedral sites of the fcc structure of C60 fullerite, used for putting up the reagent. The intercalation word is more suitable for graphite, carbon nanotubes and chaoïtes, because the dilation can become considerable. It is precisely the case of graphite, that is the more studied among these carbon structures : its

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interplanar galleries spread apart very widely in order to accommodate sometimes very thick chemical species. By direct experiments, we have shown, on the other hand, that, towards strong electron donors as alkali metals, C60 fullerite is more acceptor than graphite, that is to say C60 appears as the most oxidizing of both materials [1].

II. Graphite: Variety, Bonds, Crystalline and Electronic Structures, Anisotropy and Material Considered as a Host Structure

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Graphite appears as the most stable carbon variety in room conditions. Its stability domain is especially extensive since the coordinates of the triple graphite-liquid-vapour point in its Clapeyron’s diagram are close to 4100 K and 125 kbar [2]. The sp2 hybridised carbon atoms that form the graphene planes are closely bound one another by means of very strong covalent bonds, whose length reaches 142 pm and energy 25 eV.mol-1 [3]. The strength of these bonds is revealed also by a very high sublimation point of about 3700 K. In this 2D structure, each carbon atom is associated with three coplanar neighbours, so that the value of the C-C-C angles is exactly 120°, according to the sp2 hybridisation. The unused pz orbital of each carbon can build with neighbouring atoms πz molecular orbitals, that are of course delocalised on the whole of the graphene plane, as they are also in the case of the flat benzene molecule.

Figure 2. Crystal structure of hexagonal graphite (P63/mmc).

On the other hand, very weak Van der Waals’s bonds provide the cohesion between the successive graphene planes, that are stacked up into graphite. For this reason, two successive Graphene and Graphite Materials, Nova Science Publishers, Incorporated, 2009. ProQuest Ebook Central,

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graphene layers in graphite are 335 pm apart. But, they are not exactly superimposed and their stacking corresponds to the ABAB… sequence (Figure 2). The unit cell is hexagonal and belongs to the P63/mmc space group with the following parameters : a = 244 pm and c = 670 pm [4]. The carbon positions are : (000) and (2/3 1/3 0). And, taking the helicoïdal 63 axis into account, it appears four carbon atoms in each unit cell. In the end, graphite exhibits a very low density of 2.3. This unusual structure confers a very strong 2D character on graphite. It is a perfect example of lamellar material, whose sheets are monolayered. Its anisotropy appears in all fields. Its mechanical properties for instance exhibit a very good aptitude for the cleavage, so that graphite appears as a material often used in lubricating (oils, pencil lead, etc…). Similarly, its electrical properties are very anisotropic : graphite is indeed a poor conductor along the c-axis and it is much better conductor in the other directions, since the corresponding resistivities reach respectively 0.1-1 Ω.cm and 40 μΩ.cm [5]. Graphite can be either natural or synthetic. Well crystallised natural graphite platelets principally come from Madagascar, Sri Lanka, URSS or China. They are often mixed with other minerals like calcite or quartz and they have to be chemically purified after a manual sorting. Powder of synthetic graphite is obtained from pyrolysis of organic precursors followed by a step of graphitization. The ability of carbon to graphitize is determined during the pyrolysis. Hard carbon that is not graphitizable comes from carbonization without passing through a liquid phase. In this case, the number of graphitic slides is limited, with an distance larger than that of graphite (340-345 pm instead of 335 pm). Moreover these small crystallites are disoriented. Even after a heat treatment at 2500-3000°C, this carbon remains hard and without lubricant properties. On the contrary, when a liquid phase appears during the pyrolysis, crystallites have quite the same orientation and they are able to grow with a three dimensional organization. The graphitization is obtained by a heat treatment in the course of which most of defects disappear, the average diameter of crystallites increases and the distance between graphitic planes comes near 335 pm like in the perfect crystal. Artificial graphite powder with various granulometry can be obtained so. Otherwise, it is also possible to prepare pyrolytic graphite. A carbon deposit on a heated graphite substrate is obtained by cracking of gaseous hydrocarbide diluted in argon. Graphitic sheets are parallel to the surface and when this pyrographite is heated at very high temperature (3000°C) under high pressure, the anisotropy of the material is increased and it becomes “highly oriented pyrographite” or “HOPG” whose properties are very close to those of a single crystal. In “HOPG”, the c-axis of all crystallites, that are perpendicular to the graphene sheets, are parallel between them, with a maximal defect of 1°. However, the a and b axis are randomly oriented in the graphitic layers so that a HOPG platelet can be considered as a single crystal in the c-axis and as a powder in the perpendicular plane. An other variety of graphite called “grafoil” is obtained by compression of first exfoliated graphite [2].

III. Chemical Anisotropy Because of the nature of its bonds, the chemical properties of graphite are particularly anisotropic. In a first time, the presence of Van der Waals’s bonds explains the chemical reactivity of graphite, by comparison with the diamond one, that is almost nonexistent : for

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instance, the oxidation of graphite is rather easy, whereas it is especially difficult in the case of diamond. In a second time, the soft reagents, that are unable to destroy the covalent bonds inside the graphene planes, take advantage of the weakness of the Van der Waals’s bonds, in order to fill the interlayered galleries, leading to graphite intercalation compounds. Because these reactions are necessarily oxido-reduction reactions, a charge transfer takes place systematically between the graphene planes and the reagent. Indeed, it is well established that the intercalation into graphite is strictly impossible without electron transfer. As graphite is amphoteric (now oxidizing, now reducing), it can be, according to the cases, electron acceptor or electron donor. But, it reacts only with strong enough reducing or oxidizing reagents. Alkali metals, alkaline-earth metals and several lanthanides are very good reducing species, so that they intercalate easily into graphite at low temperature, releasing electrons into the graphene layers. This electron input creates a small dilation of the carbon-carbon distance in the covalent bonds. With these various metals, the intercalated sheets are strictly mono-atomic layers in all cases. The space between both graphene planes that surround the intercalated sheet widely varies according to the size of the intercalant. It is called « interplanar distance » (di). On the other hand, if the reagent amount is not enough to fill up all the Van der Waals’s galleries, only a few of them are full, while the others remain empty. It is impossible indeed for the intercalant to be diluted homogeneously in all Van der Waals’s gaps. In these cases, the empty intervals and the full ones follow periodically one another along the c-axis, so that the full galleries attempt to scatter at the most. This specific phenomenon leads to define a « stage » (s) for each intercalation compound : it is the number of graphene layers included between two successive intercalated sheets (Figure 3.a). The stage one is thus characteristic of the saturated compounds, but it is often possible to synthesise some compounds belonging to the stages 2, 3, 4, 5, etc…, with potassium for instance. It is usual to call « c-axis repeat distance » (Ic) the space between two successive intercalated sheets. Thus the existence of high stage graphite intercalation compounds reveals some interactions between intercalated sheets through long distances.

Figure 3. a) Model of a graphite intercalation compound (stage 3) b) Daumas-Hérold model.

The intercalated sheets can be less dense in the high stage compounds than in the first stage one. Indeed, KC8 is the chemical formula of the first stage compound whereas KC12s corresponds to the stage s compound. If we consider an intercalation reaction into graphite, the intercalant leads, in a first time, to the formation of high stages compounds, and then the progressive inlet of new amounts of reagent allows to obtain some compounds, whose stage

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regularly decreases as the intercalant takes up the empty galleries, according to the DaumasHérold model (Figure 3.b). This uncommon phenomenon is called « staging » and illustrates clearly the very high flexibility of the graphene plane. Indeed, among all the lamellar phases able to behave as host structure, the mono-layered graphene plane is truly the most flexible of them. On the other hand, it is interesting to compare the density of the intercalated sheets contained in the various first stage intercalation compounds [6]. With the little atoms (Li, Ca, Sr, Ba, Yb, Eu…), the latter are especially dense, since their chemical formula corresponds to MC6. On the contrary, in the case of the biggest atoms (K, Rb, Cs), the formula becomes MC8. For all these compounds, it is well established that the characteristic ABAB… graphitic sequence disappears for the benefit of the AAA… stacking, that leads to generate interlayered hexagonal prismatic sites, that the metallic atoms can very easily take up. All these data show clearly that the intercalated mono-layered sheets of these binary compounds are strictly commensurate with respect to the graphene planes. In all cases, the 2D unit cell of the intercalated sheets is consequently hexagonal. But, concerning the 3D one, it can be hexagonal, rhombohedral or even orthorhombic, according to the c-axis stacking mode of the successive intercalated sheets. Associated with alkali metals, numerous other elements are able to intercalate into graphite, leading to ternary compounds [7]. We find in this category weakly electropositive elements as hydrogen, mercury, thallium, bismuth, etc… or strongly electronegative ones as oxygen, halogens, sulphur, etc… In all cases, these binary intercalated species behave towards graphite as electron donors and lead generally to poly-layered intercalated sheets. We will speak about these ternary phases at length in the subsequent developments. On the other hand, very numerous oxidizing species are able to intercalate into graphite [8]. For instance, chlorine and iodine intercalate without difficulties. But various metallic halogenides (iron, copper, nickel, lanthanides chlorides…), several oxacids (H2SO4, HNO3), some oxides (Cl2O7, SO3, CrO3…) can also intercalate easily into graphite. All these chemical species intercalate while removing some electrons of graphene planes. This electronic removal causes a weak decrease in their carbon-carbon bond length. On the other hand, the previous « staging » phenomenon appears as well with these electron acceptors. It can be even particularly pronounced, since it has been reported a tenth stage graphite-sulphuric acid intercalation compound. Most of these compounds possess poly-layered intercalated sheets [9]. As examples, we find Cl-Fe-Cl and F-As-F three-layered sheets respectively in graphiteFeCl3 and graphite-AsF5 compounds, or mixed (Au-Cl) two-layered sheets in graphite-Au2Cl6 ones. In fact, such poly-layered sheets pre-exist before in the binary pristine halides, if the latter are solid in the room conditions. In these cases, they simply set up inside the Van der Waals’s galleries, after the charge transfer occurs. Consequently, these intercalated sheets are generally no-commensurate with respect to the adjacent graphene planes, that keep the ABAB… stacking of pristine graphite. In the end, it appears that both graphitic and intercalated sublattices grow parallely, using quite reduced interactions, so that both 2D unit cells remain very often quasi independent. To sum up, in order to know the main features of a given graphite intercalation compound, it is absolutely necessary to specify its chemical formula, its stage, its repeat distance and, if possible, the c-axis atomic stacking inside its intercalated sheets and the corresponding 2D unit cell. But it is not easy, for very numerous compounds, to know their 3D unit cells.

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IV. Donor-Type Graphite Intercalation Compounds

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From this part, we will consider only the graphite-electron donors compounds, because the superconducting phases appear solely in this specific category. The intercalation into graphite of the electropositive elements leads to a charge transfer, that releases electrons in the graphitic sublattice. The graphene plane appears as a macroanion and the intercalated layer is made up of cations. For this reason, it is legitimate to regard these graphite intercalation compounds as « metallic graphitides ». But, of course, the charge transfer is not complete and the s valence electron remains partially tied to metallic atom. It is possible to say that the graphitide macro-anion constitutes the reducing part of the compound. On the whole, these lamellar compounds appear as strongly reducing species and cannot be handle to the air on pain of a severe oxidation. When it is possible, the best synthesis method consists in putting the graphite material in the presence of the metal vapour, after having carefully evacuate air from the reaction tube. Thus, graphite and metal are arranged in each end of the glass tube sealed under vacuum and a temperature gradient is carried out between both reagents (Figure 4) [10]. The lower temperature is assigned to the metal, so that it imposes its vapour pressure on the whole of the tube. According to the value of the higher temperature, it is possible to synthesise first, second, third… stage binary compounds. The stage increases when simultaneously increases the temperature gradient range [6].

Figure 4. two-bulb tube for vapour phase intercalation reaction.

This method allows to prepare very pure graphite intercalation compounds, but, the vapour pressure of the metal has to be sufficiently high, even at low temperatures (200300°C). It is the case for the heavy alkali metals (K, Rb and Cs), but all the other metallic elements able to intercalate into graphite need a too high temperature, so that the reaction becoming too violent causes the destruction of the graphene planes and leads to the formation of metallic carbides. Consequently, for these metals (Li, Ca, Ba, Eu, Yb…), other synthesis methods have to be carried out. Two well established routes are recommended : solid-solid and liquid-solid reactions. The solid-solid reactions require to use a powder mixture of pure metal and pristine graphite. They have been particularly used in order to synthesise the various graphite-lithium phases [11]. Both well mixed metal and graphite powders are compressed in a pure argon atmosphere until 10 kPa and then heated under Argon or vacuum at 200°C during 24 hours.

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With lithium, the reaction product is LiCx, according to the initial Li : C ratio. Of course, the reaction temperature allows the easy lithium intercalation but remains quite low in order to avoid the formation of lithium acetylide (Li2C2). On the other hand, it is well established that temperature and pressure induced by the shocks occurring during a ball-milling can temporarily reach very high values (close to the previous conditions). Therefore, the grinding of graphite and lithium powders mixture can be used in order to synthesize graphite-lithium compounds [12]. Small amounts of n-dodecane (C12H26), which is entirely inert towards lithium, are added in order to avoid agglomerating lithium particles on the milling tools during the grinding reaction. The liquid-solid reactions are mostly more complex and especially more delicate, because it is necessary to liquefy the metallic reagent. If the melting point of the metal is low, it is easy of course to obtain a liquid reagent, but, when it is high, we have to use a mixture with a second metal in order to decrease the melting temperature. Indeed, the intercalation reaction temperature has to remain low in order to avoid the destruction of the graphene planes. The choice of the added metal is especially difficult, because, when the alloy reacts with graphite, only the first metal has to intercalate. Now, for a given alloy, reaction temperature and alloy composition strongly influence the nature of the reaction product. It is often very difficult to find the best reaction conditions able to lead to a binary intercalation compound. Sometimes, they do not exist and it is thus only possible to obtain a ternary intercalation compound or even no intercalation at all. Consequently controlling three basic parameters appears as very important in order to succeed in the intercalation into graphite of a metallic element by reaction with a liquid alloy : it is a matter of the nature of the associated metal, its concentration and the reaction temperature. For instance, LiC6 can be prepared easily using a Na-Li liquid alloy in well chosen conditions [13], CaC6 is obtained from a Ca-Li liquid alloy [14]. Of course, these reactions are carried out safe from air (under vacuum or argon atmosphere, according to the cases). After reaction, separating the solid compound from the liquid alloy is easy only if pristine graphite is a pyrolytic graphite platelet. For this reason, it is not recommended to carry out such a reaction using graphite powder. Concerning the ternary graphite-electron donors compounds, they contain two intercalated elements, whose first of them has to be metallic, while the second one can be metallic or not according to the cases. As previously, the charge transfer necessarily occurs with an increase of the negative charges inside the graphene planes, which are reduced. When is intercalated a mixture of two strongly electropositive metals (K-Rb, Rb-Cs, KCs) [15-17], the intercalant remains mono-layered, as in the binary compounds. In all other cases, on the contrary, the ternary compounds contain poly-layered intercalated sheets. More frequently, three atomic layers are intercalated between the graphene planes and this sandwich possesses a central layer of less electropositive atoms surrounded by two symmetrical layers, that are made of strongly electropositive atoms [18-19]. In order to synthesise these ternaries, the usual method is the liquid-solid reaction. A pyrolytic graphite platelet is plunged in a liquid metallic alloy or in a melted metal containing very small amounts of the second element, when this latter is weakly electropositive or strongly electronegative.

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Figure 5. Intercalation by means of two successive steps (case of potassium amalgams).

In exceptional cases, it is easier to carry out the synthesis by means of two successive steps [20] (Figure 5). In a first time, is prepared a first stage potassium-graphite, for instance, by the classical vapour-solid method, and, in a second time, this binary phase is put in the presence of hydrogen or mercury vapour. This second intercalation reaction causes an increase in the stage (from 1 to 2), and simultaneously the mono-layered intercalated sheets become three-layers. Only intercalation compounds of higher than one stage can be obtained using this method.

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V. Binary Graphite Intercalation Compounds Alkali metals graphite intercalation compounds are particularly well known, because they were the most studied among the lamellar graphite compounds. Potassium, rubidium and cesium (known as heavy alkali metals) intercalate very easily into graphite galleries [21]. They lead to intercalation phases, whose stage can vary from 1 to 2, 3, etc… The first stage compounds exhibit a specific brilliant gold colour. Their chemical formulas are KC8, RbC8 and CsC8, and their interplanar distances reach respectively 535, 565 and 592 pm, according to the increasing size of the alkali metals. Their crystal structures exhibit very pronounced likenesses. Of course, their intercalated sheets possess exactly the same geometry : each intercalated metallic atom occupies a prismatic hexagonal site, due to the AAA… c-axis stacking of the graphene planes. But, in each gallery, the quarter of the hexagonal sites only are occupied, so that it is possible to define four distinct sites into the Van der Waals’s gap : α, β, γ and δ. Although the graphene planes are exactly superimposed, the metal layers, on the contrary, avoid strictly superimposing at the most, due to the Coulomb’s repulsion. For potassium and rubidium, the c-axis sequence is AαAβAγAδ…, revealing long distance interactions between intercalated sheets. Consequently, the c parameters of KC8 and RbC8 are respectively 2140 and 2260 pm. Because of its higher interplanar distance, CsC8 adopts a shorter sequence AαAβAγ…, so that its c parameter reaches only 1776 pm. These differencies lead crystal structures, whose geometries are

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orthorhombic [2, 3] for KC8 and RbC8 (with Fddd space group, Figure 6) and hexagonal [4] for CsC8 (with P6422 space group, Figure 7).

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Figure 6. Crystal structure of KC8 (Fddd).

Figure 7. Crystal structure of CsC8 (P6422).

It is harder to synthesise sodium graphite intercalation compounds. Indeed, only high stage compounds [5] are reported, whose formulas are NaC8s, with stage number s = 4 to 8. Graphene and Graphite Materials, Nova Science Publishers, Incorporated, 2009. ProQuest Ebook Central,

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The reason for the difficulty in the synthesis of these compounds consists in two competing factors : the ionisation potential of sodium and its size. The ionisation potential increases from Cs to Li (from 3.9 eV to 5.4 eV), whereas the ionic radius strongly decreases (from 200 pm for Cs to 100 pm for Li). Of course, the lower the ionisation potential, the easier is the electron transfer from metal towards graphite. Consequently, the energy gain upon the charge transfer becomes more and more weak from Cs to Li. That is the reason that explains why a first stage sodium graphite compound is with difficulty thermodynamically stabilized. According to this argument, it can be surprising that Li is able to give without difficulty a first stage LiC6 graphite intercalation compound [11]. This observation can be explained by the very small size of Li+. Indeed, owing to its size, lithium causes a weak spacing of the graphitic galleries, corresponding to a small energy, that promotes the stability of the intercalation compounds, in spite of the previous unfavourable factor. In the case of sodium, that is an intermediate element, both factors are simultaneously unfavourable : weak ionisation potential and too large spacing of the carbon layers. In LiC6, the interplanar distance is very small (370 pm), because of the small size of Li+. The lithium atoms occupy prismatic hexagonal sites, as previously in the case of heavy alkali metals compounds. But with lithium, the intercalated sheets are more dense, so that, in each of them the third of the hexagonal sites contains a lithium atom. Consequently, we have to define only three distinct sites into the graphitic galleries : α, β and γ. In spite of that, the metallic atoms are exactly superimposed along the c-axis, according to the AαAα… sequence (the repeat distance is of course equal to the interplanar distance). Such a stacking makes two Li atoms very close through the graphene plane (370 pm), so that one can consider that exactly c-axis superimposed Li atoms are partially themselves bound by means of covalent bonds. Instead of a Coulomb’s repulsion as previously, it is, on the contrary, a covalent attraction that governs the crystal structure. The unit cell of LiC6 is hexagonal and its space group is P6/mmm [11] (Figure 8).

Figure 8. Crystal structures of MC6 compounds.

Alkaline earth metals intercalate into graphite similarly to lithium. Indeed, calcium, strontium and barium [26] lead to first stage phases, whose formulas are respectively CaC6, Graphene and Graphite Materials, Nova Science Publishers, Incorporated, 2009. ProQuest Ebook Central,

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SrC6 and BaC6. The interplanar distances increase regularly from Ca to Ba, as the corresponding ionic radii : 455, 494 and 525 pm. These metals exhibit high ionization potentials and simultaneously low vapour pressures, so that the intercalation by solid-vapour reactions appear as rather difficult. Thus, it is recommended to carry out the intercalation of these metals by solid-liquid reactions, using Li-Ca and Li-Ba well chosen alloys [27, 28]. The 2D structure of the intercalated sheets is exactly the same as for LiC6. But, due to larger ionic radii, the Coulomb’s repulsions lead to c-axis stackings quite different : AαAβ… and AαAβAγ… respectively for BaC6 and SrC6 [26] on the one hand and for CaC6 [29] on the other hand. The first stacking leads to an hexagonal unit cell (space group : P63/mmc) and the second one to a rhomboedric cell (space group : R-3m) (Figure 8). Several of the rare earth metals (Eu, Yb, Sm) have been reported to be intercalated into graphite [30]. As previously, high ionization potentials and low vapour pressures lead to difficult solid-vapour intercalation reactions. When it is possible, the solid-liquid one is preferable. Thus, in the case of europium, well chosen Li-Eu alloys are able to give first stage graphite-Eu intercalation compound. The formula of these lamellar phases is MC6, due to rather small ionic radii. And their interplanar distances reach 457, 487 and 471 pm respectively for YbC6, EuC6 and SmC6. The crystal structure of EuC6 and YbC6 corresponds to the c-axis AαAβ… sequence, so that their unit cell is hexagonal (space group : P63/mmc). High-pressure synthesis allows to prepare highly dense alkali metal graphite intercalation compounds. In these lamellar phases, the alkali metal densities can exceed considerably the maximum value observed for graphite compounds obtained by more traditional methods. Lithium gives, beyond 8 kbar, very high density compound LiC2 [31, 32]. But this latter is decomposed into less dense lamellar phases as the pressure is released. Thus, it is possible to identify successively the following compounds : Li11C24, Li9C24 and Li7C24. In spite of its rather high density, Li7C24 remains stable even at ambient pressure. On the other hand, using the ball-milling method, the LiC3 metastable phase was obtained [12]. Sodium, which is not able to give first stage intercalation compound using classical methods, leads under high pressure (35-40 kbar) to dense NaC2-3 lamellar phases [33]. But they decompose in graphite and metal below 20 kbar. In the case of heavy alkali metals, KC4, RbC4.5 and CsC4 were reported [34, 35]. These various intercalation compounds are obtained respectively beyond 5 kbar, at 20-25 kbar and at 2 kbar. Among them, only CsC4 remains metastable as the pressure is released, although it is far from equilibrium conditions. The intercalated sheets for highly dense lithium, potassium, rubidium and cesium graphite intercalation compounds are mono-layers, with classical previously reported interplanar distances. On the contrary, it is not the case with sodium, since NaC2.6 consists of three-layered metal intercalated sheets and exhibits an interplanar distance of 704 pm [33]. No information concerning its in-plane structure was reported. In LiC2, the lithium atoms occupy all the hexagonal prismatic sites derived from the AAA… c-axis stacking of the graphene planes, so that the in-plane Li-Li interatomic distance is 248 pm. This value is especially weak, since even in cubic centered pristine lithium metal, the Li-Li distance is larger (309 pm). The Li7C24 compound following the release of pressure exhibits hexagonal 2D Li7 clusters [32] (Figure 9), leading to an in-plane hexagonal unit cell, whose a parameter of 863 pm is equal to 2√3.aG (aG is the hexagonal in-plane parameter of graphene plane). Along the c-axis, its c parameter is three times higher than its repeat distance

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(1110 pm). The presence of lithium clusters, which are considered to be stabilized with the formation of Li-Li covalent bonds, appear of course as the consequence of the application of pressure.

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Figure 9. Two-dimensional structure of Li7C24 (from [32]).

Figure 10. Crystal structure of LiC3 (P63/mmc, from [36]).

The crystal structure of the ball-milled LiC3 compound exhibits an unusual small splitting of the intercalated lithium layer [36]. Indeed, in its hexagonal unit cell, that belongs to the P63/mmc space group (Figure 10), with a = 430 pm and c = 740 pm (twice the repeat

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distance), it appears a shift of the intercalated lithium layer in two planes at ± 44 pm from the medium plane of the graphitic galleries.

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Figure 11. Two-dimensional structure of CsC4 (from [37]).

The metastable CsC4 structure has been reported [37]. The in-plane unit cell of its intercalated sheets is rectangular with a = 2√3.aG and b = 2aG (Figure 11). In this compound, cesium linear chains are formed by occupying half the hexagonal prismatic sites. In every chain, the Cs-Cs interatomic distance reaches 248 pm and two adjacent chains are one hexagon ring apart from each other, so that the interchain distance is 428 pm. In pristine graphite material, the combination of sp2 σ- and π-bonds is the origin of the very strong intralayer interactions, while the overlap of π-bonds between the successive graphene layers generates the weak interlayer interactions [5]. In examining the electronic properties around the Fermi energy, which is especially important for the electronic structure of the graphite intercalation compounds, the π-electron orbitals play an essential role. They provide graphite with its exceptional properties. Conversely, the σ-bands, which exhibit larger energy than π-bands, are located far from the Fermi energy. Consequently, they do not contribute to any noteworthy change in the electronic properties when intercalated sheets are introduced between the graphene layers. On the basis of the tight binding model [38] and using Slonczewski-Weiss-McClure parameters, it was established that the electronic structure of pristine graphite shows four πbands due to the ABAB… graphitic stacking : E1, E2 and E3 (twofold degenerate). And the Fermi level crosses the E3 band, producing one electron pocket and two hole one, so that graphite appears as a semi-metal. In spite of its relative simplicity, in most cases, this model is fully efficient in order to explain the electronic properties of graphite. The numbers of charge carriers (holes and electrons) are estimated at 3.1018 cm-3. They are of course considerably smaller than for true metals. In addition, holes and electrons possess noteworthy

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smaller effective masses : 0.039m and 0.057m, respectively, where m is the free electron mass [39]. The simplest model of the electronic structure of graphite intercalation compounds is obtained from the π-band structure on the basis of the Slonczewski-Weiss-McClure tight binding model with the rigid bands scheme, where the interactions between the graphene sheets and the intercalated ones are neglected (Figure 12). It is known as Blinowski-Rigaux model [40, 41]. Because of its simplicity, it is only convenient for the electron acceptor graphite intercalation compounds. Indeed, the electronic states of the intercalated acceptor species are well below the Fermi level. The electrons in the valence π-band are transferred to the acceptor band, so that numerous holes are produced around the top of the π-band, able to play the role of charge carriers.

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Figure 12. Electronic structures of graphite and donor-type GIC (rigid bands).

In the case of electron donor graphite intercalation compounds, the intercalate band (for example, the 6s level in the case of cesium) is located close to the Fermi level. Consequently, this intercalate band has to be taken into account in addition to the graphitic π∗-band in the working out of the corresponding electronic structure. Of course, the latter is rather complicated compared to that of acceptor graphite intercalation compounds. In order to obtain convenient informations on the electronic structure of electron donor graphite intercalation compounds, it is thus necessary to use more sophisticated models than the BlinowskiRigaux one. LiC6 has been a target of most intensive studies using numerous methods of calculation, because its electronic structure is the simplest among the electron donor graphite intercalation compounds [42-47]. The interlayer state of graphite, which is unoccupied in pristine graphite, plays an important role through hybridisation between interlayer state and intercalate one [46, 48-52]. An overlap between the interlayer band and the intercalate one occurs because both of them are located in the same energy range. The resulting hybridisation gives interlayerintercalate bands featuring a combination of both bands in the graphitic interlayer space. Consequently, the intercalate electronic state is not purely that of intercalate, but possesses a strong contribution from the interlayer graphitic state. This interlayer-intercalate band exhibits a 3D nature, which is a noteworthy feature of the electronic structure of the electron donor graphite intercalation compounds (especially first stage ones). It is located between

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around 1.3 and 6.3 eV, that is to say well above the Fermi level, so that the electronic structure of LiC6 can be reasonably understood in terms of almost complete charge transfer between lithium atoms and graphene layers, leading to the presence of completely ionized Li+ cations between the graphene planes. This result is absolutely consistent with that would predict the simple rigid band scheme, if we consider that the Li 2s level is far above the Fermi energy. The behaviour of the first stage KC8, RbC8 and CsC8 compounds is quite different, because it appears a close proximity of the interlayer-intercalate state and the graphitic πband, so that the situation is rather complicated. Thus, it is useful to consider, in the case of KC8 for example, the hybridization of the graphitic π-band and the K 4s band [53-54]. The calculations show that the graphitic π∗-band is mixed with the K 4s one in the vicinity of the Fermi level, leading to only partially ionized potassium atoms (K0.6+) in the graphitic galleries. The same phenomenon occurs in both RbC8 and CsC8 cases, the interlayerintercalate band moving however to higher energy from potassium to cesium [52, 53, 55]. The alkaline earth and rare earth metals lead to first stage graphite intercalation compounds, whose formula is MC6. Among these phases, BaC6 was the most investigated [56-58]. Three bands cross its Fermi level : two of them are ascribed to the graphitic π-bands, while the third one is due to the interlayer-intercalate band. The partially occupied latter plays an important role in characterizing the electronic structure in the vicinity of the Fermi level. It contains also contributions of Ba 6s and 5d orbitals. Indeed, the hybridization between Ba 5d and graphitic π-bands has an important effect on the electronic structure of BaC6. It seems that one of both electrons in the Ba 6s band is transferred to graphitic π-band, while the second stays in the interlayer-intercalate one. In EuC6, that possesses a particular interest with regard to magnetism, occurs an interaction between Eu 4f and graphitic π-electrons, that plays an essential role, giving rise to novel magnetic behaviour in this compound [59-63]. The 4f electrons give localized states, which are responsible for localized magnetic moments, whereas the delocalized 6s electrons cause the formation of bondings with the graphitic π-electrons upon intercalation. It occurs an hybridization of 6s, 6p and 5d states of europium and appears simultaneously an overlap between the graphitic π-band and Eu spd orbitals. Consequently, a sd-hybrid band emerges as a partially filled state between the Fermi level and the π∗-band. At last, the amount of charge transferred from Eu to graphite is estimated at 0.5. This small value is ascribed to covalent admixtures present in EuC6 as well as the rather large electronegativity of europium (compared with alkali metals). Similar electronic features were observed in the case of YbC6 compound. Obtained by means of high-pressure synthesis, superdense alkali metal graphite intercalation compounds exhibit rather different features from classical binary phases. The application of pressure, leading to reduce the volume of the atoms, enhances simultaneously the contribution of p- or d-levels in the electronic structures, in spite of the predominance of the s-level [64, 65]. The p- and d-orbitals, which have directional features instead of a spherical symmetry as the s- ones, promote the covalent feature of the bonds. Thus, the presence of Li clusters (Li7C24) and Cs chains (CsC4) appear as the consequence of the covalent bond formation in the intercalated layers of these compounds [37, 66]. If we consider the very large concentration of Li in the superdense lithium compounds, it appears nevertheless that the electron transfer rate per carbon atom from Li to C exhibits

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approximately the same value in these phases as in LiC6. Consequently, the charge transfer per lithium atom is strongly reduced. This phenomenon can be explained, in Li7C24 for instance, by an obvious participation of covalent bonds, having directional p-character, in the formation of the 2D Li7 clusters. In CsC4, it was also reported that the charge transfer per cesium atom is weaker than in CsC8. This suggests the presence of Cs-Cs covalency, which is responsible for the formation of cesium chains, brought about by the presence of Cs 5dorbitals [67]. It is well established that pristine host graphite exhibits a semi-metallic behaviour. In graphite intercalation compounds, the intercalated electron donors release a large concentration of charge carriers (electrons) in graphene layers, so that these compounds become truly metallic. Indeed, their characteristic in-plane conductivity reaches about 105 Ω1 .cm-1 [68]. The 2D features of their electronic properties lead however to extremely different conductivity processes between in-plane and interplane directions. Since these compounds appear as 2D materials, their electron transport properties are particularly modified from those observed for classical 3D metals. For instance, their Debye temperature, close to 2500 K, is strongly higher than that measured for ordinary metals (it reaches indeed in most cases only 300 K). The in-plane resistivity is expressed by the means of an empirical formula, whose temperature dependence is quadratic, even though it is simply linear in the case of ordinary 3D metals [69-72]. On the other hand, the c-axis conductivity is very weak in comparison with the in-plane one. A 2D band model, widely used in the case of electron acceptors graphite intercalation compounds, is not efficient for the electron donors ones because of too strong correlations between the graphene planes. Indeed, the intercalated sheets are usually electrically conductive in these cases, so that three dimensionality has to be taken into consideration in order to rightly analyse the c-axis conductivity of these phases. Indeed, it was established that donor intercalates contribute effectively to c-axis electron transport. As a consequence of this phenomenon, it appears that the c-axis conductivity of the binary electron donors graphite intercalation compounds is always larger than that of pristine graphite. Thus, HOPG, LiC6 and KC8 possess c-axis conductivities (σc in Ω-1.cm-1 ) of 8.3, 1.8 x 104 and 1.94 x 103 respectively [73-75]. This is considered to be associated with the presence of the interlayerintercalate states in the graphitic galleries, as it has been previously reported. The partial three-dimensionality of the binary electron donors graphite intercalation compounds is also easily observed examining the room temperature σa/σc ratio. In the case of pristine graphite (HOPG), it reaches indeed 3 x 103, and frequently 104, 105 and even 106 for the electron acceptors compounds, but it falls to 56 and 14 for KC8 and LiC6 respectively. Impurity- and phonon-assisted hopping seems to play a basic role in the behaviour of the c-axis conductivity, according to Sugihara [76-78]. On the other hand, Shimamura [79] claims the importance of the presence of conduction paths, which are produced by intercalation of incomplete layered sheets (Daumas-Hérold domains for instance).

VI. Superconductivity o Binary Graphite Intercalation Compounds Among graphite intercalation compounds (GICs), only donor type compounds exhibit superconducting properties.

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The superconductivity in graphite intercalation compounds has been discovered in 1965 by Hannay et al. [80] in first stage alkali metal compounds. The transition temperatures observed range from 0.39 K to 0.55 K for KC8, from 0.023 K to 0.151 K for RbC8 and from 0.020 K to 0.135 K for CsC8. The authors didn’t observe any superconductivity down to 0.011 K for second stage compounds. After this work, superconductivity of KC8 was confirmed quite twenty years later by Koike et al. [81-83], by Kobayashi and Tsujikawa [84, 85], and the superconducting properties were investigated in detail. Later, the superconductivity of RbC8 was confirmed by Kobayashi et al. [85, 86]. Table I. Superconducting binary first GICs di (pm)

Hc2⊥/Hc2//

KC8

535

4.7 - 6.2

RbC8

565

CsC8

592

LiC2

368

GIC

NaC2 NaC3 NaC4 KC3

(at T =100 K)

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530.5

(at T =100 K)

RbC4.5 CsC4 YbC6 CaC6

References 80 81-83 84, 85 80 86 80 94, 95 95 93, 95, 96

2.3-3.8 2.3-4.5

93, 96 95

2-3.5 3 5.5 0.35-3 1.5 1.5 1.45-1.55 1.6 6 6.5 11.5 11.45 11.3

95 93, 95 97 95 93, 97 95 34 35 98 87 87 88 105

398.5 and 557.8

KC4 KC6

Tc (K) 0.39 – 0.55 0.128 – 0.198 0.15 0.023 – 0.151 0.026 0.020 – 0.135 1.9 0.9 - 1.6 5

457 451 452.4

2 2 3.5-4

In the end of the eighties, the application of high pressure on mixtures of graphite and alkali metals have led to superdense GIC’s, a new family of superconducting materials with a highest Tc of 6 K for CsC4. But these compounds are not stable in ambient conditions (temperature and pressure). Twenty-five years later, the discovery of the superconductivity in YbC6 and CaC6 [87, 88] with critical temperature of 6.5 K and 11.5 K respectively has led to a renewed interest in graphite intercalation compounds. In all systems, when the graphite intercalation compound is superconducting, the intercalated element doesn’t superconduct. All superconducting binary GICs are listed in Table I.

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KC8 Compound Most studies were performed on potassium-graphite compounds. Superconducting properties of this system were investigated by Koike et al. by low frequency a.c. magnetic susceptibility and electrical resistivity measurements using HOPG based samples. The intercalation was carried out using potassium in vapour phase. The superconducting transition that is quite narrow, appeared between 0.128 K and 0.198 K measured on 13 samples, leading to an average value close to 0.15 K. Magnetic susceptibility measurements performed with the applied magnetic field parallel or perpendicular to the c-axis revealed a remarkable anisotropy. When the applied field is parallel to the c-axis, KC8 appeared as a type I superconductor whereas when the field is applied in the perpendicular plane, type II superconductivity is observed. An anisotropic behaviour is also evidenced by the values of the critical fields : Hc2 for an applied field perpendicular to the c-axis is more than twice higher than Hc for an applied field parallel to the c-axis. This anisotropic feature declines with the decrease of the K/C ratio. However, the reduction of potassium concentration doesn’t change the value of the transition temperature up to the composition KC14.7. No transition was found down to 0.060 K for KC16.7 and KC21.6 [85] so that it is the confirmation that the second stage potassium-graphite compound is not superconducting. However, the transition temperature depends on the carbon materials used for the preparation of the samples. Indeed, Tc is 0.080 K when powdered pyrolytic graphite is used, 0.125 K using grafoil and in the best case, 0.162 K with HOPG [85]. The higher is the crystal structure of the host material, the higher is the Tc.

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RbC8 Compound In comparison, RbC8 became superconductor at 0.026 K [86] and it appeared as a type I. As in the case of graphite-potassium system, in the graphite-rubidium one, superconductivity was evidenced only in the first stage compound.

Hydrogenation of KC8 The hydrogenation of KC8 has led to superconducting quasi-binary compounds whose sheets are monolayered. This property depends on hydrogen concentration, stage and host graphite. KH0.19C8 prepared by hydrogen chemisorption from HOPG based KC8 is superconducting below 0.195 K [89]. This compound seems to be a mixture of KH0.1C8 (stage 1) and a stage 2 potassium hydride ternary compound that is not superconducting. The latter is described in VII. The superconductivity is then induced by the quasi-binary KH0.1C8. As in KC8, KH0.1C8 appeared as a type I superconductor when the applied field is parallel to the caxis whereas type II superconductivity is observed when the field is applied in the perpendicular plane. No superconductivity is observed in the ternary stage 2 compound KH0.67C8 prepared from grafoil.

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KC8 under Pressure The application of high pressure is often tried to increase the values of the transition temperature in superconducting materials. In the case of KC8, DeLong et al. [90, 91] found at an applied pressure ranging from 2 kbar to 15 kbar a first-order phase transition from a superconducting state with a Tc of 0.13 K to a an other one with a Tc of 1.7 K. The exact nature of the high pressure phase remains uncertain even if structural changes are the most probable. Later Belash et al. [92, 93], succeeded in increasing the critical temperature of KC8 applying pressure up to 13 kbar to 1.5 K. But with an applied pressure higher than 13 kbar, Tc decreases to 1.4 K at 30 kbar and to 1.13 K at 37 kbar.

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Dense Alkali Metal Compounds Graphite intercalation compounds with all alkali metals were obtained using a high pressure synthesis method. These high concentration alkali metals compounds form a group of superconducting materials with transition temperatures higher than those of classical binaries. Most of these compounds are not stable under standard conditions so that they were quenched to temperatures of 90 K to 100 K and then stored in liquid nitrogen. In the case of lithium, weighed amounts of graphite and lithium in order to obtain LiC6, LiC3 and LiC2 were treated at 77 K under a pressure ranging from 30 to 40 kbar for 6 hours [93-95]. For LiC2 samples, a superconducting transition was measured at 1.9 K, whereas no transition has been observed at a temperature higher than 0.35 K for LiC6 and LiC3. The compositions NaC4, NaC3 and NaC2 were studied [93, 95, 96]. All became superconducting after the application of the pressure. NaC3 was synthesized at 227 K under 45 kbar for 0.5 h in a copper ampoule and was then placed in a teflon container and treated at room temperature under 35 kbar for 22 h. After quenching the sample in liquid nitrogen, Xray diffraction was carried out at 100 K and two series of 00l reflexions were observed and attributed to the presence of two phases with repeat distances of 1115.6 ± 0.7 pm and 797.0 ± 1.5 pm. As in the case of lithium, there is a dependence of the critical temperature to the alkali metal concentration. However, in both cases, Tc decreases monotonously with time, even when the samples are stored in liquid nitrogen. The potassium GICs were the most studied compounds. In this system, the richest potassium compound is KC3. It was obtained at 77 K under a pressure of 30-40 kbar for 6 hours. Less dense phases, KC6 and KC8 were prepared at 77 K with an applied pressure of 3-7 kbar for 6 hours. KC8 samples are stable under normal conditions. The magnetic susceptibility of each potassium GIC versus temperature is shown in figure 6.1. The transition is abrupt with complete saturation for KC3, KC6 and KC8, whereas that of KC4 is probably due to a mixture of several superconducting phases (Figure13). In these compounds, the Tc value is controlled by the potassium content since it increases when the C/K ratio decreases but it depends also on the metal ordering in the layer. Temperature and angular dependences of Hc2 and Hc1 for both KC3 and KC6 compounds, as well as Hc2 anisotropy for KC8 were studied [95]. All compounds can be described using the

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phenomenological anisotropic effective mass model suggesting that the increase in the potassium concentration makes the electronic structure more three dimensional.

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Figure 13. Magnetic susceptibility of KCx GICs (from [95]).

For lithium, sodium and potassium dense compounds, the transition temperature raises when the alkali metal concentration increases. This suggests an important role of alkali metal electrons in enhancing superconductivity. Graphite intercalation compounds with the heaviest alkali metals, rubidium and cesium, were less studied than Li, Na, K compounds [35, 97]. Among all these alkali metals dense compounds, CsC4 exhibits the highest critical temperature of 6 K [98].

Recent Advances in YbC6 and CaC6 In 2005, Weller et al. [87] reported a superconducting transition in YbC6 and CaC6 with respective Tc of 6.5 K and 11.5 K. In the case of CaC6, in the magnetization results, no saturation of diamagnetism is obtained down to 2 K, due to the reduced samples quality. Emery et al. obtained the saturation of the diamagnetic signal after a very sharp transition [88] using bulk samples, prepared by a liquid-solid synthesis route [14]. Among the GICs, these compounds exhibit the highest transition temperatures so that a renewed interest in these materials appeared recently. Many efforts were done in experimental and theoretical studies in this field. Two kinds of pairing mechanisms have been developed for understanding the origin of superconductivity in these materials [99-103]. A conventional electron-phonon interaction could be sufficient for Calandra and Mauri [99, 100] and for Mazin et al. [101, 102]. On the other hand, Csányi et al. [103] proposed an unconventional pairing mechanism due to electronic correlations.

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CaC6

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The magnetization curve of CaC6 obtained by Weller et al. [87] does not reach the saturation of the sample due to his low quality. In this study, the authors have used the vapour transport technique described in [26]. This synthesis method is well known to lead in the case of calcium to a weak intercalation in surface. Consequently, Ellerby et al. [104] have estimated the volume fraction of CaC6 in the measured sample at 3% by X ray diffraction. However, these authors have shown unambiguously that a superconducting state appears in CaC6 below 11.5 K. Magnetization measurements done on bulk sample [88] conduced to a sharp transition at 11.5 K with a transition width of less than 0.5 K. Field dependence of the magnetic susceptibility was studied with the applied field parallel (H //ab) and perpendicular (H //c) to the graphene sheets. In both directions, CaC6 clearly appears as a type II superconductor [88, 105, 106]. The anisotropic ratio Hc2//ab/Hc2//c estimated from magnetic measurement is around 2 (Figure 14) with zero field extrapolated values of around 10 kOe and 5 kOe for Hc2//ab and Hc2//c respectively. Xie et al. have reported higher anisotropy of 3,5-4 [105].

Figure 14. Critical fields of CaC6 with H parallel (H ab) and perpendicular (H c) to the graphene plane.

From these results, Csànyi et al. [103] suggest that the relatively high Tc compared to those encountered in this family of compounds can’t be explained by a conventional electronphonon mechanism but by electronic correlations. On the opposite, Mazin [101] proposed a conventional coupling and explained the difference between the Tc of CaC6 and YbC6 by the

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weight difference between Ca and Yb atoms. More recently, Calandra and Mauri [99, 100] attribute the superconductivity of CaC6 to the coupling of the electrons in the Ca Fermi surface with Ca in-plane and C out-of-plane phonons. The first experimental indication of the pairing mechanism was obtained from the measurement of the in-plane magnetic penetration depth λab [107, 108], using a highresolution mutual inductance technique [109]. Indeed, the variation Δλab(T) present a thermally activated behaviour, which is compatible with the standard BCS s-wave model. From this model, the zero-temperature penetration depth was evaluated at λab(0) = 72 ± 8 nm and the zero-temperature superconducting gap at Δ(0) = 1.79 ± 0.08 meV. In this case, the ratio 2Δ(0)/kBTc is estimated at 3.6 ± 0.2, which is closed to the BCS value of 3.52. Furthermore, this study supports the BCS model of the theoretical work of Calandra and Mauri [99]. In fact, the expected ratio 2Δ(0)/kBTc is of 3.69 [110] with the predicted values of electron-phonon coupling λ = 0.83 and the logarithmic average phonon frequency ωln = 24.7 meV [99]. Moreover, the thermal behaviour of CaC6 indicates that this compound is in the dirty limit [107, 108]. More recently, these results were confirmed by the study of the CaC6 surface resistance using a perturbation method [111, 112]. For T 103 atoms) and over a relative long period of time (microseconds to milliseconds). Nevertheless, existing results have illustrated not only qualitatively the importance of cluster kinetic properties to

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the aggregation and coalescence processes [61-70], but also the possibilities of taking advantage of the cluster kinetics in controlled nanostructural fabrication [71,94-102]. In addition, the nucleation and growth of nanoparticles are the initial stages of many material growth processes [107,108]. Nanoparticle aggregation and coalescence occur also in later growth stages of polycrystalline, nanocrystalline and composite materials. Therefore, investigations of these kinetic properties of nanoparticles provide us with insights in understanding and control of the texture of these materials [109-113].

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1.2. Considerations of Using Graphite in Nanostructural Growth Studies In this Chapter, the results of our comparative studies of nucleation, aggregation and coalescence of Al, Ge and Sb nanostructures on highly-oriented pyrolytic graphite (HOPG) are presented. HOPG is widely used as a prototypical inert substrate mainly for three reasons related to its unique atomic and electronic structures, namely, strong sp2 in-plane bonding and weak van der Waals coupling between atomic planes. First, graphite is easily cleaved to obtain atomically flat plane over large area. Secondly, graphite has been extensively studied with STM, and its surface structures, including defects, are well known [114-119]. Finally, graphite is chemically inert but still quite conductive for performing STM and electron spectroscopic measurements. The density of surface defects on HOPG is much lower than that on conductor-supported oxide and nitride films [37-42]. A variety of materials have been deposited on HOPG, and various nanostructures have been observed in the past few decades [31-34,61,62,67,68,72-75,93-95,97-102,119-139]. A general conclusion is that, due to weak interaction between deposited material and HOPG substrate, metals and semiconductors tend to nucleate near defects and grow as 3D islands. However, the structures formed on HOPG can show distinctively different morphology, depending on the deposited species, flux and substrate temperature. Such difference largely reflects the unique properties of atoms, clusters and crystallites of an element when they encounter each other, because all these objects can be quite mobile on graphite surface. We choose Al, Ge and Sb as prototypical elements representing metal, semiconductor and semi-metal, respectively. The unique behavior of an element can be revealed more explicitly often in a comparative study. In the previous studies of nucleation and growth on HOPG, the results reported from different groups often showed noticeable disagreement with one another. These disagreements could arise from different deposition conditions, sample and instrumental artifacts, or from sample degradation in ex situ characterization process. For example, the nucleated features observed after a very small amount of deposition depend strongly on the structural details of defects where the nucleation takes place. Such defect details are often difficult to characterize after material deposition. Atmosphere and electron beam exposure in many ex situ analyses could modify the nanostructures to various extent. Therefore, we mainly used in situ STM to characterize the morphology of the nanostructures nucleated and grown on HOPG in ultrahigh vacuum (UHV, base pressure ~ 10-10 mbar). It is extremely difficult to obtain stable images for clusters of radii < 2 nm due to their high mobility on HOPG at room temperature (RT) unless they are trapped by defects created with ion-sputtering [140,141], so we started STM measurements when typical cluster size was above this value. We found that, for some elements, even quite large crystallites were disturbed by the scanning tip of STM. To obtain an accurate spatial distribution of such

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nanostructures, we also analyzed some samples using ex situ scanning electron microscopy (SEM). HOPG substrates were transferred into the UHV chamber through a load-lock shortly after cleaving in air. Before being used for deposition, they were degassed at 300-500 °C for 10 hours with a W-filament on the back side. Flat terraces of > 200 nm in width separated by steps were commonly observed on our HOPG substrates (see Figure 1(a)). The atomic structure on perfect graphite sheet is shown in Figure 1(b). Steps of height from one momolayer (1 ML = 3.4 Å) to several ML on HOPG can be easily recognized in a STM image. In addition, we found some linear features with height ~ 1-2 Å, which acted as nucleation sites with relative weak binding power. Such sub-ML linear features have been reported before [117], and they were denoted as the twist boundaries between rotated and unrotated areas. Here we suggest another possibility: a sub-surface step or sheet edge, as sketched in Figure 1(c). Since HOPG is made of thin finite-area graphite sheets stacked in highly oriented way, the sheets on top can cover the edges of underneath sheets, with some distortion (bending) on the surface above the covered edges. The bending observed on the surface depends on the covered edge height as well as the top sheet thickness. For a 1-ML covered edge, the surface bending will appear < 1 ML in height and diffused laterally. A multi-ML sub-surface edge may also appear < 1 ML in height if the covering sheet is relatively thick.

Figure 1. (a) Grey-scale STM image of a (0.5 μm)2 area of HOPG surface; (b) atomic structure of graphite basal plane, with the dot-line diamond representing a ( 3 × 3 )R30° super-cell; and (c) schematics of a sub-surface step that can act as sites of nucleation and aggregation, but with a relatively binding power.

High purity Al was evaporated with a hot W coil, while Ge and Sb were evaporated from boat evaporators made of Ta or W. A thermocouple was used to monitor the Sb source temperature. The flux was calibrated by measuring the volume of Al and Sb islands on HOPG in STM images since their sticking probability is near 1. The sticking coefficient of Ge on HOPG is much less than 1 (similar to the case of Si [129,134]), so Ge was deposited on a Si

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specimen for flux calibration. Aüger electron spectroscopy (AES) was also used in flux calibrations. In STM measurements of island size, we have considered the convolution effect of tip shape that could result in large error in lateral dimension of large-corrugation objects [50,140,141]. The flux values carry an absolute error of about 50%, but the relative error should be within 25%.

2. Aluminum: An Easy Coalescence System The nucleation and growth of Al on HOPG have been investigated by quite many groups previously. For instance, island formation of Al on HOPG surface was observed using X-ray photoelectron spectroscopy (XPS), AES and STM [120-124]. Ma et al. found that no chemical reaction of Al clusters with HOPG occurs at RT in the absence of contamination or defects [123]. However, two dimensional (2D) clusters of sputter-deposited Al up to 1 nm in thickness were imaged using STM in air by Maurice and Marcus [124]. They also observed a strong interaction with electron transfer from Al adatoms to graphite using XPS. Hinnen et al. [125], in their XPS investigation of the interfaces created by sputter deposition of Al on HOPG, found a growth mode of the Al film that was described in terms of Al cluster formation involving Al-C bonds and carbide-like component AlxC (x ≈ 1.4) at the interface, followed by the growth of a pure Al layer. The Al coverage on the surfaces imaged with STM in most of these works was on the order of ~ 0.01 ML, so the observed features depend strongly on the structural detail of defects where they are nucleated. Therefore, we started image the sample with an Al deposition ≥ 0.15 nm (~ 0.5 ML). The high oxidation tendency of Al requires a strict UHV environment for the experiment.

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2.1. From of Al Clusters to Crystallites Figure 2(a) displays a STM image after ~ 0.15 nm Al deposited on HOPG at RT. Al cluster chains are observed along the step edges at this early stage, similar to the Ag and Au growth on HOPG [74,100,130]. The spherical 3D clusters have heights in 4-7 nm range. Although none can be seen on terraces, Al clusters may also have nucleated on some isolated defect sites, but the binding between Al clusters and these defects is too weak to stabilize the clusters under STM scanning. This can explain the fluctuating scan lines in Figure 2(a), and is consistent with previous in situ XPS investigation and molecular dynamics simulation [123,142]. The observation of spherical clusters mostly at step edges indicates that the Al clusters in this size range have an isotropic surface energy and are indeed in a nearly freestanding state on HOPG. With 0.4 nm Al deposited at RT, the observed feature remains mostly spherical 3D clusters, although their heights increase to 8-12 nm range (consisting a number of atoms on the order of 104). But after an additional 0.4 nm deposition, Al islands with flat top and straight edges (although with multiple-tip artifact) can be seen in the STM image of Figure 2(b), indicating crystallite formation. These islands are still only found at the step edges, and the linear density of crystallites along HOPG step is about 50-80% of that of spherical clusters formed earlier, indicating coalescence occurred between some clusters.

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Figure 2. (a) Spherical Al clusters at step edges after deposition of 0.15 nm at RT; (b) and (c) flat-top Al crystallites at step edges after 0.8-nm deposition at RT; and (d) after 3-nm deposition. Scan area: (a) and (d) (1 μm)2, (b) (250 nm)2, (c) (0.5 μm)2.

The heights of Al crystallites are in 3.0-5.5 nm range, and the lateral sizes are about 1530 nm. This indicates that many islands reduce their heights during cluster-to-crystallite transformation. All Al crystallites in Figure 2(b) have Al(111)//C(0001) orientation. The crystallite profile is significantly lower than that of a free standing Al crystal predicted based on (macroscopic) surface energies [91,143], indicating a significant interface binding energy [31,43]. These observations suggest that, as the volume of Al nanoparticle increases, its surface energy anisotropy develops (probably accompanied with a crystallization transformation of interior structure), and the nature of its interfacial binding with graphite also changes. Figure 2(c) displays an area with crystallites along two HOPG steps. Larger-area STM images show that the upper step is next to a wide (> 1 μm) step-free terrace, whereas the lower step has relatively narrow (~ 0.35 μm) terraces on both sides. More Al atoms are available for the clusters/crystallites along the upper step than those along the lower one. The crystallites along the upper step have larger average size and clearer facet shape than those along the lower step. This indicates that the coalescence of Al clusters and transformation to low-profile crystallites are promoted by supply of Al atoms. Such alignment of Al crystallites

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along HOPG steps yields a quasi-one-dimension structure which may exhibit novel physical properties [144].

2.2. Migration and Coalescence of Al Crystallites

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After 3-nm Al deposition at RT, isolated flat-top islands are observed on terrace area along with those at step edges, as shown in Figure 2(d). The heights of isolated islands (mostly in triangular shape) are in 10-15 nm range, higher than those elongated ones at step edges (8-10 nm). These islands are formed as a result of further coalescence of crystallites. During STM imaging with a sample bias voltage VS = 0.6 V, isolated islands of quite large size (~ 200 nm in lateral and ~ 25 nm in height) can be dragged along on terrace due to tipisland interaction. When these islands are dragged to be in touch with those at step edges, they are trapped there. Similar behavior was also reported in Au growth on HOPG [100]. We found that when VS > 3 V is used, even smaller isolated islands grown on terraces (~ 10 nm high and 90 nm in width) can be imaged without being dragged. Even with such image condition, the islands on terrace are observed to migrate and coarsen with each other or with islands along steps in consecutive STM images. This reflects a low activation energy for the diffusion of such Al islands on graphite. In addition to the polar orientation, preferential azimuthal alignment also exists between the triangular Al islands and graphite. This is demonstrated in the SEM image shown in Figure 3(a) taken on a sample after 6 nm Al deposition. Notice that the graphite sheets are not all azimuthally aligned in HOPG [139]. Most of the triangular Al islands on terraces take two azimuthal orientations rotated 60° from each other. The two azimuthal orientations of triangular islands are a consequence of different atomic layer stacking sequence, i.e., abcabc vs acbacb. Since Al{111} facets are dominant on the Al island surface, similar to the case of Pd-Au crystallites on HOPG [93], the triangular edges are along 〈110〉. Both azimuthal alignments can be assigned as Al〈110〉||C〈 1010 〉, in agreement with previous experimental and computational results [124,145,146]. Similar lattice alignment was also reported for Pd and Au crystallites grown on HOPG [147,148]. The azimuthal alignment is mainly determined by the first interfacial atomic layers of Al and graphite. A single atomic layer of Al(111) is mirror symmetric with respect to [ 110 ], while this symmetry is broken when subsequent layers are considered. The atomic spacing along 〈110〉 on Al(111) is 2.86 Å, and it _

is 2.46 Å along C〈 11 2 0 〉 (see Figure 1(b)). In Al〈110(((C(
( alignment, we have 3aAl(111) matches closely with
aC(0001) in C(
( direction. Islands with several

degrees of deviation from the exact in-plane alignment are not scarce. With further increase in deposition, Al islands grow mainly in lateral direction to cover more surface area. Figure 3(b) shows a STM image taken after 10 nm Al deposition at RT. Although some isolated islands remain visible, ~ 95% of Al is integrated into the nearly continuous islands starting at HOPG steps, partially due to the coalescence of isolated terrace islands with those along steps. The heights of the islands are in 16-20 nm range, basically same as the sample with 6-nm deposition (Figure 3(a)). If deposition continues, we expect that the whole HOPG surface will be covered with a fairly uniform (111)-oriented Al film.

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Some voids in the continuous islands can be easily observed in Figure 3(b). Actually, voids exist even on apparent smooth islands such as those shown in Figure 2(d) and Figure 3(a). They provide us with information regarding the coalescence kinetics of the Al islands. Zooming in on top of Al islands on a sample similar to that in Figure 3(a), we observe voids typically 4-8 nm in depth as those shown in Figure 3(c). The bottom of these voids do not reach graphite surface, so we call them craters. The craters on an elongated island are usually aligned as a chain roughly following the HOPG steps. A large island on terrace may have several craters on top. Further zooming in on a crater reveals atomic steps and terraces (see Figure 3(d)). The average height of concentric round step loops is 2.52±0.20 Å, larger than the bulk value (2.34 Å) of atomic steps on Al(111).

Figure 3. (a) A SEM image of a HOPG with 6 nm Al deposited; (b) STM image taken after 10-nm Al deposited at RT; (c) and (d) zooming-in scans showing craters formed on Al islands in Figure 2(d). Scan area: (a) (15 μm)2, (b) (3.5 μm)2, (c) (0.5 μm)2, and (d) (110 nm)2.

The craters on the large Al islands disappear after a 25-min annealing at 350oC, indicating that they are not thermodynamically stable. Based on thermodynamic consideration, the typical Volmer-Weber growth with atomic deposition results in islands with flat or protruding top surface. In most kinetic theories of island nucleation, growth and coalescence based on atomic deposition, diffusion, attachment and detachment processes, the island top is normally flat or with a convex curvature, as those Al islands in Figure 2(a)-(c).

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The crater formation on top of Al island is a phenomenon related to Al crystallite coalescence on graphite. The coalescence of two Al crystallites does not generate a crater. Such coalescence events between two crystallites are visible in Figure 2(d), and the coarsening islands have the same orientation. A crater may be created when more than two crystallites coalesce as a group. In Figure 4(a), we show an island group (including at least 3 crystallites) in early coalescing stage, in which the crater in the center and the boundaries between smaller islands near the perimeter are easily identified.

Figure 4. (a) Coarsening of three Al crystallites results in a crater in middle; (b) schematics of island coarsening leading to crater formation; (c) and (d) images of a group of islands taken, with (d) taken 30 min after (c). The digits label the same islands in (c) and (d). Image area: (a) (200 nm)2, (c) and (d) (1 μm)2.

Based on this, a simple model is proposed for crater formation. Nucleation among Al atoms, which are quite mobile on graphite [142], forms clusters and later faceted crystallites. Relative small crystallites still can migrate on terraces [146], although with their mobility decreasing gradually due to a higher diffusion barrier and/or lower attempt frequency. When several crystallites meet, they merge into one large coherent island to minimize surface energy. In this process, Al atoms are required to fill in the bare HOPG surface area in the

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middle of the group. Previous investigations have shown that coalescence happens at RT for Al islands, and the kink and corner breaking induce a transition towards equilibrium-shape islands [149,150]. However, even though the Ehrlich-Schwoebel barrier [151,152] for an Al atom to jump down a step (or displace an edge atom) is small (~ 0.07 eV), the inter-layer mass transport is hindered at RT due to a high energy barrier (~ 0.8 eV) for atom detaching from the steps. Therefore, Al atom transport to the middle of the island group is much slower than the migration along the perimeter, yielding a crater with nearly round shape in the center. The scenario of crater formation is sketched schematically in Figure 4(b) in three stages. In our model, the remarkable translational and rotational mobilities of Al crystallites are essential. In fact, the inertness of graphite usually leads to a very low diffusion barrier not just for adatoms, but also for clusters of some metals, even those consisting of several thousand atoms. For instance, it has been demonstrated that Sb and Au clusters migrate on HOPG surfaces at a surprisingly high diffusion rate of ~10-8 cm2/s at RT [126,153], quite comparable to that of single atoms in similar conditions. Ag clusters with a diameter of ~ 14 nm were also found to be mobile on graphite surface [62]. The behavior of Al clusters on HOPG surface seems similar to that of Au and Ag. Simulation studies [68,69] have shown that small defects on graphite terraces have little trapping power to gold nanoclusters. This seems also the case for Al nanoparticles. Crystallites in a group can merge relative easily into a big coherent island should they have the same lattice orientation, although coarsening among crystallites of different orientation is also possible as grain boundary moving across the crystallites [110,111]. As shown earlier, most crystallites take two azimuthal orientations, while a few may deviate several degrees from such orientations. Thus, for a crystallite group coalescing into a single island, it is necessary that some Al islands adjust their orientation. We observed both island migration and rotation during STM scan, especially for those in contact with each other. Figure 4(c) and (d) are two consecutive STM images, taken 30 min in time separation, showing the position and orientation changes of a group of Al islands. VS = 4.6 V was used in STM scan here to reduce the tip disturbance to the islands. The islands are labeled with numbers. Islands “1” and “2” acted as center for the aggregation and coarsening of crystallites. Island “4” rotated ~ 7° and moved a short distance to get in touch and align with “1”. Island “3” however, rotated 60° and moved ~ 90 nm from the initial position to merge with “2”. Islands “5” and “6” also rotated 60° and moved ~ 100 nm from the initial positions to get in touch with island “1”. Such rather dramatic rotations and translations may consist of many small steps. After these Al crystallites get in contact and aligned with each other, their coalescence proceeds as sintering that occurs easily at the contact points, especially under a deposition flux.

3. Germanium on HOPG: A Low-Sticking and Hard Coalescence System There have been very few studies of semiconductor (including Ge and Si) deposition on HOPG [100,129,134]. Marsen and Sattler [129] reported Si nanowire formation on HOPG, whereas McBride et al. [100] only observed mesa-shaped Si multi-layer islands on etch pits of graphite. Si and Ge depositions have been carried out on silicon oxide and nitride surfaces

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which are also relatively inert [45-47,50,154,155]. The shape and surface morphology on these weakly-supported Si and Ge nanoparticles are quite different than those on a strongbinding substrate, such as Ge on Si [9,156-158]. In the initial stage of our RT deposition experiment, Ge clusters mostly nucleate and form single-row chains along HOPG step edges, same as that of Al in Figure 2(a). Later, clusters on both sides of the step as shown in Figure 5(a) are observed. With 0.9 nm Ge depositied, the height of Ge clusters is ≤ 9 nm. The cluster surface is curved with no observable atomic order.

Figure 5.STM images of Ge deposition on HOPG at RT. (a) Clusters nucleated on both sides of a step edge after 0.9-nm Ge deposition. (b) Double-layer cluster chains formed after 2.1-nm Ge deposition. Some chains (e.g., those with open-end) are growing on terrace as branches of those along the step edges. (c) Fractal-shaped islands grow along sub-surface steps on wide terrace; and (d) a zoom-in scan on the double-layer fractals in (c). Image area: (a) (0.3 μm)2, (b) (1.5 μm)2, (c) (2.5 μm)2, and (d) (0.8 μm)2.

After 2.1 nm Ge deposited, the cluster chains branch off the step edges and grow into terrace region. Such branch-off chains can be seen in Figure 5(b) as (but not limited to) those with an open-end. Most of the chains are nearly parallel with each other. The chain growth on terrace is similar to that of a Si dimer row on Si(001) [157,159], suggesting the chain end as the most favorable site for cluster nucleation or trapping [160]. Some chains change direction

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and even make a U-turn in the growth process. These chains mostly consist of two layers of Ge clusters now. The height of the lower layer is ≤ 9.5 nm, about the same as single-layer chain in Figure 5(a), while the height of the upper layer is ~ 15 nm as measured from graphite surface. Considering stacking geometry, the heights of the clusters in two layers are about the same, i.e., ≈ 9 nm. In the middle area of wide terraces as the one shown in Figure 5(c), Ge clusters form islands of imperfect fractal shape due to diffusion limited aggregation [161]. Figure 5(d) is a zoom-in STM image of the ramified islands, which also show a double-layer structure with the same heights as the double-layer chains along steps. Most of these ramified islands are connected along linear sites of weak binding power, such as the sub-surface steps sketched in Figure 1(c). The double-layer cluster chains and islands show a quite high second- to first-layer mass (or area) ratio. If we treat the cluster layers as atomic layers in film growth, the multilayer configuration forms as a consequence of limited mass transport from upper layers to lower incomplete atomic layers due to, e.g., the Ehrlich-Schwoebel barrier [151,152]. However, the second- to first-layer area ratio of the Ge double-layer cluster chains and islands is significantly higher than that evaluated assuming without any interlayer mass transport [162]. These double-layer cluster islands form due to four factors: 1) Ge atoms deposited later are more likely to form new clusters rather than being integrated into existing ones, indicating a self-limiting cluster growth similar to Co on SiNx [48] and Fe on NaCl [163]; 2) the sticking probability of Ge atoms on HOPG terrace is quite low (≤ 10% initially), similar to the case of Si on graphite [34,134], so that only those landed on or very close to defects or existing Ge clusters can stay by quickly finding binding sites; 3) the top of first-layer chains and fractal islands provides more stable sites for nucleation and/or binding of new clusters than graphite surface adjacent to the first-layer Ge clusters; and 4) Ge atoms or small clusters are mobile on HOPG and on the first-layer clusters to reach the top even at room temperature.

Figure 6. A (1 μm)2 STM image showing on the right side a few Ge nanowires self-assembled on HOPG at RT. These Ge wires have fairly uniform cross-section along the axis as atoms deposited later fill in the gap spacing near the contact points along the cluster chains.

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With further Ge deposition at RT, the double-layer cluster chains and islands grow mostly in lateral size. In fact, we did not observe third-layer clusters formed on the secondlayer. Some of the cluster chains gradually transform into Ge nanowires with fairly uniform cross-section area, as shown in Figure 6. Such Ge nanowires are more likely to form under a relative low deposition flux, suggesting that Ge atoms deposited later tend to be integrated at the contact points between Ge clusters rather than nucleation of new clusters. If the cluster chains in Figure 5 are considered as quasi-1D nanostructure of Ge, then the Ge nanowires in Figure 6 are even closer to a genuine 1D structure. Our results indicate that such Ge nanowires can be self-assembled on HOPG. 1D and quasi-1D nanostructures of other elements have been fabricated in similar processes, and their applications have been explored [71-73]. In addition, we have observed features similar to that assigned as Si nanowires by Marsen and Sattler [129] in their Si on HOPG growth study. Figure 7(a) is a STM image of an area in which nanowire bundles similar to those in Ref. [129] are observed.

Figure 7.(a) STM image of a HOPG sample with Ge deposited at RT showing nanowire bundles in middle; (b) zoom-in image on a nanowire bundle in (a); (c) bare HOPG surface showing CNT-like structure marked NW along a step edge; and (d) the CNT-like edges appear inert with respect to Ge clusters. Image area: (a) (100 nm)2, (b) (6 nm)2, (c) (250 nm)2 and (d) (150 nm)2.

The bundles, often surrounded with Ge clusters, show the surface structure of Figure 7(b) in small-area STM scans, which reveal atomic feature of a nanowire with a period 4.26 ± 0.05 Å along the axes. The nanowire structure appears like that observed on a Si nanowire reported by Ma et al. [164]. However, it can also be assigned as that of a carbon nanotube (CNT)

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[16,165,166]. In fact, the period along the nanowire axes is basically the value along a zigzag CNT. It has been reported that CNT-like scrolls can be formed naturally on HOPG by folding of graphitic sheets [167,168]. After cleaving and annealing, it is quite possible that carbon nanoscrolls are formed by wrapping of small graphitic sheets. Such CNT-like structures can be observed sometimes along HOPG step edges, as the one marked NW in Figure 7(c). The CNT-like step edges are rather inert with respect to Ge atoms and clusters. Figure 7(d) displays a STM image in which most of HOPG step edges are decorated as usual with Ge clusters, except the section marked NW. The CNT-like bundles as that shown in Figure 7(a) are expected to be unstable with respect to STM imaging of HOPG surface, so they can hardly be observed independently. With Ge clusters bound aside but not on the top surface, they can be stabilized for imaging.

Figure 8. STM images of Ge crystallites formed on HOPG after 4-nm deposition at RT and annealed at 310°C. Facets are shown in the 3D-view image in (b). Image area: (a) (0.8 μm)2 and (b) (0.2 μm)2.

The Ge clusters are stable with respect to annealing at T ≤ 225°C for 10 min. Faceted crystallites of height ~ 50 nm form from coarsening of clusters when annealed at a higher T, as shown in Figure 8(a). When Ge is deposited on HOPG held at T ≥ 175°C, nano-crystallite chains same as in Figure 8(a) are also observed. These chains form along HOPG step edges first, and later also branch off from the steps onto the terraces. Crystal facets develop on the crystallite surface when their diameters reach ≥ 40 nm. This corresponds to a threshold size of ≥ 106 atoms for a Ge crystallite to form facet, whereas this threshold is ≤ 105 atoms for Al according to the observation in Figure 2. Figure 8(b) displays a small-area image of faceted Ge crystallites. Further zoom-in scans reveal atomic-scale structures of the facets. High-index facets, such as {113} and {331}, are observed more often than low-index ones [50]. These facets are oriented randomly with respect to the substrate and un-correlated among different crystallites. In addition, these crystallites can be fairly easily displaced by STM tip, indicating a weak adhesion to the substrate, probably due to a small contact area. As more Ge is deposited at the raised temperature, the randomly-oriented crystallites cover more surface

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area, gradually forming a polycrystalline film. Comparing with Al on HOPG, the coarsening among both Ge clusters and crystallites is highly suppressed at RT.

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4. Antimony: Different Nanostructrues by Playing with Diffusion and Dissociation Rates of Molecules Among various materials deposited on HOPG or amorphous carbon, particular rich phenomena have been observed for Sb clusters (Sbn) in a size range of n = 4 to 2300 [67,9799,101,102,126,169]. Depending on the size n of Sbn, the Sb islands formed on graphite vary from compact spheres for n = 4 to ramified fractals for n ≥ 90. The fractal branch width decreases as n increases. These phenomena have been explained in terms of the interplay of Sbn arriving rate at an existing island and the time it takes for clusters in contact to coalesce. In all these studies, however, the possibility and consequences of Sbn decomposition were largely ignored. Sbn (particularly for Sb4 generated from a thermal evaporator) decomposition and/or conversion from physisorption to chemisorption state do occur under certain conditions [170]. This has strong effects on compound and alloy growth involving Sb [77,78,171]. The diffusion, nucleation and growth kinetics of chemisorbed Sb species on HOPG are expected to differ remarkably from those of physisorbed Sb4. It would be interesting to examine whether different structures form on HOPG if Sb4 decomposition is significantly activated (or similarly if the deposition flux consists of a significant percentage of Sb2 and Sb1 is used). We used thermal evaporation source operating in temperature range of 340-380 °C in the study of Sb growth on HOPG, which mainly generates Sb4 [77,78]. We observed that spherical 3D islands, extended 2D islands and 1D crystalline nanorods are formed on HOPG. The atomic-scale STM images of the surfaces of these different dimensional Sb structures have been obtained. It has been well known that Sb and Bi are semimetals that possess unique physical properties [172,173], such as low carrier densities, long Fermi wavelength, and high carrier mobilities. The nanostructures of these semimetals could show even more interesting electronic properties [174-180], such as surface superconductivity, extremely large magnetoresistance and semimetal-to-semiconductor transition. In addition, nanostructural semimetals are potentially high-efficiency thermoelectric materials [181-184]. The electronic properties of these semimetals are closely related to their surface atomic configurations. But due to experimental difficulties, although electron diffraction studies was performed almost 40 years ago [185], only the atomic structure of cleavage Sb(111) was revealed with STM very recently [186]. The crystalline Sb structures formed on HOPG allow us to image the non-cleavage surfaces when they appear. The most stable Sb bulk crystals take rhombohedral lattice structure [187] in normal conditions, which can be derived by a slight distortion of a cubic lattice [185,188]. The distorted face-center cubic representation of α-Sb is illustrated in Figure 9(a), with the ABC stacking at a 3.76-Å layer spacing. Each site represents a base of two Sb atoms, with the other atom 5.26 Å beneath the one shown in the figure. In this article, we use the rhombohedral index notation for the Sb structures, so Sb(0001) in Ref. [186] is denoted Sb(111) here. Pseudo-cubic and 4-digit hexagonal indexing systems are also used quite often in describing rhombohedral lattices [181,185-189]. The transformation between the indices in different

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systems can be found in general crystallographic textbooks [190]. For illustration and comparison, the rhombohedral and pseudo-cubic cells of α-Sb are sketched in Figure 9(b) and (c), respectively.

Figure 9. Schematics and parameters of rhombohedral Sb lattice. (a) Viewed in [111] trigonal direction, different circular symbols represent atoms in layers separated by 3.76 Å, (b) a rhombohedral unit cell, with the upper filled circle and the doted circle 5.26 Å below forming the basis; and (d) a pseudo-cubic cell.

4.1. Three Types of Sb Nanostructures Figure 10(a) displays a STM image taken on a HOPG sample with 12 Å Sb deposited at a rate of 4 Å/min at RT. Three types of Sb structures are observed, as labeled with 1D, 2D and 3D in the figure. The three large 3D spherical-top islands have heights in 50-56 nm range, and apparent lateral diameters 140-150 nm. STM tip cannot scan underneath the nanoparticles, so we cannot know their exact shape. Based on the inertness of substrate, the observed 3D particles are most likely truncated and/or oblate spheres at this stage.

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Figure 10. 3D-view STM images of Sb structures on HOPG. (a) After 1.2-nm Sb deposited at RT and a flux of 4-Å/min, with three different types of Sb nanostructures labeled as 1D, 2D and 3D; (b) after 4nm Sb deposited at RT and a 4-Å/min flux; (c) and (d) zoom-in images taken on a faceted 3D island. Image area: (a) (1 μm)2, (b) (2 μm)2, (c) (60 nm)2, and (d) (8 nm)2. Imaging condition of (d): Vs = 0.63 V, It = 0.6 nA.

In addition to these tall 3D islands, lower and extended structures are observed. The 2D islands (three of them, two unlabeled ones are in the upper part of Figure 10(a)) have heights in 3.1-3.5 nm range, with atomically flat terraces and straight step edges. The long linear (1D) feature in the upper part of Figure 10(a) has a height 20 nm and a measured width ~ 35 nm. Besides this long Sb nanorod, there are two short rods on the side of a 3D nanoparticle in the lower half of the image. The heights of these wires are about 13 nm. It should be pointed out that these Sb rods are not necessarily formed along the steps of HOPG. These 2D and 1D structures are not small graphite pieces or CNTs, because they grow as more Sb is deposited later. Figure 10(b) is an image taken on a sample after 4 nm Sb deposited. All three types of Sb structures have grown, especially the 2D islands which cover most of the surface now. More characteristics of the different Sb structures can be revealed as they grow up.

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4.1.1. 3D Sb Islands The surface of 3D islands is smoothly curved without any facet initially. In fact, some 3D islands of heights ~ 55 nm and lateral size ~ 200 nm are still not faceted. On the other hand, faceting has been observed on the surface of some relative large 3D islands. The 3D islands with facet on top can be observed in middle-left and upper-right area of Figure 10(b). These 3D islands have grown to lateral size ≥ 200 nm and have developed a flat top facet with straight edges, indicating a crystalline structure inside. But very likely the 3D islands are already crystalline before faceting [191,192]. The top facets are mostly in irregular hexagonal or triangular shape. They are parallel to the graphite basal plane and surrounded with smooth curved surface. One triangular top facet is shown in Figure 10(c). Zooming-in STM scans on such top facets (see Figure 10(d)) reveal a hexagonally ordered atomic structure with a period of 4.27±0.10 Å, basically the value on Sb(111) of bulk crystal. The faceted Sb crystallites as well as the flower-shaped islands observed in Figure 10(b) are similar to those observed by Kaiser et al. [102] using SEM. In their SEM image, the top hexagons of Sb islands are also surrounded with smooth curved surface, indicating that the surrounding feature in our STM images is not totally due to tip-shape artifact.

4.1.2. 2D Sb Islands

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As shown earlier in Figure 10(b), most of HOPG surface is covered with 2D islands as more Sb is deposited. In the STM image of Figure 11(a), flat terraces separated with atomic steps are observed. The measured average height of the atomic steps on the 2D islands is 3.96±0.20 Å. Further zoom-in scans on a flat terrace reveal a hexagonal ordered structure similar to that on 3D island top facet shown in Figure 10(d), except with a period 4.17±0.12 Å. The steps are all along 〈 110 〉 direction. Comparing with the lattice parameters of Sb(111) in α phase [187], our measured average step height is 5% larger than the bulk layer spacing (3.76 Å, see Figure 9), whereas the lateral period is shorter than the expected value (4.31 Å) by 3%. The lattice parameters of the 2D films show slight deviation from that of bulk Sb, in particular a 3% contraction in lateral spacing. It can be seen in Figure 1(b) that the period of the ( 3 × 3 )R30° superstruncture on graphite (0001) (its unit cell is outlined with dot-line diamond in Figure 1(b)) is 4.26 Å, which is 1.2% less than the period in the (111) plane of αSb. This may partially explain the shorter period observed in this study. The lattice mismatch between the 2D Sb islands and HOPG can be considered small, so one would expect that a (111)-oriented Sb film of a few atomic layers grows on graphite with a unique in-plane orientation relationship. But our results suggest that this is not necessarily the case. We found that the azimuthal orientation of the 2D islands on one HOPG terrace can be different from each other, indicating that these islands do not all have a fixed azimuthal alignment with graphite substrate. This is consistent with the observation by Scott et al. [139] using electron back scatter diffraction, in which the relative thick Bi films grown on HOPG were found consisting of domains (analogous to the 2D islands here) with 30° rotation and certain disorder in azimuthal orientation. The growth of 2D Sb islands is not in layer-by-layer mode. The number of incomplete layers increases as the growth proceeds. These layers often form triangular islands stacking

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up consecutively. On a sample with an average film thickness ≥ 5 nm, most of the surface of 2D islands is decorated with arrays of parallel monoatomic steps. Figure 11(b) shows a sample with 10 nm Sb deposition. The morphology is quite similar to that of Co growth on Pt(111) at RT [193]. This similarity suggests that inter-layer mass transport is strongly suppressed [162], which usually indicates the existence of a significant Ehrlich-Schwoebel barrier [151,152]. Factors such as strain relaxation and energetic step-step repulsion [194] may also have played certain roles.

Figure 11. 3D-view STM images of 2D Sb islands on HOPG after (a) 2.7-nm and (b) 10-nm Sb deposition. Image area: (a) (0.44 μm)2 and (b) (1 μm)2.

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4.1.3. Sb Nanorods Our STM images, as those displayed in Figure 12, indicate that the 1D Sb nanorods formed on HOPG are also crystalline. It is often observed that Sb nanorods grow out in two perpendicular directions, as illustrated in Figure 12(a). Zoom-in images on Sb nanorods reveal the top surface structures mostly as rectangular periodic or rows along the rod axis. The surface lattice parameters on the nanorods, however, vary from one area to another beyond experimental uncertainty. Figure 12(b) shows an atomic-resolution image taken on those relative lower Sb nanorods (marked “L”, with height ≤ 15 nm). A rectangular order of period (3.93±0.15 Å)×(4.40±0.15 Å) is observed away from the 90° intersection, with the shorter side along the axis of nanorods. A rectangular cell is outlined in Figure 12(b), with a bright spot inside observable. In contrast, in the right-angle elbow area, we often found a nearly square order with a period of 4.18±0.15 Å. Figure 12(c) shows an atomic-resolution image taken near the right-angle elbow of a low Sb nanorod. The average step height on the nanorod top surface is 2.83±0.20 Å. The observed lattice structure of Sb nanorods deviates significantly from α-Sb bulk. On the (110) surface of bulk α-Sb, the unit cell size is 4.31 Å × 4.51 Å. The lattice constants measured on top of Sb nanorods indicate a compressed state, and the contraction is more at the right-angle elbow than at the section away from it. These observations suggest that these nanorods start in a simple cubic (SC) phase which forms for compressed bulk Sb [188,195-197].

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Figure 12. STM images of Sb nanorods. (a) Tall (T) and low (L) nanorods growing in perpendicular directions; (b) an image on a low nanorod but away from the intersection, with a rectangular surface unit cell marked with dot-line; (c) an image taken at the right-angle intersection of a low nanorod; and (d) on a tall nanorod showing row structure. Image area: (a) (500 nm)2, (b) (4 nm)2, (c) (15 nm)2, and (d) (10 nm)2. Imaging conditions: (b) Vs = 0.63 V, It = 0.6 nA; (c) and (d) Vs = 0.4 V, It = 0.3 nA.

It has been observed for Group 5A elements such as As, Sb and Bi that a rhombohedral to SC phase transition occurs under pressure [188,195-197]. For Sb, the SC phase exists in a narrow pressure range around 7.0 GPa, in which the atomic volume is about 85% of the normal state value and the atomic spacing is 2.966±0.010 Å [195]. The 4.18±0.15 Å square unit cells and 2.83±0.20 Å step height observed on the top surface at the right-angle elbows of Sb nanorods fit closely to the SC lattice, with a

2 × 2 reconstructed (001)SC surface. The

nanorods grow out from the SC along the equivalent [110]SC and [1 1 0]SC directions. Away from the intersection, the nanorod lattice changes away from SC due to relaxation towards rhombohedral. The surface unit cell becomes rectangular, with atomic spacing expanded in the direction perpendicular to rod axis while even more contracted along the axis. The transition seems continuous, with the atomic volume remaining 85% of the normal state. These Sb nanorods have (110) top facets (or (0112) in hexagonal indexing), and their axes are along 〈 110 〉 directions (or 〈 2110 〉 in hexagonal indexing).

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Since the bonding of Sb nanorods with HOPG is weak, the compressive force is unlikely the misfit stress in a heteroepitaxial system. Nanostructures can be in a stressed state even without an external force. For example, colloidal CdSe QDs have been observed in compressive or tensile stress state depending on how the QDs’ surface is passivated [26]. The CdSe QDs are in compressive stress if the passivation layer acts as an electron donor. It is possible that some electrons transfer from the graphite substrate to Sb nanorods to induce the compressive stress. But the Sb nanorods are often observed growing in bundles. If they were charged, the electrostatic repulsion would prevent the bundle growth. Additionally, some nanorods have been observed growing on top of 2D Sb islands. Therefore, charge transfer from graphite is unlikely the driving force for lattice contraction here. Surface tension as well as the growth kinetics should be considered to explain the formation and lattice structure of the Sb nanorods. It has been found that an intrinsic compressive stress exists in many isolated 3D islands in Volmer-Weber growth [198,199]. This compressive stress is the Laplace pressure induced by the surface tension of a discrete nanostructure. Since typically the Laplace pressure is inversely proportional to a characteristic size of an object, it can reach GPa range for a nanostructure, whereas it can be ignored in a macroscopic structure. For example, based on the virtual work principle [198], in a cubic nanoparticle of edge size d with a surface tension f, the Laplace pressure is Δ P = 4 f / d . If f ~ 1 N/m and d ~ 1 nm, the Laplace pressure is a few GPa. This should favor cubic phase for Sb nanoparticles. Based on the above analysis, we propose that the Sb nanorods originate from SC-phase nanoparticles. Some of these nanoparticles can have {100}SC facets which correspond to {110} of rhombic crystal, since it was found that {110}R has a low surface energy for Sb and Bi nanocrystals and thin films grown on various substrates [139,192,200-202]. As the SC Sb nanoparticles grow in size, the Laplace pressure decreases, and the lattice structure tends to relax towards the rhombic crystal. The SC Sb nanoparticles may start in a highly symmetric shape (e.g., close to a cube), but the symmetry will be broken as the particles grow, and alternatively the lattice relaxation will proceed in an anisotropic way. An Sb nanorod can grow spontaneously from a cubic-shaped nanoparticle, since the lattice relaxation in transverse direction effectively releases the stress energy [203,204]. The Laplace pressure can still influence the growth of the nanorods. For a nanorod of length l and a square cross-section of edge size d with l >> d, assuming a surface tension f on all its surfaces for simplicity (this assumption is not critical to the following results), the Laplace pressure along the rod axis is Δ Pl = 4 f / d , while it is Δ Pt = 2 f / d transverse to the rod. That is, the longitudinal compressive stress is twice that of the transverse. Therefore, it is easier for the lattice of a nanorod to expand in transverse direction, whereas it remains highly compressed along the axis. This explains the surface lattice orientation observed in Figure 12(b). If the relaxation can be complete, the (110)R facets derived from (100)SC on an Sb nanorod should have [ 110 ] along the axis and [001] in transverse direction. Figure 12(a) and (c) indicate that it is also possible to have two perpendicular nanorods growing out of a cubic Sb nanoparticle. In this case, the symmetry-breaking relaxation takes place away from the elbow, while the elbow remains in the SC phase. On some Sb nanorods, the atomic structures observed cannot be designated as on {110}R or {100}SC facets. Rows displayed in Figure 12(d), with an average spacing 3.63±0.20 Å for the bright dots along the rows and 4.7±0.2 Å between the rows are typically observed on tall

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nanorods with heights ≥ 20 nm, as those marked “T” in Figure 12(a). The bright dots seem not equally spaced along the rows, and the rows are slightly zigzag. Due to the small number of periodically spaced rows that can be found on top of such nanorods, the uncertainty of these period data makes it hard to determine the lattice indices. A possible assignment is

{101} (or {112 0} ) with 〈 111 〉 along the rod axis [185]. Patrin et al. [205] observed elongated Sb and Bi structures with this top surface on GaAs(110). Bi nanorod growth on HOPG has also been reported [139,206]. The Bi nanorods (called strips in [139]) were also found with (110) (or {0112} ) facets on top. Due to the application potentials, semimetal nanowires have been fabricated with other self-assembly methods, mostly using anodic alumina membrane templates [181,207-211]. The nanowires obtained in some processes have their axis along 〈 110 〉 as in this study, while some show different indices, even polycrystalline form. The semimetal nanorods self-assembled on HOPG in physical vapor deposition can maintain good crystallinity. But the rods are not aligned as those grown in alumina membrane templates. On another substrate with proper lattice anisotropy and adequate interaction with Sb or Bi molecules and nanostructures, the aligned semimetal nanorod self-assembly is possible. When nanorods are preferred in certain applications, we should avoid the growth of other structures. To achieve this, the selective growth of different type of Sb nanostructures is discussed next.

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4.2. Selective Growth of Different Dimensional Sb Nanostructures It is well known that the properties of different types of nano-materials (i.e., nanoparticles, nanowires and thin films) differ from their bulk counterparts and from each other remarkably due to their dimensionality [2,5,6,212]. Therefore, the ability to selectively grow one type of nanostructural materials while suppress the others is highly desirable in nanoscience and nanotechnology [76,213,214]. We have illustrated in above section that Sb can grow in three different types of nanostructures on HOPG, namely 3D clusters or crystallites, 2D films and 1D nanorods. To selectively fabricate one type of nanostructures, it is necessary to understand the mechanism and conditions of different structural formation. We investigated Sb nanostructural growth on HOPG under different deposition flux and substrate temperature. The image shown in Figure 13(a) was taken on a HOPG sample after 1.8 nm Sb deposited with a rate of 1.8 Å/min at RT. In this condition, only 3D spherical islands are formed at early stage. Most of 3D islands are nucleated along the steps on HOPG. With further Sb deposition in this condition, 2D and 1D islands start growing. In contrast, the image shown in Figure 13(b) was taken on a sample with 5.4 nm Sb deposited at a rate of 18 Å/min and with the sample at about 100°C. Here, only 2D and 1D Sb structures are observed. We found that substrate temperature is more important than the flux in determining which type of Sb structures grow initially. At RT, even with a flux of 6 Å/min, 3D island nucleation and growth are dominant, whereas with this flux at 100°C 3D islands are totally suppressed. Raising substrate temperature further, we found that the growth cannot happen when T ≥ 135°C. In addition, Sb sublimation become significant at T ≥ 220°C from the structures grown on HOPG. After a 10-min annealing at 260°C, the nanorods almost all

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disappear, while many 2D and 3D islands remain. All Sb desorbs from HOPG after 10 min annealing at 375°C.

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Figure 13. Selective growth of Sb nanostructures on HOPG. (a) After 1.8-nm Sb deposited at RT and a flux of 1.8 Å/min; and (b) 5.4-nm Sb deposited on HOPG at 100°C and a flux of 18 Å/min. Only 3D islands grow initially in (a) whereas the growth of 3D islands is totally suppressed in (b). Image area: (a) (2.5 μm)2 and (b) (4 μm)2.

Previous studies of Sb growth on graphite have addressed mostly the nucleation and growth of compact and ramified 3D structures [97-102,169,215]. Kaiser et al. [102] observed formation of other types of structures, and they obtained dominantly branched 3D islands at a high flux (~ 60 Å/min), while a few different types of structures formed at ~ 3 Å/min. Supercooling of deposited Sb4 was considered a possible driving force for viscous fingering and dendrite crystallization. With a relative low Sb4 flux used in our experiments, however, this effect should be rather weak. Here, we explain the observed phenomena in terms of different adsorption state and diffusion rates of Sb species on HOPG. In gas phase, Sb4 is more stable than Sb2 and Sb1. The energy cost to dissociate an Sb4 into two Sb2 is 2.4 eV (i.e., 1.2 eV per Sb2), and it is 8.4 eV for breaking into four Sb1 (i.e., 2.1 eV per atom) [216,217]. The most stable configuration of Sb4 is a tetrahedron [218]. All these can change when Sb4 is adsorbed on a substrate. For example, when deposited on Si(001) near RT, an Sb4 ball (or tetrahedron) cluster first settles in a planar dumbbell precursor chemisorption state, then dissociates into two dimers [170]. The energy barrier is ~ 0.7 eV for ball-to-planar transition, and is ~ 0.8 eV for dissociation of a planar Sb4 into two Sb2. The binding energy of Sb on Si(001) is about 0.5 eV per atom with reference to Sb4 in gas phase, and a saturation coverage near 0.5 monolayer is maintained up to T ≈ 800°C [216,217], much higher than the temperature at which such a coverage can be maintained on HOPG. The bonding of Sb with HOPG is expected to be significantly weaker than that with Si. Our results show that, the initial sticking probability of Sb4 on HOPG is near 1 at RT, but it

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starts dropping noticeably at ~ 100°C. When an Sb4 lands on HOPG, it is most likely in a physisorption state. Similar to the case on Si(001), a physisorbed Sb4 can transform to a chemisorption state or even dissociate into two Sb2. But these transformations require overcoming certain energy barriers, which are expected at least as high as those on Si(001), i.e., ≥ 0.7 eV. The diffusion barrier Ed of physisorbed Sb4 on HOPG is ~ 60 meV [169], so that at RT they can already quickly find defect sites such as steps. 3D island nucleation occurs as several Sb4 clusters meet at a defect site. As more Sb4 arrive, the existing 3D islands grow, and new islands nucleate until the island density reaches certain saturation value. On the other hand, when a physisorbed Sb4 transforms to a chemisorbed Sb4 or dissociates into dimers, the diffusion barriers of these Sb species on HOPG are expected to increase significantly from that of physisorbed Sb4. We believe that the crystalline 2D and 1D structures are nucleated from these chemisorbed Sb species, and these nucleation events occur when the chemisorbed Sb species meet on graphite terrace, not necessarily at defects. This explanation is consistent with the results of Bi on HOPG which only form 1D and 2D structures [139], because the deposition flux was not mainly Bi4. The chemisorption/dissociation offers a channel competing with 3D island growth. Which channel is dominant depends on the kinetic parameters of these processes and deposition conditions. At a relative low T (e.g., 30°C) and a low Sb4 flux, the conversion to chemisorption or dissociation is strongly suppressed due to the Boltzmann factor exp[Ec/(kT)], where Ec is the barrier of chemisorption or dissociation, and k is the Boltzmann constant. Since the diffusion barrier of physisorbed Sb4 on HOPG is quite low, migration of Sb4 clusters to step edges and other defects is highly activated. Consequently, 3D island nucleation and growth are dominant, resulting in a sample shown in Figure 13(a). Increasing substrate temperature enhances the rates of both Sb4 diffusion and conversion to chemisorption (or dissociation) state. The ratio of these two rates depends on T approximately as:

Rchemisorb ⎡ ( E − Ed ) ⎤ ∝ exp ⎢− c ⎥ Rdiffusion kT ⎣ ⎦

(1)

Since Ec > Ed, the increment of chemisorption rate with T is faster than that of Sb4 diffusion, so that this ratio increases with T. Assuming Ec - Ed ≈ 0.8 eV, this ratio at 100°C is about 300 times higher than that at RT. Correspondingly, the concentration of chemisorbed Sb species increases with T, which enhances the probability of nucleation and growth of 2D and 1D structures. Increasing the deposition flux further enhances this probability, since it lets chemisorbed Sb clusters more likely meet with each other. In addition, Figure 10(a) and (b) show that, with a moderate flux and at RT, although all three types of Sb structures grow initially, most of Sb4 clusters deposited later go to 2D islands. This indicates that, once 2D islands have nucleated, they can effectively attract Sb4 deposited later so that the supply of Sb for 3D island growth drops. At high T and high flux, this effect completely suppresses 3D island growth, yielding only 2D and 1D islands on the sample as shown in Figure 13(b). At this stage, we are still searching for conditions to selectively grow either 1D or 2D Sb structures but not both. Patrin et al. [219] demonstrated 2D Bi film growth on GaAs(110) at 30 K at which the diffusion of deposited species is suppressed. Using a source mainly generating Sb2 or Sb1 [77,78] and a low substrate

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temperature, dominant growth of 2D Sb structures might be achieved. On the other hand, one could try to get dominant Sb nanorod growth by using the cracked source, a higher sample temperature and a substrate with a highly anisotropic surface lattice.

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5. Summary and Future Exploration Although graphite is a prototypical inert substrate and apparently simple 3D island growth is expected for most materials deposited on HOPG, the morphology of the resulting structures varies significantly from one material to another, and also changes with substrate temperature as well as the flux and total amount of deposition. 3D clusters nucleate and grow for all the elements studied here deposited at RT. The shape of 3D nanoparticles is nearly spherical when they are small. The spherical shape can be maintained for Sb and Ge crystallites up to a quite large size (consisting of ≥ 106 atoms). Such faceting threshold sizes, beyond which crystalline facets appear on nanocrystal surface, are significantly bigger than those of many metallic crystallites [31,43,57,106], including Al (≤ 105 atoms) in our study. The electronic energy factor, which favors spherical shape, should be insignificant in this size range. We believe that the key factor here is the surface energy of a nanoparticle that, due to limited size, can take very different values than that of macroscopic surfaces. Comparatively speaking, HOPG is nearly a perfect inert substrate for Ge, so the orientation of Ge nanocrystals is completely random. This also reflects the inertness and isotropic surface energy of Ge nanoparticles, which makes it hard for the coarsening and oriented growth of these nanoparticles. For Al and Sb crystalline nanostructures which exhibit surface energy anisotropy, HOPG shows noticeable stronger binding power to determine their polar and azimuthal orientations to certain extent. Even at RT, the 3D clusters and crystallites of Al and Sb are quite mobile on HOPG, and coalescence between these nanoparticles in contact proceeds quite easily. Although the coarsening among a group of Al crystallites leads to crater formation, a fairly uniform Al film can be obtained at a late growth stage. Besides 3D islands, 2D films and 1D nanorods are also formed when Sb is deposited on HOPG. The formation of 2D and 1D structures is related to the chemisorption and dissociation of deposited Sb4. By choosing proper deposition flux and substrate temperature, we can selectively grow either 3D islands or 2D and 1D structures. While the lattice parameters of 3D and 2D structures are close to those of α-phase Sb, the Sb nanorods show noticeable deviation in lattice type and parameters from the bulk, possibly induced by the Laplace pressure which can be rather tremendous in a nanostructure. In addition, some quasi1D nanostructures can be formed for Ge and Al, taking advantage of HOPG step edges to trap and link the clusters or crytallites. All these results indicate again that the geometric and surface properties of nanostructures can deviate significantly from that of bulk crystals and are sensitively size-dependent. Consequently, these properties affect the interactions of nanostructures with the substrates and with each other, as well as the texture of the films derived from these nanostructures. We also showed examples of selective nanostructural self-assembly. The selectivity can be enhanced based on the understanding gained from experiments over broader ranges of growth conditions (e.g., flux, sample temperature, substrate type, using surfactant). The details of nanoparticle migration, rotation and coarsening can be captured at a reduced substrate temperature. In addition, self-assembly and morphology of nearly free-standing compound

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nanostructures can be explored on HOPG and other inert substrates such as insulating films on silicon. Such exploration is beneficial to the integration of nanostructure-based electronic, optoelectronic and spintronic devices on Si-based integrated circuits.

Acknowledgements These works were partially supported by research grants from the National University of Singapore (Grants R-144-000-069-101 and R-398-000-008-112) and the Science and Engineering Research Council of Singapore (Grant R-144-000-088-305).

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SHORT COMMUNICATIONS

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Copyright © 2009. Nova Science Publishers, Incorporated. All rights reserved. Graphene and Graphite Materials, Nova Science Publishers, Incorporated, 2009. ProQuest Ebook Central,

In: Graphene and Graphite Materials Editor: H.E. Chan, pp. 233-244

ISBN: 978-1-60692-666-6 © 2009 Nova Science Publishers, Inc.

SELF-ASSEMBLED FIBRILLAR CARBON NANOTUBE HEAT TRANSFER GELS WITH ENHANCED THERMAL CONDUCTIVITIES Betty Catalina Rostro$, Scott Selinger$, Nancy Rosenberg$, Valery N. Khabashesku* and Enrique V. Barrera1,$

Department of Mechanical Engineering and Materials Science$ and Department of Chemistry and Smalley Institute for Nanoscale Science and Technology*, Rice University, Houston, TX, 77005-1892

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Abstract There are an increasing number of industrial applications that require energy-efficient heat transfer fluids. As such, fluids with high thermal conductivities are highly sought after. Increased thermal conductivities have been reported in fluids containing suspended nanoparticles – smaller than 100 nanometers (nm) – these were termed nanofluids. Nanofluids made with metal, ceramic, metal oxide, and carbon nanotube particles have shown thermal conductivities that are remarkably higher than the base liquid. The aim of this study was to increase the thermal conductivity (TC) of biodegradable synthetic and vegetable oil heat transfer fluids (HTFs). The TC of these base oils was increased by up to 96% using additives of graphene type, Single-Walled Carbon Nanotube (SWNTs), thereby leading to the formation of SWNT nanofluid-HTFs (n-HTFs). The Decagon KD2 was used to measure the TC, and Raman spectroscopy was used to study the TC mechanism. The resulting SWNT nanofluidHTFs (n-HTFs) are proposed to be defined as a self-assembled fibrillar networked gels.

Introduction There is a continued industrial need for energy efficient heat transfer fluids with high thermal conductivities. Increased thermal conductivities have been reported in fluids 1

E-mail address: : [email protected]. Enrique V. Barrera, Department of Mechanical Engineering and Materials Science - MS 321, Rice University, 6100 Main St., Houston, TX 77006. (To whom correspondence should be addressed)

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containing suspended nanoparticles – smaller than 100 nanometers (nm) – these were termed nanofluids.[1a] Nanofluids made with metal, ceramic, metal oxide, and carbon nanotube particles have shown thermal conductivities that are remarkably higher than the base liquid.[1a] A number of publications have revealed a significant enhancement in the thermal conductivity of carbon nanotube loaded nanofluids.[1a,1b] Carbon nanotubes are a novel form of elemental carbon, that exhibit high thermal conductivity properties due to their structure and size. Lubricants and cooling agents such as oil, ethylene glycol, and water are often used as traditional HTFs in engines, radiators, heat pumps, and other equipment, which require cooling and/or energy maintenance. If SWNTs are processed and solvated or suspended in HTFs, this would result in carbon nanotube heat transfer fluids, n-HTFs with increased TC. Since their discovery in 1991, SWNTs have attracted a great deal of attention due to their exception mechanical, electrical, and thermal properties. The unique SWNT properties are due to the unique structure of the tubes, which are composed of hollow rod-like cylinders of graphite sheets that are rolled up, and which function as quasi-1D crystals with translational periodicity along the tube axis. The crystalline structure and delocalized π system are responsible for the unique thermal conductivity of graphitic structures where extensive phonon and/or electron involvement is present. This study was aimed at improving the thermal conductivity (TC) of biodegradable synthetic and vegetable oil HTFs by using SWNT additives. Anisotropic and fibrous carbon nanotube roped bundles, that were microns in length, were added to biodegradable oils together with an oleylamine surfactant additive, which promoted gelation and subsequent micronetwork formation of the SWNTs in the biodegradable oil-additive mixture. This gelation allowed for the SWNT fibers to stack and slide to each other within the oil-additive matrix, which resulted in n-HTFs that could be mechanically processed via homogenization and ultrasonication. The TC of the resulting n-HTFs was measured using the Decagon KD2 and the data consistently showed a TC increase that was correlated to the SWNT loading. The heat transfer mechanism of the samples was assessed by Raman spectroscopy. The thermal conductivity increases would have resulted from the microgelled state of the SWNTs-in-oil, which would increase the thermally populated phonons within the SWNT-SWNT junctions. The SWNT thermally populated phonons could then pair up with the vibrational Brownian motion from the oil, leading to a combined SWNT phonon and oil Brownian motion heat transfer mechanism for the nHTFs.

Methods Solvents, biobased oils, and oleylamine additive were purchased from Sigma-Aldrich, while the SWNTs were HiPCO tubes provided by Carbon Nanotechnology Laboratory at Rice University. The British Petroleum (BP) 166 synthetic, poly-α-olefin oil was provided by BP. Chevron Oronite provided the ashless Succinimide and Zinc Dithiodiphosphate (ZDDP) additives. The n-HTFs were prepared by soaking the SWNTs-oil-additives in 25 mL vials. The entire mixture was mixed on a hot plate-stirrer (stirrer setting 5) for 24 hours. This was followed by solvent processing of the SWNT-oil-additive mixture with 150 mL of toluene and 10 mL of acetone on a hot-plate-stirrer (stirrer setting 5). Thereafter, n-HTF samples were homogenized for 15 minutes in 25 mL vials using the CAT X520 system that was equipped

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Self-assembled Fibrillar Cabon Nanotube Heat Transfer Gels...

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with a 20 mm generator and a sealed shaft. Samples were then ultrasonicated for 15 minutes (2 minute sonication with a 5 minute cooling interval at 75% Amplitude) in 25 mL vials using a Cole-Parmer 750 Watt ultrasonic processor with a 1/4-inch diameter tapered microtip. Figure 1-1 (a) shows the BP166 poly-α-olefin oil, and compares this to (b) BP166 with additives (1 wt% of each additive- ZDDP, Ashless Succinimide, and Oleylamine), (c) BP166 with additives and solvent processed, and (d) a fully prepared 1 wt% SWNT n-HTF in BP166 with additives and solvent processing.

Figure 1.1. Photographs of sample fluids: (a) Poly-α-olefin oil, BP166, (b) BP166-additives, (c) solvent processed BP-166-additives, (d) 1 wt% SWNT n-HTF with solvent processed BP-166-additives.

Heat transfer within the SWNT n-HTFs was tested using the Decagon KD2 system. The KD2 uses a single-needle heat pulse technique to apply a 30 second heat pulse to the medium being tested such as a powder, grease, or fluid.[2] For this study all SWNT n-HTF media were tested in 4 mL test tubes that were allowed to equilibrate for two hours. The data collected was of thermal diffusivity (TD) and thermal conductivity (TC), which are related by TC = 1 / TD. In order to standardize the KD2, three measurements of water and various oils (soybean, silicone, mineral, paraffin, and poly-α-olefin) were taken and averaged. The data from these measurements was then compared with National Institute of Standards and Technology (NIST) TC data and showed to be reproducible, it did however show a 3% error margin, this is shown in Figure 1-2 (a). Various types of carbon based n-HTFs were made in BP166 poly-α-olefin oil and tested, these ranged from carbon black, pyrographed carbon, fullerenes (C60), powdered and pristine SWNTs, and purified SWNTs, to oxidized-SWNTs (ox-SWNTs), and functionalized SWNTs such as fluorinated (F-SWNTs), and undecylated (C11H23-SWNTs).[3] The respective TC data is shown below in Figure 1-2 (b).

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Figure 1.2. TC of various fluids: (a) oils and water, (b) n-HTFs prepared with BP166 poly-α-olefin oil and different forms of carbon materials.

 

  Figure 1.2. (c). TC of SWNT-HTFs. (d) TC of purified SWNT-HTFs. Note that the TC increases with increased SWNT wt % loadings.

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  Figure 1.2. (e). TC of a variety of Fluorinated SWNT-HTFs made with BP166 poly-α-olefin oil. (f) TC of a variety of Purified SWNTs n-HTFs made with Silicone oil. Note that the TC increases with increased SWNT wt % loadings.

 

 

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Figure 1.2. (g). TC of purified SWNT-HTFs made with Soybean oil. (h) TC of purified SWNTs nHTFs made with Linseed oil. Note that the TC increases with increased SWNT wt % loadings.

From these carbon materials, SWNTs, Purified SWNTs, and F-SWNT material were chosen to make some n-HTFs in BP166 poly-α-olefin, Silicone, Soybean, and Linseed oils. The resulting SWNT n-HTFs were tested and their TC values are shown in Figure 1-2 (c)-(h). A Kaiser Raman 785 nm laser was used to assess the heat transfer mechanism of the samples, which was found to be a combination of SWCNT phonon and oil vibratory behavior, this is shown in Figures 1-3 (a)-(b). Note that by using a 785 nm laser source, fluorescence interference from the oil was significantly reduced, as the 785 nm excitation is outside the fluorescence range.[4] As the n-HTF samples were opaque and turbid they were dissolved in toluene using a 300 dilution factor. Due to this turbidity the n-HTF samples would scatter and diffuse light traveling through them, as such, elastic scattering would quickly depolarize the polarized light that is incident and which diffuses deeper into the nHTF samples.[5a] This makes it difficult to obtain a signal of singly scattered photons, however these singly scattered photons can be detected by using polarization.[5a,b] Illuminating the samples with linearly polarized light would produce two polarization states, these being states that are parallel and perpendicular to the illumination’s polarization state.[5a,b] The generated spectral line shape would then correspond to the total intensity that results from the two detected signals, these being the parallel and perpendicular Raman measurements. This procedure was used to obtain high quality spectra, whereby the resulting

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data did show some fluorescence, elastic scattering, and Raman scattering from randomly oriented molecules that had different ratios of polarized to depolarized signals. As fluorescence was present, it was necessary to allow for a one minute time delay between absorption and the re-emission of a photon as the excited molecules would tumble through Brownian motion and thus reorient their induced dipole axis, resulting in a reduced polarization.[5a,b] Such a technique required that two different separate spectra be obtained at two different times, in order to obtain the parallel and perpendicular spectra, which gave a final averaged spectrum.

Figure 1.3. (a). Raman spectrum of poly-α-olefin BP166 tested via the Kaiser 780 nm Raman. The spectral curves show vibratory Brownian motion within the oil.

Figure 1.3. (b). Raman spectrum (780 nm) of 1wt% SWNT n-HTF in poly-α-olefin. The spectral curves show a combination of SWNT phonon mechanisms and oil vibrational Brownian motion.

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Results and Discussion

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Thermal Conductivity From the calibration fluids tested in Figure 1-2 (a), we see that water has the highest TC, and that vegetable oils also showed higher TC values when compared to petroleum based oils. In Figures 1-2 (b) we note that a 1wt% loading of SWNT (0.1645 W/mK, 13.60% increase) and purified SWNT material (0.1620 W/mK, 11.88% increase) had a relatively high TC with pristine SWNT material having the highest TC (0.1816 W/mK, 25.41% increase). Functionalized SWNT material only showed a 4-7% increase with the Oxidized SWNTs (OxSWNT) showing the lowest increase. Non-SWNT materials showed relatively minor TC improvements, with a 10 wt% loading of C60 (0.1544 W/mK, 6.63% increase) showing the highest improvement versus that of the 1wt% loading of Carbon Black (0.1469 W/mK, 1.45% increase) which was the lowest. However out of the non-SWNT materials, we wanted to compare the differences between wt% and a 3 volume (vol) % loading of Pyrographed material, and the vol% sample had the highest TC (0.2244 W/mK, 54.97% increase). We also note in Figure 1-2 (e) that Fluorinated-SWNT n-HTFs had lower TC values (10 wt% loading yielded 0.1841 W/mK, 27.14% increase) when compared to Purified-SWNT n-HTFs, Figure 1-2 (f) (10wt% loading 0.2841 W/mK, 96.20% increase). The higher TC of silicone and biodegradable based oils is illustrated in Figures 1-2 (d)(h) by comparing a 10 wt% loading of purified SWNTs in the BP-166 (TC = 0.2841 W/mK, 96.20% increase) versus a 5 wt% loading of Purified SWNTs in silicone oil, (TC = 0.2131 W/mK, 58.79% increase), 5 wt% loading of Purified SWNTs in soybean oil (TC = 0.2809 W/mK, 77.56% increase) and a 5 wt% loading of Purified SWNTs in linseed oil (TC = 0.2836 W/mK, 84.28% increase). With the current processing methods higher SWNT loadings were not possible due to the n-HTFs turning into powdered SWNT material. It should, however, be noted, that consistent increases in TC were observed with increased SWNT loadings. This suggests that further TC improvements might be possible if n-HTFs with higher SWNT loadings could be formulated. Overall, the Purified-SWNT n-HTFs made with the BP-166 oils showed the highest % increase in TC, that being the 96.20% increase.

Thermal Conductivity Mechanism The higher TC values of the SWNT material are attributed to the structure and packing of the SWNTs in the oil.[6] It is here where the particle anisotropy and micronetwork formation of the SWNTs-in-oil becomes highly relevant.[6] The sp2 trigonal planar symmetry of the SWNTs is especially suitable for heat transfer since acoustic phonons and/or electrons can propagate very quickly along the tightly bound planes, but are slower to travel from one plane to another.[7] Purified SWNTs would have higher TC due to the removal of defected and graphitic impurities in the SWNT material that would interfere with the heat transfer conduction mechanisms. Since TC is an anisotropic property, fiber geometrical factors would also be relevant, making the anisotropic aspects of the nanotubes highly pertinent.[6] Therefore, at room temperature, vibrations in the SWCNT crystal lattice are the source of heat conduction, which according to quantum theory can be described by phonon interactions, and this is noted in the

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Raman spectra that is shown in Figure 1-3 (a)-(b). Note that in the Raman the SWCNT G peak is almost diminished. This occurs due to the reorientation Brownian motion of the molecules, the presence of the micronetwork interactions between the C=C bonds as well as C-H…π, N-H…π interactions, and also from the N-H vibrations which are in the 1500-1560 cm-1 energy range.[5b,8] Contributions from such interactions often make quantitative analysis highly difficult, yet the C=C and N-H…π aromatic interactions are detectable.[9-13] In fact the shoulder at 1523 cm-1 which becomes intensified with increased amine concentrations corresponds to the N-H…π aromatic interaction.[9-13] These effects become highly relevant in this study, since the phonon mechanisms of the SWCNTs and the vibrational Brownian motion of the oil which is noted in the spectra, are responsible for distributing the thermal energy in thermal conduction processes such as TC and heat capacity.[5a-b] However, ultimately it is the oil which dictates the base TC, with the viscosity and structure of the oil- vibration of the C-C and C= C bonds, C-H…π, C-N… π, NH…π interactions, micronetwork formation, and resulting gelation being the controlling factors. For liquids it is known that thermal transport occurs due to vibrations within the liquids known as Brownian motion. As the n-HTFs were gelled media that were diluted in toluene, solvent effects, intermolecular forces such as the weak Van der Waals forces, hydrogen bonding, and specific charge transfer interactions would be expected to influence the Raman spectra.[5a-b] The influence of the solvent, and alkane molecules would tend to shift and broaden depolarized Raman bands, note that this would also be caused by the rotary Brownian motion stemming from the highly anisotropic tensor of the n-HTF media.[5a-b] Biodegradable based oils showed higher TC values in Figure 1-2 (a), and this is attributed to conjugation and the presence of fatty acids, which contain hydrogen and electron containing groups such as nitrogen or oxygen.[14] Petroleum based oils would inherently suffer from lower TC values due to slower vibration along the length of the alkyl chain, due to lack of conjugation, and since a lower number of electron containing functional groups such as oxygen or nitrogen are present. Overall purified SWCNT material and biodegradable based oils showed higher TC properties than n-HTFs that were prepared with the same material in a petroleum-based oil. However, in order to fully explain the TC mechanism of the n-HTFs, the thermal contributions from the SWCNTs, additives, oil, and micronetwork formation must be accounted for.

Amine Induced Gelation Solvent-additive processing in toluene-acetone followed by homogenization and ultrasonication promoted a gelled state, where N-H…π, C-H…π and π-π interactions led to the self-assembly, or self-organizing, of the SWCNTs into three-dimensional fibroid networks within the biodegrable oil-additive media.[15-18] Further intertwining of the rod-like nanotube fibers with the oil-additive solvent molecules would serve to enhance micronetwork formation through the formation of SWCNT-SWCNT junctions, which would result in the supersaturation of the SWCNT fibers and a closely packed gelled state.[15-18] The unique interplay of H-bonding, π−π stacking, and alkyl-chain interactions within the oil-additiveSWCNT matrix, allows for the SWCNTs to self-assemble and interact with each other and with other solid surfaces, thereby making them processable.

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Self-assembly tendencies and properties are seen in liquid crystal systems, thermophilic and hydrophobic proteins, macro- or supramolecular assemblies, elastomers, gels, hydrogels, dendrimers, polymers, and combinations of these.[16-24] Other notable example of such interactions are actively seen in sol-gel materials, a variety of polymeric and biological gels, and other soft active materials.[7,15-27] When fibrous anisotropic molecules are combined with amine gelling agents such as urea, oleylamine, imidazole salts, and aromatic, or ketonic solvents, they will often show a combination of non-covalent interactions such as H-bonding, C-H…π, π−π stacking, hydrophobic forces, and van der Waals interactions, which result in the formation of self-assembled fibrillar networked gels.[16-24] This occurs due to the interplay of intramolecular hydrogen (N-H) bonding of the amine groups to the rod-like anisotropic fibrous and/or aromatic molecules, resulting in the C-H…π interaction, notably the N-H…π, and C-N… π interaction, and π-π interactions, which favor the formation of hexagonal type lattice assemblies, SWCNT-SWCNT junctions, and a fibrillar networked state, this we term micronetwork formation. Subsequent solvent and sonication processing via toluene-acetone likewise promotes intercalation of aromatic molecules such that favorable π−π stacking interactions such as T-shaped dimerization could occur.[7,15-17,27] These interactions would further promote the formation of a self-assembled fibrillar networked gel state.[7,15-27]

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n-HTF Structure The n-HTFs can be considered to have a sheath structure where the hydrocarbon and additive chains are wrapped around the bundled-roped SWNT cores, therefore creating a type of inverse micelle. It is here where active micronetwork formation occurs between the tubes and the oil-additives. Within this sheath structure, van der Waals and other non-covalent interactions such as C-H…π interaction, the C-N… π aromatic interaction, and π-π interactions from the C=C bonds would be present, this is what gives rise to the micronetwork formation. The additives help to increase the TC by further promoting micronetwork formation between the SWNTs, and they also contribute electron-rich groups due to the presence of functional groups such as N-H. This is shown in Figure 1-5 (a)-(d) where the inclusion of the amine additives gave gelled samples that were processable and where higher SWNT wt% loadings were possible. Avid micronetwork formation would lead to closely packed structures that would favor ensuing vibratory behavior which would favor higher TC values.

TC Barriers TC barriers would result from the existence of amorphous material that may be present as impurities, defects, lack of nanotube-nanotube contact and/or other changes that would hinder SWCNT crystallinity. Increased surface defects, or porosity of the SWCNTs, which would be evident at lower loadings or in the functionalized SWCNT material, would decrease the phonon mean free path and increase phonon-defect or phonon-interface interactions and as the result would limit the TC. If the outer walls of the nanotubes make good thermal contacts, then extrinsic phonon scattering mechanisms are enhanced due to nanotube-nanotube

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interactions. These interactions enhance the TC in the horizontal direction due to anisotropic considerations. In effect, the TC results from the percolation behavior of the phonons and/or electrons within the SWCNTs, and the vibrational Brownian motion that is being experienced by the oil-additive chains of the fluid media.[14,8-13]

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Figure 1.5. (a). A highly hydrophobic 1-wt% SWNT-BP166 n-HTF without oleylamine that wraps onto itself. (b) A gelled 1-wt% SWNT-BP166 n-HTF made with oleylamine that could be processed. (c) Depiction of the oil-additive mixture and the SWNTs. (d) Micronetwork formation.

Conclusion n-HTFs are a novel type of self-assembled fibrillar networked gels that exhibit greater than 90% TC increase when compared to regular HTFs. The n-HTFs, via a combination of non-covalent interactions such as metal coordination, C-H…π interactions, CN… π interactions, H-bonding, π−π stacking, hydrophobic forces, and van der Waals interactions, form a networked gelled state. The degree of anisotropic micronetwork formation dictates the conductivity increase via percolation, and the amine groups coupled with sonication, and solvent processing controls the degree of gelation, SWNT micronetwork formation, and ensuing supersaturation. A 780 nm Raman analysis suggested the TC mechanism to be SWNT phonon mechanisms within the Brillouin zone of the SWNTs coupled with oil vibrational Brownian motion and additive-electron and Hydrogen bonding. The TC enhancements of the n-HTFs have been attributed to SWNT phonon mechanisms, these being phonon-phonon, phonon-defect, and phonon-interface, all of which are present at room temperature with additional vibrations from the oil, electron-phonon interactions, and H bonding from the additives. These n-HTFs can be conveniently modeled using the worm-like chain model where the micronetwork formation can be considered to affect the percolation behavior through increased SWNT-SWNT junctions, molecular crowding, and interface activity. Furthermore this model can also be used to explain vibratory

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Brownian motion and phonon interactions of the SWNTs in the oil-additive matrix, all of which leads enhanced heat transfer and TC. While many studies have suggested that biodegradable oils suffer from inherent low thermal conductivity and thermal-oxidative properties, this work experimentally shows that biodegradable oils have higher thermal oxidative and conductivity properties than petroleum based products. The low toxicity, long lifetime, natural lubricity, good metal-wetting attraction, and antimicrobial properties of the biodegrable oils make them suitable for use in various applications. This is significant since it is known that highly conductive fluids will allow for more efficient heat transfer, which can increase efficiency, lower the weight, and reduce the complexity of existing thermal control systems that may be present in engines and/or micro-electromechanical systems (MEMS).

Acknowledgement This work was supported in part by the NSF AGEP grant # HRD-9817555, Welch Foundation grant # C-1494, and NASA URETI Cooperative Agreement #NCC-1-02038. We are grateful to Michael Strano and Erik Haroz from the former Smalley lab at Rice for help with Raman characterization, Felipe Chibante from NanoTex-BuckyUSA and Decagon, for countless hours of advice on thermal conductivity instrumentation.

References [1]

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[2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14]

1

a. H. Chen, Y. Ding, C. Tan, New J. of Phys., 9, 367 (2007).1b. P. Keblinski, J. A. Eastman, D. G. Cahill, Mater. Today, 8, 36 (2005). M. Sawamura, K. Kawai, Y. Matsuo, K. Kanie, T. Kato, E. Nakamura, Nature, 419, 702 (2002). H. Peng, P. Reverdy, V. N. Khabashesku, J. L. Margrave, Chem. Commun. 2003, 362363. S.E.J. Bell, E.S.O. Bourguignon, A.O’Grady, J. Villaumie, A.C. Dennis, Spectrosc. Eur. June/July, 17 (2002). Z. J. Smith, A. J. Berger, Optics Letters, 30, 1363 (2005). 5b. G. Maes, T. ZeegersHuyskens, J. Raman Spectrosc., 7, 325 (2005). S. T Huxtable, D. G. Cahill, S. Shenogin, L. Xue, R. Ozisik, P. Barone, M. Usrey, M. S. Strano, G. Siddons, M. Shim, P. Keblinski, Nature Mater., 2, 731 (2003). C. W. Chang, D. Okawa, A. Majumdar, A. Zettl, Science, 314, 1121 (2006). F. C. Wang, M. Feve, T. M. Lam, J-P. Pascalt, J. Polym. Sci., Part B: Polym. Phys., 32, 1315 (1994). S. Liu, S. Gangopadhyay, G. Sreenivas, S.S. Ang, H.A. Naseem, Phys. Rev. B, 55, 13020 (1997). M. Gdaniec, I. Bensemann, T. Polonski, Cryst. Eng. Comm., 7, 433 (2005). K. Pal, A.K. Banthia, D.K. Majumdar, Biomed. Mater. 1, 49 (2006). I. In, S.Y. Kim, Polymer, 47, 547 (2006). T-H. Lee, J.H. Kim, B-S. Bae, J. Mater. Chem., 16, 1657 (2006). G. Giraud, K. Wynne, J. Chem. Phys., 119, 11753 (2003).

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T. Naota, H. Koori, J. Am. Chem. Soc., 127, 9324 (2005). T. Kato, Science, 295, 2414 (2005). X. Gao, T. Hu, L. Liu, Z. Guo, Chem. Phys. Lett., 370, 661 (2003). J. Tritt-Goc, J. Boguszynska, M. Szwaj, L. Boutellier, and J. Jadzyn, Acta Physica Polonica A 108, 81 (2005). K. Yabuuchi, E. Marfo-Owusu, T. Kato, Org. Biomol. Chem., 1, 3464 (2003). M. Hashimoto, S. Ujiie, A. Mori, Adv. Mater., 15, 797 (2003). F. Camerel, C. F. J. Faul, Chem. Commun., 15, 1958 (2003). N. M. Sangeetha, U. Maitra, Chem. Soc. Rev., 34, 821 (2005). P. Xie, R. Zhang, J. Mater. Chem., 15, 2529 (2005). S.M. Liff, N. Kumar, G.H. McKinley, Nature Mater., 6, 76 (2007). 25. C. Zakri, P. Poulin, J. Mater. Chem., 16, 4095 (2006). A. Cao, S. Talpatra, Y. Choi, R. Vajtai, P.M. Ajayan, A. Filin, P. Persans, A. Rubio, Adv. Mater., 17, 147 (2005). L.H.Sperling, Introduction to Physical Polymer Science, 3rd Edition, WileyInterscience (2001), Chapters 6-14.

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[27]

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In: Graphene and Graphite Materials Editor: H.E. Chan , pp. 245-277

ISBN: 978-1-60692-666-6 c 2009 Nova Science Publishers, Inc.

VON N EUMANN A LGEBRAS G ENERATED BY AUTOMATA Ilwoo Cho∗ Saint Ambrose Univ., Dep. of Math, 518 W. Locust St., Davenport, Iowa, 52803, U. S. A.

Abstract

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The main purpose of this paper is to introduce how to construct a von Neumann algebra generated by an automaton, containing the full information of the given automaton. We show that the von Neumann algebras generated by automata are characterized by the graph von Neumann algebras in the sense of [10] and [11]. This shows that the von Neumann algebras generated by automata have the same basic properties with graph von Neumann algebras.

1991 Mathematics Subject Classification: 05C99, 18B20, 18B99, 20F10, 68Q99, 46H99, 46L99, 47L65. Key words and phrases: Automata, Automata Graphs, Automata Groupoids, Directed Graphs, Graph Groupoids, Graph von Neumann Algebras, Automata Von Neumann Algebras, Crossed Product Algebras, Amalgamated Free Products. In this paper, we will consider a certain application of the study of graph von Neumann algebras (See [10], [11], [12], [17] and [18]). We search the connections between (graph) von Neumann algebras and automata. In particular, we are interested in von Neumann algebras generated by automata, preserving the full combinatorial properties of the given automata. We show that these von Neumann algebras are nicely characterized by graph von Neumann algebras. Graph von Neumann algebras are operator algebraic objects induced by combinatorial objects, directed graphs. By considering the connection between automata and directed graphs, we can find the relation between automata and graph von Neumann algebras.. The main purpose of this paper is to introduce the construction of graphs, preserving the properties of automata, and the construction of von Neumann algebras generated ∗

E-mail address: [email protected]

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Ilwoo Cho

by automata via the corresponding graphs of automata, which is nothing but the graph von Neumann algebras. Consider a machine consisting of finite alphabet a finite tape alphabet a finite state control and an infinite work tape. The instructions are the form read, write, move left, move right and one reads / writes letters from the tape alphabet on the tape, when the tape starts out blank. We input a finite string consisting of letters in the alphabet one letter at a time, read from left to right. For each letter a in the alphabet, the finite state control performs some instructions on the work tape corresponding to an edge whose label is (a, instructions) and move to the target node of the edge. We can start at the start node and accept the string if there is some path from the starting node to an accept node labeled by the letters of the string. The language of a machine is the set of strings in the letters in the alphabet which the machine accepts. This is how automata work. We can regard the machine with such instructions as an automaton. Let the quadruple A = (Q, D, ϕ, ψ) is given, where Q and D are finite sets and

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ϕ:Q×D→Q

and ψ : Q × D → D

are functions. Sometimes, we say that Q and D are the state set and the (finite) alphabet of A, respectively, and we say that ϕ and ψ are the state transition function and the output function, respectively. In this case, the quadruple A is called an automaton. If the map ψ(q, •) is bijective on D, for any fixed q ∈ Q, then we say that the automaton A is invertible. Similarly, if the map ϕ(•, x) is bijective on Q, for any fixed x ∈ D, then we say that the automaton A is reversible. If the automaton A is both invertible and reversible, then A is said to be bi-reversible. Recently, various algebraists are studying automata and the corresponding automata groups. We consider certain graphs induced by automata and the corresponding graph groupoids (See [10], [11], [12], [15], [16], [17] and [18]), motivated by [17] and [18]. Then we can construct the graph von Neumann algebras, which is the von Neumann algebra generated by graph groupoids as in [10] and [11]. These graph von Neumann algebras are the von Neumann algebras generated by automata. i.e., the von Neumann algebras generated by automata are completely characterized by graph von Neumann algebras. A graph is a set of objects called vertices (or points or nodes) connected by links called edges (or lines). In a directed graph (or digraph), the two directions are counted as being distinct directed edges (or arcs). A graph is depicted in a diagrammatic form as a set of dots (for vertices), jointed by curves (for edges). Similarly, a directed graph is depicted in a diagrammatic form as a set of dots jointed by arrowed curves, where the arrows point the direction of the directed edges. Recall that a W ∗ -algebra is a C ∗ -algebra closed under the weak operator topology. A ∗ W -algebra containing the unity (or the vector-multiplication identity) is said to be a von Neumann algebra. We construct a graph von Neumann algebra MG = M ×α G as a groupoid crossed product algebra of a von Neumann algebra M and a graph groupoid G, generated by a given countable directed graph G, via a groupoid action (in the sense of [20]) α of G. The construction of our graph von Neumann algebras is different from the construction of the well-known graph algebras (or quiver algebras, or graph C ∗ -algebras) based on that of Cuntz-Krieger algebras (e.g., see [3], [7], [19] and [26]). Our construction of graph von

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Neumann algebras starts from the construction of graph groupoids, which are algebraic structures induced by the given countable directed graphs. So, the construction of graph von Neumann algebras is free from the Cuntz-Krieger relations. In particular, if M = C, then the graph von Neumann algebras C ×β G are all ∗-isomorphic to the von Neumann w algebra C[G] , generated by the groupoid G, under the suitable representation of G, for all groupoid actions β’s, by the linearity of β’s on C = M. In this paper, we are interested w in the cases where we have graph von Neumann algebras C[G] . However, in Chapter 2, we will introduce the general cases where M is arbitrary von Neumann algebras, because our main results (where M = C) are naturally extendable to the general cases (where M is arbitrary), up to groupoid actions. In [10], we found a close relation between directed graphs (which are combinatorial objects), groupoids (which are algebraic objects), von Neumann algebras and crossed product algebras (which are operator-theoretical objects), and amalgamated (reduced) freeness (which is a free-probabilistic object). We showed every graph von Neumann algebra induced by a countable directed graph is ∗-isomorphic to a certain amalgamated reduced free product algebra of edge-depending W ∗ -subalgebras, called amalgamated free blocks. In [11], we established the full characterization of such amalgamated free blocks of graph von Neumann algebras. They are characterized by specific well-known von Neumann algebras: the classical group crossed product algebras (where the groups are the infinite abelian cyclic group Z), and the certain W ∗ -subalgebras of operator-valued (2 × 2)-matricial algebras. This characterization shows that understanding graph von Neumann algebras reduces to the study of graph groupoids based on these two types of von Neumann algebras. Recall that an operator a is a partial isometry on a Hilbert space H, if it satisfies the product a∗ a of the adjoint a∗ and a is a projection on H. Recall also that an operator p is a projection on H, if p satisfies p∗ = p = p2 , i.e., p is an idempotent self-adjoint operator. It is well-known that an operator a is a partial isometry if and only if a∗ is a partial isometry if and only if a = a a∗ a if and only if a∗ = a∗ a a∗ . It is interesting that directed graphs express or visualize the partial isometries and their corresponding projections, under the suitable representations (e.g., [3], [7], [10], [11], [12], [15], [16], [17], [18], [21], and [26]). This provides the connection between directed graphs and Hilbert-space operators. Each directed edge can be understood as a fixed partial isometry and each vertex can be understood as a projection on the initial or final spaces of partial isometries, corresponding to the adjacent edge(s). The adjoints of the chosen partial isometries can be represented by the opposite directed edges called shadows. So, considering graph groupoids is natural to study such operator algebraic structures generated by partial isometries. Independent from the study of graph von Neumann algebras, in [15] and [16], Cho and Jorgensen constructed new graph-depending operator algebraic structures, under the C ∗ -algebra setting. They showed that graph groupoids of “finite” directed graphs can be embedded in a C ∗ -algebra generated by certain partial isometries in the fixed operator algebra, by giving the suitable representation, called the matricial graph representation, of the graph groupoids. More interesting facts are shown in [16]: they showed that if we have a finite family of partial isometries in an operator algebra B(H), then we can construct the corresponding directed graph from them, by using the iterated gluing technique in the sense of [16]. This shows that, conversely, certain Hilbert-space operators induce the corresponding directed graph.

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Let A be an automaton. We introduce the automata graph G of A, containing full information about the automaton A. By constructing the corresponding graph groupoid G of G, called the automata groupoid, we can have the von Neumann algebra generated by A0 , w as the graph von Neumann algebra C[G] . Our construction of automata graphs is basically the reverse processes of the construction of graph automata of Cho and Jorgensen, introduced and observed in [17]. Conversely, in this paper, we will define the automata graphs induced by the given automata. Our main results show that the von Neumann algebras generated by automata are fully characterized by the corresponding graph von Neumann algebras. So, this study provide the another bridge connecting Graph Theory and Automata Theory (as in [17] and [18]), via Operator Algebra.

1.

Introduction

In this chapter, we will introduce the concepts we need in this context; Free Probability, graph groupoids, and groupoid actions. And, in Section 1.4, we sketch our main results.

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1.1.

Free Probability

Let B ⊂ A be von Neumann algebras satisfying that 1B = 1A (i.e., A is a von Neumann algebra over B) and let F : A → B be a conditional expectation satisfying that (i) F is continuous linear, (ii) F (b) = b, for all b ∈ B, (iii) F (b1 ab2 ) = b1 F (a)b2 , for all b1 , b2 ∈ B and a ∈ A, and (iv) F (a∗ ) = F (a)∗ , for all a ∈ A. Then the pair (A, F ) is said to be a B-valued W ∗ -probability space (with amalgamation over B). All operators a in (A, F ) are called B-valued (free) random variables. For any arbitrarily chosen B-valued random variables a1 , ..., as in (A, F ), we can determine their B-valued free distributional data:   r ri r i (i1 , ..., in )-th joint ∗-moments : F b1 ai11 b2 ai22 ... bn ainin

and

  r r i (i1 , ..., in )-th joint ∗-cumulants : knF b1 ai11 , ..., bn ainin ,

for all (i1 , ..., in ) ∈ {1, ..., s}n , for n ∈ N, and ri1 , ..., rin ∈ {1, ∗}, where  r  def P  r  r r i i knF b1 ai11 , ..., bn ainin = Fπ b1 ai11 , ..., bn ainin µ(π, 1n ), π∈N C(n)

by the Moebius inversion, for all b1 , ..., bn ∈ B. (By the definition of joint ∗-cumulants, in terms of the Moebius inversion, the joint ∗-moments and the joint ∗-cumulants of a1 , ..., as contain the equivalent free distributional data. To consider the spectral data of the given Bvalued random variables, the joint ∗-moments are useful. To consider the B-freeness of the given B-valued random variables, the joint ∗-cumulants are useful, since the B-freeness is characterized by cumulants by Speicher. See [24].) Here, N C(k) is the lattice of all noncrossing partitions with its minimal element 0k = {(1), (2), ..., (k)} and its maximal element 1k = {(1, 2, ..., k)}, for all k ∈ N, and µ is the Moebius functional in the incidence algebra I. Also, Fπ (...) means the partition-depending B-valued moment. For example, if π = {(1, 4), (2, 3), (5)} in N C(5), then

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Fπ (a1 , a2 , a3 , a4 , a5 ) = F (a1 F (a2 a3 )a4 ) F (a5 ). Recall that the lattice N C(n) has its partial ordering, def

π ≤ θ ⇐⇒ for each block V in π, ∃ a block B in θ s.t.V ⊆ B, where “⊆” means the usual set inclusion, for all n ∈ N. Also recall that the incidence algebra I is the collection of all functionals ξ : ∪∞ n=1 (N C(n) × N C(n)) → C satisfying that ξ (π, θ) = 0, whenever π > θ, with the usual function addition (+) and the convolution (∗) defined by def

ξ 1 ∗ ξ 2 (π, θ) =

P

π≤σ≤θ

ξ 1 (π, σ)ξ 2 (σ, θ),

for all ξ 1 , ξ 2 ∈ I. If we define the zeta functional ζ ∈ I by ζ(π, θ) = 1, for all π ≤ θ in N C(n), for all n ∈ N, then the Moebius functional µ is the convolution inverse of ζ and vice versa. Thus the Moebius functional µ satisfies that P µ(0n , 1n ) = (−1)n−1 cn−1 and µ(π, 1n ) = 0, π∈N C(n)

 2k where ck = is the k-th Catalan number, for all k ∈ N. k The B-valued freeness on (A, F ) is characterized by the B-valued ∗-cumulants (See [24]). Let A1 and A2 be W ∗ -subalgebras of A having their common W ∗ -subalgebra B. We say that A1 and A2 are free over B in (A, F ) if all mixed B-valued ∗-cumulants of A1 and A2 vanish. The subsets X1 and X2 of A are said to be free over B in (A, F ) if the von Neumann algebras vN (X1 , B) and vN (X2 , B) are free over B in (A, F ), where vN (S1 , S2 ) means the von Neumann algebra generated by sets S1 and S2 . Similarly, we say that the B-valued random variables x and y are free over B in (A, F ) if the subsets {x} and {y} are free over B. Suppose the W ∗ -subalgebras A1 and A2 of A are free over B in (A, F ). Then we can create a new W ∗ -subalgebra vN (A1 , A2 ) of A, (containing B) and this W ∗ -subalgebra is denoted by A1 ∗B A2 , where “∗B ” means the B-valued free product. Assume now that A is a von Neumann algebra over B and let {Ai ⊃ B : i ∈ I} be the collection of W ∗ subalgebras of A (containing B) generates A. i.e., A = vN ({Ai : i ∈ I}). If Ai ’s are free over B in (A, F ), from each other, for i ∈ I, then A is (or is ∗-isomorphic to) the B-valued free product ∗B Ai of {Ai }i∈I . In such case, we say that A is a B-valued free product

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def

1 k+1



i∈I

algebra of {Ai }i∈I , and the W ∗ -subalgebras (containing B) are called the B-valued free blocks of A. Let A = ∗B Ai be a B-valued free product algebra. Then it has its Banach-space i∈I

expression as follows: Graphene and Graphite Materials, Nova Science Publishers, Incorporated, 2009. ProQuest Ebook Central,

250

Ilwoo Cho Banach

A = B⊕



∞

⊕

n=1



⊕

i1 6=i2 , i2 6=i3 , ..., in−1 6=in

(Aoi1

⊗B ...



⊗B Aoin )

,

with def

Aoij = Aij ⊖ B, for all j = 1, ..., n, for n ∈ N, Banach

where “ = ” means “being Banach-space isomorphic”.

1.2.

Graph Groupoids

Let G be a countable directed graph with its vertex set V (G) and its edge set E(G). Let e ∈ E(G) be an edge of G with its initial vertex (or its source) v and its terminal vertex (or its range) v ′ . Then we will denote e by e = v e or e = e v ′ or e = v e v ′ to emphasize the initial vertex of e respectively the terminal vertex of e respectively both the initial and the terminal vertices of e. In this case, we will say that the vertex v and the edge e are admissible (resp.,. the edge e and the vertex v ′ are admissible). Suppose e1 = v1 e1 v1′ and e2 = v2 e2 v2′ are edges in E(G), with v1 , v1′ , v2 , v2′ ∈ V (G). And assume that the edges e1 and e2 are connected in the order (e1 , e2 ). i.e., the vertices v1′ and v2 satisfy v1′ = v2 in V (G). Then there exists a finite path e1 e2 on the graph G. In this case, we say that the edges e1 and e2 are admissible. Notice that even though e1 and e2 are admissible (i.e., e1 e2 is a finite path on G), the edges e2 and e1 are not admissible in general. Indeed, if v1′ = v2 and v2′ 6= v1 , then e1 e2 is a finite path but e2 e1 is undefined on G. In other words, e2 and e1 are not connected in the order (e2 , e1 ). Suppose there is a finite path w = e1 e2 ... en on G, for n ∈ N, where e1 , ..., en ∈ E(G). Then we say that e1 , e2 , ..., en are admissible. (1) (1) (2) (2) (2) (1) (1) Now assume that w1 = e1 ... ek1 and w2 = e1 ... ek2 are finite paths. If e1 ... ek1 e1 Copyright © 2009. Nova Science Publishers, Incorporated. All rights reserved.

(2)

... ek2 is a new finite path on G, then we denote this finite path by the product w1 w2 of them, and we will say that the finite paths w1 and w2 are admissible. Suppose a finite path w = e1 ... ek has its initial vertex v1 and its terminal vertex vk (i.e., e1 = v1 e1 and ek = ek vk ). Then similarly we denote w = v1 w or w = w vk or w = v1 w vk , to emphasize the initial and terminal vertices information of w. Denote the set of all finite paths of G by F P (G). We call F P (G), the finite path set of G. Let w ∈ F P (G). Then the length |w| of w is defined to be the cardinality of admissible edges constructing the finite path w. Since every edge is a finite path with length 1, the edge set E(G) is contained in F P (G). Notice that all finite paths in F P (G) are regarded as words in E(G), under the admissibility. We can define the G-depending algebraic structure (F+ (G), ·) defined by a set F+ (G) = V (G) ∪ F P (G) ∪ {∅}, with its binary operation (·) which is the admissibility, where ∅ is the empty word in V (G) ∪ E(G). Notice that all elements in F+ (G) can be understood as words in V (G) ∪ E(G). Thus the empty word ∅ is well-determined as an element in F+ (G), with respect to (·). The pair (F+ (G), ·) is called the free semigroupoid of a graph G. For convenience, we will denote this pair simply by F+ (G). Remark that there are free semigroupoids having no empty element ∅. For instance, if O is a one-vertex-multi-loop-edge graph, then the free semigroupoid F+ (O) of O does not contain the empty element ∅, since all edges are

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admissible from each other, via the unique vertex. However, in general, whenever |V (G)| ≥ 2, the free semigroupoid F+ (G) contains the empty element. So, if there is no confusion, we always assume that a given free semigroupoid has its empty element. For the given countable directed graph G, we can define the shadow G−1 of G, which is the opposite directed graph of G, with its vertex set V (G−1 ) = V (G) and its edge set E(G−1 ) = {e−1 : e ∈ E(G)}, where e−1 is the opposite directed edge of e, called the shadow of e. i.e., if e = v e v ′ in E(G), with v, v ′ ∈ V (G), then e−1 = v ′ e−1 v in E(G−1 ). Remark that the admissibility on the free semigroupoid F+ (G−1 ) of the shadow G−1 is oppositely preserved by that on F+ (G). In other words, if we fix a nonempty element w in F+ (G) then there is a unique corresponding element w−1 in F+ (G−1 ), and vice versa. In particular, w = e1 ... ek ∈ F P (G), with e1 , ..., ek ∈ E(G), if and only if w−1 = e−1 k ... −1 ), with e−1 , ..., e−1 ∈ E(G−1 ). Notice that if v is a vertex in V (G), then e−1 ∈ F P (G 1 1 k v −1 = v, since V (G−1 ) = V (G). It is easy to check that (G−1 )−1 = G. Now, define the shadowed graph Gˆ of G by the directed graph with its vertex set V (Gˆ ) = V (G) = V (G−1 ) and E(Gˆ ) = E(G) ∪ E(G−1 ). Then, as a new directed graph, this graph Gˆ has its free semigroupoid F+ (Gˆ ). Remark that, in general, F+ (Gˆ ) satisfies that

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F+ (Gˆ ) % F+ (G) ∪ F+ (G−1 ). −1 −1 ˆ For instance, if e1 , e2 ∈ E(G) and e−1 2 ∈ E(G ), then e1 e2 e2 ∈ F P (G ) ⊂ −1 F+ (Gˆ ), but this element e1 e2 e2 does not contained in F+ (G) ∪ F+ (G−1 ). Define the reduction (RR) on the free semigroupoid F+ (Gˆ ) of the shadowed graph Gˆ of G by

(RR)

ww−1 = v and w−1 w = v ′ , for all w ∈ F+ (Gˆ ),

whenever w = v w v ′ in F+ (Gˆ ). (Here, if w is a vertex in V (Gˆ ), then we can regard w = w w w. In fact, if w is a vertex, then wk = w, for all k ∈ N.) The free semigroupoid F+ (Gˆ ), with this reduction (RR), is called the graph groupoid of G, under the inherited admissibility with F+ (Gˆ ). We denote this graph groupoid of G by G. Suppose w1 and w2 are elements in G. Then the reduced product of them is also denoted by w1 w2 . But notice that this reduced product w1 w2 in G is different from the (nonreduced) product w1 w2 in F+ (Gˆ ). Let w1 = e1 e2 and w2 = e−1 2 be finite paths on the ±1 ˆ ˆ shadowed graph G , where e1 , e2 ∈ E(G ). Then the product w1 w2 of w1 and w2 is + ˆ determined by the length-3 finite path e1 e2 e−1 2 in the free semigroupoid F (G ), but it is −1 determined by the length-1 reduced finite path e1 (e2 e2 ) = e1 in the graph groupoid G. In the graph groupoid G, the subset of all reduced finite paths is denoted by F Pr (Gˆ ). i.e.,

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F Pr (Gˆ ) = G \ (V (Gˆ ) ∪ {∅}). And we call it the reduced finite path set of G. Again, remark that all elements in a graph groupoid can be regarded as “reduced” words in E(Gˆ ), under the admissibility and the reduction (RR).

1.3.

Groupoids and Groupoid Actions

While (categorial) groupoids and their actions are used in many areas of mathematics (e.g., [17], [27], [34], and [58]), here we use them in connections with graphs and representations, and we open with the necessary definitions. We say an algebraic structure (X , Y, s, r) is a (categorial) groupoid if it satisfies that (i) Y ⊂ X , (ii) for all x1 , x2 ∈ X , there exists a partially-defined binary operation (x1 , x2 ) 7→ x1 x2 , for all x1 , x2 ∈ X , depending on the source map s and the range map r satisfying that: (ii-1) x1 x2 is well-determined, whenever r(x1 ) = s(x2 ) and in this case, s(x1 x2 ) = s(x1 ) and r(x1 x2 ) = r(x2 ), for x1 , x2 ∈ X , (ii-2) (x1 x2 ) x3 = x1 (x2 x3 ), if they are well-determined in the sense of (ii-1), for x1 , x2 , x3 ∈ X ,

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(ii-3) if x ∈ X , then there exist y, y ′ ∈ Y such that s(x) = y and r(x) = y ′ , satisfying x = y x y ′ (Here, the elements y and y ′ are not necessarily distinct), futhermore, if y ∈ Y ⊂ X , then s(y) = y = r(y). (ii-4) if x ∈ X , then there exists a unique element x−1 for x satisfying x x−1 = s(x) and x−1 x = r(x). Thus, every group is a groupoid (X , Y, s, r) with |Y| = 1 (and hence s = r on X ). So, roughly speaking, a groupoid is a generalized group with multi-units (or multi-identities). This subset Y of X is said to be the base of X . Remark that we can naturally assume that there exists the empty element ∅ in a groupoid X . The empty element ∅ represents the products x1 x2 , which are not well-defined, for some x1 , x2 ∈ X . Notice that if |Y| = 1 (equivalently, if X is a group), then the empty word ∅ is not contained in the groupoid X . However, in general, whenever |Y| ≥ 2, a groupoid X always contain the empty word. So, if there is no confusion, we will naturally assume that the empty element ∅ is contained in X. It is easily checked that our graph groupoid G of a finite directed graph G is indeed a groupoid with its base V (Gˆ ). i.e., every graph groupoid G of a countable directed graph G is a groupoid (G, V (Gˆ ), s, r), where s(w) = s(v w) = v and r(w) = r(w v ′ ) = v ′ , for all w = v w v ′ ∈ G with v, v ′ ∈ V (Gˆ ). Let Xk = (Xk , Yk , sk , rk ) be groupoids, for k = 1, 2. We say that a map f : X1 → X2 is a groupoid morphism if (i) f is a function, (ii) f (Y1 ) ⊆ Y2 , (iii) s2 (f (x)) = f (s1 (x)) in X2 , for all x ∈ X1 , and (iv) r2 (f (x)) = f (r1 (x)) in X2 , for all x ∈ X1 . If a

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groupoid morphism f is bijective, then we say that f is a groupoid-isomorphism. If there is a groupoid-isomorphism between X1 and X2 , then the groupoids X1 and X2 are said to be groupoid-isomorphic. Notice that, if two countable directed graphs G1 and G2 are graph-isomorphic, via a graph-isomorphism g : G1 → G2 , in the sense that (i) g is bijective from V (G1 ) onto V (G2 ), (ii) g is bijective from E(G1 ) onto E(G2 ), (iii) g(e) = g(v1 e v2 ) = g(v1 ) g(e) g(v2 ) in E(G2 ), for all e = v1 e v2 ∈ E(G1 ), with v1 , v2 ∈ V (G1 ), then the graph groupoids G1 and G2 are groupoid-isomorphic. More generally, if G1 and G2 have graph-isomorphic shadowed graphs Gˆ1 and Gˆ2 , then G1 and G2 are groupoid-isomorphic. Proposition 1.1. Let G1 and G2 be countable directed graphs with their graph groupoids G1 and G2 , respectively. If the shadowed graphs Gˆ1 and Gˆ2 are graph-isomorphic, then G1 and G2 are groupoid-isomorphic. Proof. Suppose Gˆ1 and Gˆ2 are graph-isomorphic, via a graph-isomorphism g : Gˆ1 → Gˆ2 . Then we can define the morphism ϕ : G1 → G2 , defined by  g(w) if w ∈ V (Gˆ1 ) ∪ E(Gˆ1 )     if w = e1 ...en ∈ F Pr (Gˆ ),  def g(e1 )...g(en ) ϕ(w) = with e1 , ..., en ∈ E(Gˆ ), for n > 1      ∅2 if w = ∅1 ,

where ∅1 and ∅2 are the empty word in G1 and G2 , respectively. We can easily check that ϕ is a groupoid-isomorphism, preserving the admissibility on G1 to that on G2 .

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1.4.

Automata and Fractal Groups

Automata Theory is the study of abstract machines, and we are using it in the formulation given by von Neumann. It is related to the theory of formal languages. In fact, automata may be thought of as the class of formal languages they are able to recognize. In von Neumann’s version, an automaton is a finite state machine (FSM). i.e., a machine with input of symbols, transitions through a series of states according to a transition function (often expressed as a table). The transition function tells the automata which state to go to next, given a current state and a current symbol. The input is read sequentially, symbol by symbol, for example as a tape with a word written on it, registered by the head of the automaton; the head moves forward over the tape one symbol at a time. Once the input is depleted, the automaton stops. Depending on the state in which the automaton stops, it is said that the automaton either accepts or rejects the input. The set of all the words accepted by the automaton is called the language of the automaton. For the benefit for the readers, we offer the following references for the relevant part of Automata Theory. Let the quadruple A = < D, Q, ϕ, ψ > be given, where D and Q are sets and ϕ:D×Q→Q

and ψ : D × Q → D

are maps. We say that D and Q are the (finite) alphabet and the state set of A, respectively and we say that ϕ and ψ are the output function and the state transition function, respectively. In this case, the quadruple A is called an automaton. If the map ψ(•, q) is bijective Graphene and Graphite Materials, Nova Science Publishers, Incorporated, 2009. ProQuest Ebook Central,

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on D, for any fixed q ∈ Q, then we say that the automaton A is invertible. Similarly, if the map ϕ(x, •) is bijective on Q, for any fixed x ∈ D, then we say that the automaton A is reversible. If the automaton A is both invertible and reversible, then A is said to be bi-reversible. To help visualize the use of automata, a few concrete examples may help. With some oversimplification, they may be drawn from the analysis and synthesis of input / output models in Engineering, often referred to as black box diagram: excitation variables, response variables, and intermediate variables. In our presentation above, the D (the chosen finite alphabet) often takes different forms on the side of input Di and output Do . In popular automata that models stimuli of organisms, the three sets input Di , output Do , and the state set Q, could be as in the following prototypical three examples: Example 1.1. Models stimuli of organisms: Di = {positive stimulus, negative stimulus}, Do = {reaction, no reaction}, and   reaction to last positive stimulus, Q= . no reaction to last positive stimulus

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Example 1.2. In a control model for say a steering mechanism in a vehicle: Di = {right, left}, Do = {switch on, switch off} or {lamp on, lamp off} and   right-turning direction signal Q= . left-turning direction signal Example 1.3. In a model for quantization in Signal Processing:  assignments from a bit alphabet,    with the bits referring to the value D = Di = Do = of pulses-in and pulses-out in a    signal processing algorithm for example, on a discrete multiresolution (e.g., [50]), and

   

,

  

a subset of the Cartesian product of Q = copies of D, fixing finite number of times, i.e., D × ... × D Recently, various algebraists have studied automata and the corresponding automata groups (Also, see [1], [20], [33] and [35]). We will consider a certain special case, where Q is a free semigroupoid of a shadowed graph. Roughly speaking, a undirected tree is a connected simplicial graph without loop finite paths. Recall that a (undirected) graph is simplicial, if the graph has neither loop-edges nor multi-edges. A directed tree is a connected simplicial graph without loop finite paths,

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with directed edges (See Section 5.1, more in detail). In particular, we say that a directed tree Tn is a n-regular tree, if Tn is rooted and one-flowed infinite directed tree, having the same out-degrees n, for all vertices (Also, see Section 5.1, for details). For example, the 2-regular tree T2 can be depicted by ր ··· • → ··· ր • → • → ··· ր ց ··· T2

=

• ց

ր ··· • → • → ··· ց • → ··· ց ···

Let A = < D, Q, ϕ, ψ > be an automaton with |D| = n. Then, we can construct automata actions of A on Tn . Let’s fix q ∈ Q. Then the action of Aq is defined on the finite words D∗ of D by def

Aq (x) = ϕ(x, q), for all x ∈ D, and recursively,

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Aq ((x1 , x2 , ..., xm )) = ϕ (x1 , Aq (x2 , ..., xm )) , for all (x1 , ..., xm ) ∈ D∗ , where   xk ∈ D, for all def ∞ m D∗ = ∪m=1 (x1 , ..., xm ) ∈ D . k = 1, ..., n

Then the automata actions Aq ’s are acting on the n-regular tree Tn . In other words, all images of automata actions are regarded as an elements in the free semigroupoid F+ (Tn ) of the n-regular tree. i.e., V (Tn ) ⊇ D∗ and its edge set E(Tn ) ⊇ {Aq (x) : x ∈ D, q ∈ Q}. This makes us to illustrate how the automata actions work. Let C = {Aq : q ∈ Q} be the collection of automata actions of the given automaton A = < D, Q, ϕ, ψ >. Then we can create a group G(A) generated by the collection C. This group G(A) is called the automata group generated by A. The generator set C of G(A) acts

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fully on the |D|-regular tree T|D| , we say that this group G(A) is a fractal group. There are many ways to define fractal groups, but we define them in the sense of automata groups. Now, we will define a fractal group more precisely. Let A be an automaton and let Γ = G(A) be the automata group generated by the automata actions acting on the n-regular tree Tn , where n is the cardinality of the alphabet of A. By StΓ (k), denote the subgroup of Γ = G(A), consisting of those elements of Γ, acting trivially on the k-th level of Tn , for all k ∈ N ∪ {0}. ր ··· • → ··· ր • → • → ··· ր ց ··· T2 =

• ց

levels:

0

ր ··· • → • → ··· ց • → ··· ց ··· 1 2 ···

Analogously, for a vertex u in Tn , define StΓ (u) by the subgroup of Γ, consisting of those elements of Γ, acting trivially on u. Then StΓ (k) =

∩

u : vertices of the k-th level of Tn

(StΓ (u)) .

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For any vertex u of Tn , we can define the algebraic projection pu : StΓ (u) → Γ. Definition 1.1. Let Γ = G(A) be the automata group given as above. We say that this group Γ is a fractal group if, for any vertex u of Tn , the image of the projection pu (StΓ (u)) is group-isomorphic to Γ, after the identification of the tree Tn with its subtree Tu with the root u. For instance, if u is a vertex of the 2-regular tree T2 , then we can construct a subtree Tu , as follows: ր ··· • → ··· ր • → • → ···

ր ··· • → ···

u

ր

ց ···

T2 = •

7−→ Tu = ց

ր ··· • → • → ··· ց • → ··· ց ···

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ր . • → • → ··· u

ց ···

Automata Von Neumann Algebras

257

As we can check, the graphs T2 and Tu are graph-isomorphic. So, the above definition shows that if the automata actions Aq ’s of A are acting fully on Tn , then the automata group G(A) is a fractal group. There are lots of famous fractal groups, but we introduce the following example, for our purpose. Example 1.4. Let A = < X2n , Fn , ϕ, ψ > be an automaton, where Fn is the free group with its generator set X2n = {g1±1 , ..., gn±1 }. Then the automata group G(A) is groupisomorphic to Fn . It is easy to check that all elements in Fn acts fully on the 2n-regular tree T2n , and hence G(A) is a fractal group. For example, if n = 2, then we can get the following 0-th and 1-st levels of T4 : g1 eF2

ր → → ց

g1−1 g2 g2−1 ,

where eF2 is the group-identity of F2 = < g1 , g2 > . We used the above construction to define fractaloids, the graph groupoids containing the fractal property, in [17].

1.5.

Sketch of Main Results

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In [10], [11] and [12], we considered a crossed product von Neumann algebra M ×α G of an arbitrarily chosen von Neumann algebra M and a graph groupoid G of a countable directed graph G via a groupoid action α : G → B (K ⊗ HG ), defined by αw (m)Lw L∗w = L∗w m Lw , for all m ∈ M and w ∈ G, where K is a Hilbert space where the von Neumann algebra M acts and HG is the graph Hilbert space with its Hilbert basis {ξ w : w ∈ F Pr (Gˆ )} (See Chapter 2, below). Such crossed product algebras are said to be graph von Neumann algebras induced by G over M . We showed that the study of graph von Neumann algebras is to study groupoid crossed product algebras with amalgamated reduced free probabilistic tools, where the reduction is totally depending on the admissibility of graph groupoids, in [10]. Moreover, the characterization of amalgamated free blocks of graph von Neumann algebras are given in [11]. i.e., the study of graph von Neumann algebras reduces to the study of graph groupoids and the characterized von Neumann algebras. Let A be an automaton. If we can construct a suitable directed graph G, containing the full information of A, then the von Neumann algebra vN (A) generated by the automaton w A would be characterized by the graph von Neumann algebra C[G] in B(HG ), where G is the graph groupoid of the graph G, and HG is the corresponding graph Hilbert space. In other words, if we construct the graph G preserving the combinatorial properties of the w automaton A, then the graph von Neumann algebra C[G] will represent the von Neumann algebra generated by A.

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The main result of this paper is the construction of directed graphs induced by automata. Then we can create corresponding graph von Neumann algebras, as the von Neumann algebras generated by automata. This means that the properties of the von Neumann algebras generated by automata are characterized by those of graph von Neumann algebras in [10] and [11]. As application, we introduce the labeling operators of automata, as operators in graph von Neumann algebras. Then the properties of them is completely characterized by those in [17] and [18].

2.

Graph Von Neumann Algebras

In this chapter, we will review some results of [10] and [11], because they provide the main tools of this paper. Let G be a directed graph with its graph groupoid G. Then we can define a Hilbert space HG having its Hilbert basis {ξ w : w ∈ F Pr (Gˆ )}, where F Pr (Gˆ ) is the reduced finite path set of G. This Hilbert space HG is said to be the graph Hilbert space of G. Notice that those basis elements satisfy the following multiplication rule:

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ξ w1 ξ w2 =

   ξ w1 w2

  ξ def ∅ = 0

if w1 w2 6= ∅ otherwise,

for all w1 , w2 ∈ F Pr (Gˆ ). If w1 w2 ∈ V (Gˆ ), then ξ w1 w2 is well-determined element in HG . So, for any w ∈ G, we can decide the Hilbert space element ξ w , including 0-element 0HG = ξ ∅ . Indeed, if w ∈ F Pr (Gˆ ), then ξ w ξ w−1 = ξ ww−1 , where w w−1 is a vertex in G, by the reduction (RR). Therefore, any w ∈ G induces the unique corresponding Hilbert space element ξ w ∈ HG . The above multiplication rule on HG let us define multiplication operators {Lw : w ∈ G}. i.e., each operator Lw is a multiplication operator with its symbol ξ w on HG , for all w ∈ G. It is easy to check that Lw1 Lw2 = Lw1 w2 , for all w1 , w2 ∈ G, and L∗w = Lw−1 , for all w ∈ G. Thus we can conclude that: if w is a reduced finite path, then the operator Lw is a partial isometry, since it satisfies that Lw L∗w Lw = Lw Lw−1 Lw = Lww−1 w = Lw , and if v is a vertex, then the operator Lv is a projection, since L∗v = Lv−1 = Lv = Lv2 = L2v .

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Fix a von Neumann algebra M in an operator algebra B(K), consisting of all bounded linear operators on a Hilbert space K. We define a groupoid crossed product algebra MG = M ×α G of M and G, via the graph-representation α : G → B(K ⊗ HG ), where B(K ⊗ HG ) is the operator algebra consisting of all bounded operators on the Hilbert space K ⊗ HG . The graph-representation α of G is a groupoid action of G, determining the bounded operators αw on K ⊗ HG satisfying that αw (m) Lw L∗w = L∗w m Lw , for all w ∈ F Pr (Gˆ ), and αv (m) = m, for all v ∈ V (Gˆ ), for all m ∈ M. Remark that Lw and L∗w are regarded as 1 ⊗ Lw and 1 ⊗ L∗w in MG , for w ∈ G. Definition 2.1. The above crossed product algebra MG is said to be a graph von Neumann algebra induced by G over M . Every element x in a graph von Neumann algebra MG has its expression, x=

P

mw Lw , for mw ∈ M.

w∈G

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Let MG = M ×α G be a graph von Neumann algebra. Then it has its natural W ∗ subalgebra DG defined by ⊕ (M · Lv ). This W ∗ -subalgebra DG is called the M v∈V (Gˆ )

diagonal subalgebra of MG . Define the canonical conditional expectation E : MG → DG by E



P

w∈G

mw Lw



=

P

mv Lv .

v∈V (Gˆ )

The pair (MG , E) is a well-defined DG -valued W ∗ -probability space. Definition 2.2. We will call the pair (MG , E), the M -diagonal graph W ∗ -probability space over its M -diagonal subalgebra DG . By the DG -freeness on MG , we could show that: Lemma 2.1. (See [10] and [11]) Let w1 , w2 ∈ F Pr (Gˆ ). The elements w1 and w2 are diagram-distinct, in the sense that (i) w1 6= w2−1 and (ii) the diagrams of them on G are distinct, if and only if the subsets M · Lw1 and M · Lw2 are free over DG in (MG , E), def

where M · Lw = {m Lw : m ∈ M }, for w ∈ G.  and hence we have that; Graphene and Graphite Materials, Nova Science Publishers, Incorporated, 2009. ProQuest Ebook Central,

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Theorem 2.2. (See [10] and [11]) A graph von Neumann algebra MG = M ×α G is def

∗-isomorphic to the DG -valued reduced free product algebra ∗rDG Me , where Me = e∈E(G)

vN (M ×α Ge , DG ) are the DG -free blocks of MG , for all e ∈ E(G). Here, Ge means the subgroupoid of G, consisting of all reduced words only in {e, e−1 }.  Remark that the DG -free blocks Me ’s of MG are indexed by the edge set E(G) of G, not by the edge set E(Gˆ ) of the shadowed graph Gˆ . In fact, each DG -free block Me is def

exactly identical to Me−1 = vN (M ×α Ge−1 , DG ), since Ge−1 = Ge in G. By the Banach-space expression of amalgamated free product algebras, a graph von Neumann algebra MG = M ×α G can be expressed as a Banach space, DG ⊕



⊕

w∗ ∈E(G)∗

 Mow∗ ,

where Mow∗ = Moe1 ⊗DG ... ⊗DG Moek , with Moej = Mej ⊖ DG , for all w∗ = e1 ... ek ∈ E(G)∗ , where def E(G)∗ =

E(Gˆ )

   e = 6 e2 , e2 6= e3 ∞ ∪ ∪k=2 e1 e2 ...ek−1 ek 1 . ..., ek−1 6= ek

−1 ˆ In [10], we showed that if all edges eˆ1 ∈ {e1 , e−1 1 } and e2 ∈ {e2 , e2 } are not admissible in G, then

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Moe1 ⊗DG Moe2

Banach

= {0DG }.

Thus, we can conclude that: Theorem 2.3. (See [10] and [11]) As a Banach space, a graph von Neumann algebra MG = M ×α G is Banach-space isomorphic to DG ⊕



⊕

w∗ ∈E(G)∗r

 Mow∗ ,

where Mow∗ = Moe1 ⊗DG ... ⊗DG Moen , whenever w∗ = eˆ1 ... eˆn in E(G)∗r , where  e1 ... en ∈ F Pr (Gˆ ),  def ±1  e ... en e1 = E(G)∗r = E(Gˆ ) ∪ ∪∞ 6 e±1 n=2 2 , e2 6= e3 ,  ,  1 ±1 ..., en−1 6= en 

 

under the identification, Me = Me−1 , for all e ∈ E(G). 

The above theorem represents how the reduction on the amalgamated free product “∗rDG ” works on MG . The DG -free blocks of a graph von Neumann algebra MG are characterized by the well-known two types of von Neumann algebras: Classical (group) crossed product algebras and the matricial algebras:

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Theorem 2.4. (See [11]) Let G be a countable directed graph and G, the graph groupoid of G and let MG = M ×α G be a graph von Neumann algebra. (1) If e is a loop edge, then the corresponding DG -free block Me of MG is ∗-isomorphic to vN (M ×λ(e) Z, DG ), where M ×λ(e) Z is a classical crossed product algebra, where (e)

λ(e) is a group action of Z on M, satisfying that λn (m) = αen (m), for all m ∈ M and n ∈ Z. (2) If e is a non-loop edge, then the corresponding DG -free block Me of MG is ∗isomorphic to vN (M2αe (M ), DG ), where M2αe (M ) is a ∗-subalgebra of M2 (M ) = M ⊗C M2 (C), where def

M2α (M ) = M ⊗αe vN

   0 1 Ue = . 0 0



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The above theorem shows that all DG -free blocks Me ’s of a graph von Neumann algebra MG are characterized by either vN (M ×γ (e) Z, DG ) or vN (M2αe (M ), DG ), for all e ∈ E(G). Therefore, to study a graph von Neumann algebra MG = M ×α G, we can concentrate on the combinatorial information of the given graph G and on two types of von Neumann algebras. The following corollary are the direct consequence of the previous theorem. Notice that, if M = C, then all graph von Neumann algebras C ×α G are ∗-isomorphic w to C[G] in B(HG ), for any graph-representations α, by the linearity of α on C. We call w the von Neumann algebra C[G] , “the” graph von Neumann algebra of G. w

Notation From now, we denote a graph von Neumann algebra C[G] (in B(HG )) simply by MG to distinguish from the general case. Also, we denote the C-diagonal subalgebra of MG by DG .  Corollary 2.5. Let G be a countable directed graph and MG , the graph von Neumann algebra of G, and let Me be the DG -free blocks of MG , for all e ∈ E(G). (1) If e is a loop edge, then Me is ∗-isomorphic to vN (L(Z), DG ), where L(Z) is a group von Neumann algebra generated by the group Z. (2) If e is a non-loop edge, then Me is ∗-isomorphic to vN (M2 (C), DG ). 

Example 2.1. Let GN be a one-vertex-N -loop-edge graph with its vertex set V (GN ) = {v} and E(GN ) = {ej = v ej v : j = 1, ..., N }. Then the graph von Neumann algebra MGN = w C[GN ] of GN , where GN is the graph groupoid of GN , is ∗-isomorphic to the free group factor L(FN ), generated by the free group FN with N -generators. Notice that the graph groupoid GN of GN is a group and moreover it is group-isomorphic to the free group FN

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with N -generators. Indeed, the edges e1 , ..., eN are generators of GN as a group. So, there is a natural generator-preserving group-isomorphism between GN and FN . Also, notice that the vertex v in GN is the group identity. Example 2.2. Let CN be the one-flow circulant graph with V (CN ) = {v1 , ..., vN } and def

E(CN ) = {ej = vj ej vj+1 : j = 1, ..., N, vN +1 = v1 }. Then the graph von Neumann algebra MCN contains W ∗ -subalgebras which are ∗-isomorphic to the group von Neumann algebra L(Z). Since a finite path w = e1 ... eN induces the subset Sw consisting of all w reduced words in Sw = {w, w−1 } in GCN , we have the W ∗ -subalgebra N = C[Sw ] in MCN . We can regard this W ∗ -subalgebra N as a graph von Neumann algebra induced by the graph Gw with its vertex set V (Gw ) = {v1 } and its edge set E(Gw ) = {w = v1 w v1 }. Then it is an one-vertex-one-loop-edge graph. So, by the previous example, the von Neumann algebra N is ∗-isomorphic to L(F1 ), where F1 is the free group with 1-generator, which is group-isomorphic to Z. So, N is ∗-isomorphic to L(Z) which is also ∗-isomorphic to L∞ (T), where T is the unit circle in C. Consider wk , for all k ∈ Z \ {0}. Then W ∗ w subalgebras Nk = C[Gwk ] of MCN are all ∗-isomorphic to L(Z). The set E(C3 )∗r of C3 is identical to F P (C3 ) ∪ F P (C3−1 ). Indeed, E(C3 )∗r = {∅} ∪ {v1 , v2 , v3 }

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∪ {e1 , e1 e2 , e1 e2 e3 , e1 e2 e3 e1 , ...} −1 −1 −1 −1 −1 −1 −1 −1 −1 ∪ {e−1 1 , e2 e1 , e3 e2 e1 , e1 e3 e2 e1 , ...} ∪ {e2 , e2 e3 , e2 e3 e1 , e2 e3 e1 e2 , ...} −1 −1 −1 −1 −1 −1 −1 −1 ∪ {e−1 2 , e3 e2 , e1 e3 e2 , e2 e1 e3 e2 , ...} ∪ {e3 , e3 e1 , e3 e1 e2 , e3 e1 e2 e3 , ...} −1 −1 −1 −1 −1 −1 −1 −1 −1 ∪ {e−1 3 , e1 e3 , e2 e1 e3 , e3 e2 e1 e3 , ...} = F P (C3 ) ∪ F P (C3−1 ). −1 In fact, more generally, we can conclude that E(CN )∗r = F P (CN ) ∪ F P (CN ), for all N ∈ N. Therefore, N

MCN = ∗DCN Mek k=1

for all k = 1, ..., N = DC N ⊕

= DC N ⊕



⊕

w∗ ∈E(CN )∗r

Mwo ∗

⊕



−1 w∈F P (CN )∪F P (CN )

Mwo

!

,

def

where Mwo = Meo(1) ⊗DCN ... ⊗DCN Meo(n) , whenever w = e(1) ... e(n) in E(CN )∗r , for n ∈ N. Graphene and Graphite Materials, Nova Science Publishers, Incorporated, 2009. ProQuest Ebook Central,

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We showed that, if G1 and G2 are graph-isomorphic, then the corresponding graph groupoids G1 and G2 are also groupoid-isomorphic in the sense of Section 1.3. However, the converse does not hold, in general (See [11]). We also showed that, more generally, if two directed graphs have the graph-isomorphic shadowed graphs, then the corresponding graph groupoids are groupoid-isomorphic. Based on this observation, we could get the following isomorphism theorem for graph von Neumann algebras. Theorem 2.6. (See [11]) Let G1 and G2 be directed graphs with their graph groupoids G1 and G2 , respectively. If the graphs G1 and G2 have the graph-isomorphic shadowed graphs Gˆ1 and Gˆ2 , where Gˆk are the shadowed graphs of Gk , for k = 1, 2, then the graph von Neumann algebras MG1 = M ×α1 G1 and MG2 = M ×α1 G2 are ∗-isomorphic, whenever (α1 )w1 (m) = (α2 )Φ(w1 ) (m), for all m ∈ M, w1 ∈ G1 , where Φ : G1 → G2 is the groupoid-isomorphism induced by the graph-isomorphism g : Gˆ1 → Gˆ2 .  The proof of the above theorem is based on the amalgamated free probabilistic structures of MG1 and MG2 . The following corollary is the direct consequence of the previous theorem. Corollary 2.7. (Also see [11]) Let G1 and G2 be directed graphs with their graph groupoids G1 and G2 . If G1 and G2 have the graph-isomorphic shadowed graphs Gˆ1 w and Gˆ2 , respectively, then the graph von Neumann algebras MG1 = C[G1 ] and MG2 w = C[G2 ] are ∗-isomorphic. 

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3.

Automata Graphs and Automata Groupoids Let A be a given automaton. We say that A is invertible, if ψ(q, •) : D → D is bijective,

for all q ∈ Q. Also, we say that A is reversible, if ϕ(•, x) : Q → Q is bijective, for all x ∈ D. If A is both invertible and reversible, we will say that the automaton A is bi-reversible. If the given automaton A is bi-reversible, then it is easy to construct the corresponding automata group Γ(A) induced by A. However, we are interested in the general case. So, it seems much natural to think about the groupoid G(A) induced by A. Similar to Chapter 2, if we have a suitable graph G, representing the properties of the automaton A, then we can identify the groupoid G(A) with the graph groupoid G of G. The main purpose of this chapter is to construct such graph G from A. Let A = (Q, D, ϕ, ψ) be an arbitrary automaton. For the fixed finite set Q, we can determine the set Q∗ , consisting of all finite words in Q. i.e., Q∗ = ∪∞ n=1 Qn ,

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with def

Qn = {q1 ... qn : qj ∈ Q, ∀ j = 1, ..., n}, for all n ∈ N. Suppose a word w is contained in Qn ⊂ Q∗ . Then we can define the length |w| of w by n. Similarly, we can construct the set D∗ , consisting of all finite words in D, as ∗ the disjoint union ∪∞ n=1 Dn , similarly, where Dn is the subset of D , consisting of all finite words with their length n, in D, for all n ∈ N. Then, inductively, we can extend the maps ϕ(•, x) and ψ(q, •) on Q∗ and D∗ , respectively, for x ∈ D and q ∈ Q, as follows: ϕ(q1 ... qn , x) = ϕ (q1 ...qk , ψ(qk+1 ... qn , x)) and ψ(q, x1 ... xn ) = ψ (ϕ(q, x1 ... xk ), xk+1 ... xn ) , for all k ≤ n ∈ N, where q1 ... qn ∈ Q∗ and x1 ... xn ∈ D∗ . For instance, ϕ(q1 q2 , x) = ϕ (q1 , ψ(q2 , x)) and ψ(q, x1 x2 ) = ψ (ϕ(q, x1 ), x2 ) .

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More generally, we can have that ϕ (q1 ...qn , x1 ...xm ) = ϕ (q1 ... qk , ψ(qk+1 ... qn , x1 ... xm )) , ϕ (q1 ...qn , x1 ... xm ) = ϕ (ϕ(q1 ...qn , x1 ... xk ), xk+1 ... xm ) , and ψ (q1 ...qn , x1 ...xm ) = ψ (ϕ(q1 ...qn , x1 ...xj ), xj+1 ... xm ) , ψ (q1 ... qn , x1 ... xm ) = ψ (q1 ... qj , ψ(qj+1 ... qn , x1 ... xm )) , for all q1 ... qn ∈ Q∗ and x1 ... xm ∈ D∗ , for k ≤ n, j ≤ m ∈ N. Under this extended ϕ : Q∗ × D∗ → Q∗ and ψ : Q∗ × D∗ → D∗ , we can define the actions {Aq : q ∈ Q} of A acting on the set D∗ , as follows: def

Aq (w) = ψ (q, w) , for all w ∈ D∗ , for any fixed q ∈ Q. i.e., if w = x1 ... xn ∈ Dn ⊂ D∗ , then the image of the action Aq of w is determined by

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Aq (w) = ψ (q, w) = ψ (q, x1 ... xn ) = ψ (ϕ(q, x1 ... xk ), xk+1 ... xn ) for any k ≤ n. Again, by the extended definition of ϕ and ψ, we can check that indeed {Aq }q∈Q are actions on D∗ : (Aq1 Aq2 ) (w) = Aq1 (Aq2 (w)) = Aq1 (ψ(q2 , w)) = ψ (q1 , ψ(q2 , w)) = ψ (q1 q2 , w) , for all q1 , q2 ∈ Q and w ∈ D∗ , and hence Aq1 Aq2 = Aq1 q2 , for all q1 , q2 ∈ Q. Notice that q1 q2 ∈ Q∗ , and hence the actions {Aq }q∈Q of A generate the collection of all actions {Ay : y ∈ Q∗ } of A, acting on D∗ .

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Definition 3.1. Let A = (Q, D, ϕ, ψ) be an automaton. Then actions AQ∗ = {Ay : y ∈ Q∗ } of A, acting on D∗ are called the automata actions of A (acting on D∗ ). For convenience, we will call the subset AQ = {Aq : q ∈ Q} of AQ∗ , the generating automata actions (of AQ∗ ). Recently, many algebraists have studied about the automata group Γ(A), generated by the generating automata actions AQ = {Aq : q ∈ Q} of the given automaton A. The applications of automata groups are very interesting in many math fields. In particular, it is used to study fractal structures (e.g., see [1] and [17]). In particular, in [17], Cho and Jorgensen used grouopoids induced by automata to observe the fractal property of graph groupoids, so-called the fractaloids. This shows that the fractal property of a groupoid can be explained by the spectral data of the corresponding Hilbert space operator, called the labeling operator. Let A = (Q, D, ϕ, ψ) be an automaton. Then we can construct the graph G with V (G) = D and E(G) = {(x, ψ(q, x)) : q ∈ Q and x ∈ D}. Here, the pair (x, ψ(q, x)) means the edge connecting from the vertex x to the vertex ψ(q, x). Then the edge set E(G) and the set {ϕ(q, x) : q ∈ Q, x ∈ D} are equipotent (or bijective). So, without loss of generality, we can re-define the edge set E(G) of G by E(G) = {ϕ(q, x) : q ∈ Q, x ∈ X}. Graphene and Graphite Materials, Nova Science Publishers, Incorporated, 2009. ProQuest Ebook Central,

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i.e., the Q-value ϕ(q, x) is understood as the q-th edge connecting from the vertex x to the vertex ψ(q, x). Notice here that, even though ϕ(q1 , x1 ) = q = ϕ(q2 , x2 ) in Q, for some q ∈ Q, we will regard ϕ(q1 , x1 ) and ϕ(q2 , x2 ) as “distinct” edges connecting from xk to ψ(qk , xk ), for k = 1, 2. i.e., ϕ(qk , xk ) are the q-th edge connecting from xk to ψ(qk , xk ). i.e., the set Q is understood as the labeling set in the sense of [17], and the set E(G) is the set consisting of all edges labeled by Q. We may understand the labeling as a certain weighting on edges, but slightly different. Definition 3.2. Let A = (Q, D, ϕ, ψ) be an automaton, and let G be a directed graph with V (G) = D and E(G) = {ϕ(q, x) : q ∈ Q, x ∈ D}, by identifying ϕ(q, x) ∈ Q, as the q-th edge (x, ψ(q, x)) connecting from x to ψ(q, x). Then this graph G is called the automata graph induced by A (for short, the A-graph). Example 3.1. Let Q = {q1 , q2 } and D = {x1 , x2 }, and assume that ϕ(q1 , x1 ) = q1 , ϕ(q2 , x1 ) = q1 ,

ϕ(q1 , x2 ) = q2 , ϕ(q2 , x2 ) = q1 ,

ψ(q1 , x1 ) = x2 , ψ(q2 , x1 ) = x1 ,

ψ(q1 , x2 ) = x2 . ψ(q2 , x2 ) = x1 .

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and

Then we can create the finite directed graph G such that G

=

• ⇄ • . 

Assume now that ϕ(q1 , x) = q2 in Q, and suppose ϕ(q1 , x) as an edge of the A-graph GA . Then, by definition, the Q-value q2 = ϕ(q1 , x) is the edge connecting the vertex x to the vertex ψ(q1 , x). Futhermore, we can verify that if q1 ∈ ϕ(Q × D), then the identity q2 = ϕ(q1 , x1 ) also means that the edge q1 and q2 are admissible, via the vertex x. In other words, q2 = x q2 (ψ(q1 , x)) and q1 = q1 x, by using the language of Section 1.2. i.e., the edges q1 and q2 are admissible. Let G be the A-graph, where A = (Q, D, ϕ, ψ) is a given automaton, with V (G) = D, and E(G) = {ϕ(q, x) : q ∈ Q, x ∈ D}. Then, as a new directed graph, it has its shadow G−1 , and the corresponding shadowed graph Gˆ = G ∪ G−1 . With respect to the shadow G−1 of the A-graph G, we can define the shadow automaton A−1 of A, having its A−1 -graph G−1 . Indeed, we can define a new automaton A−1 = < Q− , D, ϕ− , ψ − >, for the given automaton A, equipped with the functions ϕ− and ψ − , where

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def

Q− = {q −1 : q ∈ Q}, and ϕ− : Q− × D → Q− and ψ − : Q− × D → D defined by
ϕ− q1−1 , x2 = q2−1 ,

and

ψ − (q1−1 , x2 ) = x1 , whenever ϕ(q1 , x1 ) = q2 ∈ Q, and ψ(q1 , x1 ) = x2 ∈ D, for all q1 , q2 ∈ Q and x1 , x2 ∈ D. By using the graph-theoretical language, the image ϕ− (q −1 , ψ(q, x)) ∈ Q− means the directed edge connecting the vertex ψ(q, x) ∈ D to the vertex x ∈ D, equivalently, it is the shadow ϕ(q, x)−1 of the edge ϕ(q, x) ∈ Q. i.e., the shadow ϕ(q, x)−1 of ϕ(q, x) = ϕ− (q −1 , ψ(q, x)). Of course, we can get that

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ψ − q −1 , ψ(q, x) = the terminal vertex of ϕ− q −1 , ψ(q, x) = the terminal vertex of ϕ(q, x)−1 = x Notice that the maps ϕ− is not the inverses ϕ−1 of ϕ, in general. They just represents the groupoidal inverses. If the automaton A is reversible, then ϕ− = ϕ−1 , where ϕ−1 is the (functional) inverse of ϕ. However, in general, we can not guarantee that ϕ− is identical to the inverse ϕ−1 of ϕ. This observation also shows that it is natural to think about the groupoids generated by automata. Definition 3.3. The automaton A−1 = (Q− , D, ϕ− , ψ − ), induced by the given automaton A = (Q, D, ϕ, ψ), defined in the previous paragraph, is called the shadow (automaton) of A. By the very definition, we can get the following lemma. Lemma 3.1. Let A = (Q, D, ϕ, ψ) be an automaton with its A-graph G. Suppose A−1 = (Q− , D, ϕ− , ψ − ) is the shadow of A. Then A−1 -graph K is graph-isomorphic to the shadow G−1 of G.  So, without loss of generality, we can let G−1 be the A−1 -graph, where G is the Agraph. Let G be the A-graph. As in Section 1.2, we can create the shadowed graph Gˆ of G. Then we can construct an automaton Aˆ induced by A having its Aˆ -graph, the shadowed graph Gˆ of G. Define now the automaton Aˆ by < Q± , D, ϕ± , ψ ± >, where

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Ilwoo Cho Q± = Q ⊔ Q− , ϕ± = ϕ ∪ ϕ− and ψ ± = ψ ∪ ψ − ,

where ϕ± (q,

def



ϕ(q, x) ϕ− (q, x)

if q ∈ Q if q ∈ Q− ,

def



ψ(q, x) ψ − (q, x)

if q ∈ Q if q ∈ Q− .

x) =

and ±

ψ (q, x) =

Here, the symbol ⊔ means the disjoint union. Definition 3.4. Let A = (Q, D, ϕ, ψ) be an automaton with its shadow A−1 = (Q− , D, ϕ− , ψ − ). Let Aˆ = (Q± , D, ϕ± , ψ ± ) be the automaton defined as in the previous paragraph. This automaton Aˆ is called the shadowed automaton of A. Again, by the construction, we can get that: Lemma 3.2. Let A be an automaton with its A-graph G, and let Aˆ be the shadowed automaton of the given automaton A. Then the Aˆ -graph K of Aˆ is graph-isomorphic to the shadowed graph Gˆ of G. 

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Without loss of generality, we can regard the Aˆ -graph of the shadowed automaton Aˆ of A is the shadowed graph Gˆ of the A-graph G. Now, we can define the automata groupoids, the groupoids induced by automata. Definition 3.5. Let A be an automaton with its automata graph G. The graph groupoid G of G is called the automata groupoid (or the A-groupoid) of A. In our setting the automata groupoids are nothing but the graph groupoids of automata graphs. But notice that the automata groupoids contains the full information of the given automata and the corresponding automata actions and their groupoidal inverses. Example 3.2. Let A = (Q, D, ϕ, ψ) be an automaton with Q = {a, b} and D = {0, 1} and ϕ(a, 0) = b, ϕ(b, 0) = a, ϕ(a, 1) = b, ϕ(b, 1) = a, and ψ(a, 0) = 1, ψ(a, 1) = 0, ψ(b, 0) = 1, ψ(b, 1) = 0. We can easily check that the automaton is bi-reversible. The shadow A−1 = (Q− , D, ψ − ) of A is determined by

ϕ− ,

ϕ− (a−1 , 1) = b−1 , ϕ− (b−1 , 1) = a−1 , −1 −1 −1 −1 −1 ϕ−1 0 (a , 0) = b , ϕ0 (b , 0) = a Graphene and Graphite Materials, Nova Science Publishers, Incorporated, 2009. ProQuest Ebook Central,

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and ψ − (a−1 , 1) = 0, ψ − (b−1 , 1) = 0, ψ − (a−1 , 0) = 1, ψ − (b−1 , 0) = 1. So, we can have the shadowed automaton A± = (Q± , D, ϕ± , ψ ± ). The A-graph G is graph-isomorphic to the graph G0 , with V (G0 ) = {v1 , v2 } and E(G0 ) = {e1:12 , e2:12 , e1:21 , e2:21 }, where ek:ij means the k-th edge connecting the vertex vi to the vertex vj , for i, j, k ∈ {1, 2}. The graph groupoids G0 is nothing but the automata groupoid G(A) of A. Assume now that we have two automata A1 and A2 . We will consider the equivalence of them.

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Definition 3.6. Let A1 and A2 be automata with automata graphs G1 and G2 . We say that two automata A1 and A2 are automata-isomorphic, if G1 and G2 are graph-isomorphic. Indeed, since the automata graphs Gk contain full information of the automata Ak , via admissibility, for k = 1, 2, the graph-isomorphisms of G1 and G2 preserve the automata properties of A1 to those of A2 , and hence A1 and A2 can be understood as the equivalent automata from each other. Indeed, we may / can define the automata-isomorphisms in pure Automata Theory point of view: the automata A1 = (Q1 , D1 , ϕ1 , ψ 1 ) and A2 = (Q2 , D2 , ϕ2 , ψ 2 ) are automata-isomorphic, if there exist bijections (3.1) gQ : Q1 → Q2 and gD : D1 → D2 such that ϕ2 (gQ (q), gD (x)) = gQ (ϕ1 (q, x)) and ψ 2 (gQ (q), gD (x)) = gD (ψ 1 (q, x)) , for all q ∈ Q1 and x ∈ D1 . Indeed, the bijections gQ and gD preserve the automata properties of A1 to those of A2 . Thus, we can understand the automata A1 and A2 are equivalent mathematical objects. Observation Assume now that the automata A1 = (Q1 , D1 , ϕ1 , ψ 1 ) and A2 = (Q2 , D2 , ϕ2 , ψ 2 ) are automata-isomorphic in the sense of (3.1), guaranteed by the existence of the bijections gQ and gD . Then we can easily verify that the automata graphs Gk of Ak , for k = 1, 2, are graph-isomorphic. We can define the corresponding graph-isomorphism g : G1 → G2 such that

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Ilwoo Cho g |V (G1 ) = gD and g |E(G1 ) = gQ . Then it is a bijection from V (G1 ) ∪ E(G1 ) onto V (G2 ) ∪ E(G2 ), and it satisfies that g(q) = g (x1 q x2 ) = gD (x1 ) gQ (q) gD (x2 ) in E(G2 ),

whenever q = x1 q x2 ∈ E(G1 ), with x1 , x2 ∈ V (G1 ) = D1 . Therefore, the graphs G1 and G2 are graph-isomorphic, and hence the automata A1 and A2 are automata-isomorphic, in the sense of the above definition. Conversely, suppose that the automata graphs Gk induced by the given automata Ak , for k = 1, 2, are graph-isomorphic, via a graph-isomorphism g : G1 → G2 . Then we can construct the bijections gQ : Q1 → Q2 and gD : D1 → D2 satisfying that ϕ2 (gQ (q), gD (x)) = g (ϕ1 (q, x)) and

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ψ 2 (gQ (q), gQ (x)) = g (ψ 1 (q, x)) , in Q2 × D2 , for all (q, x) ∈ Q1 × D1 . This shows that if the automata A1 and A2 are automata-isomorphic in the sense of the above definition, then they are automataisomorphic in the sense of (3.1). Therefore, we can conclude that our automata-graphdepending definition of automata-isomorphisms is a well-defined equivalence on automata, pure automata theoretically.  The above characterization shows that it is safe to define the automata-isomorphisms, in terms of the (automata-)graph-isomorphisms. Since the graph-isomorphisms of the (automata) graphs G1 and G2 guarantees the groupoid-isomorphisms of their graph groupoids G1 and G2 , we can have the following proposition: Theorem 3.3. Let Ak be automata, for k = 1, 2. If A1 and A2 are automata-isomorphic, then the automata groupoids G1 and G2 are groupoid isomorphic, where Gk are the Ak groupoids, for k = 1, 2. More precisely, if two automata A1 and A2 have automataisomorphic shadowed automata Aˆ1 and Aˆ2 , then the automata groupoids G1 and G2 are groupoid-isomorphic. Proof. Since two automata A1 and A2 are automata-isomorphic, if and only if the corresponding automata graphs G1 and G2 are graph-isomorphic, the graph groupoids G1 and G2 , which are the automata groupoids, are groupoid-isomorphic, by Chapter 1. Also, if the given automata Ak have the shadowed automata Aˆk , and if the corresponding Aˆk -graphs Gˆk are graph-isomorphic, then the groupoids G1 and G2 are groupoid-isomorphic, again by Chapter 1. The above theorem classify the isomorphic classes of automata groupoids. Now, recall the automata actions {Awq : wq ∈ (Q± )∗ } of a given automaton A acting on D∗ , where def

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for any wq ∈ Q∗ . Indeed, they satisfy Awq1 Awq2 = Awq1 wq2 , for all wq1 , wq2 ∈ Q± , where Aˆ = (Q± , D, ϕ± , ψ ± ) is the shadowed automaton of A. The groupoid GQ± generated by {Aq : q ∈ Q± } (Recall that {Aq }q∈Q± generates {Awq }wq ∈(Q± )∗ !) is groupoidisomorphic to the automata groupoid G of A. Notice that the existence of the shadow A−1 and the shadowed automaton Aˆ provide the groupoidal inverse actions A−1 wq of Awq . Theorem 3.4. (Also see [17]) Let A be an automaton with its A-groupoid G, and let G = {Aq : q ∈ Q± } be the generating automata actions acting on D∗ , where Aˆ = (Q± , D, ϕ± , ψ ± ) is the shadowed automaton of A. Then the groupoid G(G), generated by G, is groupoid-isomorphic to the A-groupoid G.  The proof is straightforward, by definition.

4.

Von Neumann Algebras Generated by Automata

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Throughout this chapter, let A = (Q, D, ϕ, ψ) be an automaton with its A-graph G. As we observed in the previous chapter, A has its shadow A−1 , and its shadowed automaton Aˆ , having their automata graphs G−1 and Gˆ , respectively, where G−1 and Gˆ are the shadow and the shadowed graph of G, respectively. So, the graph groupoid G of G is the groupoid containing the full information of the given automaton A. Definition 4.1. Let A be an automaton having its A-groupoid G. Define the von Neumann w algebra MA by C[G] , as a W ∗ -subalgebra of the operator algebra B(HG ), where HG is the graph Hilbert space in the sense of Chapter 2. Then this von Neumann algebra MA generated by the groupoid G is said to be the automata von Neumann algebra induced by A. The above definition shows the connections not only between automata and directed graphs but also between automata and von Neumann algebras, via automata graphs and corresponding graph groupoids. This shows that we assign each ψ(q, x) to a projection on HG and assign each ϕ(q, x) to a partial isometry on HG . This connection of automata and (graph) von Neumann algebras provides a new application of the study of graph von Neumann algebras, and a tool how we connect automata to the operator theoretical objects. The nice fact is that the automata von Neumann algebras share their properties with those of graph von Neumann algebras. Remark 4.1. Let A be an automaton with its A-groupoid G. More generally, for any fixed arbitrary von Neumann algebra M, we can create a groupoid crossed product algebra MA = M ×α G, where α is a groupoid action of G, satisfying the conditions in Chapter 2. We can say that such crossed product algebras are the automata von Neumann algebras, but in this paper, we will concentrate on observing the case where M = C. However, we remark that even though we consider the crossed product algebras, all properties of such automata von Neumann algebras are characterized by [10] and [11].

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We observed, in Chapter 3, that if A1 and A2 are automata-isomorphic, then the automata groupoids G1 and G2 are groupoid isomorphic, where Gk are the Ak -groupoids, for k = 1, 2. Therefore, we can get the following isomorphism theorem on automata von Neumann algebras. Theorem 4.1. Let Ak be automata with their automata graphs Gk , and let Gk be the w automata groupoids of Ak , for k = 1, 2. Let MAk = C[Gk ] be the automata von Neumann algebra acting on the graph Hilbert space HGk , for k = 1, 2. If the automata A1 and A2 are automata-isomorphic, then MA1 and MA2 are ∗-isomorphic. Proof. Suppose A1 and A2 are automata-isomorphic. Then, by the above proposition, the Ak -groupoids Gk are groupoid-isomorphic. Therefore, the graph von Neumann algebras w MGk = C[Gk ] are ∗-isomorphic, by Chapter 2 (Also see [11]), for k = 1, 2. By the very definition of automata von Neumann algebras, MGk = MAk , for k = 1, 2. Therefore, the automata von Neumann algebras MA1 and MA2 are ∗-isomorphic. The detailed theory of automata von Neumann algebras are completely characterized by the study of graph von Neumann algebras. w Observation Let MA = C[G] be the automata von Neumann algebra induced by the automaton A. Then it is identified with the graph von Neumann algebra MG , generated by the A-groupoid G, acting on the graph Hilbert space HG , where G is the A-graph. Therefore, all theoretical facts about MG are exactly same as those of MA . For instance, we have that MA

∗-isomorphic

=

∗rDA Mq , q∈Q

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where DA = ⊕ Cx x∈D

∗-isomorphic

=

C⊕ |D| , with Cx = C, ∀ x ∈ D,

and w

Mq = C[Gq ] , for all q ∈ Q, where Gq is the subgroupoid of A-groupoid G, consisting of all reduced words in {q, q −1 } ⊂ Q± , for all q ∈ Q, etc (See Chapter 2, [10], [11], [12], and [17]). 

5.

Labeling Operators of Automata

In this chapter, we introduce the labeling operators induced by automata in a automata von Neumann algebras. Let A = (Q, D, ϕ, ψ) be an automaton and let G be the A-graph w with its corresponding graph groupoid G, called the A-groupoid. Also, let MA = C[G] be the automata von Neumann algebra, as a W ∗ -subalgebra of B(HG ), where HG is the graph Hilbert space in the sense of Chapter 2. As we observed in Chapter 4, this automata von Neumann algebra MA shares its properties with the graph von Neumann algebra MG ,

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since G is the graph groupoid induced by the A-graph G. Thus, as in [17] and [18], we can define the labeling operator TA of A. Recall that, in [17], Cho and Jorgensen defined and observed the labeling operator TG of the graph groupoid G, induced by a locally finite connected directed graph G. In particular, we showed that such labeling operators are used to study a certain fractal property of groupoids. Also, in [18], they could find the amalgamated free distributional data of general labeling operators of (graph) groupoids, and hence it represents the spectral property of graph groupoids. In this chapter, we will follow the same settings introduced in [17] and [18], and we define the labeling operator TA of the given automaton A, as the labeling operator of the A-groupoid G on HG . Notice that, in [17] and [18], we constructed the graph automata with respect to the given directed graphs. Our approach here is opposite. For convenience, we put Q = {q1 , ..., qN } and D = {x1 , ..., xn }, for the fixed numbers N, n ∈ N, and let Q− = {q−1 , ..., q−N }.

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For a fixed qj ∈ Q± (i.e., j ∈ {±1, ..., ±N }), we define the operator Tj on HG by (5.1)

Tj ξ w =

    ξ ej ξ w = ξ ej w   

0HG

if ∃ej ∈ E(Gˆ ) s.t., ϕ(qj , ej w) 6= ∅ otherwise,

for all j = ±1, ..., ±N, for all w ∈ G. Recall that [ϕ(wq , wd ) = ∅] means that ϕ(wq , wd ) is identical to the empty element ∅ of G. Definition 5.1. The operators Tj ’s on HG defined in (5.1) are called the j-th labeling operators on HG . And the operator (5.2) def

TA =

P

−1 k=−N

 P  N T Tk + i i=1

is called the labeling operator of the given automaton A on HG . As we have seen in [17] and [18], the labeling operator TA of the automaton A contains the full admissibility information of the A-groupoid G, and hence the properties of TA can be used to the analysis of the spectral properties of the operator TA , governed by the algebraic properties of G (and hence governed by A).

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Remark 5.1. In [17] and [18], we defined the j-th labeling operators and the labeling operator of the given automaton A by  if ∃ej ∈ E(Gˆ ) s.t.,    ξ wej ϕ(qj , w ej ) 6= ∅ Tj ξ w =    0HG otherwise,

for all j ∈ {±1, ..., ±N }, and w ∈ G, because, in [17] and [18], we dealt with “right” graph von Neumann algebras determined by the “right” multiplication operators, instead of using the graph von Neumann algebras in our sense, determined by the “left” multiplication operators. However, right graph von Neumann algebras and (left or usual) graph von Neumann algebras have the same free probabilistic properties. In fact, our left groupoid actions α in Chapter 2 (and [10], [11], [12], [15]) and right groupoid actions β in [17] and [18] satisfy that w ∗-isomorphic

C[α(G)]

=

w ∗-isomorphic

C[G]

=

w

C[β(G)] ,

as W ∗ -subalgebras of B(HG ). Futhermore, notice that   w w op , C[β(G)] = C[α(G)]

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and hence they are anti-∗-isomorphic, where M op means the opposite (topological ∗)algebra of a topological ∗-algebra M. This means that the j-th labeling operators in (5.1) and the labeling operator of A in (5.2) have the same (or equivalent) spectral properties with those of [17] and [18]. Thus, in the following, we usually omit the proofs. We refer readers to read [18], for more about labeling operators. Notice that we can regard the operators Tj ’s and TA , as elements in the automata von Neumann algebra MA . Indeed, we can construct the elements def

P

τj =

Lqj , for j ∈ {±1, ..., ±N }

x∈D, ϕ(q, x)=qj ∈E(Gˆ ), for q∈Q

and def

τ =

P

−1 k=−N

 P  N τ . τk + i i=1

Then, they are well-defined elements in MA , and it is easy to check that τ j ’s are equivalent to Tj ’s and τ is equivalent to TA on the graph Hilbert space HG , where G is the A-graph. Therefore, with out loss of generality, we can understand the j-th labeling operators Tj ’s and the labeling operator TA of A as elements of the automata von Neumann algebra MA : Lemma 5.1. Let Tj ’s be the j-th labeling operators and TA , the labeling operator of the given automaton A on HG . Then they are elements of the automata von Neumann algebra MA . 

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By the previous remark and lemma (and by [17] and [18]), we can characterize the properties of the j-th labeling operators Tj ’s and the labeling operator TA of the given automaton in terms of those of the A-groupoid G. First, we can have the adjoint properties of Tj ’s and TA as follows: Proposition 5.2. (See [17] and [18]) (1) Let Tk be the k-th labeling operator on HG , for k = ±1, ..., ±N. Then its adjoint Tk∗ is identified with the (−k)-th labeling operator T−k , for k ∈ {±1, ..., ±N }. (2) By (1), the labeling operator TA is self-adjoint.  Now, we will consider the DA -freeness of {Tk , T−k }’s in the graph W ∗ -probability space (MA , E), for all k = 1, ..., N. Proposition 5.3. (See [17] and [18]) Let {Tk : k = ±1, ..., ±N } be the k-th labeling operators on HG . Then the families {Tk , T−k }’s are free over DA from each other in (MA , def

E), for k = 1, ..., N, where DA = ⊕nk=1 (C · Ldj ) is the C-diagonal subalgebra of MA .  Clearly, the above DA -freeness is determined by the canonical conditional expectation E : MA → DA , in the sense of Chapter 2. By the previous observation, we can observe the DA -valued joint ∗-moments of T±1 , ..., T±N , as in [18]. So, we can conclude that: Theorem 5.4. Let Tk ’s be the k-th labeling operators on HG , for all k = ±1, ..., ±N. Then the DA -valued joint ∗-moments of them is determined by

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(5.3)

E (Ti1 ... Tin ) =

    

P

x∈D, qi1 ...qin ∈Q∗ , i1 +...+in =0

Lψ(x, qi1 ...qin ) if n is even

0DA

if n is odd,

in DA , for all (i1 , ..., in ) ∈ {±1, ..., ±N }, for n ∈ N.  The formula (5.3) provides the DA -valued free distributional data of {Tk : k = ±1, ..., ±N } in MA , in terms of their DA -valued joint ∗-moments. Fix n ∈ N and consider TAn : TAn = (T−N + ... + T−1 + T1 + ... + TN )n P

=

(i1 , ..., in )∈{±1, ..., ±N }n

Ti1 ...Tin .

Thus, we can compute that E (TGn ) =

P

(i1 , ..., in )∈{±1, ... ±N }n

E (Ti1 ... Tin ) .

Therefore, by (5.3), we can get that: Graphene and Graphite Materials, Nova Science Publishers, Incorporated, 2009. ProQuest Ebook Central,

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Ilwoo Cho

Theorem 5.5. Let TG be the labeling operator of G on the graph Hilbert space HG . Then E(TAn ) = 0DA , whenever n is odd, and E(TG2n ) =

(5.4)

W2n for all n ∈ N. 

P

Lw , for all n ∈ N, where W2n is defined by

w∈W2n

  qi1 ...qi2n ∈ F P (Gˆ ) ˆ n P = qi1 ...qi2n ∈ E(G ) , 2n k=1 ik = 0

def

This show that the spectral properties of the labeling operator TA is determined by as above, in terms of DA -valued moments. Recall that if an operator a of a B-valued W ∗ probability space (A, EB ), where EB : A → B is a conditional expectation, is self-adjoint, then the B-valued free distribution σ a of a and the operator-valued spectral measure χa of a are equivalent (See [5] and [24]). Therefore, the formula (5.4) contains the spectral measure theoretical data of the labeling operator TA .

References [1] A. G. Myasnikov and V. Shapilrain (editors), Group Theory, Statistics and Cryptography, Contemporary Math, 360, (2003) AMS. [2] A. Gibbons and L. Novak, Hybrid Graph Theory and Network Analysis, ISBN: 0521-46117-0, (1999) Cambridge Univ. Press.

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[3] B. Solel, You can see the arrows in a Quiver Operator Algebras, (2000), preprint. [4] C. W. Marshall, Applied Graph Theory, ISBN: 0-471-57300-0 (1971) John Wiley & Sons [5] D.Voiculescu, K. Dykemma and A. Nica, Free Random Variables, CRM Monograph Series Vol 1 (1992). [6] D.W. Kribs and M.T. Jury, Ideal Structure in Free Semigroupoid Algebras from Directed Graphs, preprint. [7] D.W. Kribs, Quantum Causal Histories and the Directed Graph Operator Framework, arXiv:math.OA/0501087v1 (2005), Preprint. [8] F. Balacheff, Volume Entropy, Systole and Stable Norm on Graphs, arXiv:math.MG/0411578v1, (2004) Preprint. [9] G. C. Bell, Growth of the Asymptotic Dimension Function for Groups, (2005) Preprint. [10] I. Cho, Graph von Neumann Algebras, ACTA Appl. Math., 95, (2007) 95 - 134. [11] I. Cho, Characterization of Amalgamated Free Blcoks of a Graph von Neumann Algebra, CAOT, 1, (2007) 367 - 398. Graphene and Graphite Materials, Nova Science Publishers, Incorporated, 2009. ProQuest Ebook Central,

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[12] I. Cho, Vertex-Compressed Algebras of a Graph von Neumann Algebra, (2007) Submitted to ACTA Appl. Math. [13] I. Cho, Measures on Graphs and Groupoid Measures, CAOT, 2, (2008) 1 - 28. [14] I. Cho, Direct Producted W ∗ -Probability Spaces and Corresponding Free Stochastic Integration, B. of KMS, (2007), To be Appeared. [15] I. Cho, and P. E. T. Jorgensen, C ∗ -Algebras Generated by Partial Isometries, JAMC, (2007) To Appear. [16] I. Cho, and P. E. T. Jorgensen, C ∗ -Subalgebras Generated by Partial Isometries in B(H) , (2007) Submitted to JMP. [17] I. Cho, and P. E. T. Jorgensen, Application of Automata and Graphs: LabelingOperators in Hilbert Space I, (2008) Submitted to ACTA Appl. Math: Special Issues. [18] I. Cho, and P. E. T. Jorgensen, Application of Automata and Graphs: LabelingOperators in Hilbert Space II, (2008) Preprint. [19] I. Raeburn, Graph Algebras, CBMS, no 3, AMS (2005). [20] P. D. Mitchener, C ∗ -Categories, Groupoid Actions, Equivalent KK-Theory, and the Baum-Connes Conjecture, arXiv:math.KT/0204291v1, (2005), Preprint. [21] R. Scapellato and J. Lauri, Topics in Graph Automorphisms and Reconstruction, London Math. Soc., Student Text 54, (2003) Cambridge Univ. Press.

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[22] R. Exel, A new Look at the Crossed-Product of a C ∗ -algebra by a Semigroup of Endomorphisms, (2005) Preprint. [23] R. Gliman, V. Shpilrain and A. G. Myasnikov (editors), Computational and Statistical Group Theory, Contemporary Math, 298, (2001) AMS. [24] R. Speicher, Combinatorial Theory of the Free Product with Amalgamation and Operator-Valued Free Probability Theory, AMS Mem, Vol 132 , Num 627 , (1998). [25] S. H. Weintraub, Representation Theory of Finite Groups: Algebra and Arithmetic, Grad. Studies in Math, vo. 59, (2003) AMS. [26] V. Vega, Finite Directed Graphs and W ∗ -Correspondences, (2006) Ph. D thesis, Univ. of Iowa. [27] W. Dicks and E. Ventura, The Group Fixed by a Family of Injective Endomorphisms of a Free Group, Contemp. Math 195, AMS. [28] F. Radulescu, Random Matrices, Amalgamated Free Products and Subfactors of the von Neumann Algebra of a Free Group, of Noninteger Index, Invent. Math., 115, (1994) 347 - 389.

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INDEX

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A AAA, 149, 152, 155 ABC, 212 absorption, 55, 66, 114, 115, 127, 128, 174, 238 academic, 65 acceptor, 32, 144, 145, 146, 148, 158, 181 acceptors, 149, 160, 177 accessibility, 26 acetone, 234 acetylcholine, 49 acetylene, 60, 61, 85 acid, vii, 3, 8, 13, 15, 16, 26, 28, 31, 46, 48, 49, 50, 52, 55, 67, 118, 130, 131, 132, 133, 134, 149 acidic, 47, 54 acoustic, 239 acrylic acid, 16, 50 activated carbon, 62, 63 activation, ix, 58, 72, 73, 74, 75, 76, 85, 86, 204 activation energy, 74, 204 active site, 20, 28 actuators, 7 Adams, 13, 48, 227 additives, x, xi, 60, 71, 72, 113, 116, 119, 125, 127, 135, 138, 233, 234, 235, 240, 241, 242 adenine, vii, ix, 3, 8, 28, 49, 95, 96, 102, 104, 106, 107, 108, 109 adhesion, 115, 125, 126, 128, 193, 196, 211 adhesive interaction, 194, 196 adjustment, 110 adrenaline, 8 adsorption, ix, x, xi, 22, 23, 36, 39, 40, 43, 49, 92, 95, 96, 97, 100, 106, 107, 110, 113, 115, 128, 193, 194, 195, 220 adsorption isotherms, 106 age, 210, 222 agent, 47, 96, 134 agents, 234, 241 aggregation, xi, 71, 196, 197, 198, 199, 200, 201, 207, 209 aid, 10, 21, 71

air, 61, 84, 96, 114, 117, 120, 123, 128, 133, 136, 150, 151, 174, 175, 201, 202 alcohol, 49 alcohols, 98 algorithm, 254 alkali, x, 59, 143, 146, 149, 150, 152, 154, 155, 159, 161, 163, 164, 168, 170, 171, 172, 173, 174, 175, 176, 178, 179, 180, 182, 183 alkaline, 47, 159 alkane, 240 alkanes, 97, 98 alloys, 54, 91, 155, 172, 173, 180, 182 alternatives, 35 Aluminum, 202 amalgam, 172, 176 ambient pressure, 155, 180 ambiguity, 59 amide, 22, 115, 116 amine, 48, 240, 241, 242 amines, 49 ammonia, 183 amorphous, 8, 9, 115, 212, 224, 241 amorphous carbon, 8, 9, 212 amphoteric, 145, 148 AMS, 276, 277 Amsterdam, 139, 140, 185 anaerobic, 27, 28 anisotropy, x, 143, 146, 147, 162, 163, 165, 179, 180, 184, 198, 199, 203, 219, 222, 239 annealing, 85, 205, 211, 219, 220 anode, viii, ix, 58, 59, 60, 62, 63, 64, 70, 76, 79, 84, 88, 89, 91, 92, 93, 94 anthracene, 106 antimony, 170, 173 application, vii, viii, 3, 28, 44, 45, 46, 49, 51, 53, 54, 57, 58, 71, 156, 159, 161, 163, 177, 180, 193, 194, 198, 219, 245, 258, 271 aptitude, x, 143, 147 aqueous solution, 21, 37, 67 aqueous suspension, 36 argon, 147, 150, 151, 175 argument, 154, 182 aromatic rings, 102, 194 arsenic, 170, 173

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Index

ascorbic, vii, 3, 8, 13, 15, 16, 46, 48, 49 ascorbic acid, vii, 3, 8, 15, 16, 46, 48, 49 ASI, 185, 190 Aspergillus niger, 52 assessment, 133 assignment, 138, 219 ASTM, 119, 139 atmosphere, ix, 58, 72, 117, 120, 121, 129, 134, 150, 151, 174, 175 atomic force, 133 Atomic Force Microscopy, 96, 133 atoms, ix, xi, 4, 5, 32, 36, 37, 62, 63, 65, 95, 98, 99, 102, 107, 109, 117, 144, 145, 146, 147, 149, 151, 154, 155, 159, 166, 168, 169, 173, 175, 176, 197, 198, 199, 200, 202, 203, 206, 207, 209, 210, 211, 212, 213, 222, 225 attachment, 9, 102, 134, 198, 205 automata, xii, 245, 246, 248, 253, 254, 255, 256, 257, 258, 263, 265, 266, 267, 268, 269, 270, 271, 272, 273, 274 averaging, 109

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B band gap, 6, 7 bandwidth, 38 barium, 154, 183 barrier, 20, 206, 207, 209, 216, 220, 221 barriers, 221, 241 basis set, 109, 110 batteries, 35, 92, 94 battery, viii, 54, 58, 60, 62, 63, 70, 76, 79, 83, 84, 88, 91, 92 BCS theory, 166 beams, 145 behavior, vii, 3, 21, 26, 28, 33, 35, 39, 48, 49, 53, 92, 181, 200, 204, 207, 237, 241, 242 behaviours, 116 Beijing, 48 Belgium, 113 bending, 22, 59, 201 benign, 35 benzene, ix, 80, 83, 95, 97, 98, 102, 107, 108, 109, 110, 146 beverages, 28 bias, 204 binding, ix, 22, 36, 43, 71, 77, 95, 96, 97, 98, 99, 100, 101, 103, 104, 105, 106, 107, 108, 109, 110, 117, 157, 158, 199, 201, 202, 203, 208, 209, 220, 222 binding energies, ix, 95, 96, 97, 98, 99, 100, 105, 107, 108, 109, 110 binding energy, ix, 22, 36, 95, 96, 97, 98, 99, 100, 101, 103, 104, 105, 106, 107, 108, 109, 110, 117, 203, 220 biocatalysis, 35, 36 biocompatibility, 44, 45 biodegradable, xi, 233, 234, 239, 240, 243

biofuel, vii, 3, 8, 35 biological systems, 43, 96 biomarker, 8 biomarkers, 47 biomaterials, 7, 43, 44 biomolecular, 20 biomolecules, 8, 44 biopolymer, 52 bioreactors, 35 biosensors, vii, 3, 7, 8, 16, 20, 28, 35, 44, 45, 46, 50, 51, 52 biotin, 8 bipolar, viii, 57, 66, 67, 68, 69 bismuth, 149, 170, 173, 178 blocks, 247, 249, 257, 260, 261 blood, 32 body fluid, 13, 28 Boltzmann constant, 101 Boltzmann factor, 221 bonding, 4, 98, 99, 107, 108, 115, 116, 128, 134, 144, 168, 198, 200, 218, 220, 240, 241, 242 bonds, 4, 22, 37, 115, 117, 129, 131, 132, 134, 138, 145, 146, 147, 148, 154, 159, 168, 202, 240, 241 Boron, 169 boron-doped, 182 brain, 13, 48 brain chemistry, 13, 48 British Petroleum, 234 Brownian motion, 234, 238, 240, 242, 243 buffer, 8, 14, 28, 34, 41 bulk crystal, 199, 212, 215, 222 burn, 9 burning, 60

C cables, 89 calcium, 154, 165, 172, 184 calibration, 18, 202, 239 calixarenes, 54 cancer, 8, 47 candidates, 116 capacity, 7, 62, 63, 84, 85, 92, 115, 116, 126, 240 capillary, 115 caps, 8 carbides, 150 carbon, vii, viii, ix, x, xi, 3, 4, 6, 7, 8, 9, 10, 15, 16, 28, 29, 32, 33, 36, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 54, 55, 57, 58, 59, 60, 61, 62, 63, 64, 65, 70, 71, 72, 73, 74, 76, 77, 78, 79, 80, 82, 84, 85, 86, 87, 89, 90, 91, 92, 93, 95, 96, 97, 98, 102, 105, 107, 110, 112, 117, 140, 143, 144, 145, 146, 147, 154, 159, 162, 168, 169, 170, 173, 181, 182, 184, 185, 187, 188, 189, 210, 211, 212, 223, 233, 234, 235, 236, 237, 239 carbon atoms, ix, 4, 62, 95, 98, 102, 117, 144, 145, 146, 147, 168, 173

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Index carbon materials, vii, x, xi, 3, 143, 144, 145, 162, 181, 236, 237 carbon nanotubes, vii, 3, 4, 6, 7, 8, 9, 10, 15, 29, 43, 44, 45, 46, 47, 48, 49, 54, 58, 96, 107, 110, 112, 145, 181, 182, 234 carbon-fiber, 116 carbonization, 147 carbonyl groups, 128, 135 carboxyl, 55 carboxylic, 8, 9, 10, 22, 130, 131, 132, 133 carboxylic acids, 9 carrier, 32, 182, 212 cast, 10, 21, 24, 33, 36, 38, 51, 53 CAT, 234 catalase, 46 catalysis, 27, 35, 44, 50, 53 catalytic activity, 12, 50 catechol, 49 catecholamine, 13 cation, 64 cell, viii, 5, 11, 20, 57, 66, 67, 68, 71, 73, 74, 84, 91, 147, 149, 154, 155, 156, 157, 170, 171, 172, 174, 175, 213, 215, 216, 217 cellulose, 115 ceramic, xi, 233, 234 cesium, 152, 155, 157, 158, 159, 160, 164, 170, 173, 174 channels, 12, 116 chemical bonds, x, 143 chemical degradation, 116 chemical properties, 147 chemical reactions, 130, 135, 145 chemical reactivity, x, 117, 129, 134, 143, 168 chemical stability, 7 chemical vapor deposition, 4, 179 chemicals, 116 chemisorption, 117, 129, 162, 196, 212, 220, 221, 222 Chevron, 234 China, 3, 44, 57, 81, 147 chiral, 5 chirality, 5, 6, 7 chitosan, 47, 52, 54 chloride, 28, 29, 49, 54 chlorine, 149 chloroform, 195 chromatography, ix, 95, 97, 98 classes, 270 classical, 35, 152, 155, 159, 160, 163, 247, 261 classification, 144 clay, 51, 52 cleavage, 107, 133, 134, 147, 212 closure, 13, 14 clouds, 194 clusters, xi, 32, 155, 156, 159, 160, 197, 198, 199, 200, 202, 203, 206, 207, 208, 209, 210, 211, 212, 219, 221, 222, 223, 224, 225 CNTs, 8, 214 CO2, 62

281

coatings, 116, 129 coenzyme, 50 cofactors, 28 coherence, 167, 180, 182 cohesion, 116, 145, 146, 168 coil, 201 coke, 80 communication, 52 complexity, 181, 243 composites, x, 16, 35, 36, 37, 38, 113, 114, 115, 116, 117, 118, 119, 120, 125, 126, 127, 128, 129, 134, 135, 138, 194, 195 composition, x, 113, 115, 136, 151, 162 compounds, x, xi, 15, 16, 35, 106, 143, 144, 148, 149, 150, 151, 152, 153, 154, 155, 157, 158, 159, 160, 161, 162, 163, 164, 165, 167, 169, 170, 171, 172, 173, 174, 175, 177, 178, 179, 180, 181, 182, 183, 184, 185, 193, 194 comprehension, 166 computation, 110 computer software, 102 concentration, viii, xi, 10, 15, 18, 27, 32, 44, 57, 66, 67, 68, 69, 119, 128, 129, 151, 159, 160, 162, 163, 164, 174, 193, 194, 195, 221 concrete, 254 condensation, 115 conductance, 91, 166 conduction, 136, 160, 177, 239, 240 conductive, 7, 8, 60, 71, 76, 77, 160, 200, 243 conductivity, xi, 15, 35, 45, 76, 77, 119, 136, 138, 160, 167, 177, 184, 194, 196, 233, 234, 235, 242, 243 conductor, vii, 147, 198 configuration, 5, 108, 136, 137, 167, 199, 209, 220 confinement, 199 confusion, 251, 252 congress, 140 conjugation, 194, 240 construction, 20, 245, 246, 247, 248, 257, 258, 268 constructional materials, 193 contaminant, 60, 85 contamination, 202 control, 24, 133, 138, 200, 243, 246, 254 convection, 9 conversion, 20, 24, 50, 101, 116, 212, 221 convex, 145, 205 cooling, 116, 234, 235 coordination, 242 copolymerisation, 17, 115 copolymers, 116, 129 copper, 66, 69, 149, 163 correlation, ix, 32, 95, 98, 100, 109, 132, 167, 183 correlation coefficient, 32 correlations, 106, 134, 160, 164, 165, 184 Coulomb, 152, 154, 155 couples, 38, 39 coupling, 165, 166, 167, 200 covalency, 160

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Index

covalent, 101, 117, 134, 144, 145, 146, 148, 154, 156, 159, 160, 168, 169 covalent bond, 101, 144, 145, 146, 148, 156, 159, 160, 168, 169 coverage, ix, 95, 96, 97, 98, 100, 110, 199, 202, 220 covering, 64, 65, 77, 88, 91, 201 crack, 128 cracking, 128, 147 critical temperature, x, 143, 161, 163, 179, 180, 184 critical value, 117 CRM, 276 crystal lattice, 239 crystal structure, 152, 154, 155, 156, 162, 169, 173 crystal structures, 152, 169, 173 crystalline, xi, 106, 110, 114, 115, 193, 194, 197, 199, 212, 215, 216, 221, 222, 234 crystallinity, 115, 219, 241 crystallites, xi, 117, 147, 197, 198, 199, 200, 202, 203, 204, 206, 207, 211, 212, 215, 219, 222 crystallization, 115, 203, 220, 224 crystals, 107, 212, 222, 234 CTAB, 10, 21, 24, 25, 26, 27, 33, 34 curiosity, 59 cycles, 18, 25, 60, 61, 120 cyclic voltammetry, 18, 26, 33, 93 cycling, 18, 60, 72 cytochrome, vii, 3, 8, 19, 20, 26, 28, 35, 46, 47, 51, 52, 53, 55 cytosine, ix, 95, 96, 102, 105, 106, 107, 109 cytotoxicity, 44

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D decomposition, viii, ix, 58, 76, 77, 79, 212 defects, 8, 9, 12, 147, 181, 200, 202, 207, 209, 221, 241 definition, 5, 248, 257, 265, 266, 267, 270, 271, 272 deformation, 115, 120, 125, 126, 128 degenerate, 157 degradation, 116, 200 dehydrogenase, 16, 49, 50 delivery, 7, 44 denaturation, 21, 35, 37, 52 dendrimers, 241 density, 104, 105, 106, 107, 109, 114, 119, 147, 149, 155, 168, 172, 173, 176, 177, 179, 182, 200, 202 density functional theory, 104, 105, 107, 109, 168, 177 deposition, viii, xi, 4, 35, 57, 59, 60, 63, 64, 84, 89, 197, 198, 200, 201, 202, 203, 204, 205, 207, 208, 210, 211, 212, 216, 219, 221, 222 desorption, ix, 95, 97, 98, 99, 100, 117 destruction, 114, 150, 151 detachment, 129, 198, 205 detection, 10, 13, 18, 20, 32, 45, 46, 47, 48, 49, 50, 51 deviation, 204, 215, 222 diabetes, 53

diamagnetism, 164 diamond, vii, xi, 4, 144, 145, 147, 148, 181, 182, 201, 215 Dicks, 277 diffraction, 44, 163, 165, 167, 215, 228 diffusion, viii, xi, 17, 25, 39, 52, 54, 57, 58, 59, 64, 67, 68, 69, 70, 72, 75, 76, 92, 93, 115, 128, 197, 198, 204, 205, 206, 207, 209, 212, 220, 221 diffusion process, 39, 70 diffusion rates, 220 diffusivity, 235 dilation, 145, 148 dimensionality, 160, 219 dimer, 109, 208 dimerization, 241 dimethylformamide, 10, 24 dipole, 238 diseases, 13 disorder, 215 dispersion, 24, 25, 107, 110 displacement, 120 dissociation, xi, 197, 220, 221, 222 distribution, ix, 58, 60, 71, 79, 198, 200, 276 division, 101 DMF, 10, 24 DNA, ix, 8, 47, 95, 96, 103, 105, 106, 107, 110 donor, 144, 145, 148, 158, 160, 178, 218 donors, 146, 149, 150, 151, 160, 170, 177, 184 dopamine, vii, 3, 8, 46, 48, 49 doped, 182, 183 doping, 92, 93, 184 dream, 71 drying, 120 dyes, 16, 49

E earth, 154, 155, 159, 183, 184 elastic constants, 117 elastomers, 45, 241 elbows, 217 electric charge, 36 electrical conductivity, 15 electrical properties, 7, 147 electroactivity, 43 Electroanalysis, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55 electrocatalysis, 46, 48, 52, 54, 55 electrocatalyst, 20 electrochemical detection, 20, 47 electrochemical impedance, 38, 40 electrochemical interface, 93 electrochemical measurements, 35 electrochemical reaction, vii, 3, 7, 8, 11, 12, 13, 14, 15, 16, 17, 24, 34, 40, 51, 71 electrochemistry, vii, 3, 8, 13, 28, 33, 35, 36, 45, 46, 47, 48, 51, 52, 53, 54, 55, 65

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Index electrodeposition, 54 electrodes, vii, 3, 7, 8, 9, 13, 14, 15, 19, 31, 35, 36, 40, 41, 42, 43, 45, 46, 47, 49, 50, 51, 52, 53, 54, 55, 72, 76, 79, 107, 182 electrolyte, viii, ix, 35, 38, 54, 58, 64, 65, 66, 67, 68, 69, 71, 74, 76, 77, 79, 84, 85, 91 electrolytes, 53, 67 electron, vii, 6, 7, 8, 10, 12, 19, 20, 21, 25, 26, 28, 30, 31, 32, 34, 35, 39, 40, 41, 42, 43, 46, 47, 51, 52, 53, 54, 55, 70, 144, 145, 146, 148, 149, 150, 154, 157, 158, 159, 160, 165, 167, 168, 169, 170, 177, 184, 198, 200, 202, 212, 215, 218, 234, 240 electron diffraction, 212 electron microscopy, 201 electronegativity, 144, 145, 159, 170, 174, 176 electronic structure, x, xi, 6, 7, 143, 144, 157, 158, 159, 164, 176, 177, 182, 200 electron-phonon, 164, 166, 167, 170, 180, 242 electron-phonon coupling, 166, 167 electrons, 4, 26, 117, 145, 148, 149, 150, 157, 158, 159, 160, 164, 166, 168, 169, 179, 180, 184, 199, 218, 239, 242 electron-transfer, 25, 26, 32, 38, 42 electrospinning, 45 electrostatic interactions, 37 emission, 7 emission source, 7 energy, ix, x, 7, 22, 37, 62, 64, 74, 83, 84, 95, 96, 97, 98, 99, 100, 101, 102, 104, 107, 108, 109, 110, 116, 132, 146, 154, 157, 158, 159, 176, 198, 199, 206, 207, 218, 220, 221, 222, 233, 234, 240 energy density, 62, 84 energy efficiency, 62 engines, 234, 243 entanglement, 115 entanglements, 9 environment, 11, 20, 115, 117, 118, 120, 123, 128, 129, 175, 198, 202 environmental conditions, 114 enzymatic, 16, 35, 53 enzymes, vii, 3, 7, 8, 16, 19, 20, 21, 22, 25, 26, 28, 35, 36, 37, 40, 41, 42, 43, 46, 50, 51 epitaxial growth, 224 epoxy, 116, 193 equilibrium, 114, 155, 199 equipment, 234 ESI, 91 ester, 88 ethanol, 49, 50, 99 ethers, 97 ethylene, 52, 53, 66, 84, 234 ethylene glycol, 234 ethylene oxide, 52, 53 europium, 155, 159, 172 evacuation, 89 evaporation, 4, 72 evolution, 123, 199 excitation, 237, 254 exclusion, 97

283

exfoliation, 107 expert, 80, 83 exposure, 44, 115, 135, 200 extraction, vii, viii, ix, 54, 57, 58, 60, 63, 64, 71, 72, 80, 92, 195

F fabric, 116, 117 fabricate, 9, 60, 198, 219 fabrication, vii, 3, 8, 29, 36, 128, 200 FAD, 28, 29, 30 failure, 7 family, x, 32, 115, 143, 161, 165, 179, 180, 183, 184, 247 fatigue, 118 fatty acid, 240 fatty acids, 240 feedback, 120 fermentation, 28 Fermi, 157, 158, 159, 166, 176, 177, 179, 212 Fermi energy, 157, 176 Fermi level, 157, 158, 159, 176, 179 Fermi surface, 177 fiber, viii, ix, 7, 48, 50, 52, 57, 58, 60, 61, 63, 64, 65, 71, 72, 73, 74, 75, 76, 77, 78, 79, 84, 85, 86, 87, 89, 90, 91, 92, 93, 145, 179, 239 fibers, 71, 76, 78, 79, 84, 85, 87, 234, 240 fibrillar, xi, 233, 241, 242 filler particles, 116 filler surface, 194 fillers, xi, 116, 117, 120, 125, 129, 193, 194 film, viii, 25, 33, 46, 48, 49, 53, 55, 57, 63, 64, 65, 66, 84, 85, 86, 87, 89, 90, 91, 92, 115, 116, 121, 122, 123, 125, 126, 128, 129, 130, 133, 134, 135, 136, 138, 202, 204, 209, 212, 215, 216, 221, 222 film formation, 126, 134 film thickness, 89, 91, 216 films, xi, 34, 45, 48, 50, 51, 52, 53, 54, 64, 90, 91, 121, 125, 126, 127, 128, 133, 136, 140, 197, 198, 200, 215, 219, 222, 223, 224 financial support, 138 fines, 194 fixation, 120 flexibility, 59, 115, 128, 149 flow, 50, 51, 74, 86, 97, 128 flow rate, 97 fluid, 235, 242 fluorescence, 55, 237, 238 fluorinated, 235 fluorine, 129 focusing, 7, 55 folding, 5, 211 foodstuffs, 28 forests, 8, 47 fossil, 62 fossil fuel, 62 fouling, 8, 13, 16

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FRA, 121 fractal structure, 265 fractals, 208, 212 fracture, 115, 117, 119, 120, 123, 124, 125, 128, 134 fragmentation, 133 France, 143 free radical, 134 free radicals, 134 free volume, 115 friction, x, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 128, 129, 130, 132, 133, 135, 136, 137, 138 FTIR, 9, 10, 22, 23, 84, 85, 115 FTIR spectroscopy, 9 fuel, 62 fullerene, 110, 144, 183 fullerenes, xi, 44, 58, 144, 145, 235 functionalization, 48, 54

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G GaAs, 219, 221 gas, ix, 95, 96, 97, 100, 107, 220 gas phase, ix, 95, 96, 100, 107, 220 gel, 36, 48, 241 gelation, 234, 240, 242 gels, xi, 233, 241, 242 generation, 51 generators, 262 germanium, 121 Germany, 10, 121 glass, 71, 114, 115, 128, 150 glass transition, 115, 128 glass transition temperature, 128 glucose, vii, 3, 8, 19, 28, 31, 32, 46, 47, 50, 52, 53, 54, 55 glucose oxidase, vii, 3, 8, 19, 47, 52, 53, 54, 55 glycerol, 50 gold, 16, 31, 49, 50, 52, 152, 207 gold nanoparticles, 16, 50 grades, 115 graduate students, 60 grain, 119, 207 grants, 223 graph, xii, 245, 246, 247, 248, 250, 251, 252, 253, 254, 257, 258, 259, 260, 261, 262, 263, 265, 266, 267, 268, 269, 270, 271, 272, 273, 274, 275, 276 graphene sheet, ix, 4, 5, 6, 76, 147, 165 graphite, vii, viii, ix, x, xi, 4, 7, 9, 28, 33, 34, 44, 46, 47, 51, 53, 57, 58, 60, 61, 62, 71, 79, 80, 81, 82, 84, 88, 89, 93, 95, 98, 102, 106, 107, 109, 113, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 129, 132, 133, 134, 135, 136, 138, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 157, 158, 159, 160, 161, 162, 163, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 181, 182, 184, 185, 193, 194, 195, 196, 197,

198, 200, 201, 202, 203, 204, 205, 206, 207, 209, 212, 214, 215, 218, 220, 221, 222, 234 group identity, 262 groups, 8, 9, 11, 16, 18, 20, 22, 50, 85, 115, 116, 128, 130, 131, 135, 194, 195, 200, 202, 240, 241, 242, 246, 247, 254, 256, 257, 265 growth, xi, 197, 198, 200, 202, 204, 205, 208, 209, 210, 212, 215, 216, 218, 219, 220, 221, 222, 224 guanine, ix, 95, 96, 102, 104, 106, 107, 109

H halogen, 170, 174, 175 halogenated, 98 halogens, 149 hardness, 120 Hartree-Fock method, 106 H-bonding, 240, 241, 242 HDPE, 114 heat, xi, 60, 87, 136, 147, 170, 174, 194, 233, 234, 235, 237, 239, 240, 243 heat conductivity, 194 heat pumps, 234 heat transfer, xi, 233, 234, 237, 239, 243 heating, 61, 63, 64, 85, 121, 132, 136, 145 height, viii, 57, 60, 65, 72, 91, 201, 204, 205, 208, 209, 211, 214, 215, 216, 217 heme, 8, 20, 21, 23, 26, 36, 37, 38, 40, 42, 51, 52, 55 hemoglobin, vii, 3, 8, 26, 28, 35, 36, 46, 51, 52, 54 hemoglobin (Hb), 28 heterogeneous, 20, 25, 28, 31, 34, 43 hexafluorophosphate, 35 high pressure, xi, 147, 155, 161, 163, 167, 174, 177, 181, 197 high temperature, x, 64, 69, 113, 115, 118, 130, 132, 133, 138, 150, 181 Hilbert, 247, 257, 258, 259, 265, 271, 272, 274, 276, 277 Hilbert space, 247, 257, 258, 259, 265, 271, 272, 274, 276, 277 histidine, 26 homocysteine, 49 homogenisation, 135 homogenized, 234 horse, 52 host, x, 55, 143, 149, 160, 162, 181, 182 HRP, 28, 36, 37, 41, 42, 43 HRTEM, 80, 81, 82 human, 8, 13 humidity, x, 113, 114, 115, 118, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 132, 133, 134, 135, 137, 138 hybrid, 16, 46, 50, 62 hybridization, 4, 47, 58, 59, 144, 145, 159 hydration, 15 hydride, 93, 162, 174 hydro, 107, 114, 115 hydrocarbon, 110, 241

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Index hydrocarbons, 98, 107 hydrogels, 241 hydrogen, viii, 7, 20, 26, 28, 58, 64, 93, 96, 98, 99, 105, 107, 108, 114, 115, 128, 149, 152, 162, 174, 176, 177, 240, 241 hydrogen atoms, 107 hydrogen bonds, 108, 114, 115, 128 hydrogen peroxide, 26 hydrogenation, 162, 174, 179 hydrolysis, 128, 130, 132, 134, 138 hydrophilic, 114, 115 hydrophobic, 37, 52, 129, 241, 242 hydrophobic interactions, 52 hydrophobic properties, 129 hydrophobicity, 115 hydrostatic pressure, 167 hydrothermal, 9 hydroxyl, 85, 194, 195 hydroxyl groups, 85, 194, 195 hypothesis, 129

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I ice, 204 identification, 81, 256, 260 identity, 246, 262, 266 illumination, 237 images, viii, 6, 58, 80, 81, 87, 119, 200, 201, 203, 204, 206, 207, 208, 211, 212, 214, 215, 216, 217, 255 imaging, 53, 96, 204, 211 immobilization, vii, 3, 8, 20, 21, 27, 30, 33, 40 immobilized enzymes, 51 impedance spectroscopy, 38 implants, 44 impurities, 239, 241 in situ, xi, 49, 50, 197, 200, 202 in vitro, 44, 49 in vivo, 44, 49 incidence, 248, 249 inclusion, 105, 241, 249 indexing, 212, 217 indication, 64, 166 indicators, 194 indices, 5, 7, 212, 219 indium, 53 induction, 179 industrial, xi, 233 industrial application, xi, 233 industry, 193 inert, xi, 117, 151, 197, 198, 199, 200, 208, 210, 211, 222, 223 inertness, 115, 207, 213, 222 infinite, 246, 247, 255 inherited, 251 inhomogeneities, 122 initial state, 65, 100 initiation, 60, 129

285

injection, 50, 169 inorganic, 35, 144, 194 insertion, vii, viii, ix, x, 57, 58, 60, 64, 67, 71, 72, 76, 80, 83, 92, 110, 143, 145 insight, 37, 116 instabilities, 123 insulin, 8, 47 integrated circuits, 223 integration, 44, 223 integrity, 37, 38 Intel, 141 intensity, 130, 132, 133, 237 interaction, ix, xi, 7, 20, 22, 29, 33, 39, 42, 43, 95, 96, 98, 100, 101, 107, 108, 109, 110, 115, 117, 121, 122, 125, 129, 130, 132, 159, 164, 170, 194, 195, 197, 199, 200, 204, 219, 240, 241 interaction effect, 7 interaction effects, 7 interactions, ix, 37, 52, 95, 96, 98, 100, 101, 104, 106, 107, 109, 110, 123, 129, 138, 148, 149, 152, 157, 158, 180, 198, 199, 222, 239, 240, 241, 242, 243 intercalation, x, 60, 63, 88, 110, 143, 145, 148, 149, 150, 151, 152, 153, 154, 155, 157, 158, 159, 160, 161, 162, 163, 164, 165, 168, 170, 171, 172, 173, 174, 175, 177, 178, 179, 181, 182, 184, 185, 190, 241 interface, 38, 39, 96, 116, 123, 125, 126, 130, 132, 133, 134, 135, 136, 138, 198, 202, 203, 242 interference, 71, 237 intermolecular, 240 interphase, ix, 58, 88 interval, 134, 235 intrinsic, xi, 117, 125, 135, 197, 198, 218 inversion, 248 iodine, 149, 176 ionic, 35, 48, 52, 53, 54, 55, 92, 154, 155, 176 ionic liquids, 53, 54 ionization, 55, 155 ionization potentials, 155 ions, viii, ix, 58, 79, 95, 116, 117, 129, 138, 183, 198 IR spectra, 84 iron, 23, 32, 129, 133, 149 island, 202, 204, 205, 206, 207, 212, 214, 215, 219, 221, 222 island density, 221 island formation, 202 isoelectric point, 36, 41 isolated islands, 204 isolation, vii isomorphism, 263, 272 isotherms, 106 isotope, 166 isotropic, 166, 182, 195, 199, 202, 222 Israel, 85

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J Japan, 38, 64, 65, 83, 92, 190 Japanese, 71, 92 Jung, 226

K KBr, 9, 10 kinetic parameters, 221 kinetics, xi, 32, 38, 54, 55, 62, 127, 194, 197, 198, 200, 205, 212, 218

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L labeling, 258, 265, 266, 272, 273, 274, 275, 276 lamellar, x, 113, 117, 125, 136, 143, 144, 147, 149, 150, 152, 155, 181, 184 Langmuir, 46, 51, 53, 54, 111, 139, 226, 227 language, 246, 253, 266, 267 laser, 4, 121, 237 lattice, xi, 5, 63, 173, 176, 181, 182, 183, 197, 204, 207, 212, 213, 215, 216, 217, 218, 219, 222, 241, 248, 249 lattice parameters, 183, 215, 216 lattices, 212 law, ix, 95, 96, 98, 170 laws, 194 LCP, 115 lead, 37, 40, 42, 44, 128, 145, 147, 149, 151, 152, 154, 155, 159, 160, 165, 166, 168, 170, 173, 181, 196, 199, 241 LEO, 10 lifetime, 16, 243 ligands, 110 linear, 18, 26, 32, 39, 52, 97, 101, 116, 128, 145, 157, 160, 167, 201, 202, 209, 214, 248, 259 linear regression, 97 linkage, 43, 128 links, 246 lipase, 55 lipid, 33, 34, 53 liquid chromatography, 46 liquid nitrogen, 163 liquid phase, 36, 147 liquids, 35, 53, 54, 55, 116, 240 liquor, 28 lithium, 59, 92, 93, 94, 151, 154, 155, 156, 157, 159, 160, 163, 164, 168, 170, 172, 173, 183 Lithium, 59, 93, 155 London, 92, 140, 185, 186, 190, 277 long distance, 148, 152 long period, 199 losses, 116, 120 low molecular weight, 118 low temperatures, 130, 132, 135, 150, 184

lubricants, x, 113, 117, 138 lubrication, 114, 116, 127 lysine, 52

M machines, 253 magnesium, x, 144, 168, 169 magnesium diboride, x, 144 magnetic, 159, 162, 163, 165, 166, 167, 179, 181, 197 magnetic field, 162 magnetic moment, 159 magnetism, 159 magnetization, 164, 165, 167, 181 magnetoresistance, 212 maintenance, 194, 234 mammalian brain, 13 manipulation, 38 mass spectrometry, 55 mass transfer, 57, 63, 67 mathematics, 252 Matrices, 277 matrix, x, 28, 29, 35, 47, 52, 54, 64, 65, 67, 113, 116, 117, 120, 122, 125, 182, 195, 234, 240, 243 measurement, 48, 60, 64, 66, 73, 74, 91, 128, 165, 166, 177 mechanical energy, 116, 132 mechanical properties, 7, 8, 63, 114, 115, 119, 147, 196 media, 7, 35, 235, 240, 242 mediators, 16, 21 Meissner effect, 182 melt, 86 melting, 64, 85, 114, 116, 151 melting temperature, 85, 116, 151 melts, 85 membranes, 45 MEMS, 243 mercury, 149, 152, 170, 171, 172, 176, 178, 180 Mesophase, 93 metabolic, 19 metal oxide, xi, 233, 234 metals, viii, x, 50, 57, 65, 91, 114, 143, 146, 148, 149, 150, 151, 152, 154, 155, 157, 159, 160, 161, 163, 164, 170, 172, 173, 174, 179, 182, 183, 200, 207 methane, 98 methanol, 99 methyl group, ix, 95, 96, 98, 102, 105, 109 methyl groups, 98 methylene, 17 MgB2, 168, 169, 170 micelles, 21 Microbial, 53 microdialysis, 46 microelectrode, 48 microelectrodes, 13

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Index microenvironment, 23, 26, 37 microscope, 10, 71, 117, 121, 182 microscopy, xi, 7, 44, 133, 170, 197, 198 microtubules, 44, 45 migration, 199, 207, 221, 222 minerals, 147 mirror, 204 mitochondrial, 55 mobility, 115, 116, 123, 198, 200, 206 model system, 101 models, 6, 35, 36, 96, 101, 109, 158, 180, 254 modulus, 7 MOE, 44 moisture, x, 113, 114, 115, 116, 117, 118, 128, 129, 133 moisture content, x, 113, 115, 118, 128 moisture sorption, 115 molecular dynamics, 202 molecular mobility, 115, 116, 123 molecular orbitals, 146 molecular oxygen, 20 molecular structure, 24, 117, 118, 128, 132 molecular weight, 20, 21, 118 molecules, vii, ix, x, xi, 3, 7, 8, 9, 19, 40, 95, 96, 97, 98, 99, 100, 101, 102, 107, 109, 110, 113, 115, 116, 117, 118, 123, 128, 129, 138, 145, 183, 197, 198, 199, 219, 225, 238, 240, 241 monolayer, ix, 28, 47, 53, 95, 96, 97, 98, 99, 100, 110, 220 monolayers, 50 monomers, xi, 193, 194, 195, 196 morning, 85 morphological, 199 morphology, 10, 125, 128, 133, 134, 135, 136, 198, 200, 208, 216, 222 motion, 64, 114, 117, 234, 238, 240, 242, 243 movement, 65, 70 MRS, 229 multilayer films, 34 multiplication, 258, 274 muscle, 20 muscle cells, 20 mw, 259 myoglobin, vii, 3, 8, 20, 35, 36, 46, 51, 52, 55

N N,N-Dimethylformamide, 99 NaCl, 175, 209 NAD, vii, 16, 49, 50 NADH, 8, 16, 45, 49, 50 Nafion, 10, 21, 24, 25, 27, 29, 30, 32, 46, 48, 49, 52 naming, 59 nanoclusters, 207 nanocomposites, 7, 29, 35 nanocrystal, 222 nanocrystalline, 200 nanocrystals, 198, 218, 222

287

Nanofluids, xi, 233, 234 nanomaterials, 8, 43, 197, 198 nanometers, xi, 233, 234 nanoparticles, xi, 16, 50, 51, 52, 197, 199, 200, 207, 208, 213, 218, 219, 222, 233, 234 nanorods, xi, 197, 198, 212, 216, 217, 218, 219, 222 nanoscience, 219 nanostructured materials, 198 nanostructures, 97, 198, 199, 200, 201, 203, 205, 207, 209, 210, 211, 212, 213, 214, 215, 217, 218, 219, 220, 221, 222, 223, 225, 227, 229 nanotechnology, vii, 43, 219 nanotube, xi, 4, 5, 6, 7, 9, 33, 43, 45, 46, 47, 48, 54, 144, 182, 210, 233, 234, 240 nanotubes, vii, xi, 3, 4, 5, 6, 7, 8, 9, 15, 29, 43, 44, 45, 46, 47, 48, 49, 54, 55, 58, 96, 106, 107, 110, 112, 144, 145, 181, 182, 198, 223, 239, 241 nanowires, 44, 45, 209, 210, 219 naphthalene, 106, 107 NASA, 139, 243 National Institute of Standards and Technology, 235 National University of Singapore, 197 NATO, 185, 190 natural, 59, 79, 98, 147, 166, 243, 247, 259, 262, 263, 267 negative stimulus, 254 neon, 97 nerve, 8, 47 nerve agents, 8 network, 16, 50, 116, 240 neurotransmitters, 13, 48 New York, 45, 53, 92, 111, 112, 139, 185, 190, 223, 224, 228 nickel, viii, 57, 65, 70, 71, 84, 91, 149, 276 nicotinamide, 49, 50 Nielsen, 228 niobium, 182 nitric acid, 8 nitride, 198, 200, 207 nitrides, 198 nitrogen, 11, 36, 37, 107, 119, 121, 163, 240 NMR, 70, 93 Nobel Prize, 4 nodes, 246 nonlinear, 36, 37 non-uniform, 79 normal, x, 4, 32, 113, 114, 120, 121, 123, 124, 125, 126, 127, 130, 133, 135, 136, 138, 163, 184, 212, 217 normal conditions, 163 novel materials, 4 nucleation, xi, 197, 198, 199, 200, 201, 202, 205, 208, 209, 210, 212, 219, 220, 221 nucleic acid, 8 nucleosides, 109

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O

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observations, 123, 126, 132, 203, 216 oil, xi, 9, 114, 115, 233, 234, 235, 236, 237, 238, 239, 240, 242 oils, xi, 147, 233, 234, 235, 236, 237, 239, 240, 243 on-line, 120 operator, 245, 246, 247, 258, 259, 265, 271, 273, 274, 275, 276 Operators, 272, 277 optical, 52, 121, 125, 133, 197, 198 optical fiber, 52 optical micrographs, 125 optical microscopy, 133 optical properties, 197 optimization, 99 optoelectronic, 223 organic, ix, 35, 55, 64, 65, 88, 95, 98, 109, 110, 115, 144, 147 organization, 47, 147, 224 orientation, 99, 100, 102, 109, 116, 123, 131, 136, 147, 203, 204, 206, 207, 215, 218, 222 orthorhombic, 149, 153, 171, 174 Ostwald ripening, 199 overload, 121, 123, 124, 125, 128, 135, 136 oxidation, ix, 8, 13, 14, 15, 16, 17, 18, 19, 25, 31, 32, 34, 45, 48, 49, 50, 58, 60, 63, 64, 72, 84, 85, 148, 150, 195, 202 oxidative, 8, 243 oxide, 8, 52, 53, 67, 129, 198, 200, 207 oxide electrodes, 53 oxides, 149, 198 oxygen, ix, 11, 18, 20, 26, 28, 34, 47, 58, 72, 107, 117, 149, 170, 174, 175, 176, 177, 195, 240

P pain, 150 pairing, 164, 166 palladium, 92 paper, 60, 64, 69, 70, 76, 80, 83, 85, 120, 194, 245, 247, 248, 258, 271 parameter, 96, 123, 152, 155, 166, 171, 172, 174, 175, 183 Paris, 184, 185, 186, 189, 191 parkinsonism, 13 particle shape, 199 particles, viii, xi, 8, 9, 58, 65, 70, 74, 81, 116, 119, 120, 123, 125, 126, 128, 130, 133, 134, 135, 136, 151, 194, 195, 196, 199, 213, 218, 233, 234 passivation, 88, 218 pears, 147 PEEK, 115, 116, 132 Pennsylvania, 186 peptide, 22, 37 peptide bonds, 22, 37 percolation, 45, 242

performance, x, 11, 12, 13, 18, 43, 44, 60, 64, 84, 85, 91, 92, 113, 116, 118, 121, 123, 127, 138 periodic, 64, 144, 168, 170, 173, 174, 175, 216 periodic table, 64, 144, 168, 170, 173, 174, 175 periodicity, 234 permeation, 115 peroxide, 28, 174 perturbation, 40, 104, 105, 106, 109, 166 perturbation theory, 104, 105, 109 PET, 114 petroleum, 94, 239, 240, 243 pH, 11, 14, 16, 17, 18, 21, 23, 24, 25, 26, 27, 29, 30, 31, 34, 36, 41, 42, 43 pharmacokinetics, 46 phase diagram, 167, 181 phenol, 77, 194 phenolic, 116 Philadelphia, 139 phonon, 165, 166, 167, 182, 234, 237, 238, 239, 240, 241, 242, 243 phonons, 166, 234, 239, 242 phosphate, vii, 3, 8, 14 phosphorus, 174 photoelectron spectroscopy, 202 photon, 238 photons, 237 photosynthetic, 32 physical chemistry, 84, 224 physical properties, 35, 55, 212 physics, vii, 185, 190, 224 physiological, 48 pitch, 71 planar, 5, 220, 239 plants, 32 plastic, 120, 128, 139 plastic deformation, 128 plasticization, 115 plasticizer, 115 platelet, 125, 147, 151, 175 platelets, 147 platinum, 49 play, 117, 129, 157, 158, 160, 176, 179, 180, 184, 199 PMDA, 118, 128 Poincaré, 143 poisonous, 86 polarity, 130 polarizability, 105, 106, 107, 109 polarization, 64, 65, 67, 68, 69, 77, 237, 238 polarized light, 237 polyamide, 115, 118 polyamide acid, 118 polyamides, 114, 115, 116 polyaniline, 16, 45, 50, 54 polyaromatic hydrocarbons, 98 polycondensation, xi, 118, 134, 193, 194, 195 polycrystalline, 200, 212, 219 polyethylene, 114, 115

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Index polyimide, x, 113, 116, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138 polyimide film, 128, 136 polyimides, x, 113, 115, 116, 119, 120, 121, 125, 128, 129, 130, 132, 134, 135, 136, 138 polymer, x, xi, 25, 28, 45, 46, 50, 88, 113, 114, 115, 116, 117, 118, 120, 121, 123, 125, 128, 129, 130, 134, 136, 137, 138, 193, 194, 195 polymer chains, 115, 123 polymer composites, x, 113, 116, 129, 134 polymer film, 25, 28 polymer films, 25 polymer matrix, 116, 117, 120 polymer nanocomposites, 45 polymer structure, 115 polymeric materials, 7 polymerization, 15 polymerizations, 194 polymers, x, 7, 16, 113, 114, 115, 116, 121, 125, 127, 193, 194, 241 polymorphism, 173 polypeptide, 20, 22, 36 polypropylene, 114 polystyrene, 45 polyurethane, 45 poor, 13, 24, 91, 134, 147 poor performance, 13 pore, 9, 62, 97, 100 pores, 85, 97, 127 porosity, 241 porous, 62, 85, 96, 97, 110, 127 positive stimulus, 254 potassium, 148, 152, 155, 159, 162, 163, 164, 170, 171, 172, 174, 175, 176 powder, viii, 48, 58, 60, 70, 79, 84, 85, 97, 118, 122, 135, 147, 150, 151, 235 powders, viii, 58, 120, 133, 150, 151 power, 62, 70, 84, 199, 201, 207, 209, 222 PPS, 115 pressure, xi, 4, 35, 84, 97, 121, 123, 136, 137, 147, 150, 151, 155, 156, 159, 161, 163, 167, 168, 180, 181, 183, 197, 200, 217, 218, 222 prevention, 43 pristine, 9, 44, 71, 84, 85, 145, 149, 150, 151, 155, 157, 158, 160, 169, 235, 239 probability, xi, 197, 201, 209, 220, 221, 276 probe, 7, 25, 198 production, 28, 48, 194 program, 64, 67, 84 promote, 7, 8, 20, 25, 34, 35, 40, 42, 159, 168, 241 property, x, 7, 13, 53, 59, 143, 144, 162, 177, 198, 239, 257, 265, 273 proposition, 270, 272 propylene, viii, 58, 66, 76, 77, 78, 84 protection, 96, 133 protein, 19, 20, 21, 25, 26, 29, 33, 36, 42, 52, 55 protein analysis, 55

289

proteins, vii, 3, 7, 8, 19, 20, 21, 22, 25, 26, 28, 32, 35, 36, 37, 38, 40, 41, 42, 43, 46, 50, 51, 52, 53, 54, 241 protons, 26 proximal, 26 PTFE, 114, 129 pulse, 28, 49, 53, 235 pumps, 234 purification, 8, 9, 22, 96 pyrene, 83 pyrolysis, 77, 147 pyrolytic graphite, xi, 7, 33, 34, 47, 51, 53, 98, 107, 147, 151, 162, 174, 175, 197, 200 pyromellitic dianhydride, 118 pyrrole, 17

Q QDs, 198, 218 quantization, 254 quantum, ix, 83, 95, 96, 100, 109, 110, 198, 199, 224, 239 quantum chemistry, 83 quantum confinement, 199 quantum mechanics, 110 quantum theory, 239 quartz, 38, 147

R radical, 16, 132, 135 radical formation, 132, 135 radius, 154, 199 Raman, xi, 9, 94, 121, 130, 131, 132, 133, 170, 233, 234, 237, 238, 240, 242, 243 Raman scattering, 238 Raman spectra, 240 Raman spectroscopy, xi, 170, 233, 234 ramified islands, xi, 197, 209 random, 222, 248, 249 range, viii, 18, 20, 23, 25, 26, 31, 32, 35, 38, 40, 43, 58, 64, 70, 71, 72, 74, 100, 107, 109, 128, 136, 145, 150, 158, 161, 167, 170, 175, 199, 202, 203, 204, 212, 213, 214, 217, 218, 222, 237, 240, 250, 252 rare earth, 155, 159, 184 rat, 48 reaction rate, viii, 57, 64, 65, 72, 92 reaction temperature, 151 reactivity, viii, x, 8, 57, 117, 129, 134, 135, 143, 147, 168, 197 reagent, 145, 148, 151 reagents, 145, 148, 150, 175 recall, 249, 270 reconstruction, 199 redox, 11, 14, 16, 19, 20, 23, 24, 26, 30, 31, 32, 34, 35, 38, 39, 40, 41, 46, 50, 55

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redox proteins, 32 reduction, 14, 20, 25, 26, 28, 31, 32, 34, 42, 46, 51, 53, 62, 85, 115, 120, 121, 135, 162, 196, 251, 252, 257, 258, 260 refining, 166 regenerate, 145 regression, 36, 37, 97, 98, 101 regular, 62, 74, 242 regulation, 194 relationship, x, 7, 18, 26, 113, 215 relaxation, x, 113, 114, 116, 216, 217, 218 relaxation process, 116 relaxation processes, 116 reliability, 115 research, vii, x, 7, 8, 20, 43, 44, 59, 60, 64, 77, 84, 130, 135, 138, 143, 223 research and development, 84 researchers, vii, viii, 4, 57 residues, 52 resilience, 114 resin, 77, 117 resins, 119 resistance, x, 38, 115, 116, 117, 119, 121, 127, 129, 134, 135, 166, 182 resistivity, 160, 162, 167, 180, 181 resolution, 9, 10, 52, 166 retention, 97, 106 rhombohedral, 149, 212, 213, 217 rice, 233 rings, ix, 80, 95, 97, 98, 102, 108, 110, 132 RNA, ix, 95, 96, 103, 105, 106 rods, 214, 219 room temperature, viii, xi, 38, 53, 54, 57, 64, 65, 69, 73, 74, 75, 77, 78, 91, 115, 160, 163, 177, 197, 200, 209, 242 rotations, 207 roughness, 97, 120, 125 rubbery state, 115 rubidium, 152, 155, 164, 170, 171, 172, 173, 174 Russia, 193

S safety, 59 salt, 30 salts, 55, 241 sample, viii, ix, 10, 15, 18, 21, 57, 58, 60, 61, 63, 64, 65, 66, 67, 69, 70, 71, 73, 74, 76, 81, 84, 85, 87, 89, 91, 97, 98, 120, 127, 163, 165, 166, 167, 181, 200, 202, 204, 205, 210, 213, 214, 216, 219, 221, 222, 235, 239 saturation, 127, 163, 164, 165, 181, 220, 221 saturation coverage, 220 scanning electron microscopy, 201 scanning tunneling microscopy, xi, 197, 198 scatter, 72, 123, 148, 215, 237 scattering, 55, 70, 72, 237, 238, 241 schema, 201, 206

schizophrenia, 13 Schmid, 52, 228 seals, 114 search, 183, 245 searching, 221 selectivity, xi, 13, 20, 48, 197, 222 selenium, 175 self-assembly, xi, 96, 197, 219, 222, 240 self-organizing, 240 SEM, 10, 64, 65, 77, 79, 80, 81, 85, 87, 91, 119, 201, 204, 205, 215 semiconductor, 7, 198, 200, 207, 223, 229 semiconductors, 7, 200 semi-crystalline polymers, 115 semimetals, 7, 212 sensing, 8, 10, 20, 32, 45, 47, 48, 49, 50, 68, 69 sensitivity, 6, 7, 13, 16, 121, 129, 166 sensors, 7, 45, 46, 48 separation, 11, 12, 14, 24, 30, 34, 35, 36, 43, 55, 74, 81, 97, 100, 102, 110, 123, 136, 138, 183, 207 Sequoia, 185 series, 31, 97, 163, 185, 190, 253 serotonin, 46, 49 serum, 8, 32 serum albumin, 8 Shanghai, 81 shape, 40, 62, 83, 97, 198, 199, 202, 203, 204, 207, 208, 209, 213, 215, 218, 222, 237 shares, 272 shear, x, 113, 115, 117, 118, 119, 123, 125, 126, 128, 129, 133, 134, 135, 136, 138 shear rates, 123 shear strength, 115, 119, 123, 125, 128, 134 shocks, 151 shoulder, 240 signals, 23, 237, 238 signs, 128 silica, 35 silicon, vii, 128, 207, 223 silver, 54 similarity, 216 simulation, 98, 117, 199, 202 simulations, 199 Singapore, 197, 223, 224 single walled carbon nanotubes, 54 sintering, 85, 116, 119, 207 sites, xi, 9, 47, 117, 134, 145, 149, 152, 154, 155, 157, 168, 169, 170, 171, 175, 197, 199, 201, 202, 209, 221 soccer, 4 sodium, 153, 154, 155, 164, 174, 175, 183 sol-gel, 52, 241 solid surfaces, 240 solubility, 53, 118 solutions, 11, 15, 43, 55 solvent, viii, ix, 21, 36, 57, 58, 70, 76, 79, 96, 107, 234, 235, 240, 241, 242 solvent molecules, 240 solvents, 10, 35, 53, 116, 241

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Index sorption, 115 sorting, 147 soybean, 235, 239 spatial, 198, 200 species, 39, 41, 42, 60, 145, 146, 148, 149, 150, 158, 176, 198, 199, 200, 212, 220, 221 specific heat, 166, 170, 179, 182 specific surface, 55, 62 spectrophotometric, 49 spectroscopic methods, 198 spectroscopy, 23, 37, 38, 121, 166, 170, 202 spectrum, 9, 22, 23, 37, 38, 121, 130, 131, 238 speed, ix, xi, 95, 110, 193, 195 spheres, 212, 213 spinach, 32, 33, 53 spine, 144 spintronic devices, 223 Sri Lanka, 147 stability, 7, 15, 18, 25, 26, 35, 55, 115, 145, 146, 154, 197 stabilization, 121, 168, 175 stabilize, 202 stages, 148, 173, 199, 200, 207 stainless steel, 125, 175 standard deviation, 104 state control, 246 steel, x, 7, 113, 120, 121, 122, 125, 126, 127, 134, 136, 137, 175 steric, 100, 107 stiffness, 119 stimulus, 254 STM, xi, 53, 96, 166, 170, 197, 198, 200, 201, 202, 203, 204, 205, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217 Stochastic, 277 stoichiometry, 169, 170 storage, 7, 19, 20, 25, 26, 34, 96 storage media, 7 strain, 216 strains, 7 strategies, 47 strength, 7, 115, 116, 118, 119, 120, 123, 125, 128, 130, 133, 134, 135, 136, 146, 166 stress, 128, 136, 218 stretching, 10, 22 stroke, 120 strong interaction, 123, 202 strontium, 154 structural changes, 163 structural characteristics, 55 structural formation, 219 students, 60, 66, 69, 89 substances, vii, 57, 72, 193, 194 substitution, 170 substrates, vii, 3, 8, 10, 45, 128, 198, 201, 218, 222, 223, 224 sugar, x, 96, 102, 105, 109 sulfur, 175 sulfuric acid, 67

291

sulphur, 149 summaries, 14 summer, 114 Sun, 54, 226, 228 superconducting, x, xi, 144, 150, 160, 161, 162, 163, 164, 165, 166, 167, 170, 178, 179, 180, 181, 182, 183, 184 superconducting gap, 166 superconducting materials, 161, 163, 181, 182 superconductivity, x, xi, 143, 144, 161, 162, 164, 166, 167, 170, 176, 179, 180, 181, 182, 183, 184, 212 superconductor, x, 144, 162, 165, 166, 170, 182 superconductors, 179, 180, 184 supernatant, 36 superposition, 109 supply, 132, 135, 203, 221 supramolecular, 241 surface area, viii, 11, 43, 57, 97, 98, 117, 119, 199, 204, 206 surface energy, 198, 199, 202, 203, 218, 222 surface layer, 108, 115 surface modification, 51, 60, 89 surface properties, 93, 222 surface roughness, 97 surface structure, 97, 102, 110, 128, 200, 210, 216 surface tension, 218 surface treatment, 85, 93 surfactant, 10, 21, 24, 25, 51, 53, 222, 234 surfactants, 25, 46, 51 susceptibility, 162, 163, 164, 165, 179, 181 suspensions, 21, 36 s-wave, 166, 170 swelling, 115, 128 SWNTs, xi, 4, 5, 6, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 31, 33, 34, 36, 37, 38, 39, 40, 41, 42, 43, 233, 234, 235, 237, 239, 241, 242, 243 symbols, 101, 213, 253 symmetry, 159, 167, 173, 204, 218, 239 synergistic, 136 synergistic effect, 136 synthesis, x, xi, 7, 35, 53, 54, 110, 115, 143, 150, 152, 154, 155, 159, 163, 164, 165, 174, 180, 193, 194, 195, 198, 254 systems, x, 7, 25, 30, 50, 64, 96, 108, 113, 115, 161, 168, 173, 184, 199, 212, 213, 224, 241, 243

T technological revolution, vii technology, 44 Teflon, 46, 66, 163 Tel Aviv, 85 tellurium, 175 TEM, viii, 58, 80, 94, 182 temperature, 9, 10, 21, 35, 52, 54, 60, 63, 76, 78, 84, 85, 93, 97, 114, 115, 116, 118, 119, 120, 129, 130,

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292

Index

132, 133, 134, 135, 136, 137, 138, 147, 148, 150, 151, 160, 161, 162, 163, 164, 166, 167, 179, 180, 181, 182, 184, 195, 200, 201, 211, 212, 219, 220, 221, 222, 239 temperature dependence, 160, 166 temperature gradient, 150 Tennessee, 95, 110 tensile, 7, 115, 120, 133, 218 tensile strength, 7, 115, 120, 133 tensile stress, 218 tension, 218 terraces, 201, 202, 203, 204, 205, 206, 207, 209, 211, 214, 215 textbooks, 213 thallium, 149, 170, 172, 178, 179 theory, 98, 104, 105, 107, 109, 253, 272 Thermal Conductivity, 239, 240 thermal energy, 240 thermal equilibrium, 199 thermal evaporation, 212 thermal properties, 234 thermal resistance, 115, 127 thermal stability, 35, 115, 197 thermodynamic, xi, 197, 199, 205 thermodynamical stability, 145 thermodynamics, 198 thermoplastic, 45, 119, 124, 128, 129, 132 thermoplastics, 116, 123, 138 thermosetting, 93, 136 thin film, 16, 50, 64, 72, 92, 93, 125, 218, 219, 224 thin films, 218, 219 thinking, 66 three-dimensional, 50, 144, 180, 181, 182, 240 three-dimensional model, 180 threshold, 45, 211, 222 thymine, ix, 95, 96, 102, 106, 107, 109 TILs, 35 time, x, 19, 26, 34, 60, 66, 67, 69, 71, 72, 83, 85, 88, 97, 110, 114, 122, 136, 143, 147, 148, 152, 163, 181, 182, 194, 199, 207, 212, 238, 246, 253 time consuming, 110 tin, 180 tissue, 7, 8, 48 tissue engineering, 7 title, 7 titration, 47 Tokyo, 38, 53, 77, 83, 92 toluene, 98, 102, 234, 237, 240 topological, 12, 67, 274 topology, 246 torque, 114 Toshiba, 67, 83, 84 toughness, 115 toxicity, 44, 243 toxicology, 44 transducer, 20, 120 transfer, vii, viii, x, xi, 7, 8, 20, 21, 25, 26, 28, 30, 31, 34, 35, 39, 40, 41, 42, 43, 46, 47, 51, 52, 53, 54, 55, 57, 62, 114, 115, 116, 121, 122, 123, 125,

126, 127, 128, 129, 130, 133, 134, 135, 136, 138, 143, 145, 148, 149, 150, 151, 154, 159, 160, 169, 176, 184, 202, 218, 233, 234, 235, 237, 239, 240, 243 transformation, 19, 20, 80, 167, 203, 212 transformations, 19, 50, 221 transition, 44, 53, 116, 122, 123, 124, 125, 136, 138, 161, 162, 163, 164, 165, 166, 167, 170, 179, 180, 181, 182, 183, 184, 207, 212, 217, 220, 246, 253 transition metal, 44 transition temperature, 128, 161, 162, 163, 164, 167, 170, 179, 180, 181, 182, 183, 184 transitions, 114, 117, 121, 133, 182, 253 translational, 207, 234 transmission, 115 transparent, 36 transport, x, 7, 20, 48, 93, 143, 160, 165, 167, 198, 207, 209, 216, 240 travel, 239 trend, 106, 123, 125, 128, 135 trial, 71, 76, 81 tribological, x, 113, 115, 116, 117, 118, 122, 123, 127, 128, 129, 135, 136, 138 tribology, 113, 116, 140 trichloroacetic acid, 26 tungsten, 67, 89 tunneling, xi, 38, 197, 198 two-dimensional, 5, 177, 181, 182

U uncertainty, 98, 216, 219 uniform, 43, 71, 72, 97, 204, 209, 210, 222 urea, 241 uric acid, 13, 48

V vaccine, 7, 44 vacuum, viii, 9, 57, 63, 64, 72, 84, 85, 86, 87, 89, 90, 116, 117, 118, 126, 129, 150, 151, 200 valence, 4, 150, 158, 168 values, viii, ix, 22, 25, 26, 28, 41, 43, 58, 64, 69, 70, 72, 73, 74, 76, 95, 96, 97, 98, 99, 100, 102, 104, 106, 107, 108, 109, 110, 123, 125, 151, 162, 163, 165, 166, 167, 169, 170, 181, 202, 222, 237, 239, 240, 241 Van der Waals, 96, 107, 110, 134, 145, 146, 147, 148, 152, 168, 200, 240, 241, 242 Van der Waals bonds, 134 vapor, 4, 35, 198, 219 variable, 39, 116, 124, 125 variables, 248, 249, 254 variation, 60, 62, 97, 114, 117, 123, 166, 167, 183 vector, 5 vegetable oil, xi, 233, 234, 239 vehicles, 7, 44

Graphene and Graphite Materials, Nova Science Publishers, Incorporated, 2009. ProQuest Ebook Central,

Index velocity, 114, 120, 123, 124, 125, 129, 135, 136, 137, 138 vibration, 10, 89, 240 vibrational modes, 22 violent, 150 viscosity, xi, 193, 194, 195, 240 visible, 120, 204, 206 voids, 205 Volmer-Weber, 198, 205, 218 voltammetric, 11, 15, 17, 18, 19, 24, 25, 26, 28, 30, 31, 32, 33, 41, 42, 48, 49, 52, 53

W

welding, 71 wind, 145 winter, 114 wires, 9, 209, 214 workers, 76 working conditions, 115 workstation, 11

X XPS, 22, 36, 37, 132, 202 X-ray analysis, 167

Y yield, 98, 120 ytterbium, x, 143, 184

Z zinc, 54, 84, 92, 234

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warfare, 96 water, x, 9, 10, 24, 25, 26, 36, 54, 67, 96, 106, 107, 113, 114, 115, 116, 117, 127, 128, 129, 132, 134, 138, 174, 175, 234, 235, 236, 239 water absorption, 114 water vapour, 114, 116, 127, 129 weak coupling limit, 166 weakness, 110, 148 wear, x, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 128, 129, 130, 132, 133, 134, 135, 136, 137, 138

293

Graphene and Graphite Materials, Nova Science Publishers, Incorporated, 2009. ProQuest Ebook Central,