Chemistry and Physics of Carbon VOLUME 29
Chemistry and Physics of Carbon A Series of Advances Edited by
Ljubisa R. Radovic The Pennsylvania State University University Park, Pennsylvania, U.S.A.
VOLUME 29
Marcel Dekker
NewYork † Basel
Although great care has been taken to provide accurate and current information, neither the author(s) nor the publisher, nor anyone else associated with this publication, shall be liable for any loss, damage, or liability directly or indirectly caused or alleged to be caused by this book. The material contained herein is not intended to provide specific advice or recommendations for any specific situation. Trademark notice: Product or corporate names may be trademarks or registered trademarks and are used only for identification and explanation without intent to infringe. Library of Congress Cataloging-in-Publication Data A catalog record for this book is available from the Library of Congress. ISBN: 0-8247-4088-2 This book is printed on acid-free paper. Headquarters Marcel Dekker, 270 Madison Avenue, New York, NY 10016, U.S.A. tel: 212-696-9000; fax: 212-685-4540 Distribution and Customer Service Marcel Dekker, Cimarron Road, Monticello, New York 12701, U.S.A. tel: 800-228-1160; fax: 845-796-1772 World Wide Web http://www.dekker.com Copyright c 2004 by Marcel Dekker. All Rights Reserved. Neither this book nor any part may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, microfilming, and recording, or by any information storage and retrieval system, without permission in writing from the publisher. Current printing (last digit): 10 9
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Preface
This volume contains three chapters written by distinguished scientists from Europe, South America, and Asia. When it comes to the chemistry and physics of carbon, as reflected by the authorship in this series since its inception 40 years ago, globalization (a popular term among today’s politicians and economists) has always been the rule rather than the exception or a recent trend. If anything, The New York Times editorial of May 7, 2004 is indeed correct in its conclusion that “the United States . . . is losing ground to foreign competitors [as the pre-eminent scientific and technological power in the world].” I hope that this will be a “wake-up call” to the many excellent carbon scientists across the US to reverse this trend and restore the ‘balance’ in future volumes of our series. (See also our “call to arms” in the Preface to Vol. 28.) It gives me great satisfaction to include in this series another contribution from Dr. Slobodan Marinkovic, following his Vol. 19 chapter on substitutional elements in carbons. I have first-hand knowledge of his profound scholarship: it was he who set me on the carbon science career path when he hired me a quarter of a century ago; it was he who maintained the scientific productivity and enthusiasm of the carbon materials group at the Vinca Institute in Belgrade even when the country and many of its institutions were collapsing around them. This time he offers us a systematic, indeed didactic, and comprehensive summary of a topic that is not only fascinating and even spectacular from a fundamental point of view, but has made big-time news in all the popular media: low-pressure diamond synthesis. In addition to discussing the research efforts of his own group, he provides us with the long overdue complement to the authoritative discussion of high-pressure diamond synthesis in Vol. 10 of this series. And on top of that he attempts, and in my view succeeds, “to sum up in a compact fashion the huge amount of knowledge concerning all aspects of CVD diamond so as to make it possible, or easier, to see the forest rather than the trees.” iii
iv
Preface
As we celebrate the first contribution to this series from a South American author, we report with immense sense of loss the sudden and untimely death of Eduardo Bottani. I will cherish the memory of stimulating discussions with Eduardo—low-key, mild-mannered (especially for an Argentinian!), but an enthusiastic and meticulous scientist—over the structure and some of the details of the ambitious chapter on the energetics of physisorption on carbon surfaces. Dr. Juan Tasco´n, his coauthor from the start, a well-respected and multifaceted carbon scientist, took on the monumental task of completing this chapter singlehandedly and we are proud to be able to include it in the present volume as a lasting tribute to Eduardo’s memory. The chapter is not only ambitious; it is original in structure, it is comprehensive and it attempts to cover its subject matter—deservedly very popular in this series and elsewhere—in a complementary fashion. In particular, the emphasis on adsorption energetics is well placed, to alert the experimentalists that measuring only uptakes is often insufficient. And the emphasis on theoretical interpretations and computer simulations reflects well the state of the art and the current trends in this branch of carbon surface physics. Prof. Michio Inagaki has been a prolific contributor to this series (see Vols. 23 and 26). Here he and his colleagues from both Japan and China discuss another application of intercalation compounds (see Vols. 5 and 17), which are enjoying a true renaissance since the resurgence of interest in carbon materials for electrochemical and electrocatalytic applications. They combine the unique properties of intercalation compounds with those of exfoliated carbons—materials that heretofore had not received sufficient coverage in our series—to advocate the virtues of a novel application (sorption of heavy oils and biological fluids), but they also briefly summarize the state of the art in this increasingly popular field of carbon chemistry and physics. We thus compiled three authoritative reviews on old but new topics, on old but new carbon materials . . . Another demonstration that carbon is indeed the supreme cameleon and that its chemistry and physics offer endless opportunities for doing imaginative and innovative research and developing exciting new technologies! Ljubisa R. Radovic
[email protected] University Park, PA, May 2004
Contributors to Volume 29
Dr. Eduardo J. Bottani Instituto de Investigaciones Fisicoquı´micas Teo´ricas y Aplicadas (INIFTA), UNLP-CIC-CONICET, CC 16 Suc. 4, La Plata 1900, Argentina Dr. Michio Inagaki Faculty of Engineering, Aichi Institute of Technology, Yakusa, Toyota 470-0392, Japan Dr. Feiyu Kang Department of Materials Science and Engineering, Tsinghua University, Beijing 100084, China Dr. Slobodan N. Marinkovic´ Department of Material Sciences, Institute of Nuclear Sciences “Vinc˘a”, P.O. Box 522, Belgrade, CS-11001, Serbia and Montenegro Dr. Juan M.D. Tasco´n Oviedo 33080, Spain
Instituto Nacional del Carbo´n, CSIC, Apartado 73,
Dr. Masahiro Toyoda Department of Applied Chemistry, Faculty of Engineering, Oita University, Dannoharu, Oita 870-1192, Japan
v
Contents of Volume 29
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
iii
Contributors to Volume 29 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v Contents of Other Volumes
..................................
1. Exfoliation of Graphite via Intercalation Compounds 1.1. Introduction . . . . 1 1.1.1. Reversible and Irreversible Exfoliation . . . . 2 1.1.2. Terminology . . . . 4 1.1.3. Objective of the Present Chapter . . . . 4
1.2. Exfoliation of Graphite . . . . 5 1.2.1. 1.2.2. 1.2.3. 1.2.4. 1.2.5.
Processes and Controlling Factors . . . . 5 Effect of Exfoliation Conditions . . . . 7 Effect of Intercalates . . . . 10 Effect of Host Graphite . . . . 15 Characterization of Exfoliated Graphite . . . . 17
1.3. Exfoliation of Carbon Fibers . . . . 23 1.3.1. Exfoliation of VGCFs . . . . 24 1.3.2. Exfoliation of Mesophase-Pitch-Based and PAN-Based Carbon Fibers . . . . 26
1.4. Mechanism of Exfoliation . . . . 37 1.5. Formation into Flexible Graphite Sheets . . . . 43 1.5.1. Formation Process and Controlling Factors . . . . 44 1.5.2. Properties of Flexible Graphite Sheets . . . . 46
1.6. Applications of Exfoliated Graphite and Flexible Graphite Sheets . . . . 52 1.6.1. Sorption and Recovery of Spilled Heavy Oils . . . . 53 1.6.2. Other Applications of Exfoliated Graphite . . . . 57 vii
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Contents of Volume 29 1.6.3. Applications of Flexible Graphite Sheets . . . . 62 1.6.4. Applications of Exfoliative Graphite . . . . 63
1.7. Concluding Remarks . . . . 64 References . . . . 65 2. Diamond Synthesized at Low Pressure . . . . . . . . . . . . . . . . . . . . . . 71 2.1. Introduction . . . . 71 2.1.1. 2.1.2. 2.1.3. 2.1.4. 2.1.5. 2.1.6.
Scope of the Chapter . . . . 71 Phase Diagram of Carbon . . . . 74 Chemical Bonds and Structures of Diamond and Graphite . . . . 76 Natural and Synthetic Diamonds . . . . 78 Brief History of Research on CVD Diamond Synthesis . . . . 80 Overview of the Chapter . . . . 82
2.2. Processes in the Gas Phase . . . . 83 2.2.1. Growth from Hydrocarbon/H2 Gas Mixtures . . . . 84 2.2.2. Growth from C/H/O Gas Mixtures . . . . 90 2.2.3. Growth from other Gas Mixtures . . . . 93
2.3. Nucleation of Diamond . . . . 94 2.3.1. Homogeneous Nucleation . . . . 95 2.3.2. Surface Nucleation . . . . 95
2.4. Mechanism of Diamond Growth . . . . 116 2.4.1. Surface Boundary Layer . . . . 118 2.4.2. Model of Diamond Growth . . . . 123
2.5. Diamond Growth at Low Substrate Temperature . . . . 126 2.5.1. Attainment of Necessary Substrate Temperature and Its Measurement . . . . 127 2.5.2. Methods of Diamond Deposition at Low Temperatures . . . . 128 2.5.3. Nucleation and Growth of Diamond at Low Temperature . . . . 129 2.5.4. Diamond Film Properties . . . . 133 2.5.5. Deposition of Diamond on Polymer Substrates . . . . 134 2.5.6. Future Prospects . . . . 135
2.6. Epitaxial Diamond Growth . . . . 135 2.6.1. Homoepitaxial Diamond Growth from Active Vapor Phase . . . . 136 2.6.2. Heteroepitaxial Growth of Diamond . . . . 139
2.7. Oriented Growth and Morphology of Diamond Coatings . . . . 144 2.7.1. Stimulation of Oriented Growth by Substrate Orientation . . . . 144 2.7.2. Oriented Growth as a Consequence of Different Growth Rates of Differently Oriented Crystals . . . . 145 2.7.3. Defects and Morphology . . . . 150
2.8. Doping of Diamond . . . . 151 2.8.1. Introduction . . . . 151
Contents of Volume 29 2.8.2. 2.8.3. 2.8.4. 2.8.5. 2.8.6. 2.8.7.
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Basics of Diamond Doping . . . . 152 Doping by Boron . . . . 153 Doping by Phosphorus . . . . 157 Doping by Other Elements . . . . 158 Other Diamond-Doping-Related Studies . . . . 158 Conclusion . . . . 159
2.9. Methods of CVD of Diamond . . . . 160 2.9.1. 2.9.2. 2.9.3. 2.9.4. 2.9.5. 2.9.6.
Introduction . . . . 160 Hot-Filament (HF) CVD . . . . 161 Microwave (MW) Plasma . . . . 164 DC Arc Jet . . . . 168 Radio-Frequency (RF) Plasma . . . . 174 Oxygen– Acetylene Flame . . . . 178
2.10. Applications of CVD Diamond . . . . 188 2.10.1. 2.10.2. 2.10.3. 2.10.4. 2.10.5. 2.10.6. 2.10.7. 2.10.8. 2.10.9.
Introduction . . . . 188 Mechanical Applications . . . . 188 Thermal Management . . . . 190 Applications in Electronics . . . . 191 Optical Applications . . . . 194 Electrochemical Applications . . . . 195 Composite Reinforcement . . . . 197 Detectors for Radiation and Particles . . . . 198 Conclusion . . . . 199
2.11. Summary and Conclusions . . . . 200 References . . . . 203 3. Energetics of Physical Adsorption of Gases and Vapors on Carbons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209 3.1. Introduction . . . . 209 3.2. Thermodynamic Aspects of Gas Physisorption . . . . 214 3.2.1. Classical Thermodynamics . . . . 214 3.2.2. Statistical Mechanics . . . . 227 3.2.3. Thermodynamic Quantities and Experimental Results . . . . 237
3.3. Methods and Techniques of Analysis . . . . 243 3.3.1. Direct Methods . . . . 243 3.3.2. Indirect Methods . . . . 261 3.3.3. Theoretical Methods . . . . 293
3.4. Summary and Conclusions . . . . 393 References . . . . 397 Index
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425
Contents of Other Volumes
VOLUME 1 Dislocations and Stacking Faults in Graphite, S. Amelinckx, P. Delavignette, and M. Heerschap Gaseous Mass Transport within Graphite, G. F. Hewitt Microscopic Studies of Graphite Oxidation, J. M. Thomas Reactions of Carbon with Carbon Dioxide and Steam, Sabri Ergun and Morris Menster The Formation of Carbon from Gases, Howard B. Palmer and Charles F. Cullis Oxygen Chemisorption Effects on Graphite Thermoelectric Power, P. L. Walker, Jr., L. G. Austin, and J. J. Tietjen VOLUME 2 Electron Microscopy of Reactivity Changes near Lattice Defects in Graphite, G. R. Hennig Porous Structure and Adsorption Properties of Active Carbons, M. M. Dubinin Radiation Damage in Graphite, W. N. Reynolds Adsorption from Solution by Graphite Surfaces, A. C. Zettlemoyer and K. S. Narayan Electronic Transport in Pyrolytic Graphite and Boron Alloys of Pyrolytic Graphite, Claude A. Klein Activated Diffusion of Gases in Molecular-Sieve Materials, P. L. Walker, Jr., L. G. Austin, and S. P. Nandi VOLUME 3 Nonbasal Dislocations in Graphite, J. M. Thomas and C. Roscoe Optical Studies of Carbon, Sabri Ergun Action of Oxygen and Carbon Dioxide above 100 Millibars on “Pure” Carbon, F. M. Lang and P. Magnier xi
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Contents of Other Volumes
X-Ray Studies of Carbon, Sabri Ergun Carbon Transport Studies for Helium-Cooled High-Temperature Nuclear Reactors, M. R. Everett, D. V. Kinsey, and E. Ro¨mberg VOLUME 4 X-Ray Diffraction Studies on Carbon and Graphite, W. Ruland Vaporization of Carbon, Howard B. Palmer and Mordecai Shelef Growth of Graphite Crystals from Solution, S. B. Austerman Internal Friction Studies on Graphite, T. Tsuzuku and M. H. Saito The Formation of Some Graphitizing Carbons, J. D. Brooks and G. H. Taylor Catalysis of Carbon Gasification, P. L. Walker, Jr., M. Shelef, and R. A. Anderson VOLUME 5 Deposition, Structure, and Properties of Pyrolytic Carbon, J. C. Bokros The Thermal Conductivity of Graphite, B. T. Kelly The Study of Defects in Graphite by Transmission Electron Microscopy, P. A. Thrower Intercalation Isotherms on Natural and Pyrolytic Graphite, J. G. Hooley VOLUME 6 Physical Adsorption of Gases and Vapors on Graphitized Carbon Blacks, N. N. Avgul and A. V. Kiselev Graphitization of Soft Carbons, Jacques Maire and Jacques Me´ring Surface Complexes on Carbons, B. R. Puri Effects of Reactor Irradiation on the Dynamic Mechanical Behavior of Graphites and Carbons, R. E. Taylor and D. E. Kline VOLUME 7 The Kinetics and Mechanism of Graphitization, D. B. Fischbach The Kinetics of Graphitization, A. Pacault Electronic Properties of Doped Carbons, Andre´ Marchand Positive and Negative Magnetoresistances in Carbons, P. Delhaes The Chemistry of the Pyrolytic Conversion of Organic Compounds to Carbon, E. Fitzer. K Mueller, and W. Schaefer VOLUME 8 The Electronic Properties of Graphite, I. L. Spain Surface Properties of Carbon Fibers, D. W. McKee and V. J. Mimeault The Behavior of Fission Products Captured in Graphite by Nuclear Recoil, Seishi Yajima VOLUME 9 Carbon Fibers from Rayon Precursors, Roger Bacon
Contents of Other Volumes
xiii
Control of Structure of Carbon for Use in Bioengineering, J. C. Bokros, L. D. LaGrange, and F. J. Schoen Deposition of Pyrolytic Carbon in Porous Solids, W. V. Kotlensky VOLUME 10 The Thermal Properties of Graphite, B. T. Kelly and R. Taylor Lamellar Reactions in Graphitizable Carbons, M. C. Robert, M. Oberlin, and J. Me´ring Methods and Mechanisms of Synthetic Diamond Growth, F. P. Bundy, H. M. Strong, and R. H. Wentorf, Jr. VOLUME 11 Structure and Physical Properties of Carbon Fibers, W. N. Reynolds Highly Oriented Pyrolytic Graphite, A. W. Moore Deformation Mechanisms in Carbons, Gwyn M. Jenkins Evaporated Carbon Films, I. S. McLintock and J. C. Orr VOLUME 12 Interaction of Potassium and Sodium with Carbons, D. Berger, B. Carton, A. Me´trot, and A. He´rold Ortho-/Parahydrogen Conversion and Hydrogen-Deuterium Equilibration over Carbon Surfaces, Y. Ishikawa, L. G. Austin, D. E. Brown, and P. L. Walker, Jr. Thermoelectric and Thermomagnetic Effects in Graphite, T. Tsuzuku and K. Sugihara Grafting of Macromolecules onto Carbon Blacks, J. B. Donnet, E. Papirer, and A. Vidal VOLUME 13 The Optical Properties of Diamond, Gordon Davies Fracture in Polycrystalline Graphite, J. E. Brocklehurst VOLUME 14 Lattice Resolution of Carbons by Electron Microscopy, G. R. Millward, and D. A. Jefferson The Formation of Filamentous Carbon, R. T. K. Baker and P. S. Harris Mechanisms of Carbon Black Formation, J. Lahaye and G. Prado VOLUME 15 Pyrocarbon Coating of Nuclear Fuel Particles, J. Guilleray, R. L. R. Lefevre, and M. S. T. Price Acetylene Black: Manufacture, Properties, and Applications, Yvan Schwob The Formation of Graphitizable Carbons via Mesophase: Chemical and Kinetic Considerations, Harry Marsh and Philip L. Walker, Jr.
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Contents of Other Volumes
VOLUME 16 The Catalyzed Gasification Reactions of Carbon, D. W. McKee The Electronic Transport Properties of Graphite, Carbons, and Related Materials, Ian L. Spain VOLUME 17 Electron Spin Resonance and the Mechanism of Carbonization, I. C. Lewis and L. S. Singer Physical Properties of Noncrystalline Carbons, P. Delhae`s and F. Carmona The Effect of Substitutional Boron on Irradiation Damage in Graphite, J. E. Brocklehurst, B. T. Kelly, and K. E. Gilchrist Highly Oriented Pyrolytic Graphite and Its Intercalation Compounds, A. W. Moore VOLUME 18 Impurities in Natural Diamond, D. M. Bibby A Review of the Interfacial Phenomena in Graphite Fiber Composites, K. Wolf, R. E. Fornes, J. D. Memory, and R. D. Gilbert A Palladium-Catalyzed Conversion of Amorphous to Graphitic Carbon, W. L. Holstein, R. D. Moorhead, H. Poppa, and M. Boudart VOLUME 19 Substitutional Solid Solubility in Carbon and Graphite, S. Marinkovic´ Kinetics of Pyrolytic Carbon Formation, P. A. Tesner Etch-decoration Electron Microscopy Studies of the Gas-Carbon Reactions, Ralph T. Yang Optical Properties of Anisotropic Carbon, R. A. Forrest, H. Marsh, C. Cornford, and B. T. Kelly VOLUME 20 Structural Studies of PAN-Based Carbon Fibers, David J. Johnson The Electronic Structure of Graphite and Its Basic Origins, Marie-France Charlier and Alphonse Charlier Interactions of Carbons, Cokes, and Graphites with Potassium and Sodium, Harry Marsh, Neil Murdie, Ian A. S. Edwards, and Hanns-Peter Boehm VOLUME 21 Microporous Structure of Activated Carbons as Revealed by Adsorption Methods, Francisco Rodrı´guez-Reinoso and Angel Linares-Solano Infrared Spectroscopy in Surface Chemistry of Carbons, Jerzy Zawadzki VOLUME 22 High-Resolution TEM Studies of Carbonization and Graphitization, Agne`s Oberlin
Contents of Other Volumes
xv
Mechanisms and Physical Properties of Carbon Catalysts for Flue Gas Cleaning, Harald Ju¨ntgen and Helmut Ku¨hl Theory of Gas Adsorption on Structurally Heterogeneous Solids and Its Application for Characterizing Activated Carbons, Mieczyslaw Jaroniec and Jerzy Choma VOLUME 23 Characterization of Structure and Microtexture of Carbon Materials by Magnetoresistance Technique, Yoshihiro Hishiyama, Yutaka Kaburagi, and Michio Inagaki Electrochemical Carbonization of Fluoropolymers, Ladislav Kavan Oxidation Protection of Carbon Materials, Douglas W. McKee Nuclear Grade Activated Carbons and the Radioactive Iodide Problem, Victor R. Deitz VOLUME 24 Early Stages of Petroleum Pitch Carbonization—Kinetics and Mechanisms, R. A. Greinke Thermal Conductivity of Diamond, Donald T. Morelli Chemistry in the Production and Utilization of Needle Coke, Isao Mochida, Kenichi Fujimoto, and Takashi Oyama Interfacial Chemistry and Electrochemistry of Carbon Surfaces, Carlos A. Leon y Leon D. and Ljubisa R. Radovic VOLUME 25 Carbyne—A Linear Chainlike Carbon Allotrope, Yu P. Kudryavtsev, Sergey Evsyukov, Malvina Guseva, Vladimir Babaev, and Valery Khvostov Small-Angle Scattering of Neutrons and X-rays from Carbons and Graphites, Ernst Hoinkis Carbon Materials in Catalysis, Ljubisa R. Radovic and Francisco Rodrı´guez-Reinoso VOLUME 26 Colloidal and Supramolecular Aspects of Carbon, Agne`s Oberlin, Sylvie Bonnamy, and Paul G. Rouxhet Stress Graphitization, Michio Inagaki and Robert A. Meyer High Quality Graphite Films Produced from Aromatic Polyimides, Michio Inagaki, Tsutomu Takeichi, Yoshihiro Hishiyama, and Agne`s Oberlin VOLUME 27 Carbon Materials in Environmental Applications, Frank Derbyshire, Marit Jagtoyen, Rodney Andrews, Apparao Rao, Ignacio Martin-Gullo´n, and Eric A. Grulke
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Contents of Other Volumes
1
H NMR Spectroscopy of Adsorbed Molecules and Free Surface Energy of Carbon Adsorbents, V. V. Turov and Roman Leboda Electrochemical Studies of Phenomena at Active Carbon—Electrolyte Solution Interfaces, Stanisław Biniak, Andrzej S´wia¸tkowski, and Maciej Pakuła Carbon Materials as Adsorbents in Aqueous Solutions Ljubisa R. Radovic, Carlos Moreno-Castilla, and Jose´ Rivera-Utrilla VOLUME 28 Impact of the Discovery of Fullerenes on Carbon Science, Peter J. F. Harris Molecular Models of Porous Carbons, Teresa J. Bandosz, Mark J. Biggs, Keith E. Gubbins, Y. Hattori, T. Iiyama, Katsumi Kaneko, Jorge Pikunic, and Kendall T. Thomson Adsorption of Water Vapor on Activated Carbon: A Brief Overview, D. Mowla, D. D. Do, and Katsumi Kaneko Coal-Tar Pitch: Composition and Pyrolysis Behavior, Marcos Granda, Ricardo Santamarı´a, and Rosa Mene´ndez
1 Exfoliation of Graphite via Intercalation Compounds Michio Inagaki Faculty of Engineering, Aichi Institute of Technology, Yakusa, Toyota, Japan
Feiyu Kang Department of Materials Science and Engineering, Tsinghua University, Beijing, China
Masahiro Toyoda Department of Applied Chemistry, Faculty of Engineering, Oita University, Dannoharu, Oita, Japan
1.1.
INTRODUCTION
Exfoliation phenomena of graphite have been known since the graphite intercalation compounds were found. Exfoliated graphite consists of particles exfoliated preferentially along the normal to graphite basal plane of the original flakes. A representative micrograph is shown in Fig. 1.1(a). These particles have often been called worm-like. How to exfoliate the flakes of natural graphite was first described in a US patent in 1891[1] and preparation of graphite films from exfoliated graphite in 1916.[2] This unique material has been produced in industrial scale predominantly for the raw materials of flexible graphite sheets. Therefore, exfoliation phenomena were studied mostly in order to improve the properties and performances of flexible graphite sheets. In the industry, it has been produced from residue compounds, mostly with sulfuric acid, that are formed through the mild decomposition of graphite intercalation compounds (GICs). 1
2
Inagaki et al.
Figure 1.1 SEM micrographs of exfoliated graphite with different magnifications. (a) Large spaces among the worm-like particles, (b) crevice-like pores on the surface of particle, and (c) pores inside the particles.
1.1.1. Reversible and Irreversible Exfoliation Chung[3] presented a review on exfoliation of graphite, emphasizing its properties and applications. The process and mechanism of exfoliation of graphite were discussed by Furdin.[4] In Chung’s review, exfoliation phenomena were classified into reversible and irreversible ones. The reversible exfoliation phenomenon was studied in detail on the residue compounds with bromine, which were prepared from the intercalation compounds of either pyrolytic graphite[5] or graphite single crystal[6] by their decomposition and in which a small amount of bromine remained. When these residue compounds were heated to around 3008C, they expanded to a fractional expansion of about 30 and changed to intercalation compounds, and upon
Exfoliation of Graphite via Intercalation Compounds
3
cooling they collapsed and returned to residue compounds. This expansion – collapse phenomenon was reversible, and was thus called reversible exfoliation. It may be considered to be a kind of phase transition between intercalation and residue compounds. If the same residue compounds are heated to a higher temperature (e.g., 10008C), they decompose completely and at the same time the host graphite flakes exfoliate up to about 300 in volume, particularly by rapid heating. This exfoliated graphite never returns to the original thickness upon cooling to room temperature, that is, we have irreversible exfoliation. Such exfoliation is due to the decomposition of intercalates remaining in the residue compounds, possibly in their graphite galleries, and so this is not a phase transition. These two exfoliation phenomena are schematically illustrated as curves of fractional expansion vs. heating temperature in Fig. 1.2. The latter, irreversible exfoliation is what we shall discuss and review in the present chapter.
Figure 1.2 Exfoliation of the residue compounds of graphite with bromine. (a) Reversible exfoliation due to phase transition between residue and intercalation compounds and (b) irreversible exfoliation due to the decomposition of the residue compounds at a high temperature.
4
Inagaki et al.
The products of reversible exfoliation are intercalation compounds, not exfoliated graphite, even though the increase in thickness of graphite flakes is pronounced, much larger than thermal expansion of host graphite, and depends on the intercalates. This reversible exfoliation has to be differentiated from the formation of intercalation compounds due to the reaction between graphite host and intercalates; in the former the intercalates stay inside of the sample and there is no exchange with the surroundings; but in the latter the intercalates are incorporated into the host graphite from the surroundings (intercalation reaction). The increases in interlayer spacing between graphite basal planes and in overall thickness of the graphite flakes are almost the same in both cases (reversible exfoliation and intercalation reaction) because the fundamental process responsible for the increases in interlayer spacing and in flake thickness is the same. When the intercalation reaction is performed on relatively large graphite films, irreversible exfoliation is often observed. Upon intercalation of FeCl3 into graphite films prepared from polyimide films,[7] in a molten salt of FeCl3 –KCl system above 4008C, exfoliation was observed preferentially at the edge of the graphite films. This was concluded to be caused by a high intercalation rate in the molten salt.[8] This partial exfoliation due to excessively fast intercalation will not be discussed in the present chapter, even though it is irreversible. 1.1.2. Terminology The products of irreversible exfoliation have been called exfoliated graphite. It has sometimes been called expanded graphite, but the present authors prefer to use the word “exfoliation”. It should be differentiated from thermal expansion, even though all reversible and irreversible exfoliation phenomena, as well as thermal expansion, are thermally induced. The starting materials (precursors) for irreversible exfoliation, either residue or intercalation compounds, have often been called “expandable” graphite. However, if one accepts the authors’ preference for the term “exfoliated graphite”, not expanded graphite, the precursors for irreversible exfoliation have to be called “exfoliative” graphite. 1.1.3. Objective of the Present Chapter Recently novel applications of exfoliated graphite were proposed for sorption of heavy oils[9 – 12] and biological fluids,[12,13] for which large spaces among wormlike particles were reasonably supposed to be responsible. Exfoliated graphite has a large number of pores with a wide size range; they may be classified into three kinds—large pores among the entangled worm-like particles [Fig. 1.1(a)], small wedge-shaped (crevice-like) pores on the surface of worms [Fig. 1.1(b)], and small ellipsoidal pores within the worms [Fig. 1.1(c)]. The appropriate usage of this wide range of pores in exfoliated graphite is expected to lead to its further applications.
Exfoliation of Graphite via Intercalation Compounds
5
In the present chapter, therefore, irreversible exfoliation is revisited. We review the process and the controlling factors of the exfoliation of graphite, mostly natural graphite, and of carbon fibers. We describe the techniques for its characterization by exhibiting recent results; we discuss the exfoliation mechanism and explain the formation of exfoliated graphite into flexible graphite sheets because of their large markets in high-technology industries. We also summarize the applications of exfoliated graphite, flexible graphite sheets, and exfoliative graphite, with particular emphasis on novel applications. 1.2.
EXFOLIATION OF GRAPHITE
As the utilization of exfoliated graphite had been limited thus far to the production of flexible graphite sheets, each step in the preparation process of exfoliated graphite was controlled aiming to have good graphite sheets with high strength, flexibility, thermal insulation, and chemical purity. Owing to newly developed possibilities for its applications, which will be introduced later, the controlling factors for the preparation of exfoliated graphite need to be revisited, and new characterization techniques have to be applied. 1.2.1. Processes and Controlling Factors A general procedure employed in industry for producing exfoliated graphite is shown in Fig. 1.3. In most cases, natural graphite flakes are used as starting materials. They are converted easily to GICs at room temperature in concentrated sulfuric acid to which a small amount of nitric acid is added as an oxidant. The intercalation compounds thus obtained are usually washed with water to eliminate the excess acid. In this process GICs decompose to the so-called residue compounds, which do not exhibit regular stage structure in their X-ray diffraction (XRD) patterns and contain much lesser amount of sulfuric acid intercalates. When these residue compounds are exposed to a high temperature (e.g., 10008C), the compounds, which maintain the flaky morphology of the starting graphite, decompose suddenly and exfoliate along the normal to the flakes to change their morphology to worm-like, as shown in Fig. 1.1(a). The product thus obtained is called exfoliated graphite. In the industry, thus prepared exfoliated graphite is first compressed to a certain shape, mainly to sheets with different thickness, in which the original basal planes are preferentially oriented along the sheet surface. In most cases, the compressed graphite sheets experience rolling in order to further improve the preferred orientation of the graphite basal planes. The processes of production of graphite sheets from exfoliated graphite and their controlling factors will be discussed in Section 1.5.1. The purity and structural perfection of natural graphite flakes and their sizes must be selected carefully. For fundamental exfoliation studies, single crystals and highly oriented pyrolytic graphite (HOPG) can be used, but for
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Figure 1.3
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Production procedure for exfoliated graphite and flexible graphite sheets.
the industrial processes usually flaky natural graphite powders are selected. Intercalates are also selected to have a high degree of exfoliation with a simple procedure and low cost. In the industry, sulfuric acid with additional oxidants such as nitric acid has been used mostly, where the intercalation reaction proceeds at room temperature over a relatively short period. However, other intercalates (e.g., Br2 , FeCl3 , alkali metals –organic molecules complexes, and formic acid) and different intercalation processes (e.g., electrochemical, in organic solutions at room temperature, high-temperature heating) are also investigated, which will be briefly discussed in the following sections. The different aspects of the formation process of exfoliated graphite into sheets have also been studied (Section 1.5). The influences of intercalates on the exfoliation phenomena are also discussed in the following sections.
Exfoliation of Graphite via Intercalation Compounds
7
Although the preparation process has been studied from different points of view, as is explained, the techniques used for the characterization of exfoliated graphite were not numerous: mostly scanning electron microscopic (SEM) observation of its worms, specific surface area measurements with gas adsorption at low temperature, and powder XRD studies were performed. The last two techniques, however, are not powerful because of the very low content of micropores, that is, low specific surface area and slight differences in lattice parameters between the starting graphite and the resultant exfoliated graphite. The SEM observations showed the characteristic morphology of worm-like particles of exfoliated graphite, but they did not provide a quantitative characterization. 1.2.2. Effect of Exfoliation Conditions The influence of exfoliation conditions on the nature of the resultant exfoliated graphite is studied in detail in the industry, which routinely produces exfoliated graphite and flexible graphite sheets. However, it is very difficult to find relevant experimental data in the open literature. In Fig. 1.4, the exfoliation volume is plotted against exfoliation temperature[14] for residue compounds of natural graphite with sulfuric acid, of which the original intercalation compounds have been synthesized electrochemically with an electricity consumption of 33.3 A h/kg. Exfoliation was performed by inserting the residue compounds into a muffle furnace kept at different temperatures for 10 s. The apparent volume of the sample powders, which is often called “exfoliation volume”, increases rapidly with increasing temperature up to 8008C. The increase in exfoliation volume from 800 to 10008C appears to slow down.
Figure 1.4 Exfoliation volume vs. exfoliation temperature for the residue compounds obtained from intercalation compounds prepared by electrolysis in concentrated sulfuric acid with the electricity consumption of 33.3 A h/kg.[14]
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In Fig. 1.5(a), the bulk density of the resultant exfoliated graphite from two residue compounds, both of which have been synthesized by chemical oxidation of the original graphite flakes in concentrated sulfuric acid and are used in the industry, is plotted against exfoliation temperature.[15] The bulk density corresponds to the reciprocal of exfoliation volume and is plotted in logarithmic scale because of its large change with temperature. Both Figs. 1.4 and 1.5(a) reveal a marked effect of exfoliation temperature: the higher the temperature, the higher the exfoliation volume or the smaller the bulk density up to 8008C. Above 8008C, the exfoliation volume increases and the bulk density decreases gradually, in comparison with the change below 8008C. In Fig. 1.5(b), the mass loss during exfoliation at each temperature is plotted as a function of exfoliation temperature. The two residue compounds used show small differences in mass loss, which suggests that the content of residual sulfuric acid is different in these two compounds, although no appreciable difference is detected in the bulk density of the resultant exfoliated graphite [Fig. 1.5(a)].
Figure 1.5 Bulk density (a) and mass loss (b) vs. exfoliation temperature for the residue compounds synthesized by chemical oxidation in concentrated sulfuric acid.[22]
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Figure 1.6 Exfoliated volume at 10008C for 10 s against electricity consumption for the synthesis of original intercalation compounds.[14]
In Fig. 1.6 the exfoliation volume is plotted against electrical consumption for the synthesis of H2SO4-GICs by an electrochemical process.[14] With increasing electricity consumption, the exfoliation volume increases almost linearly. The electricity consumption is considered to be proportional to the amount of intercalates in the resultant intercalation compounds, but it is difficult to know how much intercalate remains in the residue compounds after water washing. However, the latter is reasonably supposed to be governed by the former. Therefore, mass loss during exfoliation was considered to be a measure of the amount of intercalates effective for exfoliation. Figure 1.7 shows that the mass loss
Figure 1.7 Mass loss during exfoliation at 10008C for 10 s against electricity consumption for the synthesis of original intercalation compounds.[14]
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depends strongly on the electricity consumption for the synthesis of original intercalation compounds (i.e., amount of intercalates). Figures 1.6 and 1.7 reveal clearly that a larger amount of intercalates in residue compounds, which was measured by mass loss, gives a larger exfoliation volume. The correlation of exfoliation volume or bulk density with mass loss observed between Figs. 1.5 –1.7 shows that mass loss is a practical measure of the degree of exfoliation, with the effective intercalates governing the exfoliation of a given residue compound. 1.2.3. Effect of Intercalates Graphite can accept many species into the gallery between graphite layer planes to form GICs. A number of species, not only atoms and ions but also various molecules, were reported to intercalate into the graphite gallery and give various functions to GICs.[16 – 18] For example, AsF5-GICs prepared from graphite with high crystallinity could provide high electrical conductivity, comparable with metallic copper.[19] Electrochemical intercalation and deintercalation processes of lithium are successfully used in lithium ion rechargeable batteries.[20] GICs can be classified according to the fact that intercalates either donate electrons to the host graphite or accept electrons from the host: donor-type intercalation compounds (e.g., K-GIC) and acceptor-type intercalation compounds (i.e., H2SO4and FeCl3-GICs). They are also differentiated according to the number of components constituting the GICs, including carbon (e.g., binary compounds like K-GIC and ternary compounds like K-THF-GIC). Most donors (for example, K) can be intercalated into carbons where the graphite structure is not developed, but most acceptors (for example, H2SO4) can intercalate only into a well-developed graphite gallery. Intercalation compounds of graphite and carbons are known to have a wide range of stage structure and also so-called residue compounds, in contrast to other intercalation compounds of layered compounds such as sulfides and clays.[16,21] In residue compounds, which are formed through the decomposition of intercalation compounds, staging is lost, but some amount of intercalates remains in the graphite gallery (i.e., in the interlayer spaces of graphite layers, without any regularity).[22] The variety of intercalates for GICs offers various possibilities to prepare exfoliated graphite. The type of GICs was reported to have a determining influence on the apparent morphology of the resultant exfoliated graphite.[23] Exfoliated graphite prepared from acceptor-type GICs (H2SO4- and FeCl3-GICs) consists of large balloons across the original graphite flakes, as shown in Fig. 1.8(a). Donor-type GICs (Na-THF-, K-THF-, and Co-THF-GICs) on the other hand gave exfoliated graphite of small balloons with tiny graphite layers, as shown in Fig. 1.8(b). Sulfuric acid is the most conventional intercalate for achieving a high degree of exfoliation of natural graphite and so it is used most commonly in the industry. Related compounds, such as nitric acid,[4] sulfur trioxide (SO3),[24]
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Figure 1.8 SEM micrographs of worm-like particles prepared from (a) acceptor-type GIC, (H2SO4-GIC) and (b) donor-type GIC (Na-THF-GIC).[23]
and perchloric acid (HClO4)[25] have also been used for exfoliation of graphite. In addition, different metal chlorides and ternary compounds containing organic molecules, such as tetrahydrofuran (THF), with alkali metals, were explored in various research reports, as discussed subsequently. For most of these intercalates, rapid heating to a high temperature is essential for obtaining sufficient exfoliation of the host graphite. In the case of HClO4-GICs, exfoliation occurs at around 2008C, and appears to be accelerated by the exothermic decomposition of intercalates.[25] Exfoliation at room temperature was also tried using several reactions: water vapor with alkali metals,[26] hydrogen peroxide with chromium trioxide,[27] and hydrazine with molybdenum chloride.[28] FeCl3-GICs have been used in exfoliated graphite production.[29] FeCl3 decomposes into Cl2 gas and to the less volatile FeCl2 . Through exfoliation, graphite mounted by fine metal particles, particularly those of transition metals, was thought to be prepared from GICs with transition metal halides. This might open a new field in catalyst preparation. Various trials had been performed.[28,30 – 32] Starting from ternary CoCl2-THF-GICs, exfoliated graphite
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with finely dispersed particles of cobalt metal has been obtained and by its compression magnetic graphite disks can be prepared.[33] Even though several experimental trials have been performed, a practical application of these materials has not yet been realized, mainly because of heterogeneity in particle size of metals and their poor dispersion. Ternary intercalation compounds with MoCl5 and chloroform (CHCl3) also showed marked exfoliation at 10008C.[34] Two types of ternary intercalation compounds with FeCl3 and CHCl3 , types I and II, were synthesized and their exfoliation behavior was compared with that of binary compound FeCl3-GIC.[35] Both ternary compounds exfoliated even by rapid heating to 2508C. At 4008C, the so-called type II ternary showed more exfoliation than the type I ternary, and at 8008C both ternaries gave worm-like particles similar to those obtained at 10008C. In contrast, the binary compounds showed exfoliation only at 8008C, but the degree of exfoliation was much lesser than that of the ternary compounds at 2508C. These experimental results reveal that the intercalates which decompose into a large amount of gaseous species in the starting GICs are advantageous for achieving exfoliation at a lower temperature and to a higher degree, and also that the structure of ternary compounds may have an influence on the exfoliation behavior, even though the structural difference in the two types of FeCl3-CHCl3-GICs mentioned here has not been clearly understood.[35] A new GIC, n-octylammonium tetrachloroferrate(III)-GIC, was synthesized by the reaction between FeCl3-GIC and n-octylammonium chloride at 1258C and was reported to exfoliate at 4008C.[36] Exfoliation seemed to proceed slowly, but no detailed data was reported, except that the specific surface area increased from 10 m2/g in the pristine graphite to 70 m2/g after exfoliation. The reaction of metal chlorides in the graphite gallery with hydrazine gave large amounts of gaseous species at room temperature and resulted in exfoliation of the host graphite.[28] MoCl5-GICs reacted with monohydrated hydrazine at room temperature to exfoliate, but FeCl3-GICs reacted only with anhydrous hydrazine. Even at room temperature, exfoliation of flakes to worm-like particles was observed, the thickness of the flakes of original graphite increasing about 200. In Fig. 1.9, changes in the XRD pattern with annealing temperature are shown for the exfoliated graphite prepared from the reaction between MoCl5GIC and monohydrated hydrazine at room temperature.[37] Just after exfoliation at room temperature, most of the reaction products between intercalates MoCl5 and hydrazine are amorphous, though there are XRD peaks that cannot be identified. These amorphous phases crystallized to NH4Cl by annealing at 2008C and to MoO3 or MoO2 above 6008C. The exfoliation was also performed under a microgravity environment at room temperature by using MoCl5-GIC and anhydrous hydrazine, but no marked difference in the products was obtained.[38] When high-stage H2SO4-GICs was electrochemically oxidized in the perfluorooctanesulfonate (C8F17SO3)-containing electrolyte, marked exfoliation at room temperature was reported.[32]
Exfoliation of Graphite via Intercalation Compounds
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Figure 1.9 XRD patterns for the exfoliated graphite prepared by the reaction between MoCl5-GIC and monohydrated hydrazine at room temperature and then annealed at different temperatures.[37]
Organic intercalates may be preferable for obtaining a high degree of exfoliation, because they may give a large amount of gaseous decomposition products. However, intercalation compounds with only organic molecules have never been synthesized, other species such as alkali metals and metal halides being required to be intercalated with organic molecules. It is well known that various ether molecules can be intercalated into the graphite gallery by solvation with alkali metal cations.[30,40 – 42] These ternary intercalation compounds showed marked exfoliation at 10008C.[23,40,43] The degree of exfoliation was roughly evaluated by observing the size of exfoliated flakes (worms) under SEM for K- and Na-THF-GICs and their residue compounds. In Fig. 1.10, the degree of exfoliation in these four samples is plotted against exfoliation temperature, where the sample was kept for 1 min.[40] Above 8008C, both K- and Na-THF-GICs exfoliated more than 300 the thickness of the flake, but the former exfoliated at lower temperature than the latter, which was attributed to the stability of the latter in air. For the residue compounds prepared from K-THF-GICs by being left in air for 24 h, less exfoliation, about 200, was observed even at 9008C. On the other hand, Na-THF residues showed a high degree of exfoliation, comparable to that of GICs, which is also due to the stability of Na-THF-GICs in air. By using one of the ethers, THF, with sodium, vapor-grown carbon fibers (VGCFs) heat-treated at high temperatures could be exfoliated to form small sheets where graphite layers were almost perpendicular to the sheet surface,[44] details of which will be shown in Section 1.3.1. There was industrial demand to prepare flexible graphite sheets without sulfur, for which exfoliated graphite had to be prepared without using sulfurcontaining intercalates. Using residue compounds with sulfuric acid, a minute
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Figure 1.10 Changes in the degree of exfoliation with temperature for alkali metal–THF compounds.[40]
amount of sulfur remained in the resultant exfoliated graphite,[45] which gave some trouble in some special applications (e.g., sulfur eroding metals during prolonged use as a seal). This can be critical, particularly for applications in nuclear power plants, electronics, aerospace and automobile industries, and also an important issue for determining the selling price of flexible graphite sheets:[46] commercially available sheets contain sulfur at the level of 450 – 700 ppm.[47,48] Instead of H2SO4 , nitric acid was recommended.[4] Some efforts were also made to reduce the sulfuric acid content in the residue compounds by co-intercalation of either acetic acid[49] or H2O2 ,[50] but the sulfur content could not be reduced to zero in the exfoliated graphite. A few processes for the preparation of exfoliated graphite without using sulfur were proposed, two of which seemed to be promising: the ternary Na-THF-GICs[40] mentioned earlier and HCOOH-GICs.[51] The former has many advantages. It is synthesized at room temperature, has a comparable exfoliation degree to conventional ones, and gives less harmful outgassing during the exfoliation process. However, the cost of intercalates, particularly sodium metal, could not compete with sulfuric acid. The intercalation of formic acid into graphite was successfully performed through an electrochemical process and a single phase of HCOOH-GICs with stage 3 – 5 structure was obtained.[51] These GICs exfoliate at relatively low temperature (e.g., 4008C), but the degree of exfoliation depends strongly on
Exfoliation of Graphite via Intercalation Compounds
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electrochemical process conditions. In Fig. 1.11 exfoliation volume at 10008C is shown as a function of anodic current density. In order to achieve high exfoliation volume, electrochemical synthesis of intercalation compounds under low current density was recommended, probably because of homogeneous distribution of the intercalates in the graphite gallery. For HCOOH-GICs, the strongest barrier for industrial application seems to be that the electrochemical process is essential for their synthesis. 1.2.4. Effect of Host Graphite The influence of host graphite was studied upon exfoliation in concentrated sulfuric acid with hydrogen peroxide at room temperature.[52] The bulk density of the resultant exfoliated graphite was studied as a function of concentration of hydrogen peroxide for two natural graphite samples, one from Brazil, with particle size less than 50 mm, and the other from Madagascar, with larger particles, of 0.5– 1 mm. The former required a high concentration of oxidant H2O2 , though it has a much smaller particle size: in order to get a bulk density of less than 100 kg/m3 for the resultant exfoliated graphite, more than 40 vol% oxidant was needed for the former, but only a small vol% for the latter. However, the final bulk density attainable in a liquid medium was almost the same for the two natural graphite flakes of different origins. It is interesting that the exfoliated graphite prepared from the Madagascar graphite in liquid medium could re-exfoliate in the flame of a torch, its bulk density being reduced to about 20 kg/m3, though the detailed mechanism is not known. As this exfoliation process proceeded slowly in comparison with the abrupt heating to high temperature, about 1 h was needed to complete exfoliation, as shown in Fig. 1.12.
Figure 1.11 Exfoliation volume as a function of current density during 10 h electrolysis for the synthesis of HCOOH-GICs.[51]
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Figure 1.12 Change in bulk density of exfoliated graphite prepared from Madagascar graphite in H2SO4 with H2O2 at room temperature. (Adapted from Herold et al.)[52]
Figure 1.13
SEM images of exfoliated coke particle at different magnifications.[53]
Exfoliation of Graphite via Intercalation Compounds
17
Exfoliation of cokes was tried through the intercalation of K-THF complexes into pitch coke heat-treated at 28008C.[43] Exfoliation was observed above 8008C, but the thickness of the coke particles increased only about 20 after exfoliation at 8008C, much less than when using natural graphite. By chemical oxidation, intercalation of sulfuric acid into cokes did not occur, even for cokes heat-treated at high temperatures, and so no exfoliation was observed. When HClO4 was used, exfoliation was observed around 2008C and the exfoliation degree, measured by changes in specific surface area, was reported to be comparable to conventional exfoliated graphite prepared from natural graphite flakes.[25] Recently, electrochemical treatment in nitric acid of coke particles preheated at 30008C was found to result in a certain degree of exfoliation through rapid heating to 10008C.[53] The exfoliated coke particle is shown in Fig. 1.13. Pores with rather homogeneous size of 30 10 mm are observed. Carbon fibers are known to have a wide range of structure and texture.[54,55] As their behavior in intercalation, and therefore in exfoliation, is different from that of natural graphite, the exfoliation of various carbon fibers will be discussed separately (see Section 1.3). 1.2.5. Characterization of Exfoliated Graphite Techniques for the characterization of exfoliated graphite had been limited mainly because of its fragile and macroporous nature. Parameters that had been applied to most carbon materials, such as lattice constants and crystallite sizes determined by XRD and specific surface area by nitrogen adsorption at 77 K, provided only limited information. These parameters change only slightly with exfoliation. Thus, for example, the interlayer spacing, which is one of the important parameters for the graphitization process, hardly increases, and the XRD lines are broadened somewhat (i.e., the crystallite size decreases to some extent).[37] The specific surface area increases from a few m2/g to about 20 – 70 m2/g, not sufficient to be used as a measure of exfoliation degree, though some research groups have done so.[4,52] The increase in specific surface area after exfoliation of graphite is attributed not only to the increased accessibility of the layered structure but also to oxidation upon exfoliation, the latter appearing to be the more important effect. SEM micrographs have revealed a characteristic worm-like morphology of its particles, as shown in Fig. 1.1(a) –(c), but this information cannot be made quantitative. The exfoliation volume is a very important parameter for control of the exfoliation process, as discussed earlier, and also for the preparation of flexible graphite sheets, as will be discussed in Section 1.5. Instead of the exfoliation volume, which can be determined upon the preparation, the bulk (apparent) density of the resultant exfoliated graphite has also been measured, which is quite informative for its users. For different novel applications of exfoliated graphite (see Section 1.6), however, novel parameters have been required for characterizing its pore
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structure; some proposals and trials to develop the necessary techniques are presented here. Analysis of pore structure inside the worm-like particles was carried out after developing the procedure for fracturing the cross-section of the worms and with the aid of image processing.[56] The cross-sections of the worm-like particle, as shown in Fig. 1.1(c), were prepared by the procedure illustrated in Fig. 1.14: a small amount of the sample is mounted on a substrate using scotch tape, paying attention not to overlap the worm-like particles with each other; the holder for SEM observation with a conductive carbon tape was placed on top of the sample, the degradation of particles being avoided by using a spacer about 0.15 mm thick; then the SEM holder was pulled out slowly from the
Figure 1.14 particle.[56]
Procedure for the preparation of fractured cross-section of worm-like
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19
substrate. On the SEM holder, some of the exfoliated particles lay down along the surface of the holder, showing fractured cross-sections as in Fig. 1.1(c). SEM micrographs taken with an electron beam acceleration voltage of 10– 15 kV and magnification of 200 were used for further image processing. After recording the SEM image in computer memory using an image scanner with a resolution of 600 dpi, the images were digitized by selecting well-defined parts of the fractured cross-sections as an array of pixels, one pixel corresponding to 0.41 mm 0.41 mm or 0.168 mm2. The digitized SEM image thus stored was converted to a binary image by selecting a threshold value on each image. As the pores are approximately ellipsoidal, the lengths of major and minor axes, which were perpendicular to each other, were determined for the cross-sections observed by SEM, so were the area of pores and the aspect ratio (length ratio of minor to major axis) by using the image analysis software. The distribution curves of the parameters, which are measured on two commercially available exfoliated graphite samples EG-1 and EG-S, are shown in Fig. 1.15. In Fig. 1.15(a) the histograms of cross-sectional area of pores in the range of 2– 2000 mm2 are shown on two samples prepared in the industry, together with an enlargement of the part with small pore areas. The two samples show quite different distribution of pore area: EG-1 has a broad distribution over the whole range selected, whereas EG-S has a sharp distribution, around 10 mm2. In Fig. 1.15(b) and (c), the distribution of the two axis lengths, the major and minor axes, respectively, is shown for the same samples. A distinct difference is also seen in the distribution of the two axes: EG-1 has a much broader distribution in both the major and minor axes, whereas EG-S has a rather sharp distribution, whose maxima are around 8 mm in the major axis and 5 mm in the minor axis. As far as the aspect ratio shown in Fig. 1.15(d) is concerned, no difference was detected between the two samples. The average values of pore area, the two axis lengths and the aspect ratio determined on four samples, the two industrial samples mentioned earlier and two laboratory-prepared samples, are listed in Table 1.1. The two commercial samples are at opposite extremes, with large pores being dominant in EG-1 and small pores in EG-S. The average pore area for EG-S is less than half of that for EG-1, and both axes are smaller in EG-S than in EG-1, as expected from the fact that the average aspect ratio is the same in these samples. The two laboratory samples are intermediate between the two industrial samples. Increasing heating time from 20 to 60 s (EG-20 and EG-60, respectively) appears to increase the pore size after exfoliation, but the difference is not pronounced. A comparison of the laboratory samples with one of the industrial samples, EG-1, suggests that the latter has experienced much more severe exfoliation conditions, because it has a much broader distribution of not only the pore area but also the major and minor axes and higher frequency in large pore sizes. The bulk density after exfoliation had been considered as a convenient measure of exfoliation degree. However, the present results show that the exfoliation
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Figure 1.15 (a) Distribution of cross-sectional area, (b) and (c) the lengths of major and minor axes, respectively, and (d) aspect ratio for two exfoliated graphite samples EG-1 and EG-S.[56]
degree evaluated from the bulk density is not necessarily related to the pore structure in worm-like particles of the resultant exfoliated graphite; thus EG-1 has much larger pores than EG-20 and EG-60, but the bulk density of the former is only slightly higher than that of the latter two.
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Table 1.1
Preparation Conditions and Average Values of Pore Structure Parameters Determined for Four Exfoliated Graphite Samples Sample
Preparation condition
Number of SEM micrographs Number of pores used Average pore area (mm2) Average pore size (mm) (major minor axis) Average aspect ratio
EG-1
EG-S
EG-20
EG-60
Commercial
Commercial
10 2286 422 32 16
10 3511 191 21 10
Heated at 10008C for 20 s 10 1451 288 28 12
Heated at 10008C for 60 s 10 2306 308 27 13
0.53
0.54
0.51
0.54
Kang et al.[14] performed principally the same analysis on the crosssections of worms prepared by mechanical cutting of the worms mounted in a resin. Although a resin with less shrinkage during its hardening was used, there was a possibility for some deformation of the worms, as well as the possibility to deform by mechanical cleavage during the procedure summarized in Fig. 1.14. As can be seen in the SEM micrographs [Fig. 1.1(b)], a zigzag crevice-like structure on the surface of the worm-like particles, often described as analogous to the bellows of an accordion, is also characteristic of the morphology of the exfoliated graphite. An attempt was made to evaluate these bellows quantitatively by measuring the distance between neighboring bellow tips l,[14] as schematically shown in Fig. 1.16(a). In Fig. 1.16(b) and (c) the average distance l between neighboring bellow tips is plotted against electricity consumption for the electrochemical synthesis of H2SO4-GICs and also against exfoliation temperature for the residue compounds prepared electrochemically using the electricity consumption of 33.3 A h/kg. With increasing electricity consumption (i.e., increasing amount of intercalates in GICs) and exfoliation temperature the distance between neighboring bellow tips decreases; in other words, the thickness of balloons in worm-like particles becomes smaller. For a more detailed discussion of morphology changes of worms in relation to their preparation conditions, the amount of intercalates, exfoliation temperature, and host graphite type, a larger data set and a statistical treatment are required. The presence of macropores among the entangled worm-like particles was pointed out to be important for large sorption capacity for various oily materials and some organic liquids.[12,13,57 – 60] This is discussed in detail in Section 1.6.1. For such macroporous materials, mercury porosimetry is known to be useful.[61] However, it was shown that mercury porosimetry of fragile exfoliated graphite has to be done with much care, most of the macropores in the exfoliated graphite
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Figure 1.16 Characterization of the morphology of worm-like particles of exfoliated graphite.[14] (a) Scheme of worm-like particle, (b) effect of electricity consumption and (c) effect of exfoliation temperature on average distance between neighboring bellow tips l.
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Figure 1.17 Pore size distribution curves of the exfoliated graphite EG-1 measured using two dilatometers, N- and U-types, in a mercury porosimeter.[62]
being compressed before pressurization. Therefore, some modification using a new dilatometer was proposed.[62] In Fig. 1.17 two pore size distribution curves are shown for the exfoliated graphite with a bulk density of 7 kg/m3, which were measured using two different dilatometers shown schematically in the figure. Using an N-type dilatometer, which is usually supplied with the commercial instrument, it is possible to measure only pore sizes up to about 60 mm, because the sample of exfoliated graphite has been compressed by the weight of mercury before pressurization. Using a U-type dilatometer, where the sample of exfoliated graphite was placed on top of the mercury and so is not compressed in advance, very large pores, up to 600 mm, can be measured. The large pores observed by using a U-type dilatometer seem to correspond to the spaces formed by the entangled worm-like particles in the exfoliated graphite, an example being shown in Fig. 1.1(a). 1.3.
EXFOLIATION OF CARBON FIBERS
In most carbon fibers development of the graphitic structure is known to be depressed, depending strongly on the texture of carbon fibers.[54,55] In VGCFs having annual ring texture in their cross-section, graphitic structure develops markedly.[55,63] On the other hand, isotropic-pitch-based and some PAN-based carbon fibers can reach only very low graphitization degree even after heat treatment above 30008C.[64] The behavior of mesophase-pitch-based carbon fibers is intermediate between these two, depending strongly on the texture in their crosssection. Such a relationship between the graphitizability of carbon fibers and their
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structure and texture was clearly shown through the measurements of magnetoresistance.[64] Depending on the graphitization degree, the intercalation reaction proceeds easily in VGCFs, particularly those heat-treated at high temperatures, but it is not possible in isotropic-pitch-based carbon fibers. As a consequence, exfoliation occurs in the former but not at all in the latter. The literature on exfoliation of carbon fibers is still very limited. However, exfoliation phenomena were found to be influenced strongly by the texture in pristine carbon fibers. Here we discuss the exfoliation of carbon fibers separately from that of graphite flakes, because their exfoliation behavior is governed by their texture and is quite different from that of natural graphite flakes. 1.3.1. Exfoliation of VGCFs The first reports on the exfoliation of VGCFs used SbCl5 as the intercalate.[65] Later, this exfoliation process was studied in detail using ternary intercalation compounds with K and THF.[44] In Fig. 1.18 SEM micrographs are shown for samples heated at different temperatures, which reveal morphological changes from the original fiber to its complete exfoliation. From such morphological observation, the exfoliation process of VGCFs was concluded, as shown schematically in Fig. 1.19. The ternary K-THF-GICs were synthesized by immersing the stage-1 binary K-GICs of VGCFs into THF. VGCFs were used after graphitization at 30008C; they have the characteristic “rings of a tree”, that is, coaxial orientation scheme in a very high degree; and upon graphitization at 30008C their crosssection shows polygonization, consisting of polygonal domains whose c-axis orients in the radial direction of the fiber axis [Fig. 1.18(a)]. After intercalation of K-THF a crevice along the fiber axis, which seemed to pass through the ridge-like texture formed by heat treatment, was observed in most of the fibers [Fig. 1.18(b)]. The crevice thus formed divided the fiber into two parts along the fiber axis and the polygonized cross-section became round by swelling due to intercalation. Rapid heating to 250–10008C for 1–1.5 min resulted in exfoliation to different degrees, as shown in the series of SEM micrographs in Fig. 1.18(c)– (h); in all cases exfoliation occurred predominantly in the direction perpendicular to the graphite basal planes. After heating to 2508C, the polygonized feature of the fiber and the domain structure are still recognized and the exfoliation degree is about 3 to 4, in the direction perpendicular to the fiber axis, with minute pores developing in the cross-section of the fiber [Fig. 1.18(c) and (d)]. Heating to 3608C promotes exfoliation of the fiber predominantly along the radial direction so that it looks like a thin ribbon, which is a semicircle or a half fragment of the original fiber [Fig. 1.18(b)], although the degree of exfoliation is only about 10 [Fig. 1.18(e) and (f)]. Some of the ribbons thus formed have a round portion at one end [Fig. 18(e)], which is assumed to be the core of the VGCF. At 10008C, exfoliation is promoted greatly, mainly perpendicular to the
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25
Figure 1.18 SEM micrographs of the intercalation compounds of VGCFs with K-THF complexes heated in different temperatures.[23] (a) Pristine fiber, (b) after intercalation of K-THF, (c) after heating to 2508C, (d) after heating to 3208C, (e) and (f) after heating to 3608C, and (g) and (h) after heating to 10008C.
axis, and seems to be complete. As a consequence, thin ribbons with a size of approximately 20 mm in thickness and 100 –200 mm in width are formed, in which graphite layers are preferentially perpendicular to the surface of the ribbon and somewhat twisted [Fig. 1.18(g) and (h)].
26
Figure 1.19
Inagaki et al.
Scheme for the exfoliation of graphitized VGCFs.[23]
The formation of the intercalation compounds by electrochemical processing of VGCFs in nitric acid and their exfoliation were carried out.[66] The formation of intercalation compounds was confirmed by XRD. The exfoliation by rapid heating to 10008C was observed clearly, as shown in Fig. 1.20. The exfoliation of VGCFs using nitric acid was confirmed to be the same as that of the fibers using ternary intercalation compounds with K and THF.[44] 1.3.2. Exfoliation of Mesophase-Pitch-Based and PAN-Based Carbon Fibers Exfoliation of pitch-based carbon fibers heat-treated at a high temperature was first reported by Anderson and Chung.[6] From their SEM micrographs, however, marked exfoliation as observed in natural graphite flakes and VGCFs is not recognized. Marked exfoliation has been reported only very recently.[66 – 70] Intercalation was carried out by electrolysis. Carbon fibers fixed to platinum were used as the anode, immersed into concentrated nitric acid electrolyte (13 mol/dm3), then a constant current was applied using a potentiostat. The counter-electrode was platinum. Carbon fibers 5 cm in length were immersed into nitric acid from their free end. After electrolysis until an optimal electric charge was reached, the fibers were taken out from the electrolyte solution, rinsed with water, and dried at room temperature in air. The carbon fibers thus electrolyzed were inserted quickly into a furnace, whose temperature was kept
Exfoliation of Graphite via Intercalation Compounds
27
Figure 1.20 SEM micrographs of VGCFs exfoliated at 10008C.[66] (a) Original fiber, (b) cross section, and (c) lateral side of the fiber after exfoliation.
at 10008C, to exfoliate. After 5 s, the sample was rapidly removed from the furnace. Representative SEM images of exfoliated carbon fibers are shown in Fig. 1.21. The morphology of mesophase-pitch-based carbon fibers after exfoliation is clearly different from that of VGCFs (Fig. 1.18). Figure 1.22 shows the potential change vs. electric charge supplied on mesophase-pitch-based carbon fibers heat-treated at 30008C. In Fig. 1.23 XRD patterns are shown for the original carbon fibers and for those electrolyzed up to 1200 C. The potential of fibers heat-treated at 30008C increased markedly to a shallow plateau around 2.0 V during electrolysis (Fig. 1.22). The electrolyzed fibers show an additional broad peak near 118 and a very faint one around 228 2u, which are not seen in the original fibers (Fig. 1.23). The interlayer spacings measured from these additional peaks were about 0.78 and 0.39 nm, respectively, the former corresponding to the identity period for stage-2 intercalation compound with nitric acid and the latter to its second order diffraction peak. However, the two observed peaks were very broad and the peaks corresponding to higher order indices were difficult to detect. Therefore, the products are assumed to be residue compounds or intercalation compounds with highly disordered stacking sequences.
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Figure 1.21 SEM micrographs of a single mesophase-pitch-based carbon fiber after exfoliation.[66]
These intercalated carbon fibers prepared by applying an electrical charge of 1200 C were exfoliated by rapid heating to 10008C. In Fig. 1.24 the morphological changes in the fibers are demonstrated by showing SEM images of a single original fiber, one after intercalation of nitric acid by electrolysis and after rapid heating to 10008C. The original mesophase-pitch-based carbon fibers have zigzag radial texture in cross-section [Fig. 1.24(a)]. After electrolysis up to potential saturation (i.e., until completion of intercalation) a large crack is formed along the fiber axis and a number of fissures extended along the fiber axis are observed, the apparent diameter of the fiber increasing almost twice, from 5 to 10 mm [Fig. 1.24(b)]. The crack and fissures are assumed to be due to the increase in interlayer spacing from 0.34 nm for the original to 0.78 nm for the intercalation compounds of nitric acid. After rapid heating, a marked morphological change was observed,
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29
Figure 1.22 Change in the potential for mesophase-pitch-based carbon fibers heattreated at 30008C through electrolysis at 0.5 A.[66]
Figure 1.23 XRD patterns of the original 30008C-treated mesophase-pitch-based carbon fibers and after electrolysis in nitric acid.[66]
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Figure 1.24 Morphology changes of mesophase-pitch-based carbon fibers heat-treated at 30008C.[66] (a) Original single fiber, (b) after intercalation of nitric acid by electrolysis, (c) appearance, (d) cross-section, and (e) lateral view of filaments after rapid heating at 10008C.
a single fiber being converted to a bundle of thin filaments split along the original fiber axis [Fig. 1.24(c)]. The apparent diameter of the exfoliated fiber became more than 10 the original, about 50– 60 mm. It has to be pointed out that the cross-sectional view of the fiber after exfoliation [Fig. 1.24(d)] is quite similar to the fractured view of worm-like particles of exfoliated graphite (Fig. 1.1),
Exfoliation of Graphite via Intercalation Compounds
31
suggesting that exfoliation occurs at interlayer spaces of crystallites composed of fibers. From these results, this phenomenon is suggested to be an exfoliation by decomposition of intercalates between the hexagonal carbon layers of crystallites. In some fibers, breaking of thin filaments perpendicular to the fiber axis is observed in some regions of the fibers [Fig. 1.24(e)]. This lateral breaking of filaments might be due to the cracks in the original fibers. In comparison with VGCFs, the morphological change in mesophasepitch-based carbon fibers is somewhat different. The VGCFs are mostly broken into two parts and exfoliated along the radial direction of the original fibers, but the mesophase-pitch-based carbon fibers appeared to split into many thin filaments along the original fiber axis. This difference of behavior in exfoliation between VGCFs and mesophase-pitch-based carbon fibers is assumed to be due to the cross-sectional texture of the pristine fibers, the former having a coaxial orientation of hexagonal carbon layers and the latter a radial one. These results suggest that exfoliation of carbon fibers strongly depends on the texture of carbon fibers. Transmission electron microscope (TEM) micrographs of these thin filaments are shown in Fig. 1.25. From the bright-field image [Fig. 1.25(a)], every thin filament split out from the fiber appears to consist of thin sheets. Each of these filaments is concluded to consist of well-oriented layer planes, based on the analysis of 002 dark-field images and selected-area electron diffraction patterns of TEM [Fig. 1.25(b) and (c), respectively]. Such exfoliation behavior and structure analysis of fragmented filaments agree well with previous highresolution TEM analyses of thin sections of mesophase-pitch-based carbon fibers.[54,71,72] Electrochemical intercalation of formic acid was also applied to the same heat-treated carbon fibers (30008C), and their exfoliation was investigated.[69] The intercalation reaction was carried out by electrolysis in 50% formic acid. In Fig. 1.26 the XRD patterns are shown for the original fibers and after their electrolysis up to the potential saturation. The formation of intercalation compounds was confirmed from the fact that the XRD pattern for the carbon fibers after electrolysis showed a diffraction peak at the interlayer spacing of about 0.92 nm and only a trace of the 002 diffraction peak of the original carbon fiber remained. According to the result of a previous paper[51] and from the broadness of the observed peak, a mixture of stage-1 and stage-2 structures was assumed to be formed. In Fig. 1.27 SEM micrographs are shown for a single fiber after electrolysis and after exfoliation. By the intercalation of formic acid, the original fiber seems to expand and some cracks are formed along the fiber axis [Fig. 1.27(a)]. The morphological changes in the fiber after exfoliation are observed to be similar to the case of nitric acid intercalation described earlier [Fig. 1.27(b)]. In order to understand the process of intercalation of nitric acid into carbon fibers, electrolysis with a current density of 20 A/m2 was interrupted at different supplied charges, as indicated by arrows on the potential curve in Fig. 1.22.
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Figure 1.25 TEM micrographs of (a) bright-field image, (b) 002 dark-field image brightening at the edge, and (c) 002 diffraction spots.[66]
Figure 1.28 shows the XRD patterns of each sample electrolyzed up to its respective electric charges. Charging up to 150 C does not produce a detectable change in the XRD pattern. After 300 C, however, additional peaks appear, broad but apparent at around 118 and very faint at 228 2u, whose interlayer spacings are about 0.78 and 0.39 nm, respectively, as interpreted earlier. The 002 diffraction line of the original carbon fibers disappears completely above 600 C. Therefore the formation of intercalation compounds by electrochemical processing seems to be completed before 600 C, which corresponds to the beginning of potential saturation in Fig. 1.22. Above 600 C, no apparent change in XRD pattern is observed. This series of samples was subjected to rapid heating to 10008C. The appearance of carbon fibers after rapid heating is shown in Fig. 1.29, where
Exfoliation of Graphite via Intercalation Compounds
33
Figure 1.26 XRD patterns of original mesophase-pitch-based carbon fibers and after their electrolysis in formic acid.[69]
the positional relation of a bundle of carbon fibers to electrolyte and platinum anode is also indicated. Exfoliation proceeds from the free end of the fiber bundle to its fixed end with increasing electrical charge supplied. Since exfoliation is possible only on the intercalated fibers, this result indicates that nitric acid molecules are intercalated electrochemically into carbon fibers through their free end toward the fixed end with increasing charge. From SEM observation under high magnification, a single fiber was converted to a bundle of thin filaments split along the original fiber axis at every exfoliated part in electrolyzed fibers; even the free end of fibers electrolyzed up to 150 C. In the intercalation of formic acid into carbon fibers, the same behavior was recognized in potential changes, XRD patterns, and exfoliation process.[70] Therefore, these results suggested that the electrochemical intercalation behavior of carbon fibers, starting from the free end and proceeding along the fiber axis and
Figure 1.27 SEM micrograph of single carbon fiber (a) after intercalation of formic acid by electrolysis and (b) after exfoliation.[69]
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Figure 1.28 XRD patterns of carbon fibers heat-treated at 30008C after electrolysis at 150 C, 300 C, 450 C, 600 C, and 1200 C.[67]
Figure 1.29 Exfoliation behavior of a bundle of mesophase-pitch-based carbon fibers after electrolysis at 150 C, 300 C, 450 C, 600 C, and 1200 C.[67]
Exfoliation of Graphite via Intercalation Compounds
35
being accompanied by a gradual increase in potential, is common for all intercalates. The present technique of nitric acid intercalation using electrochemical processing (electrolysis) could easily apply to long fibers, 50 cm long, because only one fiber end was necessary to connect to the current source, and they were exfoliated by rapid heating at 10008C. A photograph of long fibers after exfoliation is shown in Fig. 1.30, where an SEM micrograph of an exfoliated part is also attached. Carbon fabrics, with a size of 8 cm 6 cm [Fig. 1.31(a)], were used for this electrochemical processing in nitric acid. Figure 1.31(b) and (c) exhibit the photographs of two fabrics after exfoliation, the former being connected only by their warp to the Pt-electrode and the latter by both the warp and the weft. When only the warp of the fabric was connected to the Pt-electrode, exfoliation of only the warp was observed and no exfoliation of the weft was recognized [Fig. 1.31(b)]. When both the warp and the weft were connected to the Pt-electrode, on the other hand, both fibers could be exfoliated [Fig. 1.31(c)]. These results showed that it is necessary to connect both the warp and the weft to the electric source in order to intercalate nitric acid and, as a consequence, to exfoliate both the warp and the weft, probably because the contact resistance at the places of crossing two fiber bundles is quite high. In other words, the fibers
Figure 1.30 (a) Morphology of exfoliated long fibers and (b) SEM micrograph of exfoliated part.[66]
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Figure 1.31 Morphology changes of carbon fabrics upon exfoliation.[66] (a) Original fabrics, (b) connected only by warp, and (c) connected both by warp and weft to the Pt-electrode during electrolysis.
in one direction could be exfoliated in the fabrics. In Fig. 1.31(c) the central region of the fabric is seen to become tight after exfoliation because the available space for exfoliation of both the warp and the weft is comparatively small. The exfoliation of each single fiber in the fabric to a bundle of thin filaments was confirmed under SEM. For PAN-based carbon fibers heat-treated to 25008C, formation of intercalation compounds by electrolysis even up to 1200 C could not be detected on the XRD pattern, except for some broadening of the 002 carbon peak.[70] Hence, it was not presumed that intercalation compounds were formed in carbon fibers with a low graphitization degree even by electrochemical processing. However, exfoliation was observed after rapid heating to 10008C, as shown in Fig. 1.32. After rapid heating some of the fibers show splitting into a bundle of thin filaments, but some exhibit their original state with no exfoliation. It is supposed, therefore, that partial intercalation of nitric acid can occur in the carbon fibers by an electrochemical process. No XRD peak seemed to be attributable to the fact that only a small amount of intercalates was actually intercalated. In order to make the entire fibers exfoliate, it might be necessary to perform more careful experiments, ensuring good contact of every fiber with the platinum
Exfoliation of Graphite via Intercalation Compounds
Figure 1.32
37
SEM micrograph of PAN-based carbon fibers after exfoliation.[53]
electrode and selecting the most appropriate conditions for electrolysis (e.g., current density and concentration of electrolyte). 1.4.
MECHANISM OF EXFOLIATION
Exfoliation of graphite residue compounds with sulfuric acid is a consequence of the decomposition of sulfuric acid molecules and anions (e.g., HSO2 4 ) to H2O, SO3 , SO2 , and O2 , all of which are neutral gases, at a high temperature such as 10008C. Since these decomposition reactions are endothermic, high temperature is needed for exfoliation. Rapid heating is also required in order to have a sudden formation of these gaseous decomposition products and subsequently enough exfoliation. For other intercalates (e.g., HNO3 , SO3 , HClO4 , and HCOOH) exfoliation due to the formation of gaseous decomposition products is thought to be similar to the case of sulfuric acid. Exfoliation of GICs with metal chlorides (e.g., FeCl3-GICs) by rapid heating is also due to the decomposition of metal chloride to gaseous species. However, it was pointed out that in the case of FeCl3-GICs one of the decomposition products (FeCl2) is less volatile, so that a part of them remain in the graphite gallery to hinder the diffusion of another product (Cl2) to the edge of the flake.[52] In exfoliation due to the reaction between MoCl5-GICs and monohydrated hydrazine at room temperature, the reaction occurs between hydrazine and MoCl5 in the graphite gallery to give NH4Cl and molybdenum oxides or hydroxides.[73] As this reaction is exothermic, these reaction products and also a part of the hydrazine that penetrates into the graphite gallery are vaporized. Using anhydrous hydrazine, the reaction occurs so violently that the temperature of the sample goes up, which further accelerates the exfoliation process. Using monohydrated hydrazine, the reaction proceeds gently and slowly, in comparison with anhydrous hydrazine, and the graphite exfoliates in the liquid of excess monohydrate.
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An experiment in which the change in pore structure of exfoliated graphite was studied as a function of heating temperature showed that graphite exfoliation proceeds in three steps: below 6508C, between 6508C and 8008C, and above 8008C.[74] In Fig. 1.33(a) – (c), bulk density and exfoliation volume of the resultant exfoliated graphite and mass loss during heating are plotted against exfoliation temperature. In these changes two kinks are recognized, at around 6508C and around 8008C, more clearly upon change in exfoliation volume, as shown by arrows in Fig. 1.33(b). Bulk density decreases abruptly with increasing exfoliation temperature [note that the ordinate in Fig. 1.33(a) is a logarithmic scale], corresponding to the increase in exfoliation volume and to the gradual increase in mass loss due to heating; the bulk density of about 300 kg/m3 after 5008C heating decreases to about 10 kg/m3 after 8008C. Above 9008C, the
Figure 1.33 Changes in (a) bulk density, (b) exfoliation volume, and (c) mass loss with exfoliation temperature.[22]
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39
bulk density decreases only slightly, but the exfoliation volume and mass loss increase further. The changes in the porosity inside of worm-like particles were examined on the fractured cross-sections of worms with the aid of image processing. Three samples prepared by rapid heating to 6008C, 8008C, and 10008C for 1 min were selected, based on the results in Fig. 1.33. Pore parameters (i.e., crosssectional area, lengths along the major and minor axes, and aspect ratio) together with cumulative frequency of cross-sectional area, are shown for these three samples in Fig. 1.34. Also average values of these parameters are listed in Table 1.2, where bulk density, the total number of pores used for analysis, and the fractal dimension of the pore wall surface are also shown. The increase in exfoliation temperature from 6008C to 8008C does not produce a major change in pore parameters from those reached below 6008C, but further temperature increase does: the cross-sectional area and the lengths of both major and minor axes do become larger. The aspect ratio (i.e., the ratio of the lengths of minor to major axis) is around 0.4, regardless of the exfoliation temperature, revealing that the cross-section of pores in the worms maintains approximately the same elliptic geometry. The fractal dimension is also constant, about 1.1, which agrees with the notion that the walls of ellipsoidal pores consist of smooth graphite basal planes. From the experimental results shown in Figs. 1.33 and 1.34, and Table 1.2, exfoliation is concluded to occur in three steps: below 6508C, between 6508C and 8008C, and above 8008C. Below 6508C, worm-like particles are formed by the volatilization of the decomposition products through preferential exfoliation perpendicular to the basal plane of graphite, which results in the complicated entanglement of particles. This is the reason why bulk density decreases or exfoliation volume increases abruptly, concurrently with the increase in mass loss. In the intermediate range of temperature, 650–8008C, pores inside the particles grow only slightly but the decrease in bulk density or the increase in exfoliation volume is pronounced, suggesting the growth of spaces among the particles. Above 8008C, the increase in exfoliation volume becomes slow, that is, entanglement among worms does not change that much. However, pores inside the worms grow again, accompanied by further increase in mass loss (i.e., further decomposition and volatilization of the remaining intercalates). These results suggest that for the characterization of exfoliated graphite the parameters of pores inside of worm-like particles have to be defined, as well as the bulk density or exfoliation volume. Structural annealing of exfoliated graphite, which was prepared by the reaction of MoCl5-GICs with hydrazine at room temperature, was examined after washing out the reaction products, such as NH4Cl , MoO3 , and MoO2 , with HCl and NH4OH.[73] In Fig. 1.35 the change in half width of the 002 graphite peak with annealing temperature is shown. After annealing at 2008C, the 002 peak was so broad that its half width was difficult to determine. Above 3008C, it starts to sharpen and seems to level off at about 0.38 2u, which is still far from the half width for the pristine graphite. Above 5008C, the intensity of the 002 peak increased with increasing annealing temperature and residence time,
Figure 1.34 Distribution histograms for the parameters of pores inside of worm-like particles.[22]
40 Inagaki et al.
41
Figure 1.34 Continued.
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Inagaki et al.
Table 1.2 Average Values of Pore Parameters for Exfoliated Graphite Prepared at Different Temperatures[15] Exfoliation temperature (8C)
Bulk desity (kg/m3) Number of pores used Average pore parameters Area (mm2) Major axis (mm) Minor axis (mm) Aspect ratio Fractal dimension
600
800
1000
40.3 2583
8.8 2161
6.6 2059
193 24.4 8.8 0.412 1.09
217 26.0 9.7 0.424 1.10
321 31.2 11.2 0.412 1.09
but its half width did not show a notable decrease. The half width leveled off for the sample exfoliated at room temperature is much larger than that for the sample prepared from the same starting GICs by rapid heating to 8008C. This result shows that the graphite exfoliated at room temperature contains a large amount of stacking disorder, which may be introduced by local heating due to exothermic reaction between MoCl5 and hydrazine, and only a part of which can be annealed at 8008C. Exfoliation at higher temperature (e.g., 8008C) is accompanied by partial elimination of these disordered regions. In exfoliated carbon fibers, a marked acceleration of graphitization was observed.[75,76] After exfoliation of mesophase-pitch-based and PAN-based carbon fibers heat-treated at a high temperature as 30008C using the same
Figure 1.35 Change in half width of the 002 diffraction peak of exfoliated graphite with annealing temperature.[37]
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Figure 1.36 Raman spectra for a single filament of PAN-based carbon fibers, pristine fibers heat-treated at 30008C, as-exfoliated, and after reheat-treatment at 28008C, with their interlayer spacing d002 .[76]
procedure described in Section 1.3.2, they were subjected to repeated heat treatment at high temperatures. In Fig. 1.36 Raman spectra for a single PAN-based carbon fiber heat-treated at 30008C are compared: the original, as-exfoliated, and after reheat treatment at 28008C for 10 min, together with interlayer spacing d002 measured by XRD.[76] The original PAN-based carbon fiber shows a strong D-band around 1360 cm21, which is attributed to disordered structure and a weak G-band around 1600 cm21, which is attributed to ordered graphitic structure;[77] in other words, it is not graphitized even after 30008C treatment. After exfoliation, even the D-band grows. By re-heat treatment to 28008C, however, the D-band almost disappeared, a strong G-band appeared, and d002 decreased to 0.337 nm, which is very close to that of graphite. These results show that PAN-based carbon fibers were graphitized almost completely after exfoliation. Acceleration of graphitization of mesophase-pitch-based carbon fibers was also observed.[75,76] This acceleration of graphitization in exfoliated carbon fibers is attributed mainly to the elimination of the constraint to maintain a fibrous morphology through the exfoliation to thin filaments.
1.5.
FORMATION INTO FLEXIBLE GRAPHITE SHEETS
Since large flakes of natural graphite are not commonly available, the development of a technique to prepare graphite sheets promoted the applications of graphite. Graphite sheets provided the characteristic advantages, such as
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flexibility, compactability, resilience, and easy formation into various shapes, in addition to the original properties of graphite, that is, lubricity, chemical and thermal stability, electrical conductivity, thermal conductivity, etc. Based on these properties, they have been widely used in modern technology. Detailed results on mechanical properties of commercially available flexible graphite sheets were reported in 1986.[78] In order to satisfy the severe demands from recent modern technology, a wide variety of research is still being conducted in several countries. These are reviewed next. 1.5.1. Formation Process and Controlling Factors Figure 1.37 shows schematically the manufacturing process for flexible graphite sheets. Natural graphite flakes are chemically or electrochemically intercalated to form GICs, usually sulfuric acid-GICs due to simplicity and low production cost. After rinsing and drying, residue compounds are obtained, which are called exfoliative graphite (it has been called expandable graphite, but in the present review we prefer to use the word “exfoliative”, as explained in Section 1.1.2). This product is then rapidly heated to 900– 12008C, upon which the intercalates remaining between the graphite layers are decomposed to gaseous products
Figure 1.37
The manufacturing process of flexible graphite sheets.
Exfoliation of Graphite via Intercalation Compounds
45
and yield exfoliated graphite, as described in Section 1.2. This exfoliated graphite is either molded or rolled into a sheet without any adhesives or binders. These are called flexible graphite sheets. During this forming process, several factors are very critical in determining the properties, particularly mechanical properties, of the final sheets. Besides exfoliation and formation processes, the properties of the raw residue compounds, that is, their contents of residual intercalates, moisture and ash, as well as particle size of the starting natural graphite flakes, were pointed out to be very important.[45] During intercalation with sulfuric acid and exfoliation at high temperature, most of the mineral impurities, such as silica and iron oxides, which come from the ores of original natural graphite, are removed. Therefore, the resultant graphite sheets are essentially pure carbon, but still contain some minerals, which are referred to as ash, and a small amount of sulfur, which comes from intercalates (sulfuric acid). The exfoliation temperature has a pronounced influence on the exfoliation volume, as discussed in Section 1.2.2, and also on residual sulfur content. Usually, for industrial manufacturing, the temperature is kept in the range of 900 – 12008C in order to ensure complete decomposition of the intercalated sulfuric acid and to minimize the residual sulfur oxides. If the temperature is too high, the consumed energy increases and graphite is partially oxidized. If the temperature is too low, the exfoliation volume is not sufficient and the residual sulfur content remains relatively high. The duration of exfoliation also influences the final sulfur content, and the optimum is said to be between 10 and 20 s.[14] Too short a time results in higher sulfur content in the final sheets. Tensile properties are also affected by prior exposure to high temperature and residence times.[78] Molding or rolling assists mechanical interlocking among worm-like particles of the exfoliated graphite[79] and the rolling process determines the thickness, density, as well as preferred orientation of graphite (002) planes of the finished sheets. Annealing before rolling of the sheet is usually carried out at 600 –8008C for industrial manufacturing, and this reduces the final sulfur content and provides good surface quality and texture homogeneity after the subsequent rolling process.[45] Thus fabricated flexible graphite sheets are stocked as a roll, as shown in Fig. 1.38. They are formed to different shapes and sizes by punching. Some of the industrial products, including tapes, O-shaped rings, as well as differently shaped ones, are shown in Fig. 1.39. Most of these products are used as seals, packings, and gaskets. Figure 1.40 shows schematically how many seals and gaskets made of flexible graphite sheets are used for an engine in an automobile. Flexible graphite sheets can be laminated with themselves and with various metals and plastics to form gaskets for a variety of applications. Lamination of graphite sheets is mainly aimed to increase the thickness of a gasket or packing ring, each sheet being bonded with an adhesive. The laminates thus prepared may or may not be treated thermally to decrease outgassing. Lamination
46
Figure 1.38
Inagaki et al.
A rolled flexible graphite sheet. (Courtesy of Nihon Carbon Co. Ltd.)
of a graphite sheet with a metal or plastic sheet is mainly carried out in order to improve its handling performance and mechanical strength. For example, the use of metal or polyester interlayer was claimed to improve the compressive loadcarrying ability of laminates. However, their thermal, mechanical, and chemical performance as a gasket was somewhat restricted.[80] The metal interlayers may be foils, screens, or perforated metals. The foils and screens are adhesively bonded to the graphite sheet and perforated metals are mechanically bonded.[80] 1.5.2. Properties of Flexible Graphite Sheets Flexible graphite sheets retain the fundamental characteristics of graphite; they are lubricious, chemically inert, electrically and thermally conductive, and resistant to heat and corrosion. However, the sheets have additional advantages; they are flexible, compactable, resilient, and can form into a variety of shapes, this last property being the most important for industrial applications. The Material Safety Data Sheet of flexible graphite sheets shows that a graphite sheet, which contains
Figure 1.39
Flexible graphite sheets with different shapes for seals and gaskets.
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Figure 1.40 Applications of flexible graphite sheets as gaskets and seals (1 to 27) in an engine. (Courtesy of Nippon Gasket Co. Ltd.)
no hazardous ingredients, is not a fire or explosion hazard, is not reactive, and requires no special protection or precautions. Therefore, it may be a good replacement for asbestos gaskets, particularly in places where fire safety is demanded. It is also superior to conventional elastomeric bonded gaskets, because it is more thermally stable and chemically inert with considerably less creep relaxation.[81] The physical properties of a flexible graphite sheet are listed in Table 1.3. The bulk density of a flexible graphite sheet for industrial uses is ca. 1.1 103 kg/m3, which is only one-half of the theoretical density of graphite (2.25 103 kg/m3). This makes the sheets compressible, which is required to produce an effective sealing in gasket applications. The bulk density may be controlled from 0.8 to 1.4 103 kg/m3 by the degree of compaction during its forming processes, particularly rolling.[80] The density of the sheets also affects its other properties, the increase in density increasing its recovery, tensile strength, thermal conductivity, Young’s modulus, and hardness, but decreasing its compressibility, gas permeability, oxidation rate, flexibility, and electrical conductance perpendicular to the sheet.[80]
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Table 1.3
Inagaki et al. Typical Room Temperature Properties of Flexible Graphite Sheets
Property Bulk density Thickness Tensile strength along the sheet Compressive strength Creep relaxation Compressibility Recovery Young’s compressive modulus Sealability Static friction coefficient Working temperature Thermal conductivity at 218C Along the sheet surface Perpendicular to the sheet Electrical resistivity Along the sheet surface Perpendicular to the sheet under 690 kPa Coefficient of thermal expansion Along the sheet surface Perpendicular to the sheet Specific heat at 248C Oxidation rate in air At 5008C At 7008C Carbon content Ash content Sulfur content Leachable chlorides and fluorides
Value 1.1 103 kg/m3 0.15 – 1.0 1023 m 4.4 MPa 240 MPa ,5% 40% 20% 1.4 GPa ,0.5 mL/h 0.052 (at 0.07 MPa) 22408C to 30008C
Remarks 0.8– 1.4 103 kg/m3 4.0– 6.9 MPa 1008C 22 h
Against steel Oxidation occurs above ca. 4558C in air
140 W/m K 5 W/m K 8 1026 ohm m 15 1026 ohm m
20.4 1026 m/m8C 27 1026 m/m8C 711 J/kg K Mass loss 0.03 – 0.75 g/m2 h 12– 130 g/m2 h 95.0 – 99.5 mass% ,0.5– 5.0 mass% ,500– 1000 ppm ,50– 100 ppm
Linear From 218C to 10948C From 218C to 22068C
99.8 mass% for nuclear ,450 ppm for nuclear ,20 ppm for nuclear
The typical tensile strength of flexible graphite sheets varies from 4.0 to 6.9 MPa along the sheet surface. It was found to depend on the flake size of raw natural graphite, ash content, and exfoliation volume of exfoliated graphite, as well as on the bulk density of the sheet.[84] It increased approximately linearly with bulk density, as shown in Fig. 1.41.[78] Almost the same relationship was reported recently.[82] At a given density, tensile strength decreases with increasing ash content. The slope of tensile strength s vs. bulk density r, ds/dr, is a measure of the ability of the graphite sheet to be strengthened by densification. Figure 1.42 shows that the value of ds/dr is inversely related to ash content.[78] This result shows that ash content must be low in order to achieve high strength by densification of graphite sheets. Tensile strain to failure is also reduced
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49
Figure 1.41 Relation between tensile strength and bulk density of flexible graphite sheets. (Adapted from Dowell and Howard.)[78]
somewhat by the presence of impurities. The flake size, which is often controlled by screen aperture size in industries, affects the exfoliation volume of exfoliated graphite and, as a consequence, the tensile strength of the resultant graphite sheet. Figure 1.43 shows a linear relationship between tensile strength and flake size.[82] As shown in Fig. 1.44, tensile strength increases linearly with increasing exfoliation volume (a), and so the increase in screen aperture size results in a tensile
Figure 1.42 Dependence of the slope ds/dr on the ash content of flexible graphite sheets, where s is tensile strength and r is bulk density. (Adapted from Dowell and Howard.)[78]
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Figure 1.43 Tensile strength of flexible graphite sheets vs. flake size of raw natural graphite. (Adapted from Leng et al.)[82]
Figure 1.44 Relations among tensile strength of flexible graphite sheets, exfoliation volume of exfoliated graphite, and flake size of the original graphite. (Adapted from Reynolds and Greinke.)[83]
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51
strength increase (c) through a relationship between exfoliation volume and flake size (b).[83] The compressive strength of homogeneous, unconfined flexible graphite sheets depends strongly on the test method used. It can be compacted and “flown” under high load without any appreciable cracking. The compressive strength of unconfined homogeneous sheets is often said to be about 165 MPa.[80] If the sample is confined, this value can increase to as much as 1000 MPa. Flexible graphite sheets can also be strengthened by the addition of inorganic salts, which have to be uniformly distributed internally. For example, when boric acid or its salt was dispersed into exfoliated graphite, the tensile strength of the molded sheet was reported to increase by 50 – 80%, although it became somewhat brittle.[84] Flexible graphite sheets can be used over the widest temperature range among all the sealing materials that have ever been developed, from as low as 22408C to as high as 30008C, if the atmosphere is maintained inert. In a reducing or vacuum environment, this material stiffens slightly between 1100 and 20008C, but remains usable. Above 30008C, it begins to sublime. In air or oxidizing atmosphere, pure graphite sheet may begin to oxidize at 4558C, but it can be used at a much higher temperature, about 8008C, for gasket and packing materials, because in those applications only thin edges are exposed to air.[80] In reinforced laminates the usable temperature is governed by the adhesives and inserted materials.[80] The initiation temperature for oxidation is often defined as the temperature at which a flexible graphite sheet, with a bulk density of 1.1 103 kg/m3 and thickness of 0.38 mm, loses 1% of its mass within 24 h/m2 of surface. The atmosphere used in the test is air, flowing around the entire sample. The rate of oxidation depends strongly on the concentration and type of inorganic impurities present in the sheet, which can act as oxidation catalysts or inhibitors.[80] A homogeneous flexible graphite sheet without any resin binders or organic fillers is chemically resistant to attack from nearly all inorganic or organic fluids, with the exception of highly oxidizing chemicals. It is not influenced by pH in its full range of 0 – 14. It can also be used at high temperatures with most chemicals. When flexible graphite laminates are used, the nongraphite constituents limit their chemical stability. Galvanic corrosion of stainless steel components can be a serious problem in fluid sealing. It is the result of an electrochemical reaction between a metal and graphite in the presence of an electrically conductive fluid or water. The rate and degree of pitting due to galvanic erosion are dependent on how widely separated the metal and graphite are in the galvanic series, in this system graphite being located near the cathodic scale end. This erosion is very important when graphite sheets are used for sealing of conductive fluids in contact with metal, where the metal always acts as the anode. Unless an electrically conductive fluid is present, galvanic corrosion does not occur. In order to increase resistance to erosion of the
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flexible graphite sheets, several methods have been proposed:[80] (a) addition of an inorganic, nonmetallic, passivating erosion inhibitor, which must be uniformly distributed throughout the sheets; (b) addition of metal sacrificial inhibitors such as zinc and aluminum; and (c) control of the contents of leachable chlorides and sulfur well below ca. 20 and 450 ppm, respectively. High purity of the sheet is recommended for nuclear and other applications, where corrosion of metals is of critical concern.[80] Since sulfur oxides cause corrosion of metals, their content is very important as well. It is influenced by the composition of the raw residue compounds of sulfuric acid, which in turn depends especially on the details of intercalation and exfoliation processes. For standard industrial use, maximum sulfur level of ca. 1000 ppm may meet the specifications. For nuclear power plants, however, sulfur content must be controlled below 500 ppm.[80] Some of the sheets contain very small amounts of halides (chlorides and fluorides), which catalyze corrosion, and their levels must be kept also very low in critical applications. Leachable halides in aqueous solutions accelerate pitting corrosion by permeating stainless steel’s chromium oxide film and eventually causing its complete physical breakdown. A maximum value for total amount of leachable chlorides and fluorides is about 100 ppm in most industrial grades of the sheets. For nuclear power plants, this value must be controlled below 50 ppm, even less than 20 ppm.[80] Functional properties related to the performance of flexible graphite sheet as a gasket are the following: sealability, compressibility, recovery, and creep relaxation.[80] Density of the sheets is known to affect these properties; for example, a sheet with a lower density has higher compressibility but lower resilience. Flexible graphite sheets with a bulk density of 1.1 103 kg/m3 without metal and polyester layers present usually 40–50% compressibility and 15–25% resilience,[80] resilience being virtually unaffected by service conditions, which proves that it is an effective, long-term sealing material. They possess very low creep relaxation and are thermally stable. 1.6. APPLICATIONS OF EXFOLIATED GRAPHITE AND FLEXIBLE GRAPHITE SHEETS Some applications of exfoliated graphite, including exfoliation phenomena of intercalation compounds (exfoliative graphite), were reviewed by Chung,[3] most of them being originally described in patents. Some research activity on exfoliation has still continued to this day, as discussed in different sections in this review. Recently, several novel applications of exfoliated graphite have been reported, and, as a consequence, exfoliation has been revisited by different research groups in various countries.[85] New applications of flexible graphite sheets were reviewed recently.[86] In this section a novel application of exfoliated graphite, sorption of spilled heavy oil, is reviewed first, then other recently reported applications of exfoliated graphite are also discussed. Some applications of flexible graphite sheets and
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exfoliative graphite, most of them having already been established,[3,4] are only briefly presented. 1.6.1. Sorption and Recovery of Spilled Heavy Oils Over the last decade there have been quite a few oil spill accidents of large oil tankers in the world, most of which resulted in serious disasters for the environment. Although such disastrous accidents produced massive oil spills, it was pointed out that the principal loss of oil still occurs during its routine transportation and transfer.[87] A continuous leaking of oil through pipe joints, for example, may result in serious soil contamination and sometimes even in contamination of subterranean water. This endangers the life of human beings through contamination of various plants, fishes, and water.[88] Although these oil spills are not as massive as in tanker accidents, they have occurred frequently and resulted not only in a great deal of damage to the environment, such as life cycles, but also in great loss of heavy oil in most heavy oil spill accidents. So far, some mats of polymers, such as polypropylene and polyurethane, have been used for the absorption of spilled oil. Their maximum absorption capacity is 10 – 20 g of heavy oil/g of polymer.[89,90] However, most of these polymers absorb water, in addition to heavy oil, and have no special selectivity for heavy oils, and so the effective absorption capacity of polymer mats for heavy oils must be even lower than the figures mentioned. Exfoliated graphite was found to be able to sorb a large amount of heavy oil floating on water at room temperature very quickly, more than 80 g of a heavy oil/g of exfoliated graphite within 1 min.[57,58] It was also shown that about 80% of sorbed heavy oil could be recovered by simple compression. There was another brief report on the sorption of heavy oil onto exfoliated graphite, but the reported capacity was much lower and the details were not published.[91] Preferential sorption of heavy oil spilled over water by exfoliated graphite was also demonstrated.[10] These promising results were reported in a series of papers.[9 – 11,58 – 60,92 – 97] By addition of exfoliated graphite to the heavy oil floating on water, the characteristic brown color of heavy oil disappeared as a consequence of its sorption into exfoliated graphite. Typical photographs of water with floating A-grade oil are shown in Fig. 1.45(a) and (b) before and after addition of exfoliated graphite. In this case the dark brown color disappeared within 1 min. After removing the exfoliated graphite, no additional contamination appeared in the water. When the amount of sorbed heavy oil was less than the maximum capacity of exfoliated graphite (the case of Fig. 1.45), no oil emanated from exfoliated graphite even if it was transferred onto the white filter paper, all of the heavy oil being retained in the exfoliated graphite, and no contamination of the filter paper was observed, as shown in Fig. 1.45(c). In Fig. 1.46 the sorption capacities of two exfoliated graphite samples with slightly different bulk densities (EG-1 with 6 kg/m3 and EG-2 with 10 kg/m3)
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Figure 1.45 Photographs of A-grade heavy oil (a) floating on water, (b) after its sorption by adding exfoliated graphite, and (c) after being transferred onto filter paper.
are compared using four grades of heavy oil. Density and viscosity at 258C for the four oils are listed in Table 1.4. In the case of A-grade heavy oil, as much as 83 g was sorbed into 1 g of exfoliated graphite EG-1 at 258C, 83 g being the sorption capacity of this exfoliated graphite. When 85 g of heavy oil was used, slightly more than the sorption capacity, the characteristic brown color of floating heavy oil completely disappeared, but the surrounding of the graphite lump was trimmed by a transparent oily material. When 100 g was used, a small amount of oil with brown color remained floating on the water surface even after sorption by exfoliated graphite. This sorption capacity is higher than that first reported by Cao et al.,[98] and much higher than that of polypropylene. The sorption rate of A-grade oil was so high as to be essentially completed within 1 min. Exfoliated
Figure 1.46 Sorption capacity of two exfoliated graphite samples EG-1 and EG-2 with bulk densities of 6 and 10 kg/m3, respectively, for four heavy oils with different viscosities.[57]
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Table 1.4
Density and Viscosity of Heavy Oils Used
Grade of heavy oil A-grade B-grade C-grade Crude
55
Density (kg/m3)
Viscosity (Pa s) at 258C
864 890 950 826
0.004 0.27 0.35 0.004
graphite with a bulk density of 10 kg/m3 (EG-2) had somewhat lower sorption capacity (about 70 g/g). The sorption capacity for a crude oil, whose viscosity is comparable to that of A-grade oil (Table 1.4), was similar to that for A-grade heavy oil (Fig. 1.46). Its sorption rate was also as high as in the case of A-grade oil, saturation being reached within 2 min. The sorption capacities of EG-1 and EG-2 for crude oil were 75 and 65 g/g, respectively. In the case of C-grade heavy oil, which has a relatively high viscosity (Table 1.4), the sorption capacity of exfoliated graphite was somewhat smaller than in the case of A-grade oil, but still 67 and 60 g/g for EG-1 and EG-2, respectively (Fig. 1.46). Sorption of C-grade heavy oil proceeded very slowly; about 8 h was needed for saturation. The B-grade heavy oil showed a behavior similar to that of C-grade oil in both sorption capacity (Fig. 1.46) and sorption kinetics. Figure 1.47 shows the pronounced dependence of sorption capacity on the bulk density of exfoliated graphite for A-grade and C-grade heavy oils.
Figure 1.47 Dependence of sorption capacity of the exfoliated graphite on its bulk density for A- and C-grade heavy oils.[60]
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Exfoliated graphite with bulk density above 40 kg/m3 could not sorb viscous C-grade heavy oil. In Fig. 1.48 the sorption capacity at 208C is plotted against the volume of pores in the range of 1 – 600 mm,[99] as measured by mercury porosimetry using precautions discussed in Section 1.2.5. Sorption capacity increases with increasing pore volume of the exfoliated graphite. It is reasonable to assume that large molecules in a heavy oil are sorbed into the macropores of the exfoliated graphite by virtue of the capillary phenomenon. The pore volume measured with the usual dilatometer (N-type in Fig. 1.17) gave much lower capacity.[62,99] The important contribution of large pores among the worm-like particles of exfoliated graphite for heavy oil sorption was also shown.[100,101] The pores inside the worm-like particles and crevice-like pores on the surface of the particles together with hydrophobic (oleophilic) nature of the graphite surface seemed to assist the rapid capillary pumping.[102] In Fig. 1.49 the sorption capacity of the exfoliated graphite EG-1 is plotted against the temperature of heavy oil. In the case of A-grade heavy oil, the capacity seems to increase gradually and reaches 90 g/g at 308C. In the case of C-grade heavy oil, in contrast, the temperature dependence is more pronounced: the capacity decreases abruptly below 208C and no sorption occurs below 158C. Sorption capacities for crude oil and B-grade heavy oil show an intermediate dependence. These changes in sorption capacity of exfoliated graphite with temperature may be related to the increase in viscosity of each oil with decreasing temperature. In Fig. 1.50(a) the sorption capacity of the exfoliated graphite is plotted against viscosity at different temperatures between 0 and 308C on a logarithmic scale. This figure highlights two different dependences of sorption capacity on viscosity, for less viscous oils (A-grade and crude oils)
Figure 1.48 Dependence of A-grade oil sorption capacity of the exfoliated graphite on the pore volume measured by mercury porosimetry using U-type dilatometer.[99]
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Figure 1.49 Dependence of sorption capacity of the exfoliated graphite with a bulk density of 6 kg/m3 (EG-1) for four heavy oils on ambient temperature.[9]
and more viscous oils (B- and C-grades). Both groups reveal a sharp dependence of sorption capacity on viscosity within a narrow viscosity range, at less than 0.01 kg/m s for the former group and above 0.1 kg/m s for the latter. The same measurements for a wide range of oils (mineral oils, cooking oils, motor oils) could fulfill the intermediate viscosity range and give a continuous dependence of sorption capacity on viscosity, as shown in Fig. 1.50(b).[103] This dependence of sorption capacity of various oils on their viscosity has to be discussed on the basis of fundamental properties of oils, for example, molecular size and viscosity. The sorption rate of these oils was found to depend strongly on their viscosity.[103] Pumping of the heavy oil into the exfoliated graphite was shown to be possible and its kinetics was studied in detail.[104,105] From contaminated sands, heavy oil was successfully recovered using this pumping ability of the exfoliated graphite.[106] This sorptivity of oily materials was proposed to be exploited also for lubricant supports;[107,108] a lubricating oil was sorbed into the exfoliated graphite, which gave advantages for easy handling and increased stability of the oil. 1.6.2. Other Applications of Exfoliated Graphite 1.6.2.1.
Medical Dressings
Exfoliated graphite was proposed to be used for medical dressings, especially for curing of burned skin.[13,98] It can absorb large biological molecules, such as
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Figure 1.50 Changes in sorption capacity of the exfoliated graphite with a bulk density of 6 kg/m3 (EG-1) with oil viscosity.[103] (a) For heavy oils and (b) for various oils including heavy oils.
proteins and body fluids, and so it may keep the burned skin surface dry without any infection. It does not support bacteria life and is not harmful to the human body. It is also effective for curing other injured surfaces, for example, knife cuts and skin infections.
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1.6.2.2.
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Thermal Insulators and Conductors
A lump of exfoliated graphite has low thermal conductivity because of its low bulk density, so that it can be used as packing for thermal insulation, for example, in a high-temperature furnace in inert atmosphere. By combining it with a graphite sheet, which also has low thermal conductivity perpendicular to the sheet surface, efficient insulation is expected.[109] Because of light weight, low bulk density, and effective absorbance of a wide range of electromagnetic radiation, from ultraviolet to microwave, exfoliated graphite in the size range of 10– 35 mm is thought to be useful as a battlefield obscurant.[110,111] In contrast to these insulator applications, there are efforts to use compacted exfoliated graphite as a heat conductor.[112] In Fig. 1.51 the thermal conductivity perpendicular and parallel to the compression plane are plotted against bulk density of the compacts of exfoliated graphite powders, which were produced by uniaxial compression. The compacts with bulk density of 50 –1800 kg/m3 showed very high thermal conductivity, 25 –400 W/m K in the direction parallel to the compression plane, and low values (up to 6 W/m K) perpendicular. The former values are comparable to those in metals (copper and aluminum) and, due to low bulk density, the diffusivity of the compacts is also much higher than in metals. Compacted exfoliated graphite was proposed to be used as a heat conducting medium inside the solid –gas fixed bed reactor of chemical heat pumps.[113] By controlling the bulk density of the compact prepared from exfoliated graphite, a high porosity that facilitates the permeation of working fluid and sufficient thermal conductivity, as well as good mechanical strength, were obtained, in addition to the original characteristics of graphite (e.g., high chemical resistance to corrosive gases and high electrical conductivity). The structure of compressed exfoliated graphite and its properties, particularly pore structure, were studied by modeling.[114,115]
Figure 1.51 Changes in thermal conductivity perpendicular and parallel to the compression plane with bulk density of the compacts. (Adapted from Bonnissel et al.)[112]
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1.6.2.3.
Raw Materials for Other Forms of Carbon
Grinding in cyclohexene by using a helicoidal mixer and then subjecting to a combination of tangential shearing by a mill and cavitation by a high-power ultrasonic agitation, thin flakes of graphite powders with average diameter of about 10 mm and thickness less than 0.1 mm were prepared.[4,116] These powders were named “Flat Micronic Graphite” (FMG) in English or “Graphite Micronique Plat” (GMP) in French. A typical distribution of flake sizes is shown in Fig. 1.52. Most of the flakes in this powder showed the electron diffraction pattern of single crystal graphite and they had a specific surface area of about 20 m2/g, as determined by krypton adsorption at 77 K. By simple sedimentation in a liquid medium, a highly oriented layer with a thickness of 1 mm was obtained, which could be converted to a flexible film by compression. Also the composites of this powder with polyurethane paint were prepared, and they had very high anisotropy in electrical conductivity.[116] Thin flakes of graphite, which were prepared from exfoliated graphite by sonication in alcohol, were used as a filler for the composites with methyl methacrylate and styrene.[117] By impregnation of poly(furfuryl alcohol) into exfoliated graphite, carbonization, and then activation, monolithic activated carbon was prepared.[118] The advantages of using exfoliated graphite are supposed to be as follows: porosity in the block can be controlled just by compression of exfoliated graphite and reasonable mechanical strength can be expected even after activation. As stated in Section 1.6.1, the exfoliated graphite can sorb a large amount of oily materials. Exfoliated graphite was also found to sorb a large amount of silicones, such as [CH3(CH55CH2)SiO]n and (CH3)3SiO[CH3(H)SiO]m . The sorbed silicones were polymerized at 3008C in the pores of exfoliated graphite. By heating to 16008C in inert atmosphere, this product could be converted to
Figure 1.52 Flake size distribution of a flat micronic graphite. (Adapted from Furdin et al.)[116]
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Figure 1.53 SEM micrograph of submicron SiC particles prepared by the reaction between exfoliated graphite and silicones. (Courtesy of Prof. H. Konno, Hokkaido University, Japan.)
fine particles of b-type silicon carbide SiC, 1 mm in size.[119] Even at 14008C, b-SiC powders were obtained by prolonging the heat treatment time. An SEM micrograph of the submicron size SiC particles thus prepared is shown in Fig. 1.53. In this case, the exfoliated graphite could retain relatively large amount of silicones, separate them from each other, and also react with them to form silicon carbide. Exfoliated graphite may be used as a raw material for making some graphite-based composites, which have a potential application as functional materials (e.g., absorbents, electromagnetic shielding and thermal insulator). Previous works[120,121] showed that some inorganic additives, such as boric acid and iron oxides, could be dispersed uniformly into the exfoliated graphite, which possesses low bulk density, high strength, and is conductive. A carbon or metal coating on the exfoliated graphite with a low bulk density is achieved using conventional CVD methods.[118] 1.6.2.4.
Others
The exfoliated graphite prepared from n-octylammonium tetrachloroferrate(III)GICs was used in anodes of lithium ion batteries and reported first discharge capacity of 862 mA h/g,[36] more than the theoretical value of graphite (372 mA h/g). However, no detailed data on irreversible capacity and cycling performance of this anode made of exfoliated graphite were reported. Exfoliated graphite was modified using covalently bonded dopamine (3,4dihydroxyphenethyl-amine) after introducing carboxyl functional groups by oxidation in HNO3 þ H2SO4 . This modified exfoliated graphite was reported to be biosensing.[122]
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1.6.3. Applications of Flexible Graphite Sheets 1.6.3.1.
Gaskets, Seals, and Packings
Flexible graphite sheets prepared by compression and rolling of exfoliated graphite are a very effective material for gaskets, seals, and packings at high temperatures.[3] They exhibit an outstanding fluid sealing function, which is based on the characteristics of the original graphite (lubricity, chemical inertness, excellent conductivity, and high resistance to heat and chemical corrosion) and on those of formed sheets, such as flexibility, compactability, and resilience. They can be made into a variety of shapes to fit virtually any fluid sealing application. Their chemical resistance and thermal stability make them an effective material where fire-safe sealants are required. They are safe to people’s health and so an ideal replacement for gaskets based on asbestos. They are also superior to conventional elastomeric bonded gaskets, because they are more thermally stable and chemically inert with considerably less creep relaxation. They are also preferable to other nonasbestos sheet gaskets, such as aramids, glass fiber, and mica, which have lower thermal stability and higher creep, often resulting in poor performance under load. Resilience of flexible graphite sheets may develop new applications for damping of mechanical loads.[123,124] Damping of hazardous loads, whether due to accidental loading, winds, ocean waves, or earthquakes, is required. 1.6.3.2.
Thermal Insulators
Flexible graphite sheets have unique physical and chemical properties that make them ideal for thermal radiation shielding. They can be used on any flammable liquid piping or equipment in accordance with recommendations of the gasket, pipe, or equipment manufacturer without organic fillers or resins. Flexible graphite sheets have a minimum thermal conductivity of 5 W/m K perpendicular to the sheet surface and a thermal conductivity of approximately 140 W/m K along the sheet. This anisotropy makes them thermal insulators perpendicular to the sheet and conductors along the sheet. They are commercially available for high-performance and cost-effective furnace insulation. One of the advantages of these sheets is their emissivity of 0.5 at high temperatures, which means that 50% of the heat radiated upon the surface of the sheet is reflected back to the hot zone. Graphite sheets have a high anisotropy in various properties, as shown in Section 1.5.2. By wrapping such sheets around a graphite tube heater in order to minimize heat dissipation, it was reported that a very high temperature, such as 34008C, could be attained and also the service life of graphite heater could be prolonged.[125] 1.6.3.3.
Electromagnetic shielding
Electromagnetic interference shielding, which can be accomplished by reflection and/or absorption of electromagnetic radiation by a material, is increasingly
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needed in our daily life; for example, high-frequency radiation emanating from cellular phones interferes with many electronic devices (e.g., computers). Shielding of such radiation is required with high efficiency, by light and thin layers. Flexible graphite sheets were demonstrated to be among the promising candidates.[86,126] 1.6.4. Applications of Exfoliative Graphite 1.6.4.1.
Fire-Protective Materials
Exfoliative graphite can be used as an intumescent flame retardant additive, superior to that of conventional chemical intumescents, such as polyurethane, pentaerythritol, melamine, phosphates, and aluminum trihydroxide. Its effectiveness often depends on the amount of exfoliation volume generated and the onset temperature at which the exfoliation is initiated. Exfoliative graphite can exfoliate up to 100 of its original thickness. Such tremendous exfoliation generates an extensive insulation layer and it can dramatically reduce heat release, mass loss, and smoke generation. It may provide the optimum intumescent performance for fire retardant barriers, putties, and foams.[127] The properties of exfoliative graphite as an intumescent, the onset temperature, and exfoliation volume can be controlled by the kind and amount of intercalates. Two commercially available exfoliative graphites exhibited high exfoliation volume of 100 –150 mL/g at onset temperature of 1608C and 2208C.[128] The addition of exfoliative graphite flakes was found to increase the flame retardant effectiveness of intumescent resin systems.[129] The use of graphite improved the physical characteristics of the char by increasing the thickness of the insulation layer and reducing crack formation. A newly developed intumescent resin using exfoliative graphite as an additive showed markedly improved results for ignition time, heat release, mass loss, and flame spread. The smoke index for the resin/graphite system was reduced by 75%, compared with that obtained for the intumescent resin alone.[129] Exfoliative graphite added to unsaturated polyester resin in the amount of 7.5 phr (parts by weight per hundred parts resin) or more makes the resin self-extinguishing.[130] 1.6.4.2.
Thermal Insulation Slag for Molten Metals
Exfoliative graphite can be used as an additive in making thermal-insulative slag which is used to maintain the high temperature during the melting and solidifying of metals.[131,132] The process is very simple, just adding 5– 10 vol% exfoliative graphite into a conventional retardant slag. It is available in the particle size range of 0.15 –0.3 mm, carbon content of 80 – 90%, and exfoliation volume in the range of 80 –100 mL/g. Exfoliation is up to 100 in thickness, it generates an insulating layer on the surface of molten metals. This application takes advantage of both the exfoliation and insulation properties of graphite. It was also proposed as a fire extinguisher or fire retardant agent, because it exfoliates upon contact with fire and isolates the origin of the fire.[130,133]
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CONCLUDING REMARKS
In this chapter, exfoliation phenomena via intercalation compounds of graphite and carbon fibers are reviewed by discussing the effects of exfoliation conditions, intercalates, and hosts, including natural graphite, graphitized cokes, and various carbon fibers. The characterization techniques for different pores in the exfoliated graphite are introduced and on the basis of these recent results the exfoliation mechanism is discussed. After briefly reviewing the formation of flexible graphite sheets, which has been the principal application of exfoliated graphite and has played an important role in the development of modern technology, novel applications of exfoliated graphite, flexible graphite sheets, and exfoliative graphite are introduced. So far, exfoliated graphite had been used mainly as a raw material for flexible graphite sheets through complete compaction by compressing and subsequent rolling. As a consequence, scientific and technological research related to exfoliated graphite had been aimed to develop high-quality graphite sheets. Some studies suggested the possibility of having a wide range of porosities by incomplete compaction, which may open new applications for exfoliated graphite, thanks to the characteristics of graphite itself (e.g., high electrical and thermal conductivity and high resistance to chemical corrosion). The applications as heat exchanger and matrix for chemical heat pump had been examined, but the development of other applications can be expected. The finding of surprisingly high sorption capacity of exfoliated graphite for heavy oils created a novel application of exfoliated graphite as porous materials, which exploits the various pores formed in the bulky exfoliated graphite. This promoted new research, not only on fundamental problems such as quantitative characterization of various pores in the exfoliated graphite with the aid of digital image processing, but also on technological studies such as its application as sorbents for biological fluids (e.g., blood). The exfoliation of carbon fibers was just recently carried out and active research is still going on. It may open new fields of technology, which might have some relation to nanotechnology, because a single carbon fiber can split into a number of thin filaments, most of which have highly oriented texture in an axial orientation scheme. Exfoliation of various carbon fibers may give a new insight into their structure, because the constraint to keep a fibrous texture seems to be released through exfoliation. This constraint, which exists in each carbon fiber, is assumed to play an important role in structural changes and various properties of the fibers, although it has not yet been evaluated quantitatively. The acceleration of graphitization in exfoliated carbon fibers revealed another side of its importance, though we shall have to wait until more thorough investigations are performed on it.
ACKNOWLEDGEMENT The interest of the authors in exfoliated graphite was greatly promoted through the works on its heavy oil sorption and recovery, which have been done partly
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under the financial support by New Energy Development Organization (NEDO), Japan, and also partly under the joint research program between the Japan Society for the Promotion of Science (JSPS) and the National Natural Science Foundation of China (NSFC). The authors express their sincere thanks to all the people who helped to compile the present review. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29.
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2 Diamond Synthesized at Low Pressure Slobodan N. Marinkovic´ Institute of Nuclear Sciences “Vincˇa”, Belgrade, Serbia and Montenegro
2.1.
INTRODUCTION
2.1.1. Scope of the Chapter The amazing beauty and sparkle of a diamond, described and prized by many novelists and poets, stems from much less poetic, yet superior properties of diamond. These are primarily transparency and a high index of refraction (Table 2.1). Other properties of diamond are less known, but not less important. Some among them—high hardness (in fact the highest, 10 by the Moss scale), chemical inertness, and high abrasion resistance are not without significance for diamond jewels. However, these and especially some other properties— thermal conductivity (again the highest), very low coefficient of thermal expansion, very low coefficient of friction, very high electrical resistivity, high breaking strength, and semiconducting properties of doped diamond are much more important for other applications. At present, diamond is used mostly as a heat sink, as an abrasive, and for advanced cutting tools. But, if it were not relatively scarce in nature, other applications would certainly have been much more marked. Diamond also has superior chemical properties. It does not react with common acids even at elevated temperatures, and it is stable even to strong oxidants such as hot chromic acid cleansing mixture or a mixture of sulfuric and nitric acids. However, diamond is readily oxidized at high temperatures in an oxygen atmosphere or in air. Above 870 K, diamond also reacts with water vapor and CO2 . Molten hydroxides, certain salts, and metals have a corrosive 71
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Table 2.1
Selected Properties of Diamond
Property Hardness Compressibility Theoretical compressive strength Experimental compressive strength Bulk modulus Thermal expansion coefficient Thermal conductivity Bandgap Electrical resistivity Electron mobility Hole mobility Sound propagation velocity Optical transparency range Refractive index Electron affinity
Value at 300 K 90 GPa 8.3 10213 m2/N 410 GPa 3.75 GPa 1.2 1012 N/m2 0.8 1026 K21 2100 W/m/K 5.43 eV 1012 – 1016 V cm 2000 cm2/V/s 1500 cm2/V/s 18 km/s 2.5 nm to 10 mm 2.40 Very low or “negative”
effect on diamond. Carbide-forming metals react with diamond at high temperature, while ferrous metals dissolve it. Since it is scarce in nature, diamond has to be synthesized. This has long remained the goal of many researchers, but its synthesis was achieved only half a century ago. The main reason why it was not done earlier is because the stable modification of solid elemental carbon at room temperature and atmospheric pressure is graphite, not diamond. At low temperature (room temperature and below), diamond is thermodynamically unstable at a pressure lower than about 1.4 GPa (14,000 bar), while at higher temperature the stability region is shifted to still higher pressures. Therefore the first successful synthesis of diamond was performed at very high pressure and high temperature (HPHT). The synthetic diamond thus obtained (making the principal quantity of currently produced total amount) is mostly in the form of small crystals (below 1 mm), similar to the usual size of natural diamond, although crystals appropriate for (lower quality) jewels can be also produced. By sintering a mixture of small diamond crystals with a suitable binder at high pressure, material suitable for tools can be produced. In fact, the principal application of diamond was restricted to cutting tools, abrasives, and wear resistant coatings. About 15 years ago, sintered diamond heat sinks for high power density electronic devices (e.g., laser diodes or microwave devices) were introduced. Synthesis of diamond at high pressure and high temperature is a rather complicated and expensive procedure. Therefore, many researchers endeavored to produce diamond at low pressure. In favor of the possibility of such a synthesis is the fact that its thermodynamic instability is very small—the enthalpy of formation of diamond is only slightly higher than that of graphite. In addition,
Diamond Synthesized at Low Pressure
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a large activation barrier separates the two phases so that once formed diamond will not convert spontaneously to the more stable graphite phase. Therefore diamond is said to be metastable (i.e., kinetically stable but not thermodynamically stable). In order to initiate the conversion of diamond into graphite (under normal pressure), high temperature is necessary. Early experiments aimed at low-pressure diamond synthesis by chemical vapor deposition (CVD) resulted in amorphous carbon material, or rather a whole range of materials having properties between those of diamond and graphite (Section 2.1.3). It is interesting to note that low-pressure CVD diamond synthesis was achieved for the first time almost half a century ago, nearly simultaneously with HPHT synthesis. It was done by independent experiments, first in Russia[1] and then in USA.[2] However, these early experiments, although long-lasting, gave a very small amount of diamond that could hardly be detected. Therefore no one thought of practical diamond synthesis in such a way. Only in the beginning of 1980s, Japanese researchers[3,4] have shown that pure diamond can be synthesized by relatively simple techniques at a reasonable rate using CVD. It was after this achievement that the interest for such investigations abruptly increased. Various possibilities of diamond synthesis by CVD have been investigated since, and a number of CVD synthesis methods have been developed. Owing to improvement of the CVD reactors and steady increase of their capacity, the cost of diamond production has been decreasing steadily and product quality increasing. New fields and possibilities of CVD diamond applications have been proposed. Taking these facts into account, it is reasonable to expect that CVD-diamond-based products will progressively increase on the market. At the Vincˇa Institute research regarding CVD of diamond coatings started a decade ago. CVD methods of oxygen – acetylene flame, direct current (DC) arc jet, and hot filament (HF) have been developed. Diamond-coated cutting tools have been shown to have distinct advantages over uncoated products, so that their introduction in the market is expected. The abundant literature, as well as the relevant experience of the author, forms the basis of the present chapter. In view of the popularity of the subject matter, its intended audience is perhaps broader than in the case of standard CPC chapters. For this reason the focus in the cited references is on reviews, rather than on articles treating narrower specific subjects. A logical question is what are the possible advantages of such a chapter. It represents an attempt to sum up in a compact fashion the huge amount of knowledge concerning all aspects of CVD diamond so as to make it possible, or easier, to see the forest rather than the trees. It is intended to expose all the essential facts on the phenomena and processes of diamond synthesis by different CVD methods, as well as on the properties and applications of the product. Thus it differs from the earlier reviews or monographs/books, which either cover narrower subjects (an example is the excellent chapter on the optical properties of
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diamond in Vol. 13 of the series by Davies[5]) or cover the complete field but are too voluminous (such as Handbook of Industrial Diamonds and Diamond Films, edited by Prelas et al.[6]). An additional aspect of the present chapter is that it is intended to be up-to-date, which is particularly important for fields characterized by rapidly accumulated knowledge. 2.1.2. Phase Diagram of Carbon We shall restrict the present treatment to the well-known solid phases in which elementary carbon is manifested—the “usual” cubic diamond having the sphalerite structure and hexagonal graphite, for which thermodynamic relationships are best known. The recent phase diagram of pure carbon,[7] one of the authors of which (Bundy) is a coauthor of the historical diagram from the beginning of 1960s,[8,9] is presented in Fig. 2.1. The diagram contains only two solid phases—graphite and diamond (cubic and hexagonal). Other solid forms of carbon (such as fullerenes and carbyne) are omitted from the diagram.
Figure 2.1 A recent version of the phase diagram of carbon emphasizing graphite, cubic diamond, and hexagonal diamond phases, as well as the liquid carbon. Solid lines represent equilibrium phase boundaries. (A) Commercial synthesis of diamond from graphite by catalysis; (B) P/T threshold of very fast (,1 ms) solid– solid transformation of graphite to diamond; (C) P/T threshold of very fast transformation of diamond to graphite; (D) single crystal hexagonal graphite transforms to retrievable hex diamond; (E) upper ends of shock compression/quench cycles that convert hex graphite particles to hex diamond; (F) upper ends of shock compression/quench cycles that convert hex graphite to cubic diamond; (B, F, G) threshold of fast P/T cycles, however generated, that convert either graphite or hex diamond into cubic diamond; (H, I, J) path along which a single crystal hex graphite compressed in the c-direction at room temperature loses some graphite characteristics and acquires properties consistent with a diamond-like polytype, but reverts to graphite upon release of pressure.[7]
Diamond Synthesized at Low Pressure
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According to Fig. 2.1, graphite is a stable phase under ambient conditions, while diamond becomes stable at high pressures (the lowest pressure under which diamond is stable at low temperatures is 13,800 bar). Although graphite is thermodynamically more stable, diamond will not transform to graphite under normal conditions. As was already mentioned, because of a kinetic barrier, diamond exists virtually forever at low pressures in a mestastable state. Transformation occurs at high temperatures, the threshold temperature and kinetics of transformation depending drastically on diamond purity, its crystallographic orientation, and chemical nature of the surroundings. The purest natural diamond begins to transform to graphite in ultra-high vacuum only at 16508C. The phase diagram also shows that diamond can be synthesized under drastically differing pressures and temperatures. In one of the most imaginative processes using shock-waves (upper part of the figure), nanocrystals of diamond are produced from graphite powder using an explosion. A principal commercial technique of diamond synthesis today is the catalytic HPHT process: graphite is subjected to high pressure (4.5 – 6 GPa, i.e., 45,000 – 60,000 bar) and high temperatures (1350 – 16008C) in the presence of a metal catalyst (Fe, Co, or Ni alloy) in which carbon is dissolved. Tons of diamonds of industrial quality have been produced by variations of this process every year since 1960. The CVD processes (not shown) would be at the “bottom” of the diagram in the temperature range around 1000 K. Unlike the behavior of once synthesized diamond which, in spite of thermodynamics, remains unchanged eternally under low (atmospheric) pressure, diamond synthesis is quite a different situation, where one of the main obstacles originates precisely from the thermodynamic fact that diamond is stable only at high pressure. Nevertheless, the instability of diamond with respect to graphite is very small. The difference of free energy of formation of the two phases at 1 bar amounts at 0 K to only 2.361 kJ/mol, and at 2000 K to 10.5 kJ/mol. This indicates that diamond might be synthesized at low pressure. A method that may be suitable is CVD. Because diamond transforms to graphite only at high temperature, CVD might be useful at low temperature. If so, there should be a rather wide temperature range in which diamond might be synthesized under the conditions of its thermodynamic metastability. However, since deposition is basically a surface process, it seems logical that under the conditions of CVD, surface metastability should be taken into account, rather than bulk metastability. A surface phase diagram of carbon is not yet known, but it has been established that diamond preserves its crystal structure in the surface layer up to high temperatures. Experiments in which diamond was heated in ultrahigh vacuum (10210 mbar), or in highly purified hydrogen, have shown that up to 1300 –14008C no significant change in its structure occurs. On the other hand, experiments of thermodesorption show at least two peaks: a low-temperature peak at 9008C and a high-temperature one at 11008C, the latter corresponding to the heat of hydrogen desorption for the strongest C22H bonds in hydrocarbons. These data
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indicate that there is a rather complex spectrum of states of the bonded hydrogen on the diamond surface. Theoretical considerations and experiments point to a controversial nature of diamond surface. At high temperature and/or in the absence of hydrogen, additional bonding is possible between carbon atoms on the surface, which might represent a first stage of graphitization of the diamond surface. However, if the graphitized surface is submitted to the action of atomic hydrogen, it returns to the initial (nonreconstructed) state already at room temperature. This indicates the possibility that desorption of hydrogen from the diamond surface creates “dangling” bonds. At high temperatures (around or above 1600 K), where the desorption process has advanced, the dangling bonds become saturated with neighboring carbon atoms. Thus, a process of double-bonding of carbon atoms starts to prevail. Under the conditions of deposition from an active gas phase, the situation near and on the diamond surface changes drastically. In the presence of atomic hydrogen, many homogeneous and heterogeneous chemical reactions involving active hydrocarbon molecules, radicals, and ions become feasible. Presumably, metastability of the surface diamond phase may be extended under such conditions to much higher temperatures. Indeed, the experiments show that growth of tiny diamond particles by methane decomposition is possible up to 16008C. 2.1.3. Chemical Bonds and Structures of Diamond and Graphite The striking differences in properties of graphite and diamond are due to differences in their structure which, in turn, is a consequence of the well-known difference in chemical bonding (Figs. 2.2 and 2.3). The fourth, delocalized electron in graphite is responsible for very weak p-bonds acting between the layers. Because of the large difference in the bond strength within and between the layers, the layers behave in a rather “independent” way. Therefore they are named graphene layers. The C22C bond strength within graphene layers is on the average 452 kJ/mol, which is not too different from the bond strength in diamond (347 kJ/mol). A greater value of the bond strength within the graphene layer (s-bond) corresponds to a smaller interatomic distance: 0.142 nm with respect to 0.154 nm in diamond.
Figure 2.2
(a) s-Orbitals produced by sp3 hybridization and (b) structure of diamond.
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Figure 2.3 (a) s-Orbitals produced by sp2 hybridization and (b) structure of graphite.
As already mentioned, early experiments aimed at diamond synthesis by CVD produced amorphous carbon films having properties between those of diamond and graphite. Since the properties of these materials are more or less similar to those of diamond, they have found a number of applications. However, in these “diamond-like carbon” (DLC) films, along with sp3 bonds typical of diamond, there are many sp2 bonds typical of graphite. The amorphous carbon films are in fact a wide range of materials. Accordingly, a complex nomenclature has evolved. Such films may be broadly classified as: (i) amorphous carbon films, a-C films, deposited from carbon-containing gases with low or zero hydrogen content, and (ii) hydrogenated carbon films, a-C:H films, formed from hydrocarbon-containing gases. Both types of films contain different amounts of sp2 and sp3 carbon. The classification of amorphous carbon films according to carbon bond type and hydrogen content can be represented by a triangular diagram (Fig. 2.4).[10] The corners at the base of the triangle correspond to graphite (100% sp2 carbon) and diamond (100% sp3 carbon). The apex represents 100% H, but the upper limit for formation of solid films is defined by the tie line between the compositions of polyethene, 22(CH2)n22, and polyethyne, 22(CH)n22. The majority of a-C films contain mainly sp2 carbon, but the sp3 carbon content can be varied over the range 5– 55%, the hardness of the films increasing
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Figure 2.4
Classification diagram for amorphous carbon films. (Adapted from Fig. 32.[10])
with sp3 content. The H content of a-C:H films can be varied over a wide range and their hardness is inversely related to the H content. Films with a very high sp3 content (80 –90%) and correspondingly high hardness have been termed tetrahedrally bonded amorphous carbon films, ta-C films. Hard a-C:H films were named DLC, and this term has been used as a generic name for all a-C films. Thus, as a general rule, hardness increases with sp3 carbon content, as the proportion of DLC increases. Conversely, the films become softer as the sp2 carbon content increases, reflecting the increasing content of “graphite-like” carbon or “polymerlike” carbon. Clearly, there is considerable scope for varying the properties of carbon films by careful control of processing parameters. There is evidence for segregation of sp2- and sp3-bonded carbon in a-C and a-C:H films.The structure of a-C films with a high sp2 carbon content is envisaged as clusters of warped graphitic domains bonded by sp3 carbon. In a-C:H films the extent of segregation of sp2 and sp3 carbon decreases with increasing carbon content. The sp2 carbon content of both a-C and a-C:H films increases upon heat treatment in the range of 300– 6008C, that is, there is thermal transformation in graphitic structures; ta-C films are thermally stable to 10008C.
2.1.4. Natural and Synthetic Diamonds For centuries, diamond had been found only in the gravel of rivers, so nothing had been known about its origin. Only in the late 1860s, diamond was found in South Africa, in kimberlite—a volcanic rock formed under high pressure. In fact, appropriate conditions for diamond synthesis could be found inside the earth at a depth of a few hundred kilometers. It is therefore believed that diamonds were formed in this way. It is estimated that it happened up to 2 109 years ago.
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It is generally agreed that natural diamond was formed by HPHT, which is a logical conclusion derived from the mentioned data. The possibility that diamond could be formed in nature also by a CVD process was not considered before it was shown that diamond can be synthesized in that way. Nevertheless, if some facts are taken into account, it now looks in hindsight that diamond was obtained in the nature’s “laboratory” by a CVD technique: (a) the gases liberated by heating natural diamonds (CO2 , CO, H2O, CH4 , H2 , N2), the origin of which is not clear, are exacly those used for the CVD synthesis of diamond; (b) a tubular shape of formations in which natural diamond is most often found indicates a possibility that the gases from which diamond was formed by a CVD process passed through them; and (c) analysis of tiny diamond crystals found in meteorites indicates that they were formed by a CVD process. Thus, the idea that all the diamonds found in nature were formed at high pressure should not be considered indisputable. Natural diamonds can be categorized in four types, according to their optical properties, which are related to the presence of nitrogen.[11] Their most important feature are the infrared (IR) spectra below 1400 cm21. Absorption in this region is due to traces of nitrogen, the content of which can reach 0.25 at%. A small amount of nitrogen is mostly present in the substitution sites of the lattice (Section 2.8), but higher nitrogen content is present interstitially, often as aggregates. By far the most abundant (98%) natural diamond is type Ia. Its nitrogen content is relatively high (up to 0.25 at%), predominantly present as aggregates. Its characteristic features are the presence of strong IR absorption below 1400 cm21 and optical transparency in the spectrum region above 320 nm. The electrical resistivity is above 1016 V cm, and the thermal conductivity is about 900 W/m/K. The term type Ib refers to diamonds in which nitrogen (up to 0.2 at%) is present as single substitutional atoms. Purely type Ib natural diamonds are very rare (the figure of 0.1% often quoted is a gross overestimate), but sometimes natural specimens exhibit partial type Ib character, as judged from their IR spectrum, with the balance of nitrogen present as aggregates. The colour of the type Ib diamonds is yellow to amber, they show absorption at 1130 cm21, and their thermal, optical, and electrical properties are similar to type Ia diamonds. The IIa type is very rare in nature. Its nitrogen content is very low, there is no detectable absorption below 1400 cm21, it is non-semiconducting, and its thermal conductivity is up to 2600 W/m/K. The IIb type is extremely rare, it does not contain nitrogen, but does contain a small amount of B, being a p-type semiconductor. It is generally blue, and its electrical resistivity is very low (10 – 1000 V cm). HPHT synthesis produces mostly the type Ib diamond, which commonly contains up to about 300 atomic ppm of nitrogen. The type IIb is sometimes also produced. Soon after the discovery of natural diamond in South Africa, attempts of diamond synthesis by subjecting graphite to high pressure began. For a long
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time such attempts were unsuccessful, because the pressure achieved was not sufficiently high. The first reproducible HPHT synthesis was made at the end of 1954 by researchers of the General Electric company, who used 6 GPa and 15008C. Before long a procedure using a molten metal catalyst was standardized by the same company. About 100 tons of diamond is produced annually by the HPHT procedure nowadays, which approximately corresponds to the total amount of excavated diamond since biblical times. 2.1.5. Brief History of Research on CVD Diamond Synthesis The first researchers endeavoring to produce diamond using CVD had to start from the facts, but also from some hypotheses. In CVD, one usually starts with a compound containing the element to be deposited which is easily decomposed under the conditions used. In the case of diamond deposition, an unstable carbon compound should be used. Spitsyn and Derjaguin in Russia have started in 1956 with relatively unstable gaseous compounds, CBr4 and CI4 .[1] Since diamond is chemically inert, they have chosen 9008C as the deposition temperature. This temperature was high enough to ensure decomposition, but it was also sufficiently low to ensure that the deposited diamond was not changed. However, since graphite is thermodynamically stable at low pressure, it was necessary to choose conditions that would induce diamond deposition. The authors have therefore used small diamond crystals as a substrate, hypothesizing that surface carbon atoms with sp3 bonds in the diamond crystals will provide a “template” for the new incoming carbon atoms to proceed ordering themselves in the same way.[12] For the same reason, they used as precursors compounds having sp3 bonds, assuming that carbon atoms will maintain the same bond type upon deposition. Not knowing about this work, Eversole (1958) in the USA had used more or less similar conditions.[2] Exploring wide intervals of temperature (600 – 16008C) and pressure (0.0001 – 100 bar) he performed deposition on small diamond crystals by decomposing methane (CH4), organic compounds containing CH3 groups, or carbon monoxide (CO). Already in these first experiments, the starting hypotheses were shown to be essentially true. The authors obtained diamond, although in such small amount that it could hardly be identified. In a number of subsequent “isothermal” experiments of different authors, in which the substrate temperature was virtually equal to the gas phase temperature, similar results were obtained. It seemed for a while that the problem of diamond synthesis at low pressure had been solved. However, all these experiments had substantial drawbacks. One of them is that the (linear) rate of deposition was extremely low—on the order of a thousandth of a nanometer per second! In addition, such “chemical crystallization” processes could be performed only on the diamond surface. Perhaps an even more important disadvantage was that, simultaneously with diamond, nucleation and growth of islands of “byproducts”—thermodynamically more stable nondiamond carbon—had taken place. Therefore diamond deposition could not last as long
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as it was desired—the process had to be stopped from time to time in order to “clean” the deposited diamond from the nondiamond carbon. Thus, the conditions selected were not sufficient to ensure deposition of “pure” diamond (i.e., free of sp2 carbon). This is not surprising, because the difference in stability of diamond and graphite is very small. In other words, the conditions applied were only good enough to overcome the difference in stability ensuring that, in addition to (more stable) graphite, diamond was also deposited. Nevertheless, the problem of how to prevent graphite deposition remained unresolved. The disadvantages mentioned, as well as a widespread disbelief that diamond could ever be obtained under low pressure, are probably the reasons why these first results were received without enthusiasm, even in the scientific circles. Spitsyn and coworkers continued their research and in the mid-1960s reported new findings.[13] Although these results again have not provoked much interest, they represent a foundation on which today’s entire science and technology of chemically deposited diamond has been built. The essence of the new procedure, named by the authors “high temperature, high gradient chemical transport reaction” (see Section 2.6.1), is the presence of an active gas phase. In these experiments, graphite surrounded by hydrogen at low pressure was heated to high temperature (20008C), much higher than the substrate temperature. At high temperatures graphite reacts with hydrogen. Therefore the gas phase in the immediate vicinity of graphite contained active gaseous species, such as atomic hydrogen, acetylene (C2H2), and (at a much lower concentration) C2H radicals. But the substrate (diamond crystal) was positioned very close to graphite. Since diffusion is rapid at high temperature and low pressure, the gas phase composition around the diamond substrate was virtually the same as in the immediate vicinity of graphite. Thus, the substrate, heated to 10008C, was in contact with an active gas mixture formed at high temperature. In this way the authors obtained an epitaxial diamond film growing on the initial diamond crystals at the rate of 1 mm/h (i.e., three orders of magnitude greater than in the first experiments). Diamond was obtained also when an electrical discharge was produced in the mixture of a hydrocarbon and hydrogen. The authors concluded that the deposition process led to pure diamond because graphite, even though deposited simultaneously with diamond, was continuously etched away by atomic hydrogen (and, perhaps, by other generated etchant gas species). This conclusion was confirmed in 1971 by Angus et al.[14] who found that the presence of atomic hydrogen during the deposition process would lead to preferential etching of graphite rather than diamond. Spitsyn and coworkers had also shown that diamond could be deposited on the surface of nondiamond materials, again due to the simultaneous presence of carbon-containing gas species (from which different forms of the solid carbon could be deposited) and hydrogen atoms, which predominantly gasify all the nondiamond phases.[11] The real explosion of interest in diamond deposition came only at the beginning of 1980s, after the work of Japanese authors,[3,4] who brought all
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these findings together, to build, first, an HF reactor,[3] and then a microwave plasma reactor,[4] in both of which they successfully deposited diamond. A number of methods of diamond deposition have been developed since, several of them being used for industrial production. The progress achieved meanwhile can be illustrated by figures showing that the growth rate, the coated area, and the cost of CVD diamond have been dramatically changed: growth rate increased from several millicarats/h to 20 carats/h, free-standing diamond wafers as large as 30 cm have been produced, while cost dropped by a factor of 1000.[15]
2.1.6. Overview of the Chapter The first sections of the present chapter “follow” the deposition process. Since the process begins in the gas phase, Section 2.2 deals with the gas phase, primarily the active gas phase. The conditions necessary for diamond deposition in the common CVD methods have been outlined, emphasizing the essential role of atomic hydrogen. Deviations of the actual gas composition from the expectations based on simple equilibrium thermodynamics are pointed out. A recent result that diamond can be deposited from fullerene/argon gas mixtures, that is, by a mechanism involving no (atomic) hydrogen is underlined. Section 2.3 deals with nucleation of diamond. After the conditions for (heterogeneous) nucleation are presented, various substrate materials are considered from the viewpoint of carbon– substrate interaction, with a survey of properties of the currently employed and potential substrate materials. Recent results concerning diamond nucleation in the absence of hydrogen (fullerene/argon mixture) are included. Nucleation at different interfaces is considered in some detail. Surface treatments performed in order to stimulate nucleation, as well as the influence of deposition conditions on nucleation, are presented. Knowledge relevant to diamond growth is outlined Section 2.4, with an emphasis on the underlying mechanism. The data relevant to a thin layer at the gas phase/solid substrate boundary are summarized. A model of diamond growth is discussed, in which growth occurs by CH3 radical addition on the surface dangling bonds. The relationships derived from the model are shown, in particular, the dependence of deposition rate on the concentration of CH3 radical and atomic hydrogen. In Section 2.5, Deposition of diamond at low temperature, relevant results and problems are presented, including a recent experimental and theoretical study of evolution of microstructure and incorporation of nondiamond carbon. Progress in this field would result in a substantial expansion of the domains of application of diamond through a much wider choice of substrate materials. Research in this field requires experimental skill and creativity. Although a number of issues have been successfully solved, so that diamond can be deposited nowadays even below 2008C, there remains the challenge of increasing the deposition rate and improving diamond quality.
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In Section 2.6, Epitaxial diamond growth and the results achieved in this extremely significant area are discussed. Epitaxial growth is particularly important in electronics, where single crystals are needed. One of the more important problems of epitaxial deposition is that defect formation can hardly be avoided. Defects provoke stresses of the crystal lattice, resulting in twinning. Nevertheless, the achieved thickness of the diamond film virtually free from defects exceeds 1 mm. An important problem is to achieve heteroepitaxy—the possibility of using different (cheap) materials as substrates, instead of diamond. In Section 2.7, Oriented growth and morphology of diamond coatings are considered. By oriented growth, a mosaic surface consisting of equal faces is produced, which in some applications may be a good approximation to a single crystal layer obtained by epitaxial growth. Diferent techniques of oriented growth are discussed. Section 2.8 deals with doping of diamond, very important for applications, because it results in large gap, high-temperature semiconducting diamond. However, a number of important problems must be solved in order to produce diamond-based semiconductor devices, one of the most important being the necessity of producing diamond single crystals, as a precondition for high device efficiency. The data concerning incorporation of boron, phosphorus, and nitrogen, as well as the first experiments on doping with sulphur and unsuccessful experiments of lithium incorporation into the diamond lattice are considered. In the voluminous Section 2.9, the most important experimental methods of diamond deposition have been grouped. The HF method and microwave plasma are mostly used for commercial production of diamond. The methods of DC arc plasma, radio-frequency (RF) plasma, and oxygen – acetylene flame are then analyzed. Advantages and drawbacks of these methods are also discussed. Section 2.10 deals with applications of CVD diamond. Commercialized applications and those entering the market include cutting tools, heat sinks for high-power electronic and opto-electronic devices, windows for IR radiation, and SAW filters. Numerous other applications—protective wear-resistant coatings, field emission displays, electrodes for electrochemistry, diamond fiber-reinforced composites, detectors of radiation and high energy particles—have been developed, but not yet commercialized. Applications in electronics implicate solution of certain problems, which may take time. Nevertheless, the cost for 1 carat (0.2 g) fell below 1$ in the year 2000. In addition, it has very wide potential applications. These facts warrant that applications of CVD diamond will soon considerably increase. 2.2.
PROCESSES IN THE GAS PHASE
Since diamond is chemically inert, it does not undergo chemical changes, or polymorphic transformations. However, the very chemical inertness of diamond presents an obstacle for new diamond growth on the surface of the diamond nucleus. In order to make this growth possible, the current CVD methods operate in a stationary nonequilibrium regime. The CVD process involves activation of
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an appropriate gaseous mixture via chemical reactions taking place in the vicinity of a suitably heated substrate upon which polycrystalline diamond film will deposit. The active gas (vapor) phase can be defined as a nonequilibrium, nonisothermal low-temperature plasma. It contains chemically active molecules and radicals with elevated translational, rotational, and vibrational energies. Together with ions, electrons, and photons, they react with the growing diamond surface. Therefore all CVD methods currently used for producing diamond films require a means of activating gas phase carbon-containing precursor molecules. This activation can be done by electric plasma [DC, RF, or microwave (MW)], or by thermal methods—heating to high temperatures (over 20008C) or using an oxygen–acetylene flame. Each method differs in detail, but they all share a number of features in common: the presence of carbon-containing active gas species and substrate temperature in the range of 700–11008C. Until recently, atomic hydrogen was considered an absolutely essential ingredient of the vapor from which diamond is grown, but nanocrystalline diamond has been lately synthesized from hydrogen-free gas media (and, consequently, without atomic hydrogen), using fullerene as a carbon source (Section 2.2.3). Any thorough understanding of diamond CVD requires knowledge of the chemical environment in the vicinity of the diamond film during growth. Thus we need information on factors such as the gas phase species present, the sources, interconversion, and sinks of the key reactive (radical) species, their spatial distribution and their transport through the gas, the chemistry occurring at the gas/surface interface, and the way in which all of these factors vary with, for example, temperature, pressure, and the extent of activation (e.g., filament temperature or aplied microwave power). At first sight, this may seem like a daunting array of physical and chemical processes that need to be grasped if diamond CVD is to be understood. But over the past decade, there have been a large number of studies of the gas phase chemistry, and we are now beginning to obtain a clearer picture of the important principles involved. 2.2.1. Growth from Hydrocarbon/H2 Gas Mixtures Hydrocarbon/H2 mixtures have been studied extensively, because of their (apparent) chemical simplicity and compatibility with simple HF CVD reactors (Section 2.9). This compatibility is limited, however, to strictly oxygen-free mixtures, because even trace amounts of O2 lead to rapid destruction of the filament. Molecular hydrogen is by far the most abundant gas phase species of the inlet gas, although most of it passes unaltered through the reaction chamber and is driven out by the pump. Hydrocarbon (mostly methane) usually makes up just a few percent of the initial mixture. The experimental results showing relative concentrations of CH4 , C2H4 , and C2H2 as a function of filament temperature (Tfil) in an HF CVD reactor, for three different hydrocarbons, each diluted in hydrogen, so as to achieve a 1% input mole fraction of carbon are shown in Fig. 2.5.[16] A striking result
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Figure 2.5 Mole fractions of CH4 (V), C2H2 (A), and C2H4 (O) measured 6 mm from the filament in an HF CVD reactor, as a function of Tfil , for gas mixtures of (a) 1% CH4 in H2 , (b) 0.5% C2H4 in H2 , and (c) 0.5% C2H2 in H2 . In each case, the total gas flow rate was 100 sccm and the pressure 20 torr. The measured carbon balance (†) is observed to fall with increasing Tfil . This is attributable to the Soret effect, whereby heavier species diffuse preferentially from the hottest regions of the gas.[16] (Reproduced by permission of the PCCP Owner Societies.)
was obtained from this and some other earlier studies: the gas phase composition in the vicinity of the filament heated to temperatures appropriate for optimal diamond CVD (Tfil 24008C) is essentially independent of the carbon source gas. Figure 2.5(a) shows that in the case of a CH4/H2 input gas mixture, increasing Tfil causes a progressive conversion of CH4 to C2H2; the steady state concentration of C2H4 is low in comparison. Figures 2.5(b) and (c) show analogous data for C2H4/H2 and C2H2/H2 gas mixtures. In both cases, significant conversion of the C2 hydrocarbon to CH4 is observed at relatively low Tfil , followed by CH4 to C2H2 conversion as Tfil is increased. In contrast to these experimental findings, all of the simpler kinetic simulations of C2H2/H2 gas mixtures maintained at gas temperatures 1500 – 2500 K, suggest little conversion to C1 species. Therefore, different authors tended to attribute the observed (much higher) CH4 (and CH3) densities to heterogeneous processes occurring on the reactor walls, or on the growing diamond surface. This seems unlikely, however, given the striking similarities between the C2H2/H2 and CH4/H2 data.
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Nevertheless, the mentioned results are broadly consistent with expectations based on simple equilibrium thermodynamics. Starting from thermodynamic data (Table 2.2),[17] it can be predicted that the free energy for the overall conversion 2CH4
! C2 H2 þ 3H2
(2:1)
will change sign from positive to negative (i.e., the equilibrium will start to favor products rather than the reactants) as the gas temperature increases up to 1700 K. A more elaborate calculation (Fig. 2.6)[18] shows the way in which the equilibrium composition of a mixture of 1% CH4 in H2 , at 20 torr, evolves with temperature over the range of 1000 – 2500 K. However, this analysis grossly oversimplifies the real situation during diamond CVD, because the gas mixture is not static, but flowing through the reactor in which large temperature gradients exist. The equilibrium (2.1) will be shifted toward the right (i.e., C2H2) in the vicinity of the HF, whereas CH4 should dominate in cooler regions (i.e., close to the reactor walls). These “hot” and “cool” regions are, at most, only a few centimeters apart in a typical laboratory HF reactor, so that the species of interest will diffuse through the interaction zone in a time of the order of a second or less. This finite residence time prevents the gas mixture from attaining true chemical equilibrium. Additionally, the H atom concentration throughout most of the volume of the reactor, including the region close to the substrate surface, is far in excess of that predicted on the basis of equilibrium thermodynamics. Therefore any detailed description of the gas phase processes underpinning diamond CVD must take due account of the temperature and concentration gradients, as well as species and heat transport, within the reactor.[16] Although temperature gradients and finite residence time prevent the gas from attaining chemical equilibrium, the equilibrium composition provides a rough first approximation to the actual composition. Figure 2.7 shows the equilibrium gas phase composition for the conditions existing in Spitsyn’s (thermal) method of chemical transport (Section 2.6.1), in which the starting reactants are graphite and hydrogen, and the reactor pressure is 0.01 bar. For the graphite temperature of 2300 K, the main components are molecular and atomic hydrogen, C2H2 , and C2H. Since the diamond substrate is quite close to graphite, the gas composition in the vicinity of the substrate should closely correspond to that near the graphite. In the case of high temperature arc plasma jet (see Section 2.9), which is another “thermal” activation method, the gas phase composition (Fig. 2.8) is also close to the calculated equilibrium. Typical working temperature for the chosen conditions, as determined from the Ha and Hb line intensity ratio, amounts to 5000 –6000 K, with atomic hydrogen becoming a dominant gas
Temperature measurements based on emission spectroscopy may be unreliable (see “DC Arc Jet”).
298 K
0 274.9 226.7 0 2110.5 2393.5 2241.8
H CH4 C2H2 O2 CO CO2 H2O
0 91.4 222.7 0 2113.2 2 395.1 2249.0
1200 K
DH (kJ/mol)
0 292.7 219.9 0 2118.9 2396.8 2251.6
2000 K 0 250.7 209.2 0 2137.2 2394.4 2228.6
298 K 0 41.5 158.9 0 2217.8 2396.1 2181.4
1200 K
DG (kJ/mol)
0 130.8 117.2 0 2286.0 2396.3 2135.5
2000 K
1200 K 171.8 261.3 282.0 250.0 240.7 279.4 240.5
298 K 130.7 186.3 200.9 205.1 197.7 213.8 188.8
S (J/K/mol)
185.4 305.9 321.3 268.7 258.7 309.3 264.8
2000 K
Thermodynamic Data for Selected Stable Species Involved in Diamond CVD, at Room Temperature, 1200, and 2000 K.[17]
Species
Table 2.2
Diamond Synthesized at Low Pressure 87
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Figure 2.6 Homogeneous equilibrium mole fractions for different gas temperatures assuming an input gas mixture comprising 1% CH4 in H2 at a pressure of 20 torr, calculated using the relevant forward and backward rate constants and propagating to long time.[18]
species. Owing to high atomic hydrogen content, high-quality diamond is deposited, even under the conditions that would otherwise favor formation of the nondiamond phases (e.g., relatively high methane concentration). The gas species present in considerable amounts at lower temperatures (CH4 , C2H2 , and C2H), are negligible under these conditions, whereas atomic carbon becomes the most important gas species (after atomic hydrogen); concentrations of CH and C2 radicals are several orders of magnitude lower.[19]
Figure 2.7 Thermodynamic equilibria in the diamond – hydrogen system for the 500 – 1500 K range and in the graphite– hydrogen system for the 1500– 3000 K range, at a total pressure of 10 mbar.[12]
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Figure 2.8 The equilibrium gas composition in the system Ar-H22 2CH4 for CH4/H2 ratio of 2.5% and pressure of 250 mbar.[19]
In a recent study,[16] the gas phase chemistry was investigated by means of a realistic 3D model of an existing HF CVD reactor. Particular emphasis has been given to investigations (both experimental and 2D and 3D modeling) of transient species like H atoms and CH3 radicals, their spatial distribution within the HF reactor, and the ways in which these distributions vary with process conditions, and the insight provided by such investigations into the underlying chemistry. By studying a number of different reaction mechanisms, large variations in the chemistry prevailing in different regions of the reactor are revealed. Far from the filament, atomic hydrogen concentration, [H], is still significant, but gas temperature, Tgas , is low. At low Tgas (e.g., 735 K), atomic hydrogen drives C2 ! C1 conversion via a multistep sequence of reactions, whereas at much higher Tgas values, the reverse process dominates. The C2 ! C1 conversion proceeds as follows: gas phase C2H2 molecules in the presence of H atoms react to form other hydrocarbons (C2H2 ! C2H3 ! C2H4 ! C2H5 ! CH3 ! CHx , x ¼ 0, 1, 2, 4 and C2H6 ! C2H5) in the cooler regions remote from the filament. According to the analysis, approximately half of the C2H2 molecules that participate in the reactions convert to CH3 radicals, while the remainder are reduced to C2H4 . The three-body recombination H þ CH3 þ M ! CH4 þ M
(2:2)
is sufficiently fast at low Tgas to be an efficient source of CH4 molecules, which can diffuse into the near filament region and reconvert to CH3 radicals via the “traditional” abstraction reaction H þ CH4
! H2 þ CH3
(2:3)
Using similar analysis, it was shown that the rapid thermochemical cycling among the various hydrocarbon species in the reactor generally makes the gas
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phase composition in the vicinity of the growing diamond surface essentially independent of the particular hydrocarbon source gas used. For the case of the HF-activated C2H2/H2 gas mixtures, it was shown that CH3 radical formation, hitherto often presumed to involve heterogeneous hydrogenation steps, can be fully accounted for in terms of the gas-phase chemistry. 2.2.2. Growth from C/H/O Gas Mixtures From the earliest days of diamond CVD, chemists have been exploring the use of alternatives to simple hydrocarbon/H2 gas mixtures in the quest for increased growth rates, improved film quality, or lower deposition temperatures. There are many reports of diamond CVD from C- and H-containing gas mixtures that have been supplemented by small amounts of O2 or other oxygen-containing compounds. In addition, an acetylene – oxygen flame slightly richer in acetylene has been used successfully to deposit diamond. Bachmann and coworkers[20,21] analyzed the results of many such deposition experiments (including their own), using different gas mixtures and reactor types, which they summarized within the “Bachmann triangle diagram” (Fig. 2.9). This is a C/H/O composition
Figure 2.9 Ternary C/H/O diagram. The white lens-shaped area represents a new version,[21] while the original wedge-shaped version (bordered by the dashed lines) was based on a limited number of initial experiments.[20] In the original diagram, the diamond domain extended to the hydrogen-free C2 2O line, but later experiments proved that diamond deposition is not feasible without hydrogen, the content of which must be at least 0.5% in the C/H/O mixture; thus, the point up to which the diamond region extends is slightly off the C2 2O line.[21]
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diagram in which the deposition of diamond is feasible. Bachmann found that, independent of the deposition system and gas mixture, diamond would only grow when the gas composition was close to and just above the H22CO tie-line, that is, where the ratio of the carbon-to-oxygen mole fraction in the gas mixture, X(C)/X(O), is 1. This implies that diamond growth is independent of the nature of the gas-phase precursors, and that the gas-phase chemistry is so rapid that it simply and effectively breaks down the constituent gases to smaller, reactive components. The border line of the “diamond” domain on the oxygen-rich side almost coincides with the H22CO tie-line. Below the tie-line, no growth of any carbonaceous phase is detected. Above the H22CO tie-line, nondiamond carbon is generally deposited, except in a narrow window close to the tie-line (white area in the figure) in which diamond is grown. Of course, an adequate gas-phase composition is not the only necessary condition for diamond growth. Another condition is that the energy brought to the system must be sufficient to maintain the active gas phase. However, the degree of gas activation depends on the energy density and therefore, depending on the energy, the diamond region border line can be somewhat shifted: low energy (less activation) will cause a small expansion of the diamond region into the nondeposition area, while high energy density will expand the diamond region near the hydrogen corner up to the composition H/(H þ C) ¼ 0.9. Since the diamond domain is positioned between the nondiamond region and the no-growth region, it is logical and proven experimentally[21] that the rate of diamond deposition should decrease from the carbon-rich side toward the oxygen-rich border, the phase purity growing in the same direction. In addition, the gas-phase composition, deposition conditions, and properties of the deposit are changed considerably when passing along the diamond domain, from the H-rich corner to the C22O side-line. The deposition rate (Fig. 2.10) has a maximum in the center of the diagram and drops to zero near the C22O side line. These experimental results can be qualitatively understood on the basis of equilibrium thermodynamics. Using the data from Table 2.2, the free energy of oxidation of methane and acetylene, the most often used hydrocarbons in the CVD environments, 2CH4 þ O2
! 2CO þ 4H2
(2:4)
C2 H2 þ O2
! 2CO þ H2
(2:5)
and
can be calculated. It is large and negative at all temperatures of interest in diamond CVD. The respective equilibria lie far to the product side, ensuring that, in each case, the minority reactant will be consumed fully. Consequently, if the ratio of the carbon-to-oxygen mole fraction in the gas mixture, X(C)/ X(O), is equal to unity, Eqs. (2.4) and (2.5) correspond to the H22CO tie-line.
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Figure 2.10 The deposition rate increases from the hydrogen-rich corner of the C/H/O triangle diagram, reaches maximum at the C/H/O ¼ 1 : 1 : 1 ratio, and drops to zero near the C2 2O side-line.[21]
If the X(C)/X(O) ratio is just greater than unity, the activated process gas will consist of a small amount of residual hydrocarbon in a background gas mixture of CO and H2 . Assuming that CO itself does not contribute to diamond growth, this mixture has much in common with the standard oxygen-free mixtures used for diamond deposition. Deposition of diamond can occur and, as with the traditional hydrocarbon/H2 mixtures, film quality will be compromised if the concentration of “free” hydrocarbon becomes too high. Conversely, when X(C)/X(O) , 1, the hydrocarbon source gas is entirely converted to CO and there are no “active” C1 species to promote film growth. In this connection, it is interesting to consider the equilibrium gas phase composition for the acetylene –oxygen flame (Fig. 2.11),[22] which differs from those in other gas mixtures used for diamond CVD (Figs. 2.6 – 2.8). The main difference is due to the presence of oxygen, because of which CO becomes the main gas species. The working temperature is in this case around 3300 K, i.e., between the two sources discussed earlier. An additional difference with respect to the aforementioned diagrams is the presence of a discontinuity at the reactant ratio R ¼ C2H2/O2 ¼ 1. The oxygen-containing species existing at a lower ratio (R , 1) disappear, while radicals without oxygen appear. At R . 1, that is, under the conditions used for diamond deposition, the principal gaseous species are CO, H2 , and H, then follow C2H2 and C2H, the remaining species being in minor concentrations. Recently, attention in this area has been focused on the use of CO2/CH4 gas mixtures, which provide a route to depositing high-quality diamond at lower substrate temperatures.[23] The process window using this gas mixture is found to be narrow and centered at a composition of 50% CO2/50% CH4 by volume flow rate. Both a detailed experimental study at deposition temperatures down to
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Figure 2.11 Temperature and equilibrium gas phase composition vs. R5 5C2H2/O2 in combustion flame diamond synthesis.[22]
4358C and computer simulations have been performed in order to gain insight into the major reactions occurring within the plasma. According to a model of the gas-phase chemistry developed by the group, although the number of elementary reactions can be very high, only a small number of “composite reactions” are sufficient to explain the experimental findings. The CH3 radicals are likely to be the key growth species and provide a qualitative explanation for the narrow concentration window for diamond growth. 2.2.3. Growth from Other Gas Mixtures In addition to the C/H(/O) systems, the C/H/halogen systems have also been investigated.[21] In the C/H/Cl system, the diamond region is limited to the hydrogen-rich corner of the diagram, whereas in the C/H/F system it follows the H22CF4 tie line, entering considerably the fluorine-rich area. For the time being, there is no practical application of such gas mixtures, mostly because of strong corrosive action of the halogens. Thus, the C/H and C/H/O mixtures are the only utilizable ones.
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Recently, CVD procedures have been developed in which diamond is deposited from hydrogen-free gas mixtures. Particularly interesting is an H2-free (and, consequently, H-free) procedure using a fullerene/argon mixture,[24,25] in which nanocrystaline diamond with a minor surface roughness is produced. The reaction mechanism operating in this procedure must obviously be different from those in the usual C/H(/O) mixtures. Fullerene, C60 , is much less thermodynamically stable than either diamond or graphite, so that its carbon vapor pressure at 6008C can be reached with graphite only at 30008C. Copious amounts of highly energetic C2 dimers formed (instead of CH3 radicals which finally disappear as hydrogen is progressively replaced by argon) were found to be due to fragmentation of C60 through collisions with argon molecules and ions. These dimers can insert directly into carbon22carbon and carbon22hydrogen bonds without the intervention of atomic hydrogen. Such a straightforward process for continuing the growth of the diamond lattice leads to pure diamond films composed of tiny 3–5 nm crystallites throughout the entire film thickness. These results show that there is no unique mechanism, or a model of diamond growth, capable of explaining all existing experimental results. Moreover, many reactions often proceed simultaneously owing to a complex chemical nature of the growth surface. A selective overview of the gas-phase chemistry in diamond CVD laboratory scale reactors is presented in this section. Experiment and theory are advancing in tandem, and much of the essential chemistry is now determined and understood. Questions remain, however, particularly for the reactors other than HF CVD, mainly because of insufficient experimental information. Detailed studies of the chemistry prevailing in the systems operating with other than C, H (and O)-containing gases, such as used in deposition of doped diamond, are also missing.
2.3.
NUCLEATION OF DIAMOND
Nucleation is the first and critical step of CVD diamond growth. Control of nucleation is essential for optimizing diamond properties such as grain size, orientation, transparency, adhesion, and roughness which are necessary for specific applications. Investigation of diamond nucleation can lead not only to controlled growth of diamond films suitable for various applications, but it can also provide insight into the growth mechanism. There has been considerable amount of research to elucidate the mechanisms of CVD diamond nucleation. The answer to the basic question of why metastable diamond is formed instead of the thermodynamically stable graphite is clear. Namely, under CVD conditions a diamond nucleus can be more stable at normal pressure than a graphite nucleus containing an equal number of atoms. In other words, graphite is thermodynamically more stable in the bulk, but diamond can be more stable on the surface.
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Furthermore, it is now clearly established that CVD diamond nucleation requires the existence of surface defects. Defects are needed to induce the nucleation process by lowering the enthalpy of nuclei formation. However, the real chemical and the intimate structural nature of such defects relevant to nucleation are still a matter of debate. In this section we will briefly discuss nucleation of diamond under CVD conditions, paying special attention to the understanding of its mechanism. 2.3.1. Homogeneous Nucleation Although homogeneous nucleation in the gas phase, as well as its contribution to different deposition processes, is not satisfactorily understood, the existing evidence suggests that, at least in some cases, diamond can be nucleated in such a way.[26] Theoretical arguments in favor of such nucleation have been published more than a quarter of century ago,[27] and several years later[28] it has been suggested that certain hydrocarbon cage molecules are possible embryos for homogeneous nucleation of diamond. The adamantane molecule, C10H10 , represents the smallest combination of carbon atoms with the diamond unit structure (i.e., three six-member rings in a chair conformation). The tetracyclododecane and hexacyclopentadecane molecules represent twinned diamond embryos that were proposed as precursors to the 5-fold twinned diamond microcrystals prevalent in CVD diamond thin films. A simple atomic structure comparison shows that the diamond lattice could be generated easily from such cage compounds by simple hydrogen abstraction followed by carbon addition. However, thermodynamic equilibrium calculations revealed that such low-molecular-weight hydrocarbons are not stable at high temperatures (over 6008C) in the harsh environment associated with diamond CVD. In a limited number of experiments conducted to examine homogeneous nucleation of diamond in the gas phase at atmospheric and subatmospheric pressures, the number of diamond particles collected from the gas phase was very small compared with typical nucleation densities observed on substrate surfaces. Therefore, the homogeneous nucleation mechanism cannot account for the large variety of nucleation densities observed on different substrate materials and from different substrate pretreatments. Whether and how the diamond particles formed in the gas phase could serve as seeds on the substrate surface for subsequent growth of a diamond film remains unknown. 2.3.2. Surface Nucleation There is a small number of reliable data concerning the size, structure, and chemical behavior of the diamond nucleus. In comparison with a considerable development in nucleation enhancement methods, results of fundamental scientific studies related to the nucleation process remain less well addressed. Nevertheless, such results have been considered to predict preferential conditions for diamond nucleation and growth. A narrow range of deposition conditions, such
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as pressure (supersaturation), temperature, and composition, as well as the state of the substrate surface (structure, roughness), have been derived, under which nucleation and growth of diamond are significant and graphite is etched. The crucial role of hydrogen atoms in stabilizing the diamond structure on the substrate surface relative to graphite has been revealed. Hydrogen was found to have multiple roles in permitting metastable growth of diamond by impeding the conversion of diamond to graphite below 13008C. The role of substrate surfaces in stabilizing the diamond structure has also been recognized. Basically the process of CVD of polycrystalline diamond films consists of the decomposition of a hydrocarbon and crystallization of diamond. It typically shows several distinguishable stages (Figs. 2.13 and 2.14): (a) incubation period (“preparation” for nucleation); (b) surface 3D nucleation; (c) 3D growth of nuclei to grains; (d) faceting and coalescence of individual grains and formation of continuous film; and (e) growth of continuous film. Two criteria must be satisfied for “spontaneous” (non-epitaxial) surface nucleation: (i) carbon saturation of the substrate surface and (ii) presence of high-energy sites (unsaturated valences). Growth of diamond begins when individual carbon atoms nucleate onto the surface in such a way as to initiate the formation of an sp3 tetrahedral lattice. When natural diamond is used as a substrate (a process called homoepitaxial growth), the already existing diamond lattice provides a template for ordering of the new carbon atoms, thus ensuring atom-by-atom ordering as the deposition process proceeds. But for nondiamond substrates, there is no such template for the C atoms to follow. Therefore, deposited C atoms may order so as to produce both diamond and nondiamond (sp2) forms. However, those C atoms that deposit in nondiamond forms are immediately etched back into the gas phase by reaction with atomic hydrogen. As a result, the initial incubation period before which diamond starts to grow can be prohibitively long (hours or even days). Nevertheless, it is not easy to explain why spontaneous nucleation of the new diamond crystals occurs on nondiamond substrates under the conditions where graphite, and not diamond, is the stable phase. In describing the process of surface nucleation, two parameters are used: the nucleation density, Nd (cm22) (i.e., the number of nuclei formed on 1 cm2 of surface) and nucleation rate, Nr (cm22/h) (i.e., the number of nuclei formed on unit surface in unit time). The rate of nucleation depends on the number of active sites on the substrate surface. Nucleation will stop after the nuclei have been formed on all such sites, or when the diffusion zones of the nuclei start to overlap. According to different authors, nucleation density and nucleation rate may vary from 103 to 1011 cm22, and from 103 to 1010 cm22/h, respectively, depending on the substrate material, its pretreatment, and the deposition conditions. 2.3.2.1.
Nucleation of Diamond on Different Substrates
Nucleation on different substrates proceeds in different ways. There are certain conditions that must be fulfilled by a substrate in order for the nucleation and growth to
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take place on its surface. The first condition is obvious—the substrate material must be able to withstand temperatures higher than that needed for diamond deposition. This condition excludes, for example, the low-melting metals. Another, lessobvious condition is that carbon should not be dissolved in the substrate material under the deposition conditions. This excludes the transition metals (such as Fe). Stresses caused by different coefficients of thermal expansion (CTE) between the substrate and the diamond film further limit the choice of substrate materials. Because of a very low CTE of diamond, large compression stresses will develop in the film upon cooling (after the deposition) if CTE of the substrate material is large, because the substrate tends to shrink upon cooling more than the deposited diamond film. Figure 2.12 shows the CTE of different materials with respect to that of diamond.[29] Because the CTE values of many materials are considerably larger than that of diamond, such materials are not suitable as substrates, at least if the diamond film is to adhere firmly to the substrate on its entire surface. It is possible that the film adheres firmly to the substrate despite a large difference in CTE. Such is the
Figure 2.12 Typical values for thermal expansion coefficient at 300 K for a variety of substrate materials. The majority of materials have much larger CTE than diamond.[29] (Reproduced by permission of The Royal Society of Chemistry.)
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case with a quartz substrate, where growth of diamond proceeds via formation of a thin interfacial silicon carbide layer. Thus it is possible to grow thin adherent films of CVD diamond. However, owing to a large difference in CTE, a thicker diamond film will crack into a number of “plates” which will remain firmly adherent to the substrate. Knuyt et al.[30] attempted to find a relationship between the “critical” thickness of a diamond film, D, defined as the thickness in excess of which a sudden delamination may take place, and properties of the substrate and the film, as well as the substrate temperature. The relationship (for the most frequent case when the substrate thickness is much larger than that of the film), D
4:31 g 2 Ey (DaDT)2
(2:6)
where g is a mean interfacial surface energy, Ey is Young’s modulus, Da is the difference in CTE between substrate and film, and DT is the difference between deposition temperature and room temperature, shows that critical thickness is most dependent on the difference in CTE of the substrate and the film, and on substrate temperature. For a given substrate material, the CTE difference cannot be changed, and deposition temperature must remain nearly the same. There remains the possibility to increase the film adhesion by increasing the surface energy, which can be achieved by substrate surface pretreatment. The substrate usually becomes rougher (i.e., its surface area is increased). A survey of substrate materials is presented in Table 2.3.[26] If carbon – substrate interaction is considered, the substrate materials can be subdivided in three classes: 1.
2.
3.
Little or no C solubility or reaction. These include diamond itself, graphite, and carbons (including DLC), then Cu, Ag, Au, Sn, Pb, Ge. Except on diamond, which has the best nucleation potential, little spontaneous nucleation takes place on these substrates because of a weak substrate–carbon interaction. However, nucleation readily occurs on substrates that form amorphous DLC (mostly Mo and Si) or a graphite interlayer that positively affects diamond nucleation (Ni, Pt, Cu, and Si). C diffusion. Here the substrate acts as a carbon sink, whereby deposited carbon dissolves into the metal surface to form a solid solution. This causes large amounts of carbon to be transported into the bulk, leading to temporary decrease in surface C concentration, delaying the onset of nucleation. Elements where this is significant include Pt, Pd, Rh, Fe, Ni, and Ti. For substrates with a very high C diffusion rate, sample thickness becomes a significant parameter influencing the onset of nucleation, because thin foils reach their carbon saturation more rapidly than thick plates do. Carbide formation. The carbide-forming elements can be subdivided into three groups, depending on carbide type: carbides of Ti, Zr, Hf,
660 2200
2202
1064 1770 1650
2927 2467 3497
2980 3540 1860
1895
2615 2690
Substrate material
Al (fcc) Al4C3 (rhombic)
AlN (hexagonal)
Au (fcc) Pt (fcc) Fe3C (orthorombic)
TiN (cubic) Nb (bcc) NbC (bcc)
Ta (bcc) TaC (fcc) Cr(a) , 18408C (bcc)
Cr3C2 (orthorombic)
Mo (bcc) Mo2C (hcp)
0.282 0.552 1.146 0.314 0.301
0.404 0.333 2.494 0.310 0.497 0.407 0.392 0.452 0.509 0.675 0.424 0.3294 0.4424 – 0.4457 0.330 0.445 0.289
Lattice constantb (nm)
10.200 9.180
6.700
16.600 14.480 7.100
5.430 8.600 7.820
19.300 21.450 7.400
3.300
2.700 2.950
Densityc (g/cm3)
8.00
5.1 7.8– 9.3
10211 —
6.5 6.29 6.5
10214 — 4 1028 —
9.35 7.2 6.52
14.1 9.0 6.0
4.84
23.5
Thermal expansion coefficiente (1026 K21)
— 3 10212 —
— — —
—
—
Carbon diffusivityd (cm2/s)
(continued )
2.877/2.116
2.056/1.913
3.018/2.270
2.983/2.022
1.626/1.345 2.691/2.055
1.085/0.939
Surface energyf (J/m2)
Physical Parameters of Currently Used and Potential Substrate Materials—Elements and Their Carbides, Nitrides, and Oxides[26]
Melting pointa (8C)
Table 2.3
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2776
W2C (hcp)
1852 3260
2227
Zr (b) . 8408C (bcc) ZrC (fcc) Hf(a) , 13108C (hcp)
Hf(b) . 13108C (bcc)
Zr (a) , 8408C (hcp)
3387 2627
Melting pointa (8C)
W (a) (bcc) WC (hcp)
Substrate material
Table 2.3 Continued
0.474 0.316 0.290 0.283 0.299 0.471 0.323 0.514 0.361 0.467 0.319 0.520 0.350
Lattice constantb (nm)
5.800 6.660 13.100
6.490
17.150
19.300 15.800
Densityc (g/cm3)
— 6.1 6.0
3 1028 — 10213
—
5.9
8 10211
—
3.58
4.5 4.42
Thermal expansion coefficiente (1026 K21)
—
10213 —
Carbon diffusivityd (cm2/s)
3.333/1.701
2.790/1.554
3.468/2.487
Surface energyf (J/m2)
100 Marinkovic´
1710
2447
2049
2850
SiO2 (hexagonal)
B4C (rhombohedral)
Al2O3 (hexagonal)
Y-ZrO2 (cubic)
0.446 0.3024 0.417 0.7603 0.2909 0.3464 0.4382 0.560 1.212 0.4785 1.2991 0.507 5.560
3.970
2.510
2.320
12.520 6.100 5.770 3.187
—
—
—
—
— 1 1028 — —
4.0
7.5
4.5
0.55
6.27 8.3 7.2 2.11 2.876/2.082
Note: The dash (—) denotes that the data are not available. a At 1 bar. b At room temperature, or at the temperatures at which the phases exist. c At 208C. d Calculated for 8008C for most metals, or for the lower limit of temperature range for the phases existing above 8008C. e 0–1008C for metals, diamond, and graphite; 25–5008C for ceramics. f Surface energy at 258C/surface energy at melting temperature. The surface energies do not include the effects of surface reconstruction, physisorpion/chemisorption, or other surface reactions.
3887 1902 3327 2442
HfC (fcc) V (bcc) VC (fcc) Si3N4(b) (hexagonal)
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V, Nb, Ta, Cr, Mo, W, Fe, Co, and Ni (Ni carbide is metastable) have metal characteristics, B and Si form covalent, and Al, V, and rare earth elements ionic carbides. Si, Mo, W, Nb, and Ta, which form stable refractory carbides, are most suitable for diamond deposition. Carbide interlayer with a limited thickness is formed first, and diamond deposition then follows. Si is particularly popular as substrate material. Its melting point (14108C) is high enough, Si forms a localized carbide layer and has a relatively low CTE. Suitability of W and Mo has also led to their extensive use. Mo is especially used as a substrate in methods permitting high deposition rates, because of its thermal shock resistance. The deposition rate is greater for deposition sources for which higher temperature (i.e., higher energy density) is an inherent characteristic (see Section 2.4.2), and higher energy density leads to faster substrate heating (i.e., to a larger thermal shock). The rate of nucleation on elements that form stable carbides (Si, Mo, and W) is one or two orders of magnitude greater than on non-carbide-forming elements (Cu and Au) under analogous deposition conditions. The nucleation rate is several times greater on a polycrystalline than on a single crystal substrate of a given material, the surface of which has been pretreated by the same procedure. Refractory carbides (TaC, WC and Mo2C) and certain covalent carbides (SiC and B4C) have a positive effect on nucleation. The effect of ionic carbides (Al4C3) is less known. For certain substrates (e.g., Ti) the carbide layer continues to grow during deposition, and its thickness can reach hundreds of micrometers. Obviously, a layer of such thickness can strongly affect mechanical properties, and therefore the suitability of diamond deposition becomes questionable. Boron, as well as Si-containing compounds (SiO2 , quartz, and Si3N4), also form carbide layers. The suitability of carbide-forming substrates for diamond nucleation can be judged from the fact that typical nucleation density on such substrates (without pretreatment) is of the order of 106 nuclei/cm2, while it is 1000 lesser for other substrates. Recent results[24,25] have shown that diamond nucleation can be effected without the presence of (atomic) hydrogen. The authors have used fullerene as the carbon source (although they found that similar results are obtained if methane is used instead) and argon. Under such conditions, nanocrystalline diamond was obtained with crystallite size distribution that peaks at 3– 5 nm. The explanation for nanocrystallite formation offered by the authors is that embryonic nuclei, which in the presence of hydrogen would be gasified, in the absence of hydrogen continue to grow and reach critical size. However, owing to high nucleation rates, the growth is restricted to nanocrystalline size. Nanocrystalline diamond was deposited on many different substrates. 2.3.2.2.
Nucleation on an Intermediate Layer
It is widely believed that nucleation of diamond in most cases takes place on intermediate layers of DLC, metal carbides, or graphite. The intermediate layer is formed on the substrate surface as a result of chemical reactions involving
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the active gaseous species and the surface during the incubation period and it in turn provides nucleation sites for diamond crystallites. In this way morphology, orientation, and texture of the diamond layer are controlled. The interlayer thickness can be several tenths of a nanometer (0.6 nm of graphite on Pt), several nanometers (8 nm of graphite on Ni; 8 –14 nm of DLC on Cu; 20 nm of amorphous DLC on Si; and 1– 10 nm of SiC on Si), or several micrometers (1.5 – 3 mm of Mo2C on Mo). The nucleation mechanisms, as proposed in the literature, are presented in Figs. 2.13 –2.15. Nucleation on an intermediate layer of diamond-like amorphous carbon: High-resolution transmission electron microscopy (HRTEM) study
Figure 2.13 Schematic summarizing the proposed nucleation mechanism on a DLC interlayer: I, formation of carbon clusters and change in bonding structure from sp1 to sp2; II, conversion of sp2 to sp3 bonding; III, crystallization of amorphous phase; IV – VI, growth and faceting of diamond crystal; VII, secondary nucleation and growth of diamond.[31]
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Figure 2.14 Schematic of proposed nucleation mechanism: diamond nuclei form on a carbide-forming refractory metal. Initially, carburization consumes all available C to form a carbide surface layer. A minimum C surface concentration required for diamond nucleation cannot be reached. With increasing carbide layer thickness, the C transport rate decreases and the C surface concentration increases. Nucleation starts when the C surface concentration reaches a critical level for diamond nucleation, or a surface C cluster attains a critical size.[35]
of nucleation and growth of diamond on copper provided direct evidence for the formation of a diamond-like amorphous carbon layer 8 –14 nm thick, in which small diamond nanocrystallites (2– 5 nm) were embedded, and large diamond crystallites were observed to grow from these nanocrystallites. It was suggested[31] that nanocrystallites were formed as a result of direct transformation of a-C into diamond, with the intermediate layer providing nucleation sites. Figure 2.13 depicts the detailed nucleation mechanism proposed on the basis of these experimental observations. In step I, carbon clusters are formed on the substrate surface, and a change in bonding structure from sp1 to sp2 takes place. In step II, sp2-bonded carbons are converted into a relatively stable network of sp3-bonded carbon. The continuous molecular flow of activated hydrocarbon and atomic hydrogen on the substrate surface provides sufficient energy for the sp1 ! sp2 ! sp3 conversion. At the same time, etching of unstable phases (sp1 and sp2), which is 10 faster than etching of stable phase (sp3),[31] promotes and stabilizes the sp3 phase. In step III, a transition of the bonding state in the carbon network occurs from a disordered domain with sp3-bonded carbon to diamond. Crystallization in the amorphous layer also includes chemical reactions (e.g., hydrogen abstraction, dehydrogenation of adsorbed complexes, and recombination of hydrogen atoms). During crystallization, carbon atoms rearrange into f111g planes to achieve a minimum surface energy. The crystallized regions then act as nuclei for subsequent growth. In steps IV – VI, diamond growth takes place. Carbon atoms added to the surface (step IV) diffuse inwards by a solid-state diffusion
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Figure 2.15 Schematic showing a proposed nucleation mechanism on a graphite interlayer:[36] Initial condensation of graphite and subsequent hydrogenation of the f11 00} prism planes along the edges of graphite particles are followed by kinetically preferred nucleation of diamond at the emerging graphite stacking faults, resulting in an almost perfect interface between the graphite layer and the diamond nucleus. Upper: cubic diamond on perfect hexagonal graphite. Lower: a twinned diamond nucleus adjoining a graphite stacking fault. Twin boundaries in diamond are indicated by the dashed lines, H atoms by the small open circles, and C atoms by dark solid circles. The larger open circles indicate the initial nucleus formed at the interface by tying together the graphite layer with tetrahedrally bonded C atoms. [Reprinted with permission from Nature, Lambrecht et al., 1993; Copyright (1993) Macmillan Magazines Limited.]
process. The initial diamond shape is hemispherical (step IV), but once the diamond microcrystal reaches a critical size (step V), it will acquire a faceted crystallographic shape characterized by defects such as points, stacking faults, and twins (step VI). In step VII, secondary nucleation takes place as a result of concentration fluctuation on the surface of the diamond crystal. This fluctuation leads to an uneven surface of the disordered domain, whose thickness varies from 8 to 14 nm, depending on deposition conditions. Once the thickness of the
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disordered domain exceeds a critical value (above 15 nm), there will not be enough localized thermal energy or time available for carbon atoms to diffuse into the diamond crystal, thus leading to secondary surface nucleation. Formation of a DLC interlayer has also been observed by some researchers in experiments examining diamond nucleation on Mo and Si substrates. It was found that diamond crystallites are not located directly on the substrates but on an intermediate amorphous layer. Nucleation of diamond occurs readily on disordered carbon surfaces, and the formation of this type of intermediate layers is indeed one step in the nucleation mechanism of diamond. Nucleation on an intermediate carbide layer: The suggestion that diamond nucleation on Si is preceded by the formation of a b-SiC buffer layer, and that nucleation occurs on the carbide surface[32] is supported by numerous growth experiments of diamond particles or films on Si substrates in HF and MW CVD. It was shown that the Si surface is indeed transformed to SiC under the conditions leading to diamond growth and diamond nucleation occurs on the SiC intermediate layer. Formation of a Mo carbide layer in the initial stage of diamond film deposition was also reported in DC arc and MW CVD. Our results[33] show that Mo2C is initially formed in combustion flame diamond deposition. In diamond growth experiments on Mo and Si substrates using MW CVD, Mo2C and SiC layers of ca. 1.5 mm and 10 nm thickness were observed within 1 min and after 5 min, respectively.[34] The growth rate of SiC was much less than that of Mo2C. Diamond nanocrystallites were observed after 1 min, and no further carbide layer growth was detected once the surface was covered with diamond. Systematic studies of diamond growth on carbide-forming refractory metals have shown that diamond nucleation occurs only after the formation of a thin carbide layer. A model elucidating the mechanism governing the nucleation process was proposed (Fig. 2.14).[35] Carbon is suggested to initially dissolve into the substrate, resulting in the formation of a stable carbide. Diamond nucleation occurs on the carbide layer when the surface carbon concentration reaches its saturation value. Differences in nucleation density on Ti, Hf, Nb, Ta, Mo, and W substrates can be explained by carbon diffusivities in the respective substrates. The shortest incubation period is on the metal on the surface of which supersaturation of carbon is most rapidly achieved.[35] Nucleation on a graphite interlayer: Studies of diamond nucleation on Pt showed the existence of an initial incubation period during which an oriented graphite deposit formed. This deposit subsequently disappeared and the final deposit contained only polycrystalline diamond. Other experiments on Ni and Pt by HF CVD and on Si and Cu by MW CVD have also provided direct evidence for formation of graphite on substrates prior to diamond nucleation. The graphite film was found to strongly stimulate diamond nucleation.[26]
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On the basis of these experimental results and certain calculations, a detailed nucleation mechanism was proposed (Fig. 2.15). Graphite initially condenses on the substrate surface and the {11 00} prism planes are subsequently hydrogenated. Diamond nuclei are formed preferentially on the prismatic graphite planes with kinetically preferred nucleation at the emerging graphite stacking faults, and with an almost perfect interface between graphite and diamond nuclei. A preferential epitaxial lattice registry relationship exists between graphite and diamond, that is, {111}diamond k {0001}graphite . Later experiments showed also a definite orientation within the planes, that is, ½11 0diamond k ½112 0graphite . This relationship means that the puckered six-member rings in the diamond f111g plane retain the same orientation as the flat six-member rings in the graphite basal plane. Atomic hydrogen has multiple roles in this process: by terminating the dangling surface bonds, it stabilizes the tetragonally coordinated sp3-nuclei; it also etches graphite away during diamond nucleation and serves as a reactive solvent which allows conversion of graphite nuclei into diamond nuclei, thus circumventing the large activation barrier between graphite and diamond. This mechanism is consistent with the experiment-based conclusion that incubation time needed for diamond nucleation is the shortest on the metal that can most rapidly achieve a supersaturation of carbon on the surface. The aforementioned nucleation mechanism could be the dominant means of spontaneous nucleation of new diamond crystals in the absence of diamond germs. If large diamond single crystals are to be grown, precursors for graphite nucleation should be eliminated; secondary nucleation that prevents growth of diamond single crystals is thus suppressed. Conversely, in order to grow faster highly oriented polycrystalline diamond films, it is desirable to enhance diamond nucleation using precursors for graphite formation during the initial stage of heteroepitaxial deposition, when a rapid coalescence of oriented diamond nuclei is necessary. It should be noted, however, that the nature of intermediate layer formed depends not only on substrate material and pretreatment method but also on deposition conditions. For example, during deposition by HF CVD, graphitic carbon is initially formed on Pt substrate, but on Ni a thick graphite layer is formed prior to diamond nucleation. Diamond is eventually nucleated on defect sites in these graphite deposits. Moreover, different gas compositions can produce different intermediate layers on the same substrate. Thus, on Si pretreated by diamond paste, interfacial single-crystal b-SiC was grown from 0.3% CH4 in H2 , whereas an amorphous interlayer was observed with 2% CH4 in H2 . Hence it can be concluded that the interlayer formation is a step in the spontaneous nucleation of diamond on nondiamond substrates, but this alone is not sufficient for nucleation to occur. To get sufficient conditions for diamond nucleation on intermediate layers of amorphous DLC, carbide, or graphite, surface carbon saturation and the presence of defects or high-energy sites in these layers are needed.[26] It has been shown that in most CVD processes the critical nucleus consists of a small number of atoms. Under such conditions, the free energy of formation
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of a critical nucleus can be negative, while a surface energy contribution can produce an opposite effect on phase stability, which is the case known as nonclassical nucleation process. In this case, a nanometer-sized diamond nucleus can be more stable at normal pressure than a graphite nucleus containing an equal number of atoms. It has been shown that surface energy is an important factor in stabilizing a nanocrystal of diamond. Thus diamond (sp3) nuclei smaller than 3 nm, with hydrogen-saturated surface valences, have lower energy than sp2-nuclei with the same number of carbon atoms. This is in agreement with results of numerous authors who used thermodynamic methods to conclude that hydrogen stabilizes the diamond surface. The already mentioned conclusion that follows from these results (i.e., that diamond can be more stable than graphite on the surface) is true, of course, only if the conditions mentioned are fulfilled, among which the presence of sufficient atomic hydrogen content is essential. Yet, it should be pointed out that in the case of fullerene/argon (i.e., hydrogen-free) mixture (Section 2.2.3), the role of atomic hydrogen, essential for most CVD systems, is apparently taken over by C22C dimers. 2.3.2.3.
Surface Pretreatment Methods and Nucleation Enhancement Mechanism
Since spontaneous nucleation on nondiamond substrates is usually insufficient for a continuous diamond film formation, various means have been applied to enhance nucleation density. Mechanical defects are produced on the substrate surface, tiny particles of diamond, cubic boron nitride, or of a suitable carbide are brought to it (“seeding”), a suitable interlayer is formed by coating or by producing it on the surface, the surface is modified by chemical pretreatment, positive or negative biasing is applied, or some other, more sophisticated techniques are used (e.g., ion implantation and laser irradiation). A combination of different techniques is often used. By these means, the nucleation densities of up to 1010 nuclei/cm2 have been obtained, but extremely high values (2 1011 and 1012 cm22) have been reported,[37] being only two orders of magnitude less than the maximum theoretical nucleation density (1014 cm22) calculated from the critical nucleus size (2–3 nm). The nucleation density values obtained by pretreatment of the substrate surface using diferent methods are summarized in Table 2.4. Nucleation occurs most readily on particles with high carbon and/or defect content (scratches, grain or particle boundaries, dislocations, imperfections created by electron bombardment, and edges of etch pits/craters). It follows from the reported data (Table 2.4) that ultrasonic scratching and electrical biasing are the most effective techniques, followed by, for example, scratching, seeding, covering/coating, and ion implantation. As schematically depicted in Fig. 2.16, nucleation density enhancement by scratching is principally attributed to: (a) seeding effect; (b) minimization of interfacial energy on sharp convex surfaces; (c) breaking of a number of
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Table 2.4 Typical Diamond Nucleation Densities after Various Surface Pretreatments[26] Pretreatment method No pretreatment Scratching Ultrasonic scratching Seeding Electrical biasing Covering/coating with Fe film Graphite film Carbon fibers a-C film (first scratched) C70 clusters þ biasing Y-ZrO2 , a-BN, cSiC layer Cþ ion implantation on Cu Asþ ion implantation on Si Pulsed laser irradiation þ coating with a-C, WC, cBN Carburization
Nucleation density (cm22) 103 – 105 106 – 1010 107 – 1011 106 – 1010 108 – 1011 4.84 105 106 .109 3 1010 ¼Seeding effect Enhancement Enhancement 105 – 106 Enhancement Enhancement
surface bonds, or presence of a number of dangling bonds at sharp edges f100g; (d) strain field effects; (e) rapid carbon saturation (fast carbide formation at sharp edges); and (f ) removal of surface oxides.[35] In a recent detailed study of diamond nucleation on scratched Sif100g surfaces,[38] two pathways for diamond formation and growth have been detected: a seeding pathway occurs by direct growth of the diamond seeds left by scratching; a nucleation pathway is a stepwise process including the formation of extrinsic
Figure 2.16 Schematic diagram of mechanisms for diamond nucleation enhancement on scratched substrates.[35]
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(formed by pretreatment) or intrinsic (formed during CVD) nucleation sites, with subsequent formation on them of carbon-based precursors before further diamond nucleation. The nucleation sites are believed to be either grooves made by scratching or protrusions less than 100 nm in size, produced by silicon etching – redeposition. On top of these protrusions, as well as on the bare substrate, a thin (1 nm) layer of silicon carbide rapidly forms. DLC is also present. Diamond nucleation can occur at the end of this stepwise process. Carbon-based embryos for further nucleation are believed to form on top of silicon protrusions covered either by silicon carbide or DLC. Another possible operating mechanism for nucleation enhancement by scratching consists in producing nonvolatile graphitic particles through local pyrolysis of adsorbed hydrocarbons. These graphitic clusters would be subsequently hydrogenated in the atomic hydrogen environment under the typical CVD conditions to form the precursor molecules. The effectiveness of scratching of different substrates decreases from Si to Mo to WC. Abrasives used for scratching pretreatment include diamond, oxides, silicides, nitrides, carbides, and borides. The effect of the abrasives on nucleation enhancement increases in the following order: silicides , SiO2 , nitrides , ZrO2 , carbides , borides , Al2O3 , c-BN , diamond. It has been shown that nucleation density decreases with increasing particle size of diamond paste in the polishing pretreatment, but increases with particle size in the ultrasound scratching pretreatment. In general, however, the optimum size of abrasive particles depends on pretreatment methods, deposition process, growth conditions and nature of substrate materials. Different techniques (dipping, spinning, spraying, and electrophoretic seeding) have been employed to seed diamond, Si, Al2O3 , and SiC on various substrates.[26] The residual diamond seed particles on the substrate surface are the predominant nucleation sites (or the seed particles themselves are nuclei) and diamond growth then occurs homoepitaxially on these seed particles. Nucleation density is linearly proportional to the diamond seed particle density, being approximately one-tenth of the latter. Seeding also provides the possibility for epitaxial or highly oriented growth of diamond films on nondiamond substrates. Biasing a substrate can help to reduce and suppress oxide formation on the substrate surface, remove native oxides, and overcome the energy barrier for the formation of stable diamond nuclei by more effectively activating the substrate surface and/or increasing the flux and mobility of adatoms, as schematically shown in Fig. 2.17. Thus biasing of silicon leads, in addition to creating the surface defects (point defects, steps, and sp3-bonded carbon clusters) that serve as nucleation sites, to enhanced surface diffusion and sticking probability of carbon due to ion bombardment. In general, results obtained for the bias-enhanced nucleation point to the dominant role of ion bombardment in nucleation. The nucleation sequence may be as follows: (1) formation of nucleation sites; (2) formation of carbon
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Figure 2.17 Schematic diagram of mechanisms for diamond nucleation enhancement on biased substrates: (a) negative bias, carbon-containing cations are accelerated toward the substrate surface and (b) positive bias, electrons are accelerated towards the substrate surface and bombard carbon-containing molecules adsorbed on the substrate.[26]
clusters due to enhanced surface diffusion; and (3) formation of stable diamond nuclei. In DC plasma, positive substrate biasing is effective for increasing diamond nucleation, while in MW plasma and HF CVD this is achieved with both positive and negative biasing. By varying the duration of biasing pretreatment and/or the applied voltage and current, nucleation density can be controlled over three to six orders of magnitude (Fig. 2.18). Higher absolute values of the applied substrate
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Figure 2.18 Diamond particle density as a function of substrate bias voltage, gas pressure, and CH4 concentration: (a) 2%; (b) 10%; and (c) 40%.[26]
bias voltage lead to higher nucleation densities. At the same absolute bias voltage values and for CH4 concentrations from 10% to 40%, the nucleation densities on negatively biased substrates are one or two orders of magnitude higher than those on positively biased substrates. However, the bombardment by cations in negative biasing leads to roughening of Si surfaces, whereas positively biased Si substrates maintain smooth surfaces. Therefore, positive biasing is a more suitable pretreatment for Si substrates. With increasing bias current, the grain size and nondiamond carbon incorporation in diamond films decrease, with a concomitant increase in Young’s modulus and fracture strength, while large compressive stresses in the films decrease and turn to tensile stresses.[26] Nucleation enhancement has also been achieved by covering substrate surfaces with carbon fibers, clusters, or films, as well as by their coating with thin films of metals (Fe, Cu, Ti, Nb, Mo, and Ni), C70 , a-C, DLC, Y-ZrO2 , a-BN and SiC, or hydrocarbon oil. The efficiency of the overlaid materials on nucleation enhancement decreases in the order C70 . a-C . DLC . carbon fiber . graphite film . Fe . Cu . Ti . Ni . Mo . Nb. The thickness of the overlayers ranges
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typically from a few nanometres (2–8 nm for metal films, 10–20 nm for an evaporated C layer, 100 nm for a C70 layer, and 150 nm for a Y-ZrO2 layer) to about 1 mm (less than 1 mm for a carbon film). The nucleation enhancement is attributed to the physical and chemical effects associated with changes to the substrate surface (the overlayers promote carbon saturation at the substrate surface, and provide high-energy sites or nucleation centers, as well as changes to the gas chemistry in the immediate vicinity of the substrate surface).[26] Our own systematic study was concerned with effects of different combinations of several pretreatment procedures on WC-Co substrate surface modification and some properties of diamond coatings subsequently deposited by combustion flame CVD.[39,40] The pretreatment procedures examined were: action of an oxidizing oxygen – acetylene flame at 10008C, ultrasonic scratching with a suspension of diamond particles (14 – 20 mm), ultrasonic scratching with a suspension of diamond and iron particles, and seeding with a nanometer diamond colloidal suspension. An acid treatment was always included in the pretreatment sequence. A suitable statistical method was used to establish the effect of each treatment procedure on the basis of results of a small number of pretreatment experiments. The highest diamond particle density (used as a measure of nucleation density) is achieved if pretreatment by seeding and ultrasound scratching with diamond are used. However, optimum properties of the diamond coating— minimum surface roughness and maximum adhesion—are achieved by a pretreatment sequence including flame treatment, acid, and finally seeding. Other authors attempted to modify the surface energy and surface structure of substrates using ion implantation in order to enhance diamond nucleation. Implantation of Cþ (1018 ions/cm2, 65 – 120 keV) on Cu and Asþ (1014 ions/ cm2, 100 keV) on Si enhances diamond nucleation, while Arþ implantation (3 1015 ions/cm2, 100 keV) on Si decreases nucleation density. The nucleation density enhancement was attributed to lattice damages (strain, amorphous disorder, and twinning). The implantation of Siþ ions into a mirror-polished Si wafer was found to change the surface structure. After treatment with an Siþ energy of 25 keV and an implantation dose of 2 1017 cm22 diamond could easily nucleate and grow, and a continuous film was obtained. The proposed explanation is that the implantation of Siþ ions creates nanoscale surface defects on the Si substrate which serve as the active sites for the adsorption of hydrocarbon radicals necessary for initial diamond nucleation.[41] Pulsed laser irradiation of a thin buffer layer of a-C, WC, or c-BN deposited on Cu, stainless steel, or Si substrates leads to significant enhancement of both nucleation density and adhesion of diamond films. It is speculated that the irradiation converts a portion of the a-C on the surface into diamond or results in the formation of a reaction product that facilitates diamond nucleation.[26] Carburization of substrates (Mo, W, Si, and Fe/Si) also leads to nucleation enhancement owing to the formation of carbides and the saturation of carbon at the substrate surface.
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In summary, scratching and seeding are simple and effective for diamond nucleation enhancement, but they cause surface damage and contamination. In addition, these methods cannot be easily applied to substrates of complex geometry and shape. For many applications requiring extremely smooth, clean surfaces (diamond films for electronic devices, optical windows, and smooth wearresistant coatings) these techniques are inapplicable. Therefore biasing or covering/coating of substrate surfaces is used, resulting in high nucleation densities comparable to or even higher than those achieved by seeding or scratching, yet without significantly damaging the surfaces. 2.3.2.4.
Effect of Deposition Conditions on Nucleation
Substrate temperature, gas pressure, gas composition, and means of activation critically influence nucleation density and rate. It has been noted that ideal conditions for growth may not be optimal for nucleation. Thus, biasing of Si substrates could significantly enhance nucleation, but a much poorer quality diamond film was grown if the biasing was continued during the growth. Similarly, the optimal values of gas pressure and substrate temperature for growth are different from those for nucleation.[26] Table 2.5 summarizes the optimum deposition conditions for diamond nucleation (ranges, values, or tendency), as reported in the literature. The temperature dependence of nucleation density (Fig. 2.19) with a maximum near 8608C is speculated to be caused by the change in the adsorption state and surface diffusion length of growth precursors.[26] Table 2.5
Optimum Ranges and Values of Process Parameters for Diamond Nucleation[26]
Parameters Substrate temperature MW HF Gas activation Filament temperature in HF Discharge current in DC discharge Power density Gas pressure HF, MW HF, MW (recent results) Gas composition Gas flow rate Oxygen addition MW HF Arc jet
Optimum ranges, values, or tendency
830– 8608C 850– 10008C 21008C Nd increases with increasing discharge current Nd increases with increasing power density 7 mbar 0.1 – 1 mbar Nd increases with increasing CH4 % in H2 Nd increases with increasing gas flow rate Favors nucleation Suppresses nucleation 33% O2 decreases Nd
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Figure 2.19 Temperature dependence of diamond nucleation density. Solid and dashed lines show values for 1000 and 1400 W MW power, respectively.[26]
The precursors are thought to be adsorbed on the substrate mainly by physical adsorption below 9008C, and predominantly by chemical adsorption above this temperature, accompanied by an abrupt increase in the diffusion length of the precursors around 9008C. As a result, the capture rate of the precursors (sticking probability) on the substrate surface, and hence the nucleation rate and density, drastically increase when the substrate temperature approaches 8608C. The effect of filament temperature (in HF) on nucleation is similar to that of substrate temperature, that is, with increasing filament temperature nucleation density initially increases, reaches a maximum at 21008C and then decreases, with 21008C being a possible optimum value. The drop-off for T . 21008C is explained by the observation that the etching of nucleation sites is enhanced with increasing filament temperature. In DC plasma, nucleation density of 6 109 cm22 on untreated substrates was achieved by increasing the discharge current to 1 A and the cathode temperature to 14008C. It has also been suggested that diamond nucleation can be enhanced by using high power densities, such as in plasma jet, in which H2 and CH4 dissociation is promoted. Low gas pressures (about 7 mbar), high CH4 concentration (Fig. 2.18), and/ or high gas flow rates in bias pretreatment lead to high nucleation densities. The pressure dependence of nucleation density is explained by the competition effect between b-SiC formation, which increases Nd , and etching by atomic hydrogen, which decreases the number of nucleation sites. High CH4 concentration can
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promote carburization of the substrate surface and accelerate carbon saturation at the substrate surface, while a high gas flow rate may increase the mass transfer of gaseous species to the substrate surface. Consequently, diamond nucleation density can be enhanced.[26] Recently, diamond nucleation has been conducted under very low pressures (0.1 –1 mbar) whereby a very high nucleation density (109 –1011 cm22) has been achieved on mirror-polished Si substrates, using either HF or MW plasma CVD without applying surface scratching or a substrate bias. Both diamond and graphite have been found in the nucleated samples. Similar results have been obtained on Ti substrates.[39] The addition of oxygen to the gas mixture can accelerate the saturation of carbon on the substrate surface, reduce the incubation period, and promote diamond nucleation and growth which become much faster than with oxygenfree plasma. The presence of oxygen allows the use of lower substrate temperatures, preserves a good film quality at high CH4 concentrations, and suppresses possible surface contamination by Si. However, the addition of oxygen is also reported to suppress diamond nucleation by etching nucleation sites (graphite) on Ni and Pt substrates. An optimum oxygen concentration is found to be about 33% in plasma arc jet, and 2–10% in low-pressure low-temperature MW plasma.[26] In conclusion, it is evident from the published literature that technological problems associated with nucleation of polycrystalline diamond films have been adequately addressed, as demonstrated by the development of numerous methods for nucleation enhancement, selective nucleation, and textured/oriented growth. However, scientific issues associated with the nucleation process remain less well understood. A clear picture of diamond nucleation in CVD is still needed to provide an insight into the nucleation kinetics. A comprehensive theoretical model is required in order to achieve a thorough understanding of the nucleation process and to obtain more reproducible and predictable results.
2.4.
MECHANISM OF DIAMOND GROWTH
The complex chemical and physical processes that occur during diamond CVD comprise several different but interrelated features. The process gases first mix in the chamber before diffusing toward the substrate surface. On the way, they pass through an activation region (e.g., an HF or electric discharge), which provides energy to the gaseous species. This activation causes molecules to fragment into reactive radicals and atoms, creates ions and electrons, and heats the gas to temperatures approaching a few thousand kelvins. Beyond the activation region, these reactive fragments continue to mix and undergo a complex set of chemical reactions until they strike the substrate surface. At this point the species can either adsorb and react with the surface, desorb again back into the gas phase, or diffuse around close to the surface until an appropriate reaction site is found. If surface reaction occurs, one possible outcome, if all conditions are suitable, is diamond.
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The reactions occurring in the gas phase in which active gaseous species are formed have been discussed in Section 2.2. In Section 2.3, we have described how diamond nuclei could be formed from these active species. What remains is to see how the nuclei grow to form a continuous diamond layer. Several most important reactions taking place at the surface of diamond during growth are shown in Table 2.6.[14] Although carbon atoms in the bulk of diamond are fully bonded by sp3 bonds, the surface atoms are not. At the surface there are “dangling bonds” (i.e., free valences), which need to be saturated in some way in order to prevent cross-linkage and subsequent reconstruction of the surface (i.e., formation of sp2 bonds typical for graphite). Since atomic hydrogen is abundant in the vicinity of the surface (Section 2.2), it readily reacts with the dangling bonds, ensuring their necessary termination (Table 2.6, reaction 1 on substrate) and, hence, stabilization of the diamond lattice. Atomic hydrogen may, however, react with these hydrogenated carbon atoms, abstracting hydrogen and recreating dangling bonds (reaction 2). This reaction is exothermic, because the H22H bond is very strong. Yet, instead of hydrogen, the free radical CH3 (which is present in much lower concentration than atomic hydrogen) will sometimes be bonded to the free valence (reaction 3). But, even if the free radical is bonded, this does not necessarily lead to diamond growth, because surface reconstruction (sp2hybridization) is possible. Here again atomic hydrogen helps by efficiently etching the graphitic structures. The etching of graphite is known to be more rapid than its growth and the net effect is disappearance of graphite. However, in the case of diamond, its etching is much slower and the net effect is diamond growth.[12] There are many publications in which the identification of the gaseous species responsible for diamond growth has been studied. The excellent recent review by Goodwin and Butler[18] which includes this and other aspects of the theory of diamond CVD has already been mentioned. The growth species proposed include C, C2 , C2H, CH3 , C2H2 , CHþ 3 , as well as diamondoids, such as adamantane.
Table 2.6
Standard Enthalpy and Free Energy Changes of Some Important Reactions During HF CVD of Diamond[14]
Reaction
T (K)
DH (kJ/mol)
DG (kJ/mol)
On filament 1. H2 ! 2H
2500
þ456
þ155a
On substrate (S) 1. H þ S ! S2 2H 2. S2 2H þ H ! S þ H2 3. CH3 þ S ! S2 2CH3
1200 1200 1200
2393 254 2339
2284 225 2197
a
At 26.6 mbar and 2500 K, the equilibrium mole fraction of atomic hydrogen is 0.16.
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However, since diamond can be grown in systems which have few ions present (e.g., HF CVD), this suggests that the dominant growth species must be neutral. In addition, numerical simulations have shown that diamond growth can be accounted for by a single species and a single surface mechanism.[18] Based on a number of studies aimed at growth species identification, there is a general consensus today that CH3 is the dominant radical in conventional CVD processes. The data suggesting this conclusion were obtained from direct (in situ) detection of the radicals using various spectroscopic methods (mass spectrometry resonant enhanced multiphoton ionization spectroscopy), IR absorption, results of kinetic modeling of the experimental deposition rate and gas phase chemistry, as well as a number of isotope labeling methods. Yet, recent papers[42] suggest, inconsistent with earlier studies, that C2 is the important species for diamond growth in oxygen – acetylene flame—this is indicated by clear relations between the local variation in growth rate and quality of the diamond layer and the distribution of H and C2 in the boundary layer. In the DC arc jet, the important gaseous species can be atomic carbon. In the system fullerene/Ar (without the presence of hydrogen) or hydrocarbon/Ar (i.e., without input hydrogen), this role is apparently taken over by the C2 dimer, but if hydrogen is also present, the species responsible for growth (which may be CH3 , C2 , and CH) change as the gas mixture composition is changed. However, different gas-phase species are responsible for diamond growth not only in different CVD methods. It is often the case that in a given CVD method, two or more simultaneous processes occur and therefore a single species (i.e., a single growth model) cannot explain all the observations. The situation becomes even more complex because, in addition to the gas phase, it is necessary to consider processes at the substrate surface that is kept at a temperature well below that of the gas. Moreover, due to reactions occurring at the surface, the composition of the gas near the surface is perturbed. As a result, a boundary layer is formed through which species diffuse.
2.4.1. Surface Boundary Layer The conditions within the surface boundary layer in the immediate vicinity of the substrate differ substantially from those in the bulk gas phase. Within several gas phase reactive mean free paths, the composition of the gas is perturbed by the effect of reactions occurring at the surface, forming a chemical boundary layer. When the gas phase is dominated by convectively driven transport, as in plasma jets or torches, a fluid or momentum boundary layer is also formed. In these situations, only a small fraction of the gaseous species generated actually reaches the deposition surface. The chemical composition of the flux of species arriving at the deposition surface may differ from the bulk gas well away from the surface due to chemical reactions caused by the temperature and concentration gradients in the boundary layer.
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The presence of the chemical boundary layer has a profound effect on the arrival rate of reactants to the surface, and hence can severely limit growth rates. Thus in the case of diffusion through a gas consisting mainly of molecular hydrogen at 30 torr, it can reduce the H atom flux by a factor of 30 and alter the concentrations of other chemical species which are reactively coupled to the H atom.[43] Similarly, a forced convective flow, as is encountered in plasma jets and torches, can form a momentum boundary layer as well. The thickness of this layer is dependent on the fluid mechanics and viscosity (composition and pressure). High-rate deposition processes, such as DC arc jets, differ in both the fraction of dissociated hydrogen and the diffusion distance. Arc jets can have dissociation fractions over a factor of 10 higher than HF or MW systems (typically 0.001 to 0.01 for an MW system ) and the high directed velocity of an arc jet can thin the boundary layer by a factor of 10, thereby increasing the H atom flux to the surface by a factor of over 100.[43] The boundary layer is not easily susceptible to investigation. Its thickness (d) may be very small and, unlike the gas phase that can be investigated by optical emission spectroscopy, the boundary layer does not emit radiation. First estimates relative to the boundary layer were therefore obtained by computer modeling of the deposition process. In the case of oxyacetylene flame CVD, first estimates of the boundary layer thickness gave 0.1 mm.[44] Harris[45] proposed a mechanism of homoepitaxial diamond growth from CH3-radicals. It begins with the bicyclononane molecule (BCN) as a model compound representing the diamond surface. Adamantane, often treated as a prototype of diamond, is obtained by adding carbon from CH3 radicals. The diamond f100g surface of infinite dimensions is considered to be made up from an ensemble of BCN molecules. The author suggests a conceptually and computationally simple method for predicting diamond growth rate. The proposed mechanism is feasible in spite of the substantial uncertainties in the calculation, related to the use of a model compound rather than diamond. Starting from the growth mechanism proposed by Harris, Goodwin[46] carried out a numerical simulation of diamond synthesis for oxyacetylene flame and DC arc jet, both methods characterized by high deposition rate. In a hot, axially symmetrical gas jet, striking the water-cooled substrate perpendicularly, the boundary layer thickness can be expressed by the relation d (m/ra)1/2, where m and r are jet viscosity and density outside the boundary layer, a is a stagnation-point velocity gradient parameter, expressed by the relation a 2u/R (where u is the mean axial jet velocity) and R is the estimated jet diameter at the substrate. Using this method, the boundary layer thickness was estimated to be about 1 mm in the case of oxyacetylene flame (Fig. 2.20). Thus the boundary layer thickness for oxyacetylene flame obtained by Goodwin (1 mm) differs from the value of 0.1 mm estimated by Matsui
Dissociation of molecular hydrogen may vary in different CVD environments from 1% to 40%.
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Figure 2.20 Temperature and selected gas species profiles in oxyacetylene flame (R ; C2H2/O2 ¼ 1.1, Ts ¼ 1250 K), as a function of the distance from the substrate surface. The gas species concentrations sharply drop within the boundary layer as the distance decreases.[46]
et al.,[44] although in both studies the methyl radical is assumed to be the dominant diamond precursor. More recent measurements give values ranging from a few tenths of a millimeter to over 1 mm, depending on the process parameters. The boundary layer thickness has been shown to depend less on the substrate temperature and more on the flame-to-substrate distance (d ). It depends also on the radial distance.[42] Goodwin’s study shows that CH3 is the only species present in a relatively important concentration at the substrate, concentrations of other species (C, C2H, and C2) being very low. The deposition rate, calculated assuming that CH3 radical is the only species responsible for diamond growth, agrees with the experimental results of Matsui et al.[22] Thus, the presence of methyl radical alone can explain the diamond growth. Concentrations of a number of gaseous species in the oxyacetylene flame were shown to drop sharply (by several
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orders of magnitude) within the boundary layer in the immediate vicinity of the substrate (Fig. 2.20). These effects are much smaller in the DC arc jet, because of very high jet velocity (larger a) and, consequently, thin boundary layer (Fig. 2.21). In this case, although the presence of methyl radical alone can account for diamond growth, high C atom concentration indicates that it may also play a role.[46] In the mentioned study,[42] laser induced fluorescence (LIF) has been employed to measure in situ distribution of the radicals C2 , CH, and OH in the oxyacetylene flame. The peak intensity of the radiation (natural or LIF) is on the flame front, that is, at the tip of the primary cone (Section 2.9.6). The substrate was positioned at a small distance (d ) from the flame front. Since the boundary layer does not emit radiation, and the radiation intensity sharply increases beyond it, the boundary layer thickness has been defined as the distance between the
Figure 2.21 Temperature and concentrations of the most important gas species in the arc jet (0.5% CH4 in H2 , 290 mbar), as a function of the distance from the substrate. The decrease in concentration of the gas species in a thin boundary layer is much less than in the oxyacetylene flame.[46]
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substrate surface and the position where the emission intensity is 10% of the maximum value. The boundary layer thickness was thus found to amount to several tenths of a millimeter and to be less dependent on the substrate temperature and distance d, except for the CH radical, in the case of which the boundary layer thickness increases with increasing d, so that a change in d from 0.68 to 2 mm corresponds to a change in d from 0.35 to over 1 mm. An interesting result of a more recent study of the same authors[47] is that atomic hydrogen is omnipresent, including the entire boundary layer. Clear relations, agreeing with theoretical models, were observed between the local variations in growth rate and quality of the diamond layer and the distribution of H and C2 in the boundary layer just above the substrate. In the case of HF, numerical modeling gave 5 –10 mm as the boundary layer thickness (Fig. 2.22), a value two orders of magnitude higher than that for the arc plasma jet. In a study of growth of large crystals,[48] essential differences were found between the oxyacetylene flame and the HF. According to the authors, the boundary layer thickness, very different in these two methods (0.1 mm was taken for the flame), plays an important role in the growth and morphological development of large diamond crystals.
Figure 2.22 Temperature (2500 K) and concentrations of the most important gas species calculated for HF (0.5% CH4 in H2 , containing 1% of atomic hydrogen, 40 mbar), as a function of the distance from the substrate. The boundary layer is much thicker than in the oxyacetylene flame.[43]
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The boundary layer thickness in the case of inductive thermal RF plasma (thermal gradient from 40008C to 12008C, Section 2.9.5), estimated on the basis of a numerical model, amounts to 2 mm. 2.4.2. Model of Diamond Growth One can summarize the preceding section by limiting oneself to the conditions under which methyl radical is a dominant gaseous species responsible for diamond growth. Owing to the presence of high concentration of atomic hydrogen, almost all dangling bonds on the diamond surface are saturated by hydrogen. The number of reactive sites on which the carbon-containing atomic species (CH3) could be adsorbed is therefore limited. Figure 2.23 shows one of the possible reaction schemes[49] (compare also the data from Table 2.6). Atomic hydrogen abstracts hydrogen from a surface carbon atom leaving a dangling bond which will most probably be again saturated by hydrogen. However, a CH3radical will sometimes be bonded to the dangling bond, by which one carbon atom can be added to the diamond lattice. Such a process of hydrogen abstraction followed by methyl radical bonding can also happen on the adjacent carbon atom. Further hydrogen abstraction from the bonded methyl group creates a reactive radical, which may react with the neighboring methyl group, closing a ring. Thus, two carbon atoms are included into the diamond lattice. Hence, diamond growth can be considered to consist of successive additions of carbon atoms to the existing diamond lattice, which is assisted by atomic hydrogen. Any graphitic carbon formed is being removed (gasified) by reacting with atomic hydrogen. Nevertheless, the growth process cannot progress so easily. Namely, the active species (a hydrocarbon radical or molecule) must be bonded to a free (dangling) bond on the surface carbon atom. However, this is difficult because the interatomic distance in the diamond lattice is very small (0.154 nm) and the neighboring surface carbon atoms are saturated with hydrogen. This makes a crowded barrier through which the incoming active species must penetrate to reach the free dangling bond, surmounting the repulsion between the incoming and surface hydrogen atoms. Even if bonding occurs, the bond may be significantly strained and weakened by the steric environment, making the bonded species susceptible to thermal desorption. As a result of these difficulties the effective sticking probability is very low, which is reflected in a low growth rate. This problem makes many otherwise plausible hydrocarbon addition mechanisms unworkable. In the systems containing oxygen, the OH radical could play a role similar to that of atomic hydrogen, the difference being that the former is even more effective in removing graphitic carbon.[49] Therefore, faster deposition and higher diamond quality result. Nevertheless, the role of OH should be considered with reservation, as already mentioned. The scheme described is a very simplified picture of diamond growth. The real mechanism depends on the gas-phase chemical reactions, the CVD method
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Figure 2.23 A schematic of the reaction process occurring at the diamond surface leading to stepwise addition of CH3 species and diamond growth.[49]
used, and even on the nature of surface (i.e., crystal facets on which deposition takes place). Defects play an important role in diamond growth. Nevertheless, most models of diamond growth to date have been focused on formation mechanisms
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of diamond from gaseous species and very little discussion has addressed competing processes which lead to the formation of nondiamond carbon and defects. There are several “generic” models in which defects (nondiamond carbon) are formed during diamond growth.[18] Starting from a model in which defects form due to reactions or steric interactions between nearby surface species (e.g., a species attaching and blocking a neighboring hydrogen from being able to be removed, thus creating an sp3 defect), expressions relating deposition rate and defect density with surface concentration of CH3-radical and atomic hydrogen have been derived.[50,51] The results are shown in Fig. 2.24. High deposition rate (G) and low defect concentration (D) (i.e., high diamond quality) can be obtained if high concentrations of CH3 radical and atomic H are simultaneously maintained (e.g., the curves of deposition rate 1000 mm/h and defect content 0.01 cross in the upper right corner of the diagram). A given deposition rate can be achieved even with a lower CH3-radical concentration, provided that a high atomic H concentration is present. Thus, the atomic H concentration at the surface is the primary factor limiting the achievable growth rate for a specified film quality. Concerning different deposition methods, Fig. 2.24 shows that standard low-pressure HF and low-power MW plasma systems operate in a regime in which the growth rate depends on atomic H concentration. On the other hand, arc jet reactors may operate well into the saturation regime. Here the growth rate is independent of atomic H concentration, but film quality still increases with it. Atmospheric pressure combustion torches and RF plasma torches operate in a transitional regime between these two limits. It can be noticed that gas-phase temperature in different deposition methods differs greatly (6000 K in the arc jet and 2500 K in HF reactors). A diagram relating growth rate to gas phase temperature (i.e., to the power density) shows that this dependence is quite distinct (Fig. 2.25).
Figure 2.24 Contours of constant growth rate (G) and constant defect concentration (D) in a diagram with coordinates atomic H concentration/methyl radical concentration. (Adapted from Fig. 2.[50])
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Figure 2.25 Growth rate of a given CVD method greatly depends on its energy density, that is, on the gas phase temperature.[21]
The highest growth rate is achieved by means of the methods having highest power density, that is, highest gas-phase temperature (DC arc jet and inductive thermal RF plasma). Here the gas phase (plasma) is at a relatively high (atmospheric or close to atmospheric) pressure, permitting high energy density. Owing to high pressure, there is a large number of collisions, leading to equilibration of electron and gas-phase species temperatures (isothermal plasma). On the other hand, low-pressure plasma (DC, MW, or RF) has a low energy density. The plasma is nonisothermal and its temperature is low due to a small number of collisions at low pressure, which prevents energy transfer from the electrons to the gaseous species. In summary, although much remains to be done, our knowledge of diamond growth has progressed considerably: we have a good picture of the gas-phase environment at the substrate and the factors (chemistry and transport) that create it; the multiple roles of atomic hydrogen are understood; there is a strong evidence for CH3 as the principal growth species in most systems; and the basic outlines of the diamond growth mechanism are understood, at least for the common CVD methods. 2.5.
DIAMOND GROWTH AT LOW SUBSTRATE TEMPERATURE
Current processes of diamond CVD (Section 2.9) require high temperatures (typically 800– 10008C) and are feasible therefore with only a limited choice of substrate materials. However, diamond growth at low temperatures would be very significant because the list of substrate materials could then be considerably expanded, including low-temperature materials such as polymers. Lowtemperature diamond deposition would be important especially for application
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in electronics, because stresses due to a difference in thermal expansion between diamond and substrate materials, as well as damage or change of performances of pre-fabricated devices, would be avoided. Therefore many efforts have been made to lower the substrate temperature in diamond CVD. According to hitherto published papers, successful diamond growth has been performed below 2008C, while certain authors claim that it is feasible even below 1008C. It seems, however, doubtful whether substrate temperature has been correctly measured in the latter case. Namely, the existing temperature gradient between substrate surface and water-cooled holder may not have been taken into account. The problems related to the low-temperature diamond CVD that have to be solved involve, in addition to technical issues, the need to achieve satisfactory nucleation and growth of good quality diamond. 2.5.1. Attainment of Necessary Substrate Temperature and Its Measurement In order to accomplish low-temperature growth, it is necessary not only to cool the substrate, but also to minimize the heat flux directed to it. One of the most efficient ways to do this is to reduce the gas pressure during deposition. However, substrate cooling is nevertheless indispensable, because the involved surface processes are exothermic, for example, energy release of chemically or electronically activated species to form the diamond structure. All the issues otherwise present in diamond CVD are accentuated in low-temperature deposition. Thus, choice of materials for substrate cooling is important because they should have high heat conductivity; wall thickness of the cooler has to be small but sufficient to withstand pressure of water or another fluid (such as ethylene glycol), and still maintain a sufficient heat conductivity. Great care must be taken to ensure thermal contact between the substrate and the holder. Even if the surface of the holder is mirror-polished, thermal contact is not sufficient. Therefore a paste of high thermal conductivity, such as silicon grease, should be used [Fig. 2.26(b)]. The importance of employing such a paste is evident from the result that substrate temperature is more than 1008C lower if it is used.[52] As far as temperature measurement is concerned, the temperature gradient between the cooling fluid and substrate surface must be kept in mind. Optical pyrometers are excluded for temperature measurement at low temperatures. A radiation thermometer working in the IR can be applied in a broad temperature range, but cannot be used for semiconducting substrates. Substrates such as Si are almost transparent for IR radiation, and the thermometer will not measure the temperature of the substrate, but rather of the holder under it which is lower. A thermocouple can also be employed in a broad temperature range, but care should be taken to ensure good thermal contact between thermocouple and substrate. If the thermocouple is fixed at the back side of the substrate [Fig. 2.26(a)], it will measure the temperature of the holder, rather than the substrate. Many
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Figure 2.26 Substrate holder cooled by circulating water or ethylene glycol: (a) conventional technique and (b) suitable technique for low-temperature diamond CVD.[52]
papers report actually the temperature of the holder, which is several hundred degrees lower than the substrate temperature. The correct way is to fix the thermocouple to the substrate surface and to cover it with an insulator to avoid detection of the plasma potential [Fig. 2.26(b)]. 2.5.2. Methods of Diamond Deposition at Low Temperatures The reactive gaseous species are formed in the plasma by collisions of electrons with neutral gas molecules. However, low gas pressure makes both ignition and sustaining of the discharge difficult, because of a reduced number of collisions due to the low gas density. In order to compensate for the deficit of gas molecules, the number of collisions can be increased by increasing the electron density. If a magnetic field is used to retain the electrons, a magnetoactive microwave plasma is obtained. Electron cyclotron resonance (ECR) can also be employed as a means of heating by MWs, as well as propagation of resonant waves from the side of stronger magnetic field, which is termed ECR discharge. Figure 2.27 represents a system for low-temperature diamond growth using magnetoactive MW plasma, and in Table 2.7 are presented typical working conditions. A very similar apparatus is used for ECR plasma deposition.
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Figure 2.27 System for magnetoactive MW plasma diamond deposition at low temperature. Substrate holder is positively biased (usually þ30 V) with respect to grounded chamber.[52]
2.5.3. Nucleation and Growth of Diamond at Low Temperature In the current CVD methods, such as HF or MW plasma, it is very important to remove the nondiamond phases by their reaction with atomic hydrogen. However, if the substrate is held below 4008C, etching of nondiamond carbon by atomic hydrogen is much less efficient, and other ways are used to reduce the nondiamond carbon content: carbon concentration is reduced, oxygen is admited, or fluorine is used instead of hydrogen. Oxygen-containing precursor gases, such as CO, CO2 , or CH3OH, are popular means of introducing oxygen in the plasma. Table 2.7
Typical Conditions of Diamond Growth Using Magnetoactive MW Plasma at Low Temperature[52]
Hydrocarbon gas Carrier gas Total pressure MW, power Substrate Substrate temperature Substrate bias
CH3OH (0.9 L/h) H2 (5.1 L/h) 10 Pa 1.3 kW Si pþ[100] treated by diamond powder in ultrasonic field 200– 6008C þ30 V
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The process of diamond CVD involves production of chemically active species, their transport to the substrate surface, adsorption at the surface, and migration to the active sites where diamond growth occurs. Production of active species depends on the plasma characteristics and is almost independent of the nature of substrate surface. Adsorption and surface migration drastically change with temperature. Generally, as the substrate temperature is lowered, adsorption will increase, but the migration path will be reduced, and therefore the probability that an active species will arrive to a growth site will diminish. Instead of diamond, nondiamond carbon will grow. Polymer films will form especially below 2008C. It is therefore indispensable to introduce a sufficient quantity of hydrogen or oxygen, but this results in a reduced diamond growth rate. Figure 2.28 shows the temperature dependence of diamond growth rate by the magnetoactive MW plasma CVD on a Si substrate seeded with nanocrystalline diamond powder. A similar situation is in the HF method. Below 2008C diamond deposition is much more difficult, more because of very rapid growth of polymer films than because of reduced diamond growth rate. Hatta and Hiraki[52] nevertheless succeeded to deposit diamond even at 1508C, by increasing oxygen concentration in the starting gas mixture. In a study of evolution of microstructure and incorporation of nondiamond carbon between 5608C and 2758C using MW plasma and a Si substrate,[53] three temperature ranges have been distinguished. Figure 2.29 shows the relation between the surface morphology of individual grains and the nucleation mechanisms. In a model of low-temperature diamond deposition,[53] the relative arrival rates of growth species to the deposition surface and their removal by surface migration are considered. At elevated temperatures (560 –4308C), the growth species captured at the diamond surface migrate to ledges or kinks of a growing
Figure 2.28 Dependence of diamond growth rate on substrate temperature in magnetoactive MW plasma deposition under typical working conditions.[52]
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Figure 2.29 Relation between surface morphology of individual grains and competing diamond nucleation mechanisms. (a) Elevated temperatures: preferred nucleation in re-entrant corners and resulting[112] texture; (b) transition temperature: re-entrant corner nucleation in competition with 2D nucleation; (c) low temperatures: re-entrant corner nucleation and 2D nucleation on all four f111g planes and resulting [100] texture.[53]
layer, where carbon atoms become incorporated into the diamond lattice. The ledges are preferentially generated by nucleation at energetically favorable sites, usually screw dislocations or re-entrant corners. Thus the films grow by nucleation at re-entrant corners and lateral motion of growth ledges, which leads to[112] oriented grains with smooth f111g facets and nearly defect-free crystals. Crystallite size is of the order of 1 mm. The growth rate is not limited by surface migration, because all the growth species arriving at the surface have enough time to reach the growing sites (ledges or kinks). By lowering the substrate temperature, surface diffusion and the average migration length are decreased. When this length becomes significantly shorter
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than the distance to the ledge, only species near the ledges can reach the growth sites by migration. Since the arrival rate of growth species does not depend on substrate temperature, it remains unchanged and can no longer be balanced by surface migration of growth species to ledges. Thus the adsorbed growth species become enriched between the ledges. Near the low-temperature limit 2D nucleation on the growing facets between the ledges becomes the dominant nucleation mechanism as a result of insufficient surface migration. 2D nucleation dominates below the transition temperature, implying that formation of parallel twins becomes possible on all f111g planes. As the formation of parallel twins by 2D nucleation requires only a small additional energy, this process causes a simultaneous formation of both twinned and nontwinned nuclei. Impingement of these nuclei on a growing f111g facet results in incorporation of nondiamond carbon at the intersections, deteriorating the crystal quality, as evidenced by Raman spectroscopy, and reducing the crystallite size to only 10 nm, as measured by X-ray diffraction (XRD). Nondiamond carbon was detected in the form of amorphous inclusions at incoherent twin boundaries and probably at higher order twin boundaries. Also, if 2D nuclei grow together, nondiamond carbon is incorporated during growth at their interface. The authors’ observations concerning texture and surface morphology of layers deposited at 3108C are consistent with the concept of 2D nucleation.[53] The same authors suggest that, in order to improve the film quality at low deposition temperatures through avoiding 2D nucleation, lowering of the incoming flux of growing species would be necessary. This can be achieved by lowering either total pressure or carbon content in the gas phase. Enhancement of surface migration, which seems to be stimulated by the presence of oxygen, is an alternative approach. The results of Rudder et al.[54] show that polycrystalline diamond films can be deposited at substrate temperature of 3008C at the rate of 0.4 – 0.8 mm/h using a mixture of water vapor and various alcohols at a pressure of about 1 mbar and with RF power of 800 –1000 W. Another group[23] used a CO2/CH4 gas mixture in an MW plasma reactor to deposit diamond films at temperatures down to 4358C, which is lower than it would be possible with a traditional CH4/H2 system. The mixture used is somewhat unusual, because it contains no input hydrogen. The results suggest that CO might be involved in the surface termination of the growing diamond film and that CH3 is the dominant growth species. Before starting the growth process, it is necessary to ensure sufficient nucleation density by seeding, biasing, or scratching the substrate surface. Figure 2.30[55] shows the temperature dependence of incubation period (i.e., the delay of onset of growth after starting the deposition) for a Si substrate pretreated ultrasonically with diamond powder; the incubation period can be
Transition temperature lies between the elevated and low temperature ranges.
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Figure 2.30 Incubation period for diamond nucleation on an Si substrate, conventionally pretreated by ultrasonic agitation of diamond powder, steeply increases as substrate temperature is lowered. (Adapted from Fig. 5.[55])
determined from a plot of film thickness vs. deposition time. It follows that the incubation period abruptly increases if the substrate temperature is below 5008C. Because of low nucleation density, it is difficult to obtain a continuous film at low substrate temperatures. Even if continuous film is obtained, for example, by increasing the carbon concentration in the input gas, the deposited diamond has a low quality. Since spontaneous nucleation is practically excluded, surface pretreatment by conventional methods of scratching or biasing is often useless. The only method that ensures a continuous diamond film is seeding with a nanocrystalline diamond powder (synthesized by an implosion process). By using a colloidal solution of such powder previously purified by acid, seeding density higher than 1011 cm22 has been obtained. In this way, the time needed to initiate diamond growth at 2008C is shortened by more that 5 h—the incubation period otherwise needed if conventional ultrasonic scratching is used. In addition, diamond quality is higher if pretreatment by seeding is employed.[55] 2.5.4. Diamond Film Properties The quality of diamond films obtained at low temperatures is lower than that of the films prepared by conventional procedures, even if under the microscope they show similar morphology. Figure 2.31 shows Raman spectra from which it is evident that a full width half maximum (FWHM) of the diamond line (at about 1330 cm21) for a film fabricated by the conventional MW method amounts to 6 cm21, while for a film fabricated at 2008C it is 21 cm21. In addition, the line is shifted to low wavenumbers. Finally, a band with a maximum at about 1600 cm21 corresponding to nondiamond carbon is present. Thus, it can be
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Figure 2.31 Raman spectra show that the quality of diamond film fabricated at low temperature is lower than that obtained by conventional MW plasma CVD (e.g., FWHM of diamond line is much larger, indicating lower crystallinity; nondiamond carbon band at 1600 cm21 is present): (a) magnetoactive MW plasma under optimal conditions and (b) conventional MW plasma [CO/H2 gas mixture (10%), Si substrate pretreated in ultrasonic bath].[52]
concluded that the properties of low-temperature diamond films will have to be improved to ensure their application. Further details about this important topic can be found in Hatta and Hiraki[52] and the references therein. 2.5.5. Deposition of Diamond on Polymer Substrates To be applied in industry, a diamond-coated polymeric material should have better properties than are those of the polymer itself, as it would be logical to expect, but the polymer properties should not be changed during deposition. This is difficult to achieve, however, for two main reasons: (a) thermal conductivity of polymers is much lower than that of conventional substrates (such as Si) and therefore substrate surface will be heated despite cooling from the back side and (b) while etching nondiamond carbon by hydrogen or oxygen during diamond deposition, the polymer substrate must also be etched, because otherwise a polymer film would grow rapidly. The first difficulty can be eliminated by using lower gas pressures and thinner substrates.[52] It is much more difficult to eliminate the second difficulty, because of a very rapid growth of nondiamond carbon below 2008C owing to enhanced adsorption of hydrocarbons on the
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substrate surface and their polymerization. What can be done is, first, to lower carbon concentration and, second, coat the substrate by a suitable material resulting in the formation of an interlayer during deposition. Thus, a polyimide film 125 mm thick has been protected by a 0.3 mm thick a-Si film; a diamond film has been finally deposited using magnetoactive MW plasma.[52] 2.5.6. Future Prospects The basic problems that remain to be solved are an increase in the diamond deposition rate and an improvement of diamond quality. The deposition rate in the magnetoactive MW plasma increases with MW power. However, at high power it is difficult to maintain the substrate at low temperature (2008C). Higher power results in higher growth rate, presumably because of greater production of gaseous species responsible for diamond growth. It is necessary therefore to keep the high power, but reduce the substrate heating. This should be feasible if pulse heating is used. Namely, power is high during the pulse, but average power (and hence heating of the substrate) is reduced by introduction of a time interval between the pulses. Pulsed heating should also allow control of radical densities, which is expected to result in improvement of diamond film quality.
2.6.
EPITAXIAL DIAMOND GROWTH
The need for and the advantages of single crystal diamond films are reasonably self-evident. Only the single crystal material will fully exhibit all of the extreme and unique properties we associate with diamond. Electronics is a field in which the need for monocrystalline diamond is most obvious. Although we now live with silicon-based electronics, the future will demand electronics for various novel applications: information electronics for mobile communications and multimedia; electronics for power transmission systems; and enviromental electronics for harsh environments, such as high temperature and/or aggressive media. Thus, high-performance electronic devices—high power, high frequency, low loss, excellent thermal and radiation resistance— are required. Since properties of Si are inadequate for such devices, wide-gap semiconductor materials such as SiC, GaN, and diamond have been recognized as promising for producing high-power and/or high-frequency electronic devices for harsh environments. Generally, high-quality semiconductors with atomically flat surfaces, low defect density, and low residual impurities are required for electronic devices. Among the wide-gap semiconductor materials, diamond is the best because of its superior physical and electrical properties. Especially, the problem of high density of structural defects that occurs in compound semiconductors, does not exist in diamond, which is a one-element semiconductor. Diamond is an important material for high-temperature, high-speed, high-power, and high-radiation-tolerant
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electronic devices. To manufacture such devices, single crystals or monocrystalline epitaxial films are required. 2.6.1. Homoepitaxial Diamond Growth from Active Vapor Phase Epitaxial growth of diamond with thicknesses of 1 mm or more has become feasible only after the advent of diamond synthesis from an active vapor phase. A reasonable diamond deposition rate and its epitaxial growth were achieved first by Spitsyn.[13] The active gas phase was obtained using “high-temperature high-gradient chemical transport reaction” (HGCTR) (Fig. 2.32).[12] Graphite is heated to 20008C in hydrogen atmosphere at short distance (1 mm) from a diamond single crystal maintained at 10008C. Because of the large temperature difference, the gas phase composition around graphite should be different from that near diamond (i.e., a high concentration gradient should exist). For instance, hydrogen is much less dissociated at 10008C than at 20008C. Thus, at 10008C there should be much less atomic hydrogen, and the content of active gaseous species, produced by its reactions, would accordingly be less. However, owing to the high temperature gradient, low gas pressure, and a very small graphite –diamond distance, diffusion is fast (i.e., the transport of active species toward the diamond surface is fast). Therefore the gas-phase composition near the diamond surface is roughly the same as that near the surface of graphite.
Figure 2.32 A schematic showing the first apparatus in which an active gas phase was used for the (epitaxial) synthesis of diamond in the graphite–hydrogen–diamond system. Owing to a large temperature difference and a small distance between graphite and the diamond substrate, there is a large temperature gradient. Because of rapid diffusion, the gas phase composition near the diamond substrate is almost the same as that near graphite.[12]
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According to a thermodynamic calculation for a total pressure of 0.01 bar, the gas contains a mixture of very active components—atomic hydrogen and very active hydrocarbon molecules and radicals (C2H2 , C2H, C3H, and CH2) (Fig. 2.7). Because of the active medium, a (linear) epitaxial deposition rate of 1 mm/h has been achieved. The absence of nondiamond carbon was explained by its reactions with atomic hydrogen leading to gasification. Under the conditions of such special chemical transport reaction, the first man-made epitaxial diamond films were obtained as early as in 1966.[12] The processes involved are obviously complex, particularly during the initial stage, and depend on a number of gas-phase-related and substrate-related parameters. Epitaxial growth of diamond on densely packed faces of natural diamond is probably one of the simplest. By the epitaxial growth on the f111g face of a semiconductor diamond substrate, a continuous (pinhole-free) diamond layer with a thickness of 25 – 50 nm has been deposited.[12] 2.6.1.1.
Kinetics of Homoepitaxial Diamond Growth
First studies related to the kinetics of homoepitaxial growth of diamond were made in the chemical transport regime.[12] Based upon the dependence of epitaxial film growth rate on the graphite –diamond distance, and taking into account thermodynamic data, the conclusion was that acetylene is the most important carbon carrier from graphite to the diamond surface. The following principal mechanism of epitaxial diamond growth in the chemical transport process was proposed: T1 ¼20008C
T2 ¼10008C
Step 1
Step 2
C (graphite) þ (H, H2 ) ! C2 H2 ! C (diamond) þ H2 (2:7) A study of step 2 macrokinetics led the authors to suppose that the actual acetylene partial pressure (PC2H2) near the diamond surface was nearly equal to its equilibrium value at the graphite surface. From the equation G ¼ aPC2H2e2b/RT, derived for the growth rate (G) of an epitaxial [111] film, it follows that the preexponential term is equal (within an order of magnitude) to the calculated number of collisions of C2H2 molecules/cm2/s. Only 1025 –1024 of such collisions are effective (i.e., lead to C2H2 conversion to diamond at 883–1063 K). Kinetic investigations by various deposition methods (HGCTR, MW-discharge with UV illumination, DC-discharge, and MW-torch) indicate, surprisingly, that the activation energy derived from an Arrhenius plot (for growth rate) is close to 105 –125 kJ/mol (somewhat lower activation energy in the case of MW-discharge is probably associated with an additional activation of the vapor phase and/or diamond seeds due to UV-illumination). Another paper[56] reported an activation energy of 96 kJ/mol for diamond deposition by HF. Closeness of activation energy values for different diamond deposition methods suggests a common surface critical stage (rate-determining step) of CVD diamond growth.
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Homoepitaxial growth kinetics studies for the f100g, f110g, and f111g crystal faces (Fig. 2.33)[57] show that the f110g face has the highest growth rate, which is consistent with the absence of f110g facets in polycrystalline films. The dependence of the growth rate on CH4 fraction is different for each orientation; it is linear for f100g, slightly sublinear for f110g, and sigmoidal for f111g. The temperature dependence differs for each orientation as well. In the range 735 – 9708C, the kinetics could be described by activation energies of 33 + 13, 75 + 8, and 50 + 17 kJ/mol for f100g, f110g, and f111g growth, respectively. All three orientations show a higher activation energy (of the order of 210 kJ/mol) in the temperature range of 675 – 7358C. Another study[58] gave trends consistent with the above, but a maximum growth rate was found between 8008C and 9008C. Interestingly, the activation energies measured for homoepitaxial growth at 700 –9008C are all significantly lower than those measured for polycrystalline films. The reasons for this are not entirely clear, because it would be expected that the polycrystalline results be an average of the homoepitaxial ones. The result that the f100g, f110g, and f111g surfaces have growth rates that depend differently on temperature and gas composition can be used to control the morphology of polycrystalline films, which is determined by the ratio of the [100] and [111] growth rates (Section 2.7.2). Homoepitaxial diamond growth has been mostly studied in connection with semiconducting electronic devices. There are many studies related to such devices based on natural, HPHT, and polycrystalline CVD diamonds. However, only few of them report on the high-quality diamond suitable for electronic devices.
Figure 2.33 Dependence of homoepitaxial growth rate of different diamond facets on (a) CH4 fraction and (b) temperature.[57]
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2.6.1.2.
139
Defects in Homoepitaxially Grown Diamond Film
It is difficult to produce a high-quality homoepitaxial diamond film with low density of defects, mainly due to the formation of twinning structures. Twinning on the f111g plane is the most common structural defect observed in CVD diamond. Owing to high rigidity of diamond, twinning can start inside the diamond [111] film volume already at a thickness of only about 300 nm. The critical thickness for extended defect formation, estimated from the differences in the lattice constants and mechanical moduli of the film and substrate, amounts to 1 mm, which is in reasonable agreement with the experimental result.[12] Prevention of formation of twinning structures might make a breakthrough in producing large, high-quality diamond films. Another significant defect usually observed during growth of diamond (and other crystals with the diamond structure) are stacking faults, a well-known type of defect occurring in epitaxial silicon films. Stacking faults have been found in epitaxial diamond films deposited on the f111g crystal surface. Relations have been found between the type of stacking error and morphology, so that many morphologies commonly observed in CVD diamond can be explained by the interaction of various combinations of stacking errors.[14] Dislocations are also observed, but point defects such as isolated vacancies or interstitial carbon seem to be rare or nonexistent in as-grown diamond.[18] The presence of structural defects leads to development of voids inside the film, which produce a shrinkage of the lattice. Thus, the lattice constant of the polycrystalline diamond film is 0.0004 nm less than that of the purest type IIa natural diamond crystal.[12] Therefore, there is a lattice misfit between a natural diamond substrate and the epitaxial film, and stresses are developed in the system during film growth and/or during cooling. Maximum thickness of homoepitaxial diamond film virtually free of defects amounted to 5 mm in the early works, whereas it has reached several hundred micrometers and even 1.3 mm in recent experiments.[12] 2.6.2. Heteroepitaxial Growth of Diamond Homoepitaxial growth has been achieved on natural diamond and HPHT synthetic diamond. However, natural diamond is rare and expensive, while highpressure-synthesized diamond crystals have only been obtained in small sizes (,0.5 mm). Therefore, heteroepitaxial diamond growth on cheaper and more commonly available materials remains a great challenge, but also a very difficult problem. Many researchers have been trying to solve the problem how to use nondiamond substrates for preparation of single crystal diamond films. Table 2.8 presents an outline of currently used or potential substrate materials for diamond epitaxy. There are certain conditions that a substrate material has to satisfy to be suitable for heteroepitaxy. In addition to the properties already discussed (Section 2.3.2), it had been long considered that both substrate and film must
— 0.246 0.671
3797 — —
2727 1412 1084
c-BN (cubic) Si (diamond-cubic) Cu (fcc)
0.3615 0.542 0.361
0.3567 — 0.252 0.142
3057 — — —
Lattice constantb (nm)
Diamond (cubic) (hexagonal) a-axis c-axis Graphite (hexagonal) a-axis c-axis
Melting pointa (8C)
3.490 2.340 8.960
2.260 — —
3.515 3.520 — —
Densityc (g/cm3)
— 7 10215 —
— — —
— — — —
C diffusivityd (cm2/s)
0.59 7.6 17.0
— negative 25
0.8 — — —
Thermal expansion coefficiente (1026 K21)
Physical Properties of Curently Used or Potential Substrate Materials for Diamond Epitaxy[26]
Substrate material
Table 2.8
1.46 f111g 2.08 f100g
2.80 f101¯0g 0.17 f0001g
5.3 f111g 6.5 f110g 9.2 f100g
Surface energyf (J/m2)
140 Marinkovic´
1667 3160
(b) .9008C (bcc) TiC (fcc)
0.295 0.468 0.329 0.432 4.110 4.920
4.500
— 3.210
8.900
7.400 7.870 8.900
— 4.63 8.9 9.9 6.52
7 1029 2 1026 —
12.5
.14.6 12.1 13.3
1 1028 —
—
2 1027 8 1027 2 1028
2.570/1.723
2.709/2.003
2.939/1.923 2.364/1.773
Note: The dash (—) denotes that the data are not available. a At 1 bar. b At room temperature, or at temperatures at which the phases exist. c At 208C. d Calculated at 8008C for most metals, or at the lower limit of temperature range for the phases existing above 8008C. e 0–1008C for metals, diamond, and graphite; 25– 5008C for ceramics. f Surface energy at 258C/surface energy at melting temperature. The surface energies do not include the effects of surface reconstruction, physisorption/chemisorption, or other surface reactions.
—
0.251 0.407 0.354 0.435
—
1494 2697
0.356 0.286 0.352
1536 — 1455
(b) .3908C (fcc) b-SiC (cubic) Ti (a) ,9008C (hcp)
Fe (g) 912–14008C (fcc) (a) ,9128C (bcc) Ni (fcc) Co (a) (hcp)
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have similar lattice parameters, identical crystal symmetry, and bond type. An additional condition is the similarity of surface energies. A “critical” difference of 15% in the lattice constant empirically derived for polar lattices[12] would seem to be too high for the extremely rigid diamond lattice. Experiments related to heteroepitaxial growth of one substance on another have shown that bond type can be different and that the “critical” difference in lattice parameters is not precisely defined. Heteroepitaxy depends also on bond strength at the phase boundary, on rigidity of both lattices, as well as on process temperature and supersaturation. The crystals that best satisfy the above conditions are c-BN, b-SiC, graphite, wurtzite BeO, nickel, and copper. The experimental data are abundant for c-BN, b-SiC, Si, f0001g graphite, w-BeO, and Ni. c-BN: To date, c-BN is the best substrate on which diamond heteroepitaxy can be easily achieved, because of its close similarity with diamond in lattice parameter (1.3% misfit) and surface energy (4.8 J/m2 for the f111g surface of c-BN, 6 J/m2 for the low-index surfaces of diamond). Although many researchers have confirmed heteroepitaxial growth on c-BN by various CVD methods, further development in this field is limited by the small size of high-quality c-BN single crystals, which does not exceed 2 mm. The f111g surfaces of c-BN are terminated either by boron or by nitrogen. The nitrogen-terminated f111g surface is rather flat compared with the boron-terminated one which has many pits on the surface.[59] The nucleation and growth behavior of CVD diamond on the two surfaces is correspondingly different. The boron-terminated surface is readily covered with diamond, while the nitrogen-terminated surface is not. This difference in behavior can be explained by the difference in the bond strength.[60] The bond strength of B22C is larger than that of B22H, while the bond strength of N22C is smaller than that of N22H. Therefore, the hydrogenated nitrogen-terminated surface is stable and hydrogen will not be replaced by carbon, because this would be energetically unfavorable. However, the hydrogenated boron-terminated surface will become covered by carbon, that is, hydrogen will be replaced by carbon, which is more strongly bonded to boron. SiC: The second best candidate for diamond heteroepitaxy is b-SiC. In spite of a large lattice misfit of about 22%, diamond growth on b-SiC was successful.[59] The substrate was biased, the role of the applied bias being probably either cleaning the surface or enhancing the carbon concentration near the substrate. Diamond was deposited from the CH4/H2 mixture using MW plasma. The following crystallographic relationships were found to exist between the deposited diamond and the substrate: {100}b-SiC k {100}D and ½011b-SiC k ½011D . Continuous [110]-oriented monocrystalline diamond films, 2 3 mm2 6 mm in size, were obtained by this process. Diamond was also deposited on a-SiC f0001g substrates.[59] Oriented diamond particles with the following crystallographic relationships were obtained in this case: {0001}a-SiC k {11 1}D and ½112 0a-SiC k ½110D . Si: For practical purposes, the realization of diamond epitaxy directly on Si is particularly attractive, because Si wafers are easily available and extensively
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used in the electronics industry. Epitaxial growth of diamond on Si is highly desirable, particularly in view of a convenient integration of diamond electronics with Si technology. A well-oriented diamond film can be grown on the f001g plane of a silicon single crystal, through the formation of b-SiC. Thus, epitaxial growth of diamond on Si is essentialy equivalent to that on SiC. Nevertheless, the technique of b-SiC formation on Si is not well established yet and therefore diamond heteroepitaxy on b-SiC films has progressed more than that on Si. However, b-SiC is not an essential interfacial layer required for diamond heteroepitaxy on Si. In spite of a very large lattice misfit (52%), the [001]-oriented diamond films can be epitaxially grown directly on the f001g plane of Si single crystal, also by applying a negative electrical potential to the substrate[61,62] (Fig. 2.34).[63] Heteroepitaxial growth of diamond f001g on Si f001g was realized by both MW and HF CVD. The maximum area of the epitaxial (single crystalline) diamond layer grown directly on Si can reach 20 20 mm2.[41] Graphite: In contrast to diamond, graphite has a typically anisotropic layer structure with interlayer spacing (0.335 nm) much larger than the interatomic distance within the layer (0.142 nm). Nevertheless, the lattice spacings of graphite {112 0} and diamond f110g planes are quite similar (0.123 and 0.126 nm, respectively). It has been shown[64] that diamond deposited on highly oriented pyrolytic graphite (HOPG) has the following crystallographic relationships: {0001}G k {11 1}D and ½112 0G k ½110D . These relationships mean that the puckered six-member rings in the diamond f111g plane retain the same orientation as the flat six-member rings in the graphite f0001g basal planes (Fig. 2.15). Although heteroepitaxial diamond growth has been achieved on an HOPG substrate, impurities such as Mo, Fe, and their carbides have prevented accurate and fundamental studies. The fundamental issue for future study is to observe the interface between the f111g plane of diamond and the f0001g plane of
Figure 2.34 High-resolution lattice image along the [110] direction of the diamond– silicon interfacial region, showing direct diamond growth on silicon.[63]
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graphite on an atomic scale to examine whether chemical bonds are formed or not.[59] BeO: The wurtzite structure of BeO is similar to that of lonsdaleite (hexagonal diamond) and the first neighbor positions are similar to those of cubic diamond. The Be22O bond length in BeO is by 7% larger than the C22C bond length in diamond. Some of the diamond particles deposited on a BeO single crystal had the following crystallographic relationship: {0001}BeO k {11 1}D and ½112 0BeO k ½110D , although the particles were rotated by 68 with respect to the ½112 0 direction.[65] Ni: This does not look suitable for epitaxial diamond growth because carbon is strongly dissolved in it. In addition, a catalytic effect of the metal on the decomposition of hydrocarbons into sp2-bonded structures may easily result in graphite formation during diamond deposition. However, the lattice mismatch between Ni and diamond is only 1.2%. By applying a complex procedure oriented growth of diamond on Ni has been achieved (see Section 2.7.1). In conclusion, recent achievements in preparation of homoepitaxial diamond films suggest that they indeed have high potential for electronic devices. However, in order to produce CVD diamond films commercially, a number of important issues for research and development still remain. One of the most important among them is large area heteroepitaxial growth.
2.7. ORIENTED GROWTH AND MORPHOLOGY OF DIAMOND COATINGS 2.7.1. Stimulation of Oriented Growth by Substrate Orientation Large area heteroepitaxial growth of monocrystalline diamond remains a difficult problem. If the real heteroepitaxy is not yet achieved, however, it is at least possible to prepare oriented polycrystalline diamond films with texture and crystalline order between those of a typical CVD diamond coating and a genuine single crystal layer. In particular, it is often desirable to have the diamond surface with smooth f100g facets, rather than f111g surfaces which are rough on an atomic scale. A simple way to achieve oriented growth is based on the fact that a substrate surface with a regular relief pattern can orient growing microcrystals. An example is a [100]-oriented single crystal Si substrate etched by a special technique to form either a f111g-faceted sawtooth profile or a square array of quadrant pyramidal pits. Seeding by tiny f111g-faceted diamond single crystals that enter the corresponding surface grooves or holes provides the nuclei for subsequent growth. A small deviation from perfect orientation (0.2 –0.88 for pyramidal pits and 1 – 58 for sawtooth profile) was attained using this technique,[12] as confirmed by XRD. This technique was used with Si single crystals, but many other materials could be used as substrates for oriented diamond growth.[12] In another technique, a properly oriented substrate immersed in MW plasma is biased (by applying several hundred volts) to increase nucleation density.
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An oriented diamond layer has been obtained in this way on a b-SiC single crystal, whereby about 50% diamond nuclei were oriented within 38 with respect to the b-SiC crystal, with their f100g faces parallel to the f100g face of b-SiC, and their [110] directions parallel to the [110] direction of b-SiC.[66] It is significant that both heteroepitaxy (Section 2.6) and oriented growth occur on (single-crystalline) substrates with lattice parameters differing considerably from that of diamond (22% for b-SiC and even 52% for Si). That is, not many materials have lattice parameters close to that of diamond. One of these is Ni (a ¼ 0.352 nm compared to 0.357 nm for diamond). However, as mentioned in Section 2.6.2, high carbon solubility in Ni, as well as a catalytic effect of Ni on decomposition of hydrocarbons with formation of graphite are unfavorable. On the other hand, Ni is an efficient medium for diamond crystallization under HPHT conditions. Therefore, in order to achieve oriented nucleation of diamond on Ni single crystals, but also on polycrystalline metal, a complex multistage procedure has been developed:[67] surface pretreatment by diamond powder (0.25 mm particle size) to leave fine diamond particles on the surface, annealing at 9508C in hydrogen to reduce surface oxides and recrystallize Ni, brief thermal treatment at 12008C to partially dissolve diamond particles in Ni and orient them, and finally growing diamond by deposition at 9508C under suitable conditions. Well-crystallized and highly oriented diamond nuclei were obtained by this procedure. Recently, superior-quality, oriented growth of diamond crystallites on iridium layers has been reported. The Ir layers have been deposited on the f001g cleavage planes of MgO[68] or on mechanically polished f100g planes of SrTiO3 .[69] Iridium has a lattice constant of 0.384 nm, which is close to that of diamond (0.3567 nm), and it does not form carbide under the deposition conditions. Thus Ir would seem to be an excellent substrate for diamond heteroepitaxy. By using bias-enhanced nucleation and subsequent growth by an MW plasma process, highly oriented diamond crystallites have been grown on Ir. The size of the crystallites was ca. 1 mm, while the X-ray diffraction polar and azimuthal spread for the crystal orientations were less than 18. Oriented growth of diamond on Pt and Co substrates has also been reported.[41] However, it is questionable whether these approaches will have practical applications. 2.7.2. Oriented Growth as a Consequence of Different Growth Rates of Differently Oriented Crystals 2.7.2.1.
Preferred Orientation
It is well known that, for a kinetically controlled growth system, crystal morphology is determined by the appearance of facets which have the slowest growth rate in their normal direction and by the corresponding relative growth rates. The growth rates on different diamond faces are different. Because the f110g surface is a stepped face and encounters no repulsion between adjacent
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hydrogen atoms (Section 2.4.1), it should have the highest growth rate. In fact, the growth rate of the f110g surface via the CVD method is the highest among the low-index surfaces, and therefore the surface of CVD diamond crystals appears with f100g faces and f111g faces. A preferred orientation of certain diamond faces parallel to the substrate has been often reported in polycrystalline diamond coatings prepared by CVD. The existing data indicate that the preferred orientation depends on the substrate nature. Thus the f111g faces are preferentially parallel to the substrate surface when deposition is effected on a diamond-seeded Si, but the f110g faces are parallel to the microcrystalline diamond substrate. In the experiments of Wild et al.,[70] the evolution of preferred orientation of diamond coatings with their thickness has been studied. It has been found that there is no preferred orientation at the beginning of deposition (i.e., the crystals are randomly oriented), but the number of f110g faces parallel to the substrate surface increases with increasing coating thickness. The explanation offered by the authors on the basis of a 2D growth computer simulation invokes different growth rates of differently oriented crystals during deposition: crystals having f110g faces parallel to the substrate surface grow faster, as illustrated by Fig. 2.35. That is, 2D “crystals” with the faces parallel to the substrate surface (crystals with [10]-orientation) grow more slowly, being rapidly overgrown by crystals that evolve from nuclei with a corner protruding in the growth direction ([11]-oriented crystals). Such behavior is simply a consequence of the anisotropy of growth velocity:pthe ffiffiffi growth velocity of a square in the direction of a corner is greater by a factor 2 with respect to that in the direction perpendicular to a face. Computer simulation clearly illustrates the consequences of this “evolutionary selection” with increasing film thickness: (a) a preferred orientation of the crystallites develops and (b) the average grain size increases. Simulation with a large
Figure 2.35 2D computer simulation of the polycrystalline diamond film growth. The X and Y axes are normalized with respect to the mean nuclei distance, d0 .[70]
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number of nuclei (2 105) shows that the intensity ratio of differently oriented crystals (I11/I10) increases with the film thickness similar to the experimentally obtained behavior of X-ray intensity ratio I220/I111 . 2.7.2.2.
Growth Parameter a
Wild et al.[70,71] made a key contribution to the understanding of regularities determining oriented growth and morphology. They defined a parameter a:
a¼
pffiffiffi V100 3 , V111
(2:8)
where V100 and V111 are growth velocities in the [100] and [111] directions, respectively. The direction of smaller growth velocity determines the morphology: if V111 is much less than V100 , octahedral crystals (with triangular faces) are obtained, while cubic crystals result in the opposite case. Thus for a 1 a cubic morphology is obtained (the direction of fastest growth is [111]), for a 3 there is octahedral morphology ([100] being the fastest growth direction), while cubo-octahedral crystals are obtained for a between 1 and 3. Figure 2.36 represents the row of morphologies obtained for different a values. 2.7.2.3.
Influence of Deposition Conditions on Parameter a
[71]
Wild et al. have shown that the parameter a depends on deposition conditions—methane concentration and substrate temperature. This offers a possibility to control a and, consequently, film morphology, which depends on the growth velocity ratio in the [100] and [111] directions. On the basis of X-ray texture analysis of a number of diamond films deposited by MW plasma, a diagram was set up showing the dependence of film texture and morphology on the mentioned parameters (Fig. 2.37). The authors use the terms “fiber textured films”, and “epitaxially textured films”. The first denotes films in which crystal faces are parallel to the substrate plane, but with a random in-plane orientation. In the epitaxially textured films, the in-plane orientation is also determined by the orientation of the underlying substrate crystal, but with faces distributed around a main orientation. Thus, according to these authors, texture develops as a result of competing growth of
Figure 2.36 Idiomorphic crystal shapes for different values of the growth parameter a, as defined by Eq. (2.8). The arrows indicate the largest diameter (i.e., the direction of fastest diamond crystal growth, V ).[71]
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Figure 2.37 Dependence of the diamond film texture and morphology on methane concentration and deposition temperature.[71]
differently oriented crystals, the resulting fiber axis being equal to the direction of fastest growth, V. The angle between the axis perpendicular to the substrate (single crystal) and the growth direction [100] of preferentially oriented diamond crystals, denoted t100 , is related to the parameter a: cos(t100) ¼ 1/jVj. For the perfectly [100]-oriented diamond films, t100 ¼ 08 (f100g-faces are parallel to the substrate), while for perfectly [110]-oriented films t100 ¼ 458 (because the angle between f100g and f110g crystal faces amounts to 458). By varying the growth conditions, the parameter a and, consequently, the angle t100 can be varied considerably. At low methane concentrations and high deposition temperatures, the films exhibit pronounced [110] textures. The surface consists of f111g facets, inclined by 35.38 with respect to the substrate surface. At intermediate methane concentrations and intermediate temperatures a transition of the fiber axis from [110] to [100] occurs. A further increase in methane concentration or decrease in deposition temperature leads to a sudden deterioration of film morphology. At a ¼ 3, the film becomes fine-grained and no facets can be distinguished on the surface. Apart from the mentioned parameters, other deposition parameters can also influence the a value. One of those, studied in the laboratory of the present author, is the linear gas velocity during diamond deposition by an
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Figure 2.38 Preferred orientation [110] of diamond crystals, the measure of which is the X-ray intensity ratio, I220/I111 , steeply decreases as the gas flow rate increases. The intensity ratio 0.25, corresponding to the absence of preferred orientation, is reached at flow rates above 250 L/h. Preferred orientation [111] occurs only at still higher flow rates.[72]
oxygen –acetylene combustion flame[72] (Section 2.9.6). The intensity ratio of the X-ray diffraction lines, I220/I111 , has been used as a measure of preferred orientation. The dependence of the logarithm of the intensity ratio, I220/I111 , on total (acetylene þ oxygen) gas flow rate, FRtot , shows a clear relationship with a negative slope (Fig. 2.38).[72] The scattering of the results is presumably due to the fact that other parameters influencing preferred orientation have been different in different deposition experiments. It can be seen that the preferred orientation [110] (i.e., I220/I111) decreases by a factor 50 in the range of the total flow rate (or linear gas velocity) studied. Thus, the preferred orientation [110] rapidly decreases with increasing gas velocity, so that at the highest gas velocities it is changed to a preferred orientation [111]. It can be assumed, in accordance with Wild et al.,[70,71] that crystals with faces f110g parallel to the substrate surface grow faster at low flow rates. The surface consists preferentially of f111g facets, inclined with respect to the substrate surface by 35.38. However, with increasing flow rate, the relative rate of growth is gradually changed in favor of the faces f111g parallel to the substrate surface. Eventually, at high enough flow rates, their rate of growth becomes faster. At this point morphology is changed too, the octahedral crystals at the surface being replaced by the cubic ones. It is interesting to compare these results, in which the dependence of morphology on the gas velocity has been studied, with results of other authors relative to the influence of supersaturation and substrate temperature. Namely, “slow” processes at low supersaturation in the oxygen – acetylene flame CVD lead to octahedral crystals on the surface, whereas high supersaturation results in cubic crystals. The same is valid for the gas velocity in our experiments—low
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and high gas velocity lead to octahedral and cubic morphology, respectively. Thus, gas velocity plays a role analogous to that of supersaturation. In addition, our experiments show that the type of dependence on the total flow rate (gas velocity), as found for preferred orientation, is also valid for the ratio of crystallite sizes (L) in the [110] and [111] directions (i.e., for L220/ L111).[72] It was found furthermore that the decrease in this ratio with the gas velocity is a consequence of an increase in the L111 value (by an order of magnitude!), because the L220 values remain virtually unchanged as the gas velocity is increased. Since L reflects the size of coherent domains in a given crystal direction, its increase can be considered to represent a crystallinity increase. Thus, an increase in the total flow rate will cause not only an increase in the relative rate of growth in the [111] direction, but also a better crystal order in this direction. One possible explanation seems to be that both oriented growth and crystalline perfection may have a common cause in an increased flow of oxidizing gaseous species (O, CO, and OH) in the flame when the gas velocity increases. 2.7.3. Defects and Morphology The morphology of diamond crystals obtained by CVD techniques is known to vary in a wide range: spherical microcrystal clusters, cubic, cubo-octahedral, octahedral shapes, and flat hexagonal plates are all possible. Complex shapes formed by multiple twinning (e.g., decahedra and icosahedra) are also obtained. The most frequent are perhaps the clusters with many facets, formed by twinning, especially when the deposition regime suitable for octahedral f111g facets is applied. Using numerical simulation of crystal shapes and structure, Wild et al.[71] have shown that the twinning tendency also depends on the parameter a. By controlling a, films with a pronounced texture [100] having smooth f100g faces can be prepared. High a values (e.g., ca. 2.5) suppress twinning, while low a (e.g., ca. 1.5) lead to texture and morphology deterioration caused by twinning. Defects formed during growth may help and accelerate further crystal growth, and the interaction of various combinations of stacking errors may lead to complex morphologies, as shown in Table 2.9. Table 2.9
Relation of Observed Morphology to Types of Stacking Errors During Growth of f111g Faceted Diamond Crystals[14]
Type of error Two stacking errors on parallel f111g planes (intrinsic or extrinsic stacking fault or microtwin) Three stacking errors on parallel f111g planes Two stacking errors on nonparallel f111g planes Three stacking errors on nonparallel f111g planes Single stacking error
Morphology Hexagonal platelet Truncated hexagonal platelet Decahedra (pseudo 5-fold symmetry) Icosahedra Triangles (macle)
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In conclusion, considerable progress made in the preparation of oriented diamond films represents an important step in the development of CVD diamond technology.
2.8.
DOPING OF DIAMOND
2.8.1. Introduction Diamond, being an electrical insulator, can be converted by doping into a semiconductor, which opens a wide range of potential applications in electronics and optoelectronics. Covalent bonds of the carbon atom in diamond are exceptionally strong and short, thus making a crystal with unique physical, chemical, and mechanical properties not existing in any other material. These include: an exceptionally high thermal conductivity, an extremely high electrical breakdown field, a negative electron affinity (NEA), very high electrical resistivity of undoped diamond and yet, if boron-doped (p-type), semiconducting properties at practically any desired level with high carrier mobilities. The resistivity range of diamond thus extends to more than 18 orders of magnitude,[73] the largest of all known semiconductors. Recently, phosphorus-doped (n-type) diamond has been unambiguously prepared, thus opening the possibility of producing diamond-based bipolar electronic devices, which are the basic units of many electronic devices, as well as of electron emitting devices. Such properties make diamond a prime candidate for applications not possible with silicon. These may include high-temperature applications, electronics for outer space, and instrumentation for nuclear reactors. As a semiconductor, (doped) diamond has several distinct advantages.[74] First, it has the highest electron and hole velocities at high electric field. This makes diamond the material of choice for high-speed and high-frequency devices. Second, it has the highest breakdown voltage of all semiconductors. Since power is a function of voltage squared, this enables diamond to be a semiconductor material for high-power devices. Third, it has the widest band gap of all semiconductors, so that a diamond device can operate at high temperatures or with low leakage current at normal operating temperatures. Fourth, hole mobility in diamond does not exceed that of electrons in silicon, but is nearly equal to the mobility of electrons in diamond, thus rendering it ideal for bipolar devices. Fifth, its dielectric constant is half that of other semiconductors, thus significantly reducing parasitic loss and also lowering device capacitance, and rendering it ideal for use in the microwave and milimetre-wave ranges. Unfortunately, diamond is among the materials that are most difficult to synthesize and apply as semiconductors for electronic devices. From many studies related to semiconducting devices based on natural, HPHT, and polycrystalline CVD diamonds, only few of them report on the high-quality material suitable for electronic devices. Since single-crystal material alone can have extreme and unique properties as expected from diamond, single-crystal CVD diamond
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films, prepared by homo- and/or heteroepitaxial growth, are needed to fulfill such requirements. Indeed, the majority of potential diamond applications in electronics requires single crystals. One would actually expect that the devices using homoepitaxial diamond achieve even better carrier mobility and dielectric strength than the corresponding devices with natural single crystals. Homoepitaxial diamond growth on natural and synthetic diamond substrates can be used to manufacture active electronic devices, but heteroepitaxial diamond growth of suitable quality is a more difficult problem. Incorporation of foreign atoms into the diamond lattice is a statistical process of substitution of carbon atoms from the lattice by foreign atoms, thus producing a substitutional solid solution. Another possibility, for smaller atoms, is their introduction into the interstitial positions (between the normal positions of the atoms in the lattice). Doping of a crystal during its growth is achieved through (intentional or unintentional) the introduction of foreign elements in the crystallization medium. Since in the CVD the medium is in a vapor state, foreign elements must also be in the form of vapor, either of the element or its compound. The methods most often used are HF and MW plasma, whereby the inlet gas mixture (excepting dopants) consists of hydrogen with 1% CH4 . The doping level, position, and electronic state of foreign atoms introduced into the diamond lattice chiefly depend on the homogeneous and heterogeneous kinetics of reactions involving the foreign atoms, their molecules, and radicals. Complicated processes take place within the vapor phase and on the vapor/ growing film boundary. Depending on their rate and reversibility, these processes can proceed in equilibrium or as nonequilibrium doping. It is therefore necessary to estimate first the equilibrium solubility of the foreign atom in the diamond lattice. 2.8.2. Basics of Diamond Doping The list of elements that can replace the carbon atoms in diamond is rather short, due to the densely packed and rigid diamond lattice, which hinders the incorporation of atoms larger than carbon. Thus, incorporation of n-type foreign atoms (P or As), routinely performed in Si, is difficult with diamond. The number of elements capable of forming “shallow” levels within the diamond gap should be even smaller. Formation of equilibrium substitutional solid solutions of foreign elements in diamond can be understood taking into account geometrical and energetic factors.[12] One of the main conditions that the foreign atom E should satisfy to be able to enter some of the positions normally occupied by carbon in the diamond lattice is that its covalent radius, rE , does not differ much from the carbon radius (rC). The energetic factor is also significant. Thus, energetically suitable are atoms forming strong E22C bonds. Table 2.10 contains geometric and energetic parameters of certain light elements, significant for their substitutional solubility in diamond.
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Table 2.10
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Geometric and Energetic Parameters of Some Element-Carbon Single
Bonds[12]
Element C B N S P
Covalent radius r (nm)
Relative difference of covalent radii (rE 2 rC)/rC (%)
Element2 2carbon bond energy (kJ/mol)
Difference between C2 2C and E2 2C bond energies (kJ/mol)
0.077 0.085 0.070 0.104 0.110
0 þ10 29 þ35 þ43
347.5 372.6 305.6 259.6 263.8
0 þ25 242 288 284
It follows from Table 2.10 that boron and nitrogen atoms are most suitable for carbon substitution, as is indeed known, from both natural and synthetic diamonds. Although the calculated boron radius is 0.085 nm, the experimental values are considerably (at least by 0.012 nm) smaller, being very close to the value for carbon. The B22C bond is stronger than the C22C bond, thus satisfying the energetic condition. Being both geometrically and energetically suitable, nitrogen is the impurity found most frequently, both in natural and in synthetic diamonds (prepared at high pressure). The upper limit of nitrogen concentration in substitutional solid solution amounts to 4 1018 cm23 (which corresponds to 0.002 at%). Nitrogen (and other electrically inactive elements, like the bonded hydrogen atom) can considerably influence the electronic and other characteristics of diamond films doped by electrically active elements (boron, phosphorus and, perhaps, sulfur and lithium). Two other elements were also predicted to act as donors in diamond: Na (group I element, together with the already mentioned Li) as an interstitial impurity, and As (group V element, together with N and P) in substitutional sites. 2.8.3. Doping by Boron The effect of doping by boron is that diamond becomes a p-type semiconductor with an acceptor level 0.37 eV above the valence band. At the B content of about 1017 –1018 cm23, overlap of the wave functions on the adjacent acceptor centers leads to the formation of an impurity band, thus reducing the effective energy gap. At B content of 1020 – 1021 cm23, diamond becomes a semimetal with a very low resistivity (only 0.001 V cm). By using a chemical transport reaction and B-containing graphite as a source of C and B, Spitsyn[12] has deposited epitaxial films of diamond 0.05 – 2 mm thick with p-type conductivity. The f111g face of a diamond crystal served as the substrate. Figure 2.39 shows that the incorporated B content exhibits a maximum of 2.6 at% at 8008C, which corresponds to a minimum of
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Figure 2.39 Electrical resistance and boron content of epitaxial diamond film [111] as a function of deposition temperature.[12]
resistivity of 2 103 V cm. This value is much higher than the corresponding value for B-containing diamond synthesized at high pressure. According to the explanation offered, up to 8008C a nonequilibrium solid solution of B in diamond is formed, while at higher temperatures conditions for solid solution formation are close to the equilibrium ones, so that B content sharply drops. If the incorporated B content is below 0.1 at%, about 80 –90% B is in substitutional positions of the diamond lattice. It has also been found that up to ca. 0.1 wt% B, the diamond lattice constant is reduced by 6 1025 nm. As the incorporated B content is increased (up to about 1 wt%), the B atoms enter preferably into the tetrahedral interstitial positions, producing lattice expansion, with zero internal stress.[12] This behavior is (qualitatively) similar to that found for B incorporation into (pyrolytic) carbon,[75] where B presumably occupies positions of the carbon atoms up to the substitutional solubility limit (about 1%), and above that it enters the interstitial positions. The B substitution causes a decrease of interlayer spacing (the lattice constant perpendicular to graphene planes), while the interstital B provokes an increase of the interlayer spacing. However, more recent results of other authors[76] show, contrary to Spitsyn’s work, that the diamond lattice constant linearly increases with incorporated B content, although the slope of the straight line is changed at the B concenration
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of 2.7 1020 cm23. According to their results pertaining to homoepitaxial diamond obtained by MW plasma, boron incorporation induces a large expansion of the diamond lattice, especially above the semiconductor –metal transition. The maximum lattice constant increase amounts to 0.16% at B concentration of 8 1020 cm23. The authors suggest a contribution of both the different size of B and C atoms and hole concentration in the impurity band of boron. Hall effect measurements by different authors have confirmed that B is introduced into the substitutional positions of the diamond lattice, the sign of the Hall constant revealing hole conductivity.[12] From systematic studies of electrical conductivity and its temperature dependence for B-doped homoepitaxial diamond with a wide range of B concentration (5 1016 – 8 1020 cm23), it has been found that the resistivity decreases by eight orders of magnitude, from 105 to 1023 V cm (Figure 2.40).[77] The steep drop of resistivity (from 102 to 1022 V cm) for B concentrations between 2 1019 and 3 1020 cm23 is ascribed to an additional hopping component between nonionized and ionized boron levels, while at the highest B levels the conductivity decreases with temperature, indicating metallic behavior. On the other hand, no saturation of resistivity is observed toward low B level. Since resistivity of the undoped diamond has been found to be around 1013 V cm, it is logical to expect that B-controlled resistivity extends to even lower concentrations than explored in the study.
Figure 2.40 Room temperature resistivity of B-doped diamond vs. B concentration.[77] (Reprinted from CARBON, Lagrange et al., Copyright 1999, with permission from Elsevier.)
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Behavior of B atoms in the diamond lattice can be described, by analogy with doped silicon, using a simple theoretical model of hydrogen-like impurities.[78] According to the model, a donor (V group) atom in the lattice is similar to the hydrogen atom: its four electrons are used for bonding to the neighboring carbon atoms, while the fifth valence electron remains unpaired. Thus the donor atom behaves as a positive ion keeping by Coulomb force its electron which is not used for bonding in the host lattice. The electronic states of the bonded electron can be deduced by analogy with the Rydberg series of the hydrogen atom. This model is equally applicable to the behavior of acceptor impurities. It predicts an acceptor activation energy DEa ¼ 0.36 eV for group III substitutional impurities in diamond, which is in agreement with the experimentally determined values of 0.35– 0.37 eV for the boron acceptor level above the valence band. In a recent study,[79] a thick (0.4 mm) free-standing low concentration B-doped diamond polycrystalline film was prepared and its acceptor and donor defects investigated. Only a fraction of the B atoms substitutionally incorporated in diamond act as acceptors, presumably because their action can be compensated partly by impurity nitrogen atoms acting as donors. In addition, a considerable number of both boron and nitrogen atoms can be located at interstitial and clustering sites or at grain boundaries. Thus, the total concentration of B atoms may be much higher than the uncompensated acceptor concentration. The situation is even more complex because the total concentration of electrically active defects in diamond films is significantly higher than that of substitutionally incorporated B and N only. Also, the concentration of acceptors may be higher than that of uncompensated B atoms, that is, not only B-related defects contribute to total acceptor concentration. High total concentration of trapping centers (such as defects) reduces the average carrier concentration and increases the degree of compensation. The authors conclude that trapping compensation plays probably a major role. It is interesting to consider the B-doped diamond films from the viewpoint of electrochemistry, diamond electrodes in particular.[80] Diamond electrodes, fabricated by CVD, provide electrochemists with an entirely new type of carbon electrodes; stable, conductive, chemically robust, and economical. Indeed, diamond films are strikingly stable compared with conventional carbon electrodes (Section 2.10.6). The structural and chemical robustness of diamond is a consequence of its high atomic density, the highest of any terrestrial material, and of its strong, directional covalent bonding. The electrical properties of diamond electrodes are dominated by boron, which promotes p-type semiconductivity. Single crystalline and polycrystalline B-doped diamond thin-film electrodes have been prepared by homoepitaxial deposition and by growth on a tungsten wire, respectively. Incorporation of B atoms during both epitaxial growth and deposition of polycrystalline diamond films has been studied under the conditions of various electric gas-phase activation processes.[12] The average B concentration in the diamond film obtained with neocarborane (C2B10H12) vapor precursor introduced
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into the deposition zone under the conditions of DC discharge amounted to 0.1 at%. According to the authors, most of the diamond film volume is probably in the form of [111] and [100] growth pyramids, providing a rather high doping efficiency. The B/C ratio in the diamond film, as compared with that in the gas phase, was approximately the same for different incorporated B contents both in epitaxial and in polycrystalline diamond films, and the average distribution coefficient was about 50. The high doping efficiency is understandable if geometrical and energetic factors (Table 2.10) are taken into account. 2.8.4. Doping by Phosphorus The search for a suitable donor impurity in diamond which has a donor level shallow enough to yield reasonable electron-related conductivity at room temperature is one of the major open topics in diamond science and technology. Since the Fermi level for n-type semiconductors lies in the upper part of the band gap, it is conceivable that all processes which require electron liberation through the diamond surface will be enhanced. An obvious candidate to be considered as a shallow n-type dopant is phosphorus, by analogy with P-doped n-type Si. However, on the basis of geometrical and energetic factors (Table 2.10), incorporation of phosphorus into the diamond lattice would be hardly possible. In contrast to the case of P-doped Si, P-doping of diamond turned out to be a major problem, which has been solved only recently. Using a chemical transport reaction, Spitsyn reported P-doping of diamond.[12] Its resistivity amounted to 104 –101 V cm. The activation energies, obtained from the respective Arrhenius diagrams, amounted to 0.10 and 0.03 eV at phosphorus concentrations of 0.003 and 0.3 at%, respectively. According to the author, the incorporated P was mainly (about 85%) present in substitutional sites of the diamond lattice, causing n-type conductivity. Relatively high incorporated P concentration is a consequence of its chemistry, resembling in many aspects carbon chemistry. These findings can be compared with those relevant to the deposition of (pyrolytic) carbon in the presence of PCl3 ,[81] resulting also in incorporation of a relatively high P concentration (up to about 5 wt% P), which is apparently present predominantly in substitutional positions, although a small fraction exists as a separate phase (i.e., elementary phosphorus). Using MW plasma deposition with PH3 as a source of P, other researchers have found that the resistivity of resulting epitaxial diamond film amounts to 106 V cm, much higher than Spitsyn’s result. The difference, according to Spitsyn, can be perhaps ascribed to a high concentration of bonded hydrogen and/or other defects. The author’s conclusion is that better control of the presence of electrically inactive impurities, hydrogen in particular, would probably allow more efficient doping by electrically active elements. Although the early reports on CVD diamond growth in the presence of P did show the existence of some P-related electrical features, they did not
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provide direct evidence that electron conduction in the conduction band of diamond was indeed achieved by P-doping. The first clear proof of n-type doping of diamond due to phosphorus was provided by Koizumi et al.[82] who have grown diamond homoepitaxially in an MW reactor in the presence of PH3 . Detailed Hall effect measurements as a function of temperature have proven unambiguously that n-type features, typical of a doped semiconductor, were indeed obtained. The gas mixture contained only 0.15% CH4 in H2 and up to 1000 ppm PH3 with respect to hydrogen. The donor level due to the incorporated P is rather “deep” (around 0.5 eV), as confirmed by a wide variety of experimental tests. Despite many efforts worldwide, no reproducible way of obtaining P-doped n-type diamond with a reasonably high carrier mobility has been found. Therefore, much work is still needed to bring n-type diamond to the state at which the p-type diamond is at present. 2.8.5. Doping by Other Elements Several additional elements were predicted to act as donors in diamond: group I elements (Li and Na) residing at interstitial sites and group V elements (N, P, and As) at substitutional sites.[83] Nitrogen is a well-known donor which readily enters substitutionally into the diamond lattice. However, its donor level is very deep (about 1.4 eV) below the conductive band and its low conductivity is useless. Nevertheless, in the recently prepared nitrogen-doped (n-type) nanocrystalline diamond films, using fullerene as a precursor,[25] conductivity changes of many orders of magnitude have been found as a function of the amount of nitrogen introduced into the synthesis gas. Conductivities that rival that of graphite are achieved and the films display semimetallic behavior. The authors suppose that the effects found are related to the presence of high fraction of grain boundary carbon atoms in the nanocrystalline films (much higher than in the usual microcrystalline films) and the substantially lower energy needed to place a nitrogen atom into a substitutional site in a grain boundary than in the bulk. Apparently no clear indication for the incorporation of Li in diamond, or for its electrical activity, exists in the literature.[83] Attempts to dope diamond by Na and As did not yield convincing electronrelated conductivities. Computer simulations have indicated that substitutional S in diamond should have a rather shallow donor level (0.2 eV) with a formation energy lower than that of P. Indeed, sulfur has recently been reported to have a donor level in diamond, but these results need further verification.[83] 2.8.6. Other Diamond-Doping-Related Studies Influence of surface states is one of the insufficiently studied issues in spite of its importance.[84] The abundance of hydrogen at the growing diamond surface plays a crucial role not only in the growth process (Section 2.4), but also in some
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electronic properties of diamond: (a) the hydrogen present at the surface is the origin of negative electron affinity of f100g and f111g diamond surfaces and (b) the hydrogen present at the surface and/or in the subsurface region induces a superficial highly p-type conductive layer. This surface conductivity due to “hydrogen doping” is observed in diamond films grown without addition of any bulk impurity. The p-type characteristics of the undoped diamond, comparable to those of B-doped diamond and forming the basis for a special kind of field effect transistor, are due to hydrogen termination of the surface and coverage by physisorbed (hydrocarbon) adsorbates. Thus, hydrogen is necessary, but hydrogen alone is not sufficient to induce the high surface conductivity of diamond. Recently, a dramatic effect of trace amounts of B- or N-containing species (introduced into the gas phase during CVD diamond growth) on the morphology and/or quality of the resulting diamond films has been reported.[85] The doping efficiency of B has been found to be close to unity, while that of N is only 1023. Thermodynamic modeling of the gas-phase CVD environment has confirmed that the effect can be accounted for by changes in the concentrations of the gas phase precursor species rather than incorporation of the dopant into the diamond lattice. The influence of additions of PH3 , N2 , and B(C2H5)3 on diamond growth mechanism has been studied using HF CVD.[86] Deposition of faceted diamond was possible with relatively low concentrations of phosphorus (PH3/CH4 up to 0.005) and boron [B(C2H5)3/CH4 up to 0.009] and relatively high nitrogen concentrations (N2/CH4 up to 10), but concentrations of activated species (HCP, BH2 , and HCN) formed during deposition were found to be similar to each other under the conditions where faceted-to-nonfaceted morphology transition occurred. Defect-induced growth (incorporation of phosphorus in the diamond lattice and its deformation) and surface reactions of the HCP species represent the principal influences on diamond growth in the case of phosphorus. In the case of boron, well-faceted diamond growth is possible up to high boron concentrations. Boron is incorporated into the diamond lattice, but surface reactions seem to have less influence on diamond morphology. Gas-phase reactions seem to be strongly involved. Surprisingly, and in contrast to the effects of other additives, a very weak diamond peak appears in the Raman spectra.[86] Nitrogen addition causes formation of HCN or CN species during deposition. According to the authors, formation of these species can diminish carbon saturation in the system and thus improve diamond quality. In addition, CN radicals seem to stabilize the diamond surface by preferential etching.[86] 2.8.7. Conclusion One of the major problems that should be solved in order to fabricate diamond electronic devices is the need to incorporate foreign atoms reliably and reproducibly. Doping by atoms with a small number of valence electrons (boron) (i.e., fabrication of p-type semiconductors) can be considered experimentally
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solved. In order to introduce boron into the diamond lattice, it is sufficient to add a small quantity of the B-containing gas [e.g., B2H6 , B(CH3)3 , and B2O3] to the deposition gas mixture. Much more difficult is the problem of incorporation of atoms with more electrons, hence larger than carbon atom, by which n-type semiconductors are obtained. The main reason is the densely packed and rigid diamond structure. Diamond atom density, including surface density, is greater than that of any other material known. Therefore other atoms and molecules are simply too large to be incorporated in the diamond surface. Even hydrogen has not enough space on the non-reconstructed (100) surface. This is the reason why waiting for the n-type semiconducting diamond has been so long: first reports (of the NIRIM group) (see Section 2.8.4) with unambiguous proof that phosphorus enters substitutional sites in the diamond lattice appeared only recently. New results pertinent to doping nanocrystalline diamond films with nitrogen, leading to changes of many orders of magnitude in the conductivity depending on the amount of nitrogen, seem promising.
2.9.
METHODS OF CVD OF DIAMOND
2.9.1. Introduction Currently there are many CVD methods of diamond synthesis. In all these methods there is a large thermophysical and thermochemical instability at the interface between the vapor phase and deposition surface. However, such instability is not only desirable, but also indispensable. As has been mentioned, the interest for CVD of diamond has abruptly increased when its rate of deposition has become acceptable. From Fig. 2.25, it can be seen that the deposition rate becomes significant only for temperatures well above 15008C. Since graphitization of diamond takes place at these temperatures, the substrate obviously must be kept at a considerably lower temperature. Thus, it was indispensable to turn to nonisothermal systems, in which gas temperature is significantly higher than that of the substrate surface. In addition, the nonequilibrium gas phase in the vicinity of the substrate must contain not only “active” carbon-containing species but also a considerable amount of atomic hydrogen, so that some means of activation has to be applied. The numerous diverse existing metods of diamond CVD can be classified into several categories, depending on the applied gas-phase activation. This activation can be either thermal (e.g., HF), electric discharge (e.g., DC, RF, or MW), chemical (such as an oxyacetylene torch), or photochemical (making use of a low-wavelength laser). Yet, “pure” activation of a given category does not exist in any of these methods. On the other hand, a combination of different means of activation can be intentionally applied. Whilst each method differs from the others in detail, they all share some common features. Thus, owing to activation, there is a nonequilibrium gas phase near the substrate, and substrate temperature should be within the range
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of 700 –11008C. The substrate temperature is restricted to this relatively narrow range in order to ensure the necessary conditions for nucleation and growth of diamond. 2.9.2. Hot-Filament (HF) CVD HF (Fig. 2.41) is probably the most popular and one of the few commercialized diamond CVD methods. It can be considered a variant of the original Spitsyn’s
Figure 2.41
Side and top views of a typical HF laboratory reactor.[87]
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“chemical transport” method (Fig. 2.32). Matsumoto et al.[3] were the first to describe the process, and the procedures used today are mostly based on their work. The reactor design ensures the generation of a sufficient amount of atomic hydrogen and hydrocarbon radicals, as well as their transport to the growing diamond surface. Hydrogen with a low methane concentration flows near the filament made of tungsten, tantalum, or rhenium, which is resistance-heated to 2000 –26008C. The filament is positioned near the substrate which is heated to the necessary temperature either by the filament or by independent heating. The gas pressure is usually several tens of millibars. The principal role of the HF is to dissociate molecular hydrogen. The atomic hydrogen formed in this highly endothermic step drives a series of exothermic reactions, thus producing an active gas phase near the filament. Since the substrate is close to the filament, composition of the gas phase near the substrate is practically identical to that near the filament. By reacting with the introduced methane, atomic hydrogen produces the CH3 radicals, considered to be the principal growth species, but secondary reactions produce acetylene which in many cases can also play a role. The composition of the bulk gas phase, as well as that close to the substrate surface, depends on a number of parameters, including composition of the original gas mixture, pressure, level of the gas phase excitation (or its average temperature), and flow rate. The method operates in a diffusion-controlled regime. HF processes operate at significantly lower gas activation temperatures than plasma processes, and consequently produce less atomic hydrogen. In order to increase its amount, lower gas pressure is used. Lower gas pressure also leads to an increase in the rate of transport of active species. The generated atomic hydrogen takes part in a recombination reaction, which occurs only in the presence of a “third body”, M, which in this case is another gas molecule: 2H þ M ! H2 þ M þ 452 kJ=mol
(2:9)
The rate of recombination strongly increases with the reactor pressure. On the other hand, the equilibrium atomic hydrogen concentration depends little on pressure. The net effect is less destruction, that is, higher concentration, of atomic hydrogen as the pressure is lowered. However, lower working pressure leads to a relatively low deposition rate, which is one of the main disadvantages of the method. Rapid diffusion of atomic hydrogen from the area near the filament makes its concentration lower than the equilibrium concentration; however, near the substrate, owing to the rapid diffusion, atomic hydrogen concentration is much higher than its equilibrium concentration at the substrate temperature. Recombination is not the only process lowering the atomic hydrogen concentration. The same effect is produced by its reactions with hydrocarbon molecules: H þ CH4 ! CH3 þ H2
(2:10)
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For example, H concentration was found to be 30% lower if methane concentration is 5% higher. At low methane concentration, its small increase leads to a sudden decrease in H concentration, while the effect is less pronounced at higher methane concentrations. Typical deposition conditions are presented in Table 2.11. In the C22H system, conditions of carbon deposition on a substrate can be estimated on the basis of calculated equilibrium gas phase composition in the filament vicinity. Such results are in agreement with experimental results.[87] By oxygen addition (thus moving to the C22H22O system), partial pressure of all hydrocarbons is lowered, etching of nondiamond carbon is enhanced (by OH groups), and concentration of radicals is increased. If instead of methane some oxygen-containing compound is used (ethanol, methanol, acetone, or diethylether), higher deposition rates can be achieved, but the diamond quality is lowered. Certain authors have found, however, that for a given C/H ratio, the deposition rate is lower than that with methane if acetone, methanol, and dimethyl-propanol are used.[87] Within a typical range of operating conditions, the HF method produces polycrystalline diamond coating, whose morphology depends on the operating conditions. Good quality diamond is obtained by this method, which allows deposition rates of 1– 10 mm/h, because the quality of the deposited diamond is higher at low deposition rates. The deposition rate can be augmented by increasing the filament temperature, and/or decreasing the filament – substrate distance. A distinct deposition rate increase can be achieved by increasing the gas flow rate, because thereupon transport by convection becomes dominant. Apart from the low deposition rate, another disadvantage of the HF method is a possibility of diamond contamination by the material evaporating from the filament. Furthermore, tungsten and tantalum filaments slowly react with carbon producing the respective carbides; the filament becomes brittle and has to be replaced. It is mentioned in the literature that metal filaments are more efficient than carbide filaments in view of atomic hydrogen generation. A more
Table 2.11
Range of Typical Operating Conditions for HF CVD of Diamond[87]
Operating parameter Pressure Substrate temperature Substrate-to-filament distance Filament temperature Filament materials Source of carbon Gas composition
Typical range 1 – 100 mbar 600– 12008C 1 – 20 mm 2000 –26008C Tungsten, tantalum, rhenium CH4 , C2Hx(x¼2,4,6) , CH3OH and other alcohols, H2CO 0.1 – 7% hydrocarbon in hydrogen and 0 – 3% oxygen
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expensive rhenium does not make carbide; carbon rapidly diffuses through the metal making it ductile, thus extending its life.[87] Despite the drawbacks, HF deposition has remained popular because of its low capital cost and simplicity. Also, HF reactors are directly scaleable to large sizes (e.g., .20 20 cm) and can be used to coat complex shapes and internal surfaces. 2.9.3. Microwave (MW) Plasma As in the HF method, MW plasma and other electric activation methods usually employ a mixture of methane (1 – 10%) and hydrogen under low pressure (10 – 100 mbar). Deviating from earlier research, oxygen-containing compounds are often used today in order to increase the deposition rate and improve diamond quality. 2.9.3.1.
Reactors Using 2.45 GHz Plasma
As already mentioned, along with HF CVD, MW plasma is the most often used medium for diamond growth under metastable conditions. In this method, suggested for the first time by a group of Japanese researchers from the National Institute of Research of Inorganic Materials (NIRIM)[4] soon after having reported on the HF method of diamond growth, the gas activation was performed by a 2.45 GHz MW generator. In the NIRIM reactor, below 1 mbar there is a large difference between temperature of heavy species (molecules, radicals, and ions) and electrons (which are mediators in the energy transfer from the electromagnetic field to the gas phase). In a strong electromagnetic field generated by MW radiation, the electrons acquire energy that corresponds to a temperature of several thousand degrees. The heavy gas species (neutrals or ions) remain nevertheless “cold”, because they are either not influenced by the rapidly changing electric field or cannot follow it fast enough. Thus, the electric field does not act on them at all, or acts only weakly. However, although the NIRIM-type reactors are started up at low pressure (,1 mbar), they are usually operated at 10– 100 mbar during deposition. At this pressure, the number of collisions of the “hot” electrons with the heavy species is much greater, the latter being heated up as well (Fig. 2.42). The NIRIM-type reactors are simple, their damaged or contaminated parts can be easily replaced, they are subject to ready variation of substrate position relative to the plasma, and offer plasma spectroscopy and easy substrate observation during deposition. Yet, these reactors have certain disadvantages, primarily a limited size of substrates (2 – 3 cm2) and possibility of severe contamination of the growing film, which makes their industrial applications questionable. MW reactors made by ASTeX (Applied Science and Technology, Woburn, MA, USA), in which the principal disadvantages mentioned are avoided, utilize plasma having an elliptical cross-section, distant from the reactor walls. Probably the most popular reactor of this type, shown schematically in Fig. 2.43, utilizes
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Figure 2.42 Electron and heavy particle (neutrals and ions) temperatures in nonisothermal and thermal MW plasmas, as a function of gas pressure. The NIRIM reactors are started up in the border region between nonisothermal and thermal plasma, but thermal region (in which the temperatures are equilibrated) is used for the deposition in order to achieve higher deposition rate.[21]
an MW system of 5 kW/2.45 GHz, in which diamond growth rate amounts to 4 –14 mm/h, depending on the gas composition. The phase purity of the deposit is affected by the growth rate. An RF induction heater, necessary in a lower power reactor of this type (1.5 kW), is usually obsolete with 5 kW, where substrate
Figure 2.43 Cross-section of a 2.45 GHz, 5 kW ASTeX HPMS (high-pressure) MW reactor, equipped with an RF induction heater and a graphite substrate stage, used for diamond deposition onto 10 cm diameter substrates.[21]
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cooling may become necessary. This reactor type is widely used in research and development, and for prototyping and in small-scale production of diamond. If operated under well-defined deposition conditions, these systems run extremely stably and can deposit diamond continuously and unattended for several days or even weeks. This stability is absolutely necessary in order to grow top quality, 0.5 –1 mm thick diamond disks for heat sink applications, with thermal conductivities of more than 1300 W/m/K, within 1 week. Despite its importance for the development of CVD diamond technology and first steps toward its industrialization, this reactor type has some important drawbacks. At higher plasma power and low reactor pressures, the plasma discharge is not stable above the substrate, but tends to jump to the silica window. At 5 kW discharges, quick and complete destruction of the window occurs. In addition, growth rate and phase purity of the deposit are radiusdependent, the nondiamond carbon content being considerably higher at the edge of a plate 10 cm in diameter. As a result of research directed at reactor improvement, deposition of highly oriented diamond films with substantially improved thermal conductivities (up to 2200 W/m/K) for top quality heat sinks, as well as low wear coatings for cutting tools, has become feasible.[21] Full size industrialization of 2.45 GHz MW plasmas for diamond growth, however, still requires larger deposition areas, more homogeneous and more uniform deposits, and higher deposition rates. Further research and introduction of a magnetron 8 kW/2.45 GHz has led to an improvement of deposit uniformity and homogeneity, along with an increase in growth rates. In order to increase the deposition area, the size of MW plasma can be increased by operating at low pressures. However, increasing the plasma size in this way has its limits. Below 0.1 mbar, reduced number of collisions results in insufficient production of radicals and ions. Therefore, in one type of the MW CVD reactors, strong magnetic fields that force free electrons to resonantly move in closed loops (ECR) are used. Yet, at less than 0.1 mbar, where ECR starts to become significant, deposition rate, crystal size, and phase purity are all markedly reduced. Thus, although ECR is an interesting way of creating large area nonisothermal plasmas, it turned out to be unsuitable for growth of high-quality diamond. In contrast, by using a 5 kW reactor capable of operating at atmospheric pressure, a relatively high growth rate has been achieved (30 mm/h, compared with 0.5 –1 mm/h with the NIRIM 1 –1.5 kW reactors).[21] However, in this specific reactor design, the plasma is in close contact with the metal MW antenna, and another drawback is its extremely small deposition area (5 cm2). Nevertheless, this work is significant because it demonstrated that MW thermal plasmas have a clear advantage over nonisothermal plasmas. Interaction of the plasma with the substrate, as well as a small deposition area, can be a serious problem. Several research groups attempted to overcome these drawbacks by working with remote plasma generation and transport of growth species via high-velocity gas stream MW reactors.[21] With disc-shaped
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substrates, the largest diameter of 20 cm has been achieved. The disadvantage in this case is a relatively low quality of the deposited diamond. Namely, the radicals responsible for diamond growth have ample time to react or recombine after emerging from the reactor and before reaching the substrate. Outside the generator the gas phase will cool and fine-grain diamond with substantial amounts of nondiamond carbon tends to form. Such films can be suitable for some applications (low-wear coatings or electron emitting layers), but their thermal conductivity is usually insufficient for heat sinks.[21] Advantages and drawbacks of 2.45 GHz plasmas: A variety of 2.45 GHz deposition systems and reactors allows to conclude that a relatively small wavelength (12.2 cm) corresponding to this frequency permits a suitable small size and mass of the necessary components. With magnetron sources of up to 8 kW, high-rate diamond synthesis is possible and even (pilot) production is feasible. Nevertheless, there are also substantial disadvantages associated with the use of 2.45 GHz systems for diamond deposition. The main disadvantages are limited power density, plasma size, and mass deposition rate. Magnetron sources with more than 8 kW output power are not available. Higher powered klystron sources (30 and 50 kW) do exist, but they are rather complex, more expensive, and not very common. None of the presently existing reactor designs include klystrons. As the size of the plasma at constant power decreases with increasing pressure, these power limitations restrict the achievable linear deposition rates to smaller substrate areas. For high-rate largearea growth of phase pure diamond, higher MW power levels than those offered by 2.45 GHz magnetrons are necessary. In addition, relatively small wavelength (12.2 cm) plasmas are fairly sensitive to small objects that disturb the electrical field distribution inside the reactor. Such plasmas tend to concentrate at tips and edges, which may lead to nonuniform temperature, film thickness, and phase purity. It is therefore rather difficult to coat complex shapes and 3D objects. These difficulties can be overcome, for example, by the use of 915 MHz plasmas. 2.9.3.2.
Reactors Using 915 MHz Plasma
Owing to longer wavelength (32.8 cm) corresponding to this frequency, wave guides of such reactors have considerably larger sizes. However, power limitations of the 2.45 GHz reactors are no longer present. Substrates of up to 30 cm diameter can be mounted in such a unit. Diamond was demonstrated to grow at a rate of about 10 mm/h over the entire 20 cm diameter substrate with a thickness variation of +20%. A total mass deposition rate of nearly 1 g of diamond per hour, the highest diamond production rate so far attained, exceeds the total mass deposition rate of 5 kW/2.45 GHz systems by a factor of 10 to 100, while the coating area is four to five times greater. Therefore the 915 MHz systems are promising for serious industrial use, for example, mass production of heat sinks or tool coatings.[21]
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2.9.4. DC Arc Jet A plasma jet or “arc jet” is a generic expression for a high-pressure DC plasma discharge in which convection plays a significant role in transport processes.[88] In this method, the gas is heated to a very high temperature (typically 5000 – 6000 K) by means of an electric arc. There are two basic variants of the method. The arc is generated between electrodes (usually graphite), and the gas stream flows through the arc perpendicular to its axis. In another more sophisticated method, the arc is generated within a specially designed plasmatron and the gas mixture flows with a high velocity through the plasmatron parallel to the arc axis, thereby being heated to the plasma state. The plasma jet emerges with high velocity from the plasmatron and is directed to a water-cooled substrate. Typical carrier gas contains argon and hydrogen. Argon is needed to stabilize the plasma and H2 is essential as a source of atomic hydrogen. The initial gas mixture also contains a small percentage of methane. Irrespective of the initial gas mixture composition, in typical processes plasma predominantly consists of hydrogen, methane, acetylene and, if oxygen-containing compounds are added, carbon monoxide. Methane concentration in the plasma stays at a level of about 0.5% for the ratio C/H2 0.01 in the initial gas mixture, but acetylene content increases. The effect of the added oxygen is primarily to suppress acetylene and, if a sufficient quantity is added, to virtually eliminate the hydrocarbon in favor of CO. In a typical process, the arc is confined to a chamber that contains a nozzle from which the plasma comes out. The arc chamber itself, or arc jet body, may sit in a second chamber which is maintained at a pressure lower than that of the arc chamber, forcing the issuing plasma to expand. It is this pressure difference that is primarily responsible for the necessary dynamic conversion of thermal energy in the arc to kinetic energy of the flow. The temperature in the core of the arc may reach 40,000 K, and plasma conductivity increases with increasing temperature. This behavior leads to a discharge that has a negative impedance, a feature characteristic of an electric arc, which poses a significant challenge to designers of high-efficiency arc power supplies. The increased average gas temperature due to ohmic heating exceeds that which can be generated by thermal activation methods such as HF CVD. As a result of the high temperatures, the reactant gas decomposition process is much more vigorous, and a greater fraction of the plasma jet H2 is dissociated to produce atomic hydrogen, one of the most important chemical precursors in the diamond CVD processes. The very high velocities (1 – 10 km/s) that result from the expansion or acceleration process allow for a more efficient delivery of H atoms to the substrate because of reduced boundary layer thickness (Section 2.4.1). The expansion to lower pressures enhances the diffusive transport of atomic hydrogen from the plasma jet to the substrate (the diffusion rate scales inversely with pressure), which is driven primarily by the reaction of H atoms at the substrate surface. If all these factors are taken into account, one can derive an expression for the
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fraction of plasma jet H atoms that is delivered to the substrate surface in terms of the expansion pressure, pe (mbar), plasma jet velocity, u0 (cm/s), substrate diameter, ds (cm), and reaction probability of atomic hydrogen on the substrate, g:[51] ½Hs 1 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi ½H0 1 þ 950g pe ds =u0
(2:11)
Here, [H]0 and [H]s are the mole fractions of atomic hydrogen in the incident plasma jet and at the substrate surface, respectively. It is evident, that the maximum delivery of atomic hydrogen to a substrate from an arc jet is favored by reduced pressure and increased jet velocities. The advantages of such high enthalpy arc jet flows in the deposition of diamond films are clearly seen from the data on the diamond growth rate, which is nearly three orders of magnitude higher than values of the first HF and MW plasma experiments reported. Namely, shortly following the work in which deposition of diamond by DC thermal plasma was reported for the first time,[89] Ohtake and Yoshikawa[90] reported diamond growth rates exceeding 900 mm/h with a carbon conversion efficiency of about 8%. On the other hand, high heat fluxes and small deposition area are serious disadvantages which significantly restrict application of the DC plasma jet. Nevertheless, free-standing diamond plates were obtained for the first time using this method. 2.9.4.1.
DC Arc Jet Reactor for Diamond CVD
A schematic illustration of a typical DC arc jet in use as a source for diamond CVD is presented in Fig. 2.44. Electrical energy is converted to thermal and kinetic energies of a flowing gas mixture. Like in other diamond CVD methods, a major constituent of the gas mixture is hydrogen, while methane,
Figure 2.44
Schematic view of typical arc jet diamond CVD apparatus.[88]
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as a source of carbon, is most often introduced into the plasma jet. The plasma temperature is sufficiently high (3000 – 5000 K) to substantially dissociate the gas. The plasma jet impinges onto a cooled substrate surface (Ts 1000 – 1500 K). Molybdenum is often used as the substrate, although other materials have also been employed. In this method, pretreatment of the substrate by polishing with diamond paste is not essential, although it greatly enhances the nucleation density. In most designs, the electric arc in which the gas is nearly fully ionized is sustained between a concentric cathode rod and a surrounding cylindrical anode. After the arc has been ignited, the voltage drop required to dissipate the total power is established. The current is generally concentrated in the hot region of the plasma due to the thermal pinch effect. At sufficiently high current densities, a self-induced magnetic field further constricts the plasma. The arc column diameter is strongly influenced by conduction and convection of energy away from its core to the colder surrounding gas. The plasma conductivity in the core of a fullyionized arc varies as T 3/2. As a result, an increase in arc current further raises the temperature, and this results in increased conductivity which thereby reduces the arc voltage. Except for regions very near the electrodes, there is a linear potential variation along the arc column from the cathode to the anode. In this respect, the arc column behaves as a resistor with a negative impedance. The actual length of the arc column is also dependent on electromagnetic and gas-dynamic forces acting on it. Increased mass flow rates tend to increase the arc length and reduce the diameter, thereby increasing the resistance to current flow, and hence raise the operating voltage. The arc voltage established for any given operating current is therefore strongly influenced by the plasma gas mixture and flow conditions, such as the operating discharge chamber pressure and mass flow rates. A schematic illustration of the DC arc jet reactor for diamond deposition designed at the Vincˇa Institute is presented in Fig. 2.45.[19] The plasmatron (a) is mounted on the upper lid of the vacuum deposition chamber (b). The chamber and both its lids are double-walled to provide efficient water cooling. A silica window on the chamber is provided for observation and/ or spectroscopic measurements. The water-cooled copper substrate holder (c) can be moved in the vertical direction to position the substrate into the desired plasma region. It has been verified that the air leakage is sufficiently low: the oxygen content cannot exceed 4 ppm in any case, which is two orders of magnitude less than the content that might influence the deposit properties. The original design of the plasmatron, presented in Fig. 2.46, contains the cathode (upper) and the anode part. The cathode itself, made of a tungsten/ thorium alloy, is squeezed into the water-cooled supporter. Due to high current density (106 –107 A/m2) and heavy ion bombardment, the cathode is heated to the melting point of tungsten (about 3640 K). However, a high cathode temperature is necessary to ensure thermionic emission making the major part of the current passing through the plasma. The plasma column is constricted and therefore the electron emitting cathode area is very small, usually covering only part of
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Figure 2.45 Schematic view of the apparatus for DC arc jet deposition of diamond: (a) plasmatron; (b) chamber; (c) water-cooled substrate holder; (d) substrate; (e) vacuum pump; (f ) manometer; (g) optical system; (h) optical cable; and (i) photo-detector.[19]
the cathode surface. Ion bombardment must be sufficient to heat the cathode to a temperature that can support the high current density. The relationship between the cathode current, Jcat , and its temperature, Tcat , is:[88] 2 ðfw =kTcat Þ Jcat ¼ ATcat e
(2:12)
Figure 2.46 Cross-section of DC arc plasmatron designed at the Vincˇa Institute: K and A are cathode and anode parts, respectively; W is cathode, and AN is anode; 1 is insulator where primary gas mixture (P) is introduced; 2 (and S) is secondary gas mixture entrance.[19]
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where A ¼ 1.2 106 A/m2/K2, k is the Boltzmann constant, and fw is the electrode work function. In order to achieve the maximum current density for a given anode temperature, it is desirable to select the cathode material with a low work function. The work function of the W/2% Th alloy often used as a cathode material is only 3.35 eV. Owing to the arc plasma constriction and heavy ion bombardment, the cathode tip is usually in a molten state. The surface area of a molten W 1 mm in diameter can support a current of 11 A, which corresponds to 1.4 107 A/m2. The primary gas mixture consisting of hydrogen and argon is introduced near the cathode (tangentially for the sake of arc stabilization), while the secondary mixture (H2 þ CH4) is injected through an opening toward the plasma. Direct methane injection into the plasma (instead of its introduction with the primary mixture) permits good mixing of a cold secondary gas with the plasma jet, but its additional advantage is that reaction between methane and the tungsten cathode is avoided. That is, such a reaction leads to the formation of WC, the melting point of which is 500 K lower. The electron current is collected at the anode which is usually water-cooled to a temperature well below that of the arc. Thus, contamination of the plasma (and, therefore, of the synthesized diamond) due to both electrodes is reduced. The voltage – current characteristic of the plasmatron designed at Vincˇa is represented well by a hyperbolic function, its power covers the range of 1.8 – 5 kW, and its power efficiency amounts to about 50%, which is satisfactory. 2.9.4.2.
Gas Mixture Composition
Since the gas mixture composition is the main factor determining the arc voltage, it must be taken into account when the primary plasma gas is to be selected, but cost and efficiency (possibility of operating without ballast resistance) are of course also important. For arc welding, argon is used in most cases and the generators working at the corresponding voltage (20 –80 V) are readily available. Therefore, the usual choice is argon, a relatively cheap inert gas. Hydrogen is often added to argon, because even its low content (below 20%) considerably changes the voltage –current characteristic. Nevertheless, a significant drawback of argon is that considerable energy has to be expended for its heating. Transport of atomic hydrogen to the substrate is in most diamond deposition reactors diffusion-limited. It follows from Eq. (2.11) that, for typical conditions (pe ¼ 260 mbar, ds ¼ 2 cm, u0 ¼ 3 105 cm/s, g ¼ 0.1), the value of [H]s/[H]0 is equal to 0.2. Hence, a relatively small fraction of atomic hydrogen is transported to the substrate, which reduces the deposition rate. Even more important is the presence of the boundary layer (Section 2.4.1), because of which measured (or calculated) gas-phase concentrations of active gas species are not necessarily the same at the substrate. In order to circumvent, or at least minimize, this problem lower working pressure (1 mbar) and higher (supersonic) plasma jet velocity (9 105 cm/s) are used. Under such conditions, transport of
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atomic hydrogen is not necessarily limited by diffusion. Supersonic expansion at low temperature may also contrubute to minimize costs. 2.9.4.3.
Progress in the Study of Arc Jet Diamond Deposition
From morphological changes and other results, it has been concluded that large variations exist in the plasma composition along the jet. This is partly due to the diffusion of atomic hydrogen toward the substrate, which is larger than the diffusion of heavier hydrocarbon radicals. Other results suggest that f111g surfaces are more susceptible to defect formation than the f100g ones. By addition of oxygen to the gas mixture improved crystallinity of the f111g faces has been achieved.[88] In agreement with the results pertaining to other deposition methods, it has been found that the quality of the deposited diamond is rapidly degraded as the CH4/H2 ratio increases. This suggests that the chemical mechanism controlling diamond-vs.-graphite synthesis is nearly the same in the plasma jet method as in other methods in which the diamond growth rate can be orders of magnitude lower. It has been shown that this is possible if methyl radical is the gas species responsible for growth and if the surface growth mechanism follows that proposed by Harris (Section 2.4.1). However, in thermal plasmas such as DC arc jets, atomic carbon may be as abundant as CH3 , which suggests that in many thermal plasmas operating at moderate pressures atomic carbon can account for the observed growth rates.[91] The plasma temperature has often been determined from the intensity ratio of Ha and Hb lines in the emission spectrum of atomic hydrogen. However, because of indications that there is a departure from local thermodynamic equilibrium in the plasma (MW, as well as DC arc), parallel temperature measurements have been performed by: (a) emission spectroscopy, using the rotational and vibrational state distributions in electronically excited CH and C2 radicals and (b) LIF measurements of the rotational and vibrational state distributions in the electronic ground state. Much higher temperature values were obtained from the emission spectroscopy measurements (3000–7000 K) than from LIF (1200–2200 K). This indicates that the interpretation of plasma properties based on optical emission spectroscopy is unreliable because of the nonequilibrium nature of the plasma column.[88] The original design in which the substrate can be moved in vertical direction[19] allowed Vilotijevic to study deposition of diamond in different plasma jet regions. The author has differentiated three zones (A, B, and C) as suitable for diamond deposition (Fig. 2.47). In the A zone, well-defined crystals are obtained and the growth rate is by far the highest (500 mm/h) but on a relatively small surface area. In the C zone, the plasma column is much wider, the deposited area is thus larger, and the growth rate is reduced to only 20 mm/h, resulting in ball-like morphology. However, these differences are not followed by any important changes in crystallinity and phase purity, so that in all the three regions a relatively good-quality diamond is obtained.
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Figure 2.47 Schematic presentation of plasma jet with A, B, and C zones, suitable for diamond deposition.[19]
In the initial deposition stage no incubation period could be observed, although carbidization of the molybdenum substrate surface was found to precede diamond nucleation, or both processes proceed at the same time. As the substrate temperature is lowered, the diamond nucleation density on molybdenum was found to increase markedly: in the range from 1600 to 1150 K it increases by a factor of 10.[19] A particularly interesting result of applied research is the highest growth rate, 100 –200 mm/h, ever attained in homoepitaxial diamond CVD.[92] A triple arc jet design was employed in this study, a natural single diamond crystal was used as a substrate and its temperature amounted to 1200 –14008C. Concerning DC arc applications in the future, the expectation is that they will be determined primarily by the ability to reduce variable costs such as the power required to deposit a specified mass of diamond. 2.9.5. Radio-Frequency (RF) Plasma RF plasma is generated by power sources with frequencies of hundreds of kilohertz to tens of megahertz, and in this sense it lies between DC and MW plasma. Several types of RF plasmas have been used to deposit diamond. These may be distinguished primarily by the type of coupling of the plasma to the RF power source, either capacitive or inductive, and by the total gas pressure. Roughly, plasmas can be classified into glow discharge and thermal plasmas, depending on whether their total pressure is much lower or much higher than about 10 kPa (100 mbar), respectively. Thermal RF plasmas are almost always inductive, while glow discharge plasmas of both capacitive and inductive types have been used for diamond CVD.[93]
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Glow discharges are characterized by electron temperatures much higher than the temperature of heavy species, the latter being slightly higher than room temperature. The electron temperature usually exceeds 2 eV (above 20,000 K). The ionization mechanism is usually electron impact. In contrast, thermal plasmas are characterized by heavy species temperatures that are roughly equilibrated with the electron temperature. The heavy species must be hot enough, at least several thousand kelvins, to maintain a sufficiently high degree of ionization that will sustain the plasma. 2.9.5.1.
Capacitive RF Plasma
Parallel-plate capacitive RF discharges, operating at a frequency of 13.56 MHz are routinely used in the microelectronics industry for etching and deposition processes involved in the manufacture of integrated circuits. Therefore such generators are mostly used in research as well. Yet, capacitive discharges have been notably less successful than the competing technologies for depositing diamond. The major reason is that the electron energies are apparently too low (typically about 3 eV, compared to about 10 eV for MW plasmas) to attain sufficient hydrogen dissociation. Another reason may be that in parallel-plate capacitive discharges with high enough pressures to be practical for diamond CVD, highly energetic ions are present which bombard and damage the diamond coating or inhibit diamond growth. In one approach aimed at overcoming the limitations of capacitively coupled RF, the plasma is magnetically enhanced by an external magnetic field parallel to the electrodes. The electrodes are formed of separate rings which surround the plasma tube, and the deposition substrate is perpendicular to the tube axis. Potential advantages of this approach over the parallel-plate geometry are that (1) the magnetic field suppresses the loss of electrons from the plasma, thereby promoting plasma densities as high as those in MW plasmas; and (2) sputtering from the electrodes is avoided. However, the attained deposition rate is too low (about 10 nm/h only). In another study, the reactants flow through a tubular water-cooled RF electrode and are accelerated through a graphite nozzle to form a supersonic plasma jet, which impinges in stagnation flow upon the deposition substrate. Yet, diamond growth rates of only 0.2 mm/h were achieved and the diamond film contained significant amount of nondiamond carbon.[93] In summary, the results suggest that capacitive RF plasmas are unlikely to compete successfully with more established methods of diamond CVD. Indeed, in a recent research study in which capacitive RF plasma is used, the parallelplate configuration is abandoned and plasma density is enhanced by a magnetic field, or a supersonic plasma jet is formed.[93] 2.9.5.2.
Inductive RF Glow Discharge
Inductive plasmas are often referred to as being “electrodeless”, because the RF current passes through a coil that surrounds the plasma tube, which has the
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Figure 2.48 Apparatus used in the first published paper on diamond deposition in induction RF plasma.[94]
advantage that no electrode or filament comes into contact with the reacting gases. Although the diamond literature concerning the inductive RF glow discharge is even scarcer than that on capacitive discharges, the results appear more promising in that inductive glow discharges produce continuous, well-faceted diamond films which look similar to those produced by the more widely used methods. After the first reports on diamond CVD using inductive RF glow discharge by Matsumoto[94] (Fig. 2.48) and, somewhat later, another research group,[95] in which a substrate is placed parallel to the gas flow, in a more recent research by a group from the University of North Carolina,[54] a different geometry with the substrate perpendicular to the gas flow has been used. By using H2/CH4 plasma at 7 mbar, RF power 2 kW, and substrate temperature 8008C, a continuous diamond film with well-defined crystals has been obtained, at a deposition rate of 1 mm/h. However, particularly interesting results of this group are concerned with deposition of polycrystalline diamond films at 3008C at 0.4 –0.8 mm/h (Section 2.5.3). The feed gas consisted of a mixture of water vapor and various alcohols, the gas pressure was 7 – 13 mbar, and RF power 800 –1000 W.[54] 2.9.5.3.
Inductive Thermal RF Plasma
Induction plasmas in the thermal plasma regime have much in common with DC thermal plasmas, and to a lesser degree with combustion flames. Whether the electric current input to the plasma is provided by a DC arc or RF induction, in either case the electrical power primarily heats a mostly neutral gas to a very high temperature (about 10,000 K) at a relatively high, often atmospheric pressure. Differences between different systems may be attributed more to differences in geometry than to inherent differences between DC and RF plasmas. On the other hand, there are some differences between RF and DC thermal plasmas which may in some cases be important. In DC torches electrode erosion inevitably occurs, which is a potential source of contamination, while induction plasmas are electrodeless (hence, no contamination), more uniform, and have a
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larger volume, which is conducive to coating large areas uniformly. However, if either type of plasma is expanded through a nozzle (other than the anode of a DC arc jet), the conditions above the substrate have more to do with the nozzle parameters (geometry and pressure ratio) than with the type of plasma upstream of the nozzle. Typically in RF thermal plasmas the main plasma gas is argon, and hydrogen rarely exceeds 20% of the input volume flow rate. A pure atmospheric pressure hydrogen RF plasma apparently has never been achieved. Argon (or other inert gas) helps to stabilize the plasma and to reduce the high heat flux to the walls associated with hydrogen. Carbon is almost always introduced as methane, with similar methane/hydrogen ratios as in other deposition methods. The first reported use of an RF thermal plasma for diamond deposition was by Matsumoto et al.,[96] following Matsumoto’s work with RF glow discharge. The conditions applied were 60 kW, 4 MHz, atmospheric pressure, 20 mm diameter substrate, directly inserted into the 45 mm diameter plasma tube, with the plasma impinging in stagnation-point flow. A 10 min run produced a continuous polycrystalline film, with thickness ranging from 6 mm in the center to 12 mm at the edge of the substrate. According to the results of a group at the University of Minnesota working on mathematical modeling, maximum plasma temperature in a thermal RF reactor exceeds 10,0008C. A thin (about 2 mm) boundary layer exists above the substrate, across which the temperature drops from about 40008C to the substrate temperature of about 12008C. In this environment the injected reactants are virtually fully dissociated in the hot flow, and recombination takes place in the boundary layer. It is possible that under these conditions a considerable role in diamond growth is played by C1-radicals (including atomic carbon), in addition to the methyl radical, which is suggested by the agreement of experimental results with a numerical model based on this hypothesis.[93] In experiments performed with the aim of comparing a conventional atmospheric pressure RF plasma with a DC arc jet expanded to 5 kPa (50 mbar), deposition rates of 50– 60 mm/h and over 400 mm/h were obtained with RF plasma and DC jet, respectively, but the films obtained with the RF plasma were more uniform over a larger area (5 cm2). A group of Japanese authors[97] obtained diamond mass deposition rates of about 4 carats/h by RF plasma deposition of continuous films at a linear growth rate of 30 mm/h over 10 cm diameter substrates. In the reactor used in their work (Fig. 2.49), the substrate was placed beneath an expanded plasma obtained by operating at a reduced pressure of 200 mbar. The conditions used were 40 kW at 3.4 MHz, flow rates of Ar 80 L/min, and H2 20 L/min. As with DC thermal plasmas and combustion flames, in RF thermal plasmas the substrate surface is exposed to a high heat flux (typically 0.1 – 1.0 kW/cm2), and the substrate must be actively cooled to maintain a low enough temperature for diamond deposition. Since substrate temperature is one of the most important parameters for film growth, its control represents an important engineering
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Figure 2.49 Schematic illustration of RF thermal plasma reactor for diamond deposition at 30 mm/h over 10 cm diameter substrate.[97]
problem that must be solved. Successful approaches to solving this problem are substrate cooling by a jet of sprayed water and by a gas flow (Ar – He). In summary, unlike the low-pressure plasmas, RF inductive thermal plasmas have enabled (a) growth rates of several tens of micrometers per hour, considerably higher than in the low-pressure methods; (b) good film quality; and (c) good film uniformity over relatively large areas. However, the level of industrial interest in RF plasmas is much less than for MW plasma, DC arc jet, or HF. This may be due to relative unfamiliarity of industry with RF thermal plasmas and to relatively less developed RF torches for stable operation under diamond CVD conditions. Substrate temperature control is also a crucial engineering challenge, although this is shared by other high-heat-flux techniques. 2.9.6. Oxygen – Acetylene Flame The oxygen –acetylene flame CVD is the simplest and most elegant method of diamond synthesis. After the first experiments of Hirose and co-workers[98] who introduced the combustion flame diamond synthesis, common commercial burners have been used by many researchers. In this method the plasma is virtually isothermal.
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The elegant simplicity of the method stems from a number of its characteristics: 1. The process is operated in an open atmosphere, without the need for vacuum chambers, protective atmospheres, or pumps required in all the other diamond synthesis methods. 2. The required energy is derived from the combustion reaction. Thus, there is no need for power supplies, electrodes, or wave guides used in other diamond CVD methods, such as MW, HF, and the arc jet. Apart from the simplicity of the apparatus, the combustion process differs from other processes also by the fact that it is an oxygen-dominated process, while almost all other approaches to diamond synthesis are hydrogen-dominated systems. The presence of oxygen-based species (atomic and molecular oxygen, OH radicals) can induce a modification of the growing diamond surface, which, in turn, can lead to a higher diamond growth rate. That is, in the systems in which hydrogen is a dominant species, the diamond surface is surrounded by a hydrogen-supersaturated atmosphere with a low density of surface dangling bonds. On the contrary, in the oxygen-dominated systems, the presence of oxygen species may lead to a higher density of the surface dangling bonds, and consequently, higher growth rates.[21] In addition, it is well known that atomic oxygen gasifies the nondiamond carbon considerably more efficiently (100 – 1000 times faster) than atomic hydrogen,[99] and it is therefore logical to expect a better quality of the deposited diamond. An additional aspect of the flame-assisted synthesis is a lesser formation of defects in the deposited diamond. Namely, of all the activation processes, the flame possesses the least density of energetic electrons, which makes the substrate surface much less prone to damage due to electron bombardment. This may partly explain a higher quality of the flame-synthesized diamond, as far as electrical properties are concerned. 2.9.6.1.
Conical Nozzle-Stabilized Flame
Principle of the method and apparatus: In contrast to other diamond CVD methods which employ electrical or thermal activation, this method uses the energy of a chemical reaction. In the study by Hirose et al.,[98] as well as in many later papers by different authors, the flame from a conventional welding burner was directed toward a substrate mounted on a water-cooled copper holder (Fig. 2.50). Under carefully defined conditions, a diamond film of approximately circular shape is formed on the substrate. The film diameter depends on flame width, which, in turn, depends on the nozzle exit diameter of the burner. In our experiments,[39] 1 mm diameter of the nozzle results in about 6 mm film diameter. The main process parameters are substrate temperature (usually ranging from 650 to 11008C), acetylene-to-oxygen flow rate ratio, R (typically
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Figure 2.50 Schematic view of diamond deposition apparatus using acetylene – oxygen flame. Framed is enlarged view of the flame with primary zone (A), secondary zone (acetylene feather) with substrate (B), and outer flame (C).[40]
between 1.03 and 1.1), total gas flow rate, and the distance, d, from the substrate to the flame front (tip of the primary zone cone) (Fig. 2.50); d may vary from several tenths of a millimeter to several millimeters. Although the method is simple and the investment cost is very low, it provides a relatively high linear growth rate (over 100 mm/h, but it usually amounts to several tens of micrometers per hour), as well as a good quality of the film. Thus, it stimulated considerable interest of researchers who studied its different aspects. Figure 2.50 presents the flame structure. If the gas mixture is rich in acetylene (i.e., R ¼ C2H2/O2 . 1) the flame consists of three zones: 1.
Primary zone is the brightest and it is next to the nozzle exit, in which primary combustion proceeds: C2 H2 þ O2 ! 2CO þ H2 þ 448:8 kJ=mol
2.
3.
(2:13)
The C2 and C2H radicals are predominant in this zone, its brightness being due to their emission. Secondary zone, the so-called acetylene feather, is less luminous. The unburnt acetylene reacts in the same way in this zone, part of the oxygen coming from the surrounding air. This zone is rich in hydrocarbon radicals, predominantly C2 and CH. It is in this zone that the substrate must be positioned. Tertiary zone is a long outer flame, rich in oxygen radicals, owing to diffusion of oxygen from the ambient air. In this zone, secondary combustion takes place: 2CO þ H2 þ 3=2O2 ! 2CO2 þ H2 O þ 852:9 kJ=mol
(2:14)
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As the acetylene-to-oxygen ratio is reduced, the length of secondary zone (acetylene feather) is shortened. When the ratio drops to unity, this zone disappears. Thus, at R , 1 only the primary zone and the outer flame exist. On the other hand, if the ratio is strongly increased (to exceed 1.15), the secondary flame contains solid particles of sp2 carbon. Therefore a suitable ratio for diamond deposition is between 1 (slightly more than 1) and 1.15 (less than 1.15). Separation of primary and secondary combustion reactions: An original approach[100] permitting separation of reactions (13) and (14), and thus elimination of secondary combustion, was achieved by exploiting the chamber in which the deposition takes place. A slightly higher-than-atmospheric pressure is maintained in the chamber in order to prevent the ambient air from penetrating into it. The continuous flow of acetylene and oxygen is adjusted to maintain their ratio at 1.13, thus ensuring that the oxygen introduced into the chamber is completely consumed. The combustion products (CO and H2) are continuously removed from the chamber, together with the excess of acetylene, so that the secondary combustion [reaction (14)] occurs outside the chamber, using the ambient oxygen. The advantage of this procedure lies in the fact that the heat produced by combustion in the chamber is much lesser than that produced by deposition in the open atmosphere, because only primary combustion takes place in the chamber, and its energetic effect [reaction (13)] is only about one-third of the total effect. The authors have been able to apply four simultaneous flames in the chamber in order to coat with diamond all the four corner edges of a tungsten carbide cutting insert substrate, without its overheating.[100] A basically similar approach permitted to deposit diamond on larger flat surfaces, by moving the flame with respect to the substrate. Instead of the chamber, a flame cover is used. The outside air is prevented from entering the cover by maintaining a continuous flow of the acetylene/oxygen mixture (with a considerable excess of acetylene), while the combustion products and excess acetylene are removed (through a narrow gap between the cover and the copper plate on which the substrate is mounted) and burnt reacting with the ambient oxygen. Inert gas curtain: Another possibility of preventing the ambient air from diffusing into the flame lies in creating an inert gas “curtain” surrounding the flame. The authors of this approach[101] have obtained a considerable length of the acetylene feather by using an argon curtain in spite of a low R value, because the hydrocarbon radicals created close to the nozzle exit were protected from air oxidation. By using the inert gas curtain, a very uniform and dense film of microcrystalline diamond was obtained. The inert gas curtain has also been applied in our laboratory for diamond deposition on larger substrates by moving the substrate with respect to the flame. Without the gas curtain, the deposited diamond would be gasified by the outer flame rich in oxygen.
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2.9.6.2.
Flat Flame
Despite advantageous growth of high-quality diamond at rates exceeding 100 mm/ h, the practical utility of the original combustion CVD process has been limited by radial inhomogeneities and the small deposition area. For example, with the nozzle having an exit diameter of 1 mm, the diameter of the flame at the substrate level amounts to only about 2 mm, although the total area on which diamond is deposited is larger (about 6 mm in diameter). As the gas composition in the center differs from that on the periphery (because the latter contains more oxygen originating from the ambient atmosphere), the characteristics of the film will vary: diamond crystals on the periphery are larger and of better quality. Aimed at elimination or attenuation of this and other drawbacks, various modifications of the original method have been attempted in order to (1) enlarge the deposition area; (2) reduce the substrate temperature without sacrificing the deposition rate; and (3) achieve deposition on complex substrate surfaces. Moving the flame and using multiple torches in the chamber led to certain improvements, but the most significant modification is a procedure which makes use of a flat flame. That is, in the original method the burning velocity is very high and the gas flow rate is relatively low, resulting in a flame stabilized on the burner rim. However, in order to get a larger-diameter flame (i.e., to cover larger area) the flame should be blown off and stabilized close to the substrate surface. This requires an increase in gas velocity, to make it closer to the burning velocity. Yet, such solution is not practical because the gas flow rate should be too high. Another possibility is to control (diminish) the burning velocity, which could be accomplished by changing the gas compostion. Murayama and Uchida[102] achieved this by adding hydrogen to the gas mixture. Deposition at atmospheric pressure: As shown in Fig. 2.51, such a flame detaches from the nozzle to become stabilized close to the substrate surface. The diameter of the flame is considerably larger than in the burner-stabilized
Figure 2.51 Nozzle-stabilized flame is conical and covers small substrate area, while substrate-stabilized flame is flat and covers larger area.[99]
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flame. Murayama and Uchida,[102] who were the first to introduce a uniform flat flame stabilized close to the substrate, achieved a relatively high diamond deposition rate and were able to coat substrates with curvature. A schematic view of an atmospheric pressure flat flame burner similar to that of Murayama and Uchida is presented in Fig. 2.52.[103] A premixed mixture of acetylene, oxygen, and hydrogen is accelerated through a converging nozzle at a high speed (40 –55 m/s); the acetylene/ oxygen ratio (R) amounts to 1.02– 1.05, while hydrogen/oxygen ratio is 0.5. This flow impinges on the substrate 15 mm in diameter and a premixed flat flame is stabilized approximately 1 mm from the substrate surface. An additional annular flow of hydrogen gas shields the premixed gases and prevents formation of a conical flame stabilized on the burner rim. The substrate temperature is 780 – 8808C. A uniform polycrystalline high-quality diamond film is thus obtained on a molybdenum substrate, with a deposition rate of about 70 mm/h. By decreasing
Figure 2.52 Schematic view of atmospheric pressure flat flame diamond deposition apparatus. Outer nozzle diameter is 3 mm, and substrate diameter is 15 mm.[103]
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the substrate temperature to 530– 6308C, the deposition rate is drastically reduced (to about 1.5 mm/h). Another, “trumpet bell” design, had a goal to optimize the use of the inlet gases and to approach the properties of an ideal stagnation flow.[99] Thus an atmospheric pressure flat flame offers the possibility to coat large areas at a relatively high rate (25 – 40 mm/h). One of the main difficulties of atmospheric pressure operation is that pure acetylene –oxygen mixture burns so fast that either flashback or blow-off can occur readily. Various attempts to overcome this difficulty resulted in a more complicated reactor design or addition of hydrogen to the inlet gas mixture in order to obtain a more stable flame. Deposition at reduced pressure: The atmospheric flat flame does solve some of the problems related to diamond CVD, but there remains the difficulty of a very high heat flux, typically in the range of 0.5– 1 kW/cm2. If a flat flame is produced at a reduced pressure this problem can be overcome and, what is more, deposition of diamond can be effected on a still larger area, up to 20 cm2. Perhaps the most important advantage of the method is that the energy brought to the substrate is sufficiently low to make its cooling unnecessary, which allows diamond deposition onto components whose cooling is difficult to accomplish. However, a disadvantage of the low-pressure approach is a low deposition rate (several micrometers per hour). This is a consequence of the reduced radical flux to the substrate. In addition, the requirement for vacuum systems and chambers to achieve reduced pressures detracts from the inherent simplicity of the combustion process and adds to the cost of equipment. A design of low-pressure combustion apparatus,[104] based on the original design[105] is shown in Fig. 2.53. The burner is mounted in a water-cooled stainless steel vacuum chamber in an upward flow configuration. The burner
Figure 2.53
Schematic view of low-pressure flat flame diamond deposition reactor.[104]
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consists of a water-cooled cylindrical brass mixing chamber capped off at the top with a brass disk with an array of 131 uniformly spaced 1 mm diameter holes drilled in it through which the premixed reactants flow. The diameter of the array is 2.6 cm. A molybdenum rod 1.6 cm in diameter serves as a substrate. The rod is threaded into a water-cooled copper block to maintain the desired surface temperature. The pressure is maintained at 40 torr, the substrate – burner distance is 5 mm, and the total flow rate of the premixed gas is 7.2 L/min, which corresponds to a cold gas velocity of about 430 cm/s. Under optimized conditions of substrate temperature and acetylene-to-oxygen ratio, high-quality translucent diamond film consisting of well-faceted crystals is produced, exhibiting Raman FWHM of about 2.5 cm21. Diamond growth rate under these conditions is about 4 mm/h, but is found to drop off substantially at high substrate temperatures, with little or no carbon deposited beyond 10708C. Another approach involves packing a tube with thin-walled silica tubes to create a honeycomb structure. Typical operating conditions were: R ¼ 1; Ts ¼ 600– 8008C; burner –substrate distance, 8 –15 mm; P ¼ 60 mbar; cold gas velocity, 600 cm/s. The goal of both structures is to produce a velocity profile at the burner exit which is uniform across its diameter. Because of the possibility of coating large surfaces, the flat flame technique is being studied further, not neglecting deposition at low pressures (LPFD) and low temperatures (5008C), by which diamond can be deposited on a special glass (e.g., Pyrex), whose thermal expansion is comparable to that of diamond. Both atmospheric and low-pressure flat flames employing oxygen/ethylene and oxygen/methane mixtures, as well as a number of other mixtures, are studied primarily in view of replacing the expensive acetylene by a cheaper gas. Of particular interest is methane, a principal constituent of natural gas and a lot cheaper than other hydrocarbon gases. To conclude, the radial uniformity and scaleable nature of flat flames make them an attractive option for diamond deposition. Concerning comparison of atmospheric pressure and low-pressure techniques, as summarized in Table 2.12,[106] the low-pressure operation, despite lower absolute growth rates, offers advantages in reactor design, stability, and temperature control which are important for the reproducible production of quality material. Despite the important advantages of flat flames, their application is still under question because of high operational cost. Essential disadvantages of the more promising low-pressure flame are low deposition rates and high cost of acetylene. In order to make this technique competitive, the deposition rate should be increased three to six times, unless some other improvements (as already discussed in this section) are made. 2.9.6.3.
Using Advantages Offered by Flame Deposition
Among the advantages of the oxygen –acetylene flame, of particular interest is the possibility of simple and rapid change of chemical reactions during deposition, which allows not only to alter the characteristics of diamond, but also to
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Table 2.12 Comparison of operating flat flames at reduced (50 – 70 mbar) and atmospheric pressure[106] Aspect Growth rates (mm/h) Carbon conversion efficiency (%) Vacuum chamber required? Deposition temperatures (8C) Temperature control Acetylene flame stable? Safety Burner design
Reduced pressure 4 – 5.5 0.005 Yes 400– 1000 Easy Yes Advantage Simple
Atmospheric pressure 25 –40 0.005 No 700 –1200 Difficult No: H2 addition needed Complex
deposit nondiamond phases.[99] In the flame method, the distance between the nozzle exit and the substrate is usually small (less than 1 cm) and the gas velocity is high, so that the time for active gas species transport to the substrate is very short. Therefore any changes in the gas composition are immediately reflected in alteration of the deposited product. In order to prevent uncontrolled variations of deposition conditions, among which the deposition temperature is one of the most important parameters, various techniques by which these variations are significantly reduced are used. One such technique is the control of substrate temperature, regulated by means of a sprayed water jet. The jet strength is regulated by means of a computer connected to a thermocouple and a regulation valve. The control of temperature and other deposition parameters enabled a group of Dutch researchers to carry out homoepitaxial diamond growth on the f100g and f110g facets of a natural diamond crystal IIa.[107] A 0.4 carat diamond film with dimensions 6.5 9 mm has been deposited on the f110g facet. It was verified that the films grown on a number of substrates are single crystals, their quality being comparable to the substrate quality. A group of American researchers[108] has used a three-step procedure to grow diamond crystals having diameters up to 1 mm. An Si f100g single crystal served as the substrate, but its surface was covered, using a flame treatment, with microcrystalline graphite on which diamond nucleation occurred. As the thickness of the deposited diamond film increases, its uniformity decreases. Statistical variations in the growth rate can produce a pronounced coating roughness. For example, at a thickness of 100 mm, roughness (expressed as the distance between peaks and recesses) can be as high as 100 mm! How large the variations in deposition rate, and therefore in crystal sizes, may become was demonstrated in our work,[109] in which combustion flame diamond growth experiments were run up to 4 h. The diamond films (Fig. 2.54) contained, in addition to the densely populated octahedral crystals making a
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Figure 2.54 Particularly large diamond crystal is sticking out from the main crystal population which makes a continuous film. A square f100g facet is just formed at the tip of the large crystal.[109]
continuous layer (about 50 mm in thickness), a number of individual large (ca. 250 mm) cubo-octahedral crystals sticking out above the layer. The large crystals are terminated by flat square f100g facets up to 200 mm in size parallel to the substrate (i.e., perpendicular to the growth direction). This phenomenon was explained by a temperature difference between the large crystals and average crystals, due to their different heating. To prevent large differences in crystal size, process conditions can be altered[99] so that diamond and nondiamond carbon are alternatively deposited, because diamond nucleation readily takes place on nondiamond carbon. Another possibility is to periodically alter the deposition parameters in order to etch the growing diamond surface, thus reducing the size of the crystals grown above the average thickness. This approach can decrease the roughness to only 10 mm, at a deposition rate of 30 mm/h, considerably higher than that in the HF method. The alternating deposition of DLC and diamond might enhance the coating toughness, which would have a positive effect on the cutting properties of diamond-coated tools. In conclusion, it may be said that the oxygen –acetylene flame CVD is one of the methods that will probably be used in the future to produce diamond commercially. Its advantages are the following: 1. Possibility to deposit diamond in an open atmosphere, making the scale-up easier than in other methods. 2. Substantial deposition rates and possibility of achieving good quality of the deposited diamond. 3. Increased flexibility owing to numerous possible modifications of flame geometry. The flame stabilized on the nozzle and the flame
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4.
5.
stabilized on the substrate have diferent characteristics and, therefore, different applications. Deposition at reduced pressure reduces the energy brought to the substrate, making substrate cooling unnecessary. Application of the method is thus extended to substrates whose cooling is difficult to achieve. Rapid transport of active species from flame to substrate allows rapid changes of chemical reactions and, consequently, of the deposited material properties. Further flexibility increase, not existing in other methods, is thus possible. Simplicity, low cost, and small dimensions of the equipment allow its adjustment for specific applications.
The most important disadvantage is relatively high cost of acetylene, because of which the flame CVD is not competitive with other methods, such as MW, HF, or arc jet. There are several routes to overcome this difficulty: (i) reduction of cost of acetylene in a large-scale plant production; (ii) replacement of acetylene by another fuel gas; and (iii) higher deposition rate (e.g., in the low-pressure flat flame, the deposition rate is more than one order of magnitude less than that achievable over small areas with the atmospheric flame method). 2.10.
APPLICATIONS OF CVD DIAMOND
2.10.1.
Introduction
CVD diamond applications are closely linked to the extreme properties of diamond, but also to the technological flexibility of CVD methods and the possibility to combine synthetic diamond films with other diamond and nondiamond materials and products. All these properties are important for present and future applications of both dielectric and conductive diamonds. CVD diamond can be used as a film, free-standing film and plate, as well as in the form of components of composite materials and in hybrid technological processes. Table 2.13[110] contains an overview of properties and related applications of CVD diamond. 2.10.2.
Mechanical Applications
2.10.2.1.
Cutting Tools
The extreme hardness and wear resistance make diamond an ideal material for cutting tools—machining non-ferrous metals, chlorides, fluorides, polycarbonates, quartz, sapphire, NaCl, Si3N4 , SiC, Ti, WC, ZnS, plastics, chip-board, and composite materials. Industrial HPHT diamond has been applied for such purposes since 1960s and remains a lucrative commercial material today. In these applications, fine diamond grit is either glued to a suitable tool (saw blades, lathe tools, drill bits) or consolidated with a suitable binder phase (e.g., Co or SiC) to make a hard, tough, and durable composite. CVD diamond is
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Properties and Applications of CVD Diamond[110]
Properties High hardness Mechanical High modulus High stiffness Low friction Thermal High thermal conductivity Transparency Optical Optical emission Photoconductivity
Polycrystalline film applications Hard coatings (A) (cutting tools; medical knives) SAW filters (A) Speaker cone (A) Sliding parts (A) Heat sink (A) IR laser window (A)
UV detector (A)
High resistivity Electrical High break down field
Thermistor (A)
Semiconductivity Negative electron affinity Corrosion resistance
Field electron emitters (B)
Surface stability Biocompatibility
Single crystal film applications
Anticorrosive coatings (B) Electrochemical electrodes (B) Chemical sensors (B) Biocompatible coatings (B) Biosensors (B)
Heat sink UV laser window UV detector UV LED UV laser High -power devices High-temperature devices Radiation resistant devices High reliability devices 3D devices
Chemical sensors (B) Biosensors (B)
Note: The sign (A) denotes that the application is practiced, (B) indicates that the application is fundamentally feasible by the present technology, and (* ) shows that the property is extrinsic and the application requires relevant extrinsic property. SAW stands for surface acoustic wave.
beginning to be used for similar purposes. The most dramatic progress and technical success have involved thin-film-diamond-coated WC – Co tools. The range of materials machined has been substantially expanded to include carbon-loaded plastics, graphite, green ceramics, and Al –Si alloys with SiC content up to 30%.[15] These materials, in particular Al –Si materials that are beginning to be used in aerospace and automobile industries, are unsuitable for machining by traditional tools, but are excellent candidates for diamond-coated WC cutting tools. Today reliable diamond-coated tools in the market are capable of running at higher revolutions per minute, taking deeper cuts, lasting longer by factors of 5 –10 times, and providing a better finish than uncoated WC.[15]
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Our results concerning machining of an Al/12%Si alloy[111] have demonstrated advantages of diamond-coated tools (D-tool) with respect to the uncoated ones: (a) wear of the D-tool is up to 5 lesser under the same machining conditions and (b) surface roughness of the machined part is up to 3 lesser with the D-tool. Good results have also been obtained in machining glass-fiberreinforced plastics. A disadvantage of the D-tool is that it cannot be used for machining steel and other ferrous materials because of solubility of C in Fe. 2.10.2.2.
Wear-Resistant Coatings
In addition to the applications in which diamond coatings are substituted for natural diamond, there is a number of those where CVD diamond opens new possibilities. One such application is wear-resistant coatings. Protection of mechanical parts by ultrahard coatings in, for example, gear boxes, engines, and transmission mechanisms, can substantially prolong the life of the components with less lubrication. It should be pointed out that in the case of iron-based materials the application of diamond is still a big challenge. That is, in any application where friction is considerable, the diamond-coated part will be heated and, if ferrous materials are applied, the diamond coating will eventually react with iron and become dissolved in it. Therefore intensive research aimed at suitable intermediate layers that could allow application of diamond coatings on ferrous and steel parts is under way. Diamond is also used for coating magnetic disks, where surface smoothness and hardness are essential. Fine-grain polycrystalline diamond films can be used as coatings of wire dies and water jet nozzles. 2.10.2.3.
Micromechanical Devices and Sensors
The ability to produce thin diamond films that can be precisely patterned on a microscale, coupled to their stiffnesss and wear resistance, highlights another potential application—micromechanical components, such as cogs and gears. Although this technology is still in its infancy, some such structures—pressure and temperature sensors—have already been demonstrated.[49] The extreme stiffness of diamond also opens up its application for highperformance speakers. 2.10.3.
Thermal Management
Modern high-power electronic and opto-electronic devices suffer from severe cooling problems owing to the production of large amounts of heat in a small area. In order to cool these devices, it is essential to spread the narrow heat flux by placing a layer of high thermal conductivity material between the device and the cooling system (such as radiator, fan, or heat sink). CVD diamond has a thermal conductivity that is far superior to copper over a wide temperature range, together with the advantage of being an electric insulator.
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Now that large-area CVD diamond plates with thermal conductivities of 20 W/cm/K are available, this material is beginning to be used for a variety of thermal management applications. These include submounts for integrated circuits, heat spreaders for high-power laser diodes, or even a substrate material for multichip diodes. The result of this application should be higher speed operation, since devices can be packed more tightly without overheating. Reliability can also be expected to improve, since, for a given device, junction temperatures will be lower when mounted on diamond.[49] A dramatic demonstration of the virtues of diamond has been shown through incorporation of a GaAs monolithic MW integrated circuit power high-electronmobility transistor soldered to a diamond substrate and molded into a plastic package. The package operated continuously at 20 W for 96 h without thermal or electrical degradation, which represents a 10-fold improvement over conventional plastic packaging. Although the price is still unattractive for high-volume low-power plastic-packaging applications, it is cost-competitive in high-end electronic-packaging applications, such as RF power amplifiers.[15] Aside from the cost issue, the manufacture of CVD diamond for thermal management poses a technical challenge: the need for a reliable, adherent metallization scheme. This challenge has been met by different metallization processes used in conjunction with several solders, depending on the application temperature.[15] 2.10.4. Applications in Electronics 2.10.4.1.
Passive Applications
The most important passive application of CVD diamond is cooling of electronic devices, which has been already summarized (see Section 2.10.3). 2.10.4.2.
Active Electronic Devices
Devices with single-crystal or highly oriented polycrystalline diamond: The difficulties that should be overcome in order to convert diamond into a semiconductor by doping, thus opening a number of potential applications in electronics, are discussed in Section 2.8. The first problem—heteroepitaxial growth of doped diamond single crystal with satisfactory quality—is very complex. Therefore a number of researchers directed their efforts toward developing technologies that use either oriented substrate or adequate control of deposition conditions, to produce polycrystalline coatings with highly oriented diamond crystals (Section 2.7). The next problem, which has recently been partly solved,[49] is the need to pattern the diamond layers in a definite way to produce features of similar size to those used in microcircuitry, typically a few micrometers. The solution of the problem is based on the ability to coat the deposited diamond layer with a suitable non-erodible mask and then to etch away the uncoated parts by oxygencontaining plasma. Another possibility is to employ a technique of “selective
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Figure 2.55
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Selective area deposition of a patterned diamond film on Si.[49]
area deposition”, by which diamond is grown on only certain parts of the substrate. Whichever technique is used, diamond films can now be patterned to geometries suitable for all but the most demanding devices (Fig. 2.55). In a typical procedure, a single-crystal Si substrate is coated with a thin SiO2 film, which is then patterned by employing standard methods of photolithography and dry etching, whereby the Si surface is exposed. The part is then subjected to ultrasonic roughening, after which the oxide layer is removed by dissolving it in HF. Then diamond is deposited, whereby its nucleation preferentially occurs on the roughened Si surface. The final and probably the most difficult problem to solve, in order to be able to create diamond devices, is that of doping the diamond reliably and reproducibly. As has been already pointed out (Section 2.8), incorporation of the elements producing p-type semiconductivity (e.g., boron) is relatively straightforward, but doping with the n-type elements (e.g., phosphorus) is difficult because of the densely packed and rigid diamond structure, making doping with elements larger than C very difficult. Yet, very encouraging are the recent results achieved in the NIRIM which show that doping by P is feasible (Section 2.8.4). In spite of the difficulties, diamond-based devices are gradually emerging and may become the material of choice for electronic applications involving high power and/or high temperature. Diamond Schottky diodes operating at up to 10008C have been already demonstrated. Transistor structures have also been attempted, with varying degree of success. On the basis of the various field effect transistor devices that have been fabricated, an extremely highpower handling density of 30 W/mm2 has been predicted.[49] Figure 2.56[73]
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Figure 2.56
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Diamond field emitter with a self-aligned suspended gate structure.[73]
shows a diamond field emitter with a self-aligned gate structure, which provides a true three-terminal or triode emitter device configuration. The radius of curvature of the sharpened tip apex is less than 5 nm. The tips are fabricated in arrays to multiply their effect and achieve circuit level utilization. Even with these successful developments, it must be mentioned that diamond electronics is still in its infancy. Polycrystalline-diamond-based devices: Surface acoustic wave devices. One type of electronic devices that can use impure, thin polycrystalline CVD diamond (as opposed to single-crystal diamond), is the surface acoustic wave (SAW) filter. A SAW filter is a device that can transform RF electronic signals into mechanical vibrations, and vice versa. Such filters are used in the communications industry, where highfrequency radiowaves need to be generated by electronic circuitry, and subsequently broadcast by a transmitter. These radiowaves are then collected by a receiver and must be reconverted back to electronic signals for further processing. The limiting factor in most current SAW devices is the maximum speed with which signals can propagate through the device from one set of circuitry to the other, and this depends largely upon the speed of sound (the acoustic wave) along the surface of the device material. For future high-performance devices, a SAW material is needed which can operate at 10 GHz or higher frequencies, and diamond is the obvious candidate. That is, the speed of sound is proportional to the square root of the ratio of the elastic modulus to material density. The elastic modulus of diamond is the highest of all the materials known; thus, the speed of sound through diamond is extremely fast (17.5 km/s, i.e., 53 times faster than the speed of sound in air). In practice, the diamond film is part of a multilayered structure, with a piezo-electric material such as ZnO, LiNbO3 , or LiTaO3 , deposited on top of the diamond film to convert the mechanical vibrations of diamond to electric signals. Some companies (such as Sumitomo in Japan) are already exploiting diamond-based SAW filters in commercial mobile phone equipment,
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and it is likely that within a few years a diamond SAW filter will be an essential component of all high-frequency communications equipment, including telephone networks, cable television, and the Internet.[49] In Schneider et al.,[112] a (nondestructive) photoacoustic technique based on SAW was used to determine Young’s modulus, thickness, and density of diamond and DLC films. Field emission displays. Another device that can use polycrystalline CVD diamond, and which is causing a great deal of interest at the moment, is a flatpanel display. The electronic properties of diamond are such that when it is biased negatively in vacuum, electrons are ejected from its surface. This process is also common in most metals, except that in metals the electrons have to overcome an energy barrier (quantified by the work function) to escape from the surface. In diamond this barrier has been measured and found to be very small, maybe even negative, and this has given rise to the term “negative electron affinity”. In practice, this means that devices based on the electron emission properties of diamond could consume very low power levels and hence be extremely efficient. The electrons emitted from the surface are accelerated using a positively biased grid to strike a phosphor screen, causing light to be emitted. Each emitting diamond crystal, or group of crystals, would form a “pixel” on a flat panel display screen. Unlike their major competitors, liquid crystal displays (LCD), diamond cold cathode field emission displays (FED) would have high brightness, a large viewing angle, and be insensitive to temperature variations. Also, because of their relative simplicity, it is possible that diamond FEDs could be scaled up to large areas that would be impossible with LCDs, maybe even several square meters. A new type of cold diamond cathode for electron emission from the negative-electron-affinity diamond surface has been proposed.[113] 2.10.5.
Optical Applications
Diamond offers potential for both passive and active optical applications, but current usage is only passive. Passive applications take advantage of its high thermal conductivity, corrosion resistance, and hardness, as well as its low absorption coefficient and low coefficient of friction. Diamond is beginning to find uses in optical components, particularly as a free-standing plate for use as an IR window in harsh environments. The first diamond window was used for the IR emission sensor of the Venus explorer. Conventional IR materials, especially in the 8 – 12 mm wavelength range (such as ZnS, ZnSe, and Ge), suffer the disadvantage of being brittle and easily damaged. In contrast to these materials, diamond has high transparency, durability, and resistance to thermal shock and is therefore an ideal material for such applications. Although the materials mentioned could be protected by a diamond coating, a more suitable solution is a free-standing diamond window with thickness in the millimeter range. As far as polycrystalline windows are concerned, an essential condition is to achieve a smooth surface, because roughness
Diamond Synthesized at Low Pressure
Figure 2.57
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Optical quality free-standing diamond window.[49]
makes the transmitted signal scattered and weaker, with a loss of resolving power. Recently nanocrystalline diamond films with very low roughness were prepared[15,49] and they seem to be most suitable in this respect. Figure 2.57 shows an example of optical quality diamond window. Optical quality diamond thin films, deposited by the HF technique, have been found to be suitable for use as near-IR antireflective filter windows and X-ray windows.[114] CVD diamond lenses with excellent thermal and optical properties have been recently fabricated by depositing diamond on preformed substrates (Fig. 2.58).[115] Optical matching is another passive usage of diamond. Its refractive index of 2.4 is lower than that of most semiconductors and higher than that of typical dielectrics. Diamond generally has a lower refractive index than materials from which IR detectors are made (Si, Ge, group II –VI elements, and Pb salts). Therefore, it is the preferred material for coating applications. In addition, much progress has been achieved for longer wavelength detectors with higher refractive indices. The efficiency of Si and Ge solar cells has been substantially augmented by diamond coatings. Cost has been the most important factor prohibiting commercial application of CVD diamond optics. The commercially available 2.5 cm diameter window can now be purchased for several hundred dollars (in contrast to several thousand dollars for the first commercial windows). As manufacturing processes mature, further cost reduction is expected and commercial applications should expand. 2.10.6. Electrochemical Applications Three broad classes of electrochemical applications, which make use of the reactions occurring at the solid-electrode/liquid-electrolyte interface, can be
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Figure 2.58 Highly transparent 5 cm CVD-diamond wafer with diamond lenses from 3 to 5 mm in diameter and sag heights up to 380 mm.[115]
identified:[80] (a) synthesis (or destruction), in which an applied potential is used to bring about a desired chemical oxidation or reduction reaction; (b) qualitative and quantitative chemical analyses by means of the voltage –current electrode characteristics; and (c) power generation. All these applications require stable, conductive, chemically robust, and economical electrodes. Diamond electrodes, being typically in fact thin diamond coatings fabricated by CVD methods on Si, Mo, or W substrates, satisfy these conditions in a wide range of applications. An important characteristic of diamond electrodes is their stability compared with conventional carbon electrodes. Diamond coatings are stable during anodic polarization in acidic fluoride, acidic and neutral chloride, and alkaline media. For example, chlorine can be evolved on diamond thin films in 1.0 M HNO3 þ 2.0 M NaCl at a current density of 0.5 A/cm2 for up to 12 h with no evidence of damage, while glassy carbon catastrophically fails within 2 min under such conditions. Ozone can be generated in H2SO4 at B-doped diamond thin films using current densities of 1 –10 A/cm2, usually without any damage.[80] Although diamond coatings are not completely inert, especially at anodic potentials, their stability in a wide range of potential allows electrochemical reactions that would otherwise be difficult or impossible to carry out. Examples are reduction of nitrate and nitrite ions on polycrystalline diamond or a direct reduction of Liþ to Li on a diamond single crystal from a solid polymer electrolyte. These results indicate that diamond electrodes may be used to study a wide range of electrochemical reactions at very large negative potentials, without interference of parallel parasitic processes. By virtue of a low background current on diamond, the signal-to-noise ratio is much more favorable (often 5– 10 times) than on a glassy carbon, the routine
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Figure 2.59 Polycrystalline, B-doped diamond thin-film electrode grown on a 250 mm diameter tungsten wire. Insert shows magnified view of interface.[80]
detection limits are in a number of cases at a ppb level, and electrodes work stably for a long time, in contrast to carbon (sp2) electrodes. Doped CVD diamond films can also be used for electrochemical applications, particularly in harsh or corrosive environments. Conductive B-doped diamond electrodes were found to have a very large potential window in water. This is a great advantage over other electrode materials, such as Pt, which dissociate water at higher electrode potentials resulting in unwanted evolution of hydrogen and oxygen. For diamond-based electrodes, this hydrogen evolution rate is much slower, allowing much higher electrode potentials to be used. This allows the otherwise inaccessible chemistry of redox couples to be studied. Diamond electrodes might find applications in analysis of contaminants, such as nitrates, in water supplies, and even in the removal of those contaminants. Figure 2.59 shows an electrode made of tungsten wire coated with B-doped diamond.[80] It can be concluded that its unique properties make diamond extremely attractive for applications in electroanalysis and electrochemical synthesis. These might include chemically and structurally stable sensor electrodes for in vitro or in vivo biomedical applications, and sensors for long-term environmental studies, or for use in molten salts or in highly radioactive environments. Diamond electrodes might also find uses in chemically aggressive environments, for example, electrosynthesis of fluorinated compounds, anodic destruction of organic wastes, ozone synthesis, or molten-salt processes. Reactions at unusually high cathodic potentials, such as reduction of active metals, may be performed on diamond. However, the long-term stability, especially of polycrystalline electrodes on high anodic potentials and current densities, remains to be established. 2.10.7. Composite Reinforcement Recently, diamond fibers and wires have been fabricated (Fig. 2.60) with exceptional specific stiffness (high ratio of elastic modulus to density).[49] Diamond is
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Figure 2.60
Diamond-coated tungsten wire grown in an HF reactor.[49]
deposited on the outer surface of a metallic wire or nonmetal fiber. Thus obtained diamond fibers have elastic modulus values close to those expected for diamond. If growth rates can be increased to economically viable levels, such diamond fibers may find uses as reinforcing agents in metal-matrix composites, allowing stronger, stiffer, and lighter load-bearing structures to be manufactured for use in aerospace applications. By etching away the metal core using a suitable chemical agent, diamond pipes or hollow diamond fibers can also be fabricated. Hollow diamond fibers and 2D diamond fiber mattings or weaves have been demonstrated, and they could form the basis of smart composite structures that would react to external influences in a desired way. That is, substances for sealing or cooling or sensors could be introduced into empty canals.[49] 2.10.8.
Detectors for Radiation and Particles
CVD diamond is already beginning to find a market as a “solar-blind” detector for UV light and high-energy particles. Free-standing and silicon-supported polycrystalline diamond films have been used to fabricate photoconductive and photodiode structures for UV light detection. Planar and sandwiched UV photoconductive detectors appear to have a good spectral selectivity.[116] High-performance UV detectors have been demonstrated and are now in commercial production.[49] The advantage of CVD diamond as a particle detector over other materials is its radiation hardness, low atomic number, high atom density, and robustness in hostile environments. It is possible to impose a very high electric field across diamond, under which electrons and holes created by an incident particle separate and are collected by electrodes on the film surface. Radiation hardness is one of the supreme advantages of diamond over more conventional detector materials. Diamond can be used to detect high-energy particles, such as alpha- and betaparticles, protons,[117] protons, pions, and neutrons,[118] and might be used as replacement for Si-based detectors in high-energy radiation environments, provided that the sensitivity can be increased. Since diamond has a similar response to damage by X-rays and gamma-rays as human tissue, its application as a dosimeter for radiation exposure is also possible. The technical challenge has been to
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deposit diamond of the highest electrical quality so that the charge carriers generated by ionizing particles can be collected in sufficient quantity. The collection distance—the relevant figure of merit—has improved dramatically, increasing nearly 100-fold over the past 10 years. It exceeds natural type IIa diamond today by more than eight times.[15] Despite these achievements, the question whether diamond of detectorgrade quality can be grown cost effectively remains to be answered. In addition to cost, the dose-dependent sensitivity at low dose is a further obstacle to commercial use of CVD-diamond radiation detectors because they require undesirable engineering measures to compensate for the observed nonlinearity. However, signal processing can diminish the problem.
2.10.9. Conclusion Notwithstanding the rapid progress made in the past decade in the science and technology of diamond film CVD, commercialization of this amazing material is still in its infancy. Yet, some devices are already in the marketplace. These include cutting tools, SAW filters, speakers, sliding parts, heat sinks for highpower density electronic devices, windows for IR radiation, UV radiation detectors, and thermistors. All these applications are based on polycrystalline films. Future applications, which are perhaps several years ahead, will be based on single crystal films, but they require further improvements in diamond quality and purity, epitaxial growth, and doping. This is particularly true for some more complicated applications in electronics, where other materials (such as GaN) may become commercial sooner. Specific surface properties of diamond have already made possible some applications related to those dependent on its bulk properties. Such are the SAW filters and electrodes for electrochemical applications. Until recently, the high price of diamond coatings when compared with other existing materials represented an essential factor preventing broad CVD diamond applications. Yet, with the advent of high-power diamond deposition reactors and improvement of technology, the price of CVD diamond has been reduced in 10 years from 5000 to 5$ per carat, and in the year 2000 it has dropped for the first time to a value below 1$/carat (1 carat ¼ 0.2 g). This and the constant efforts of researchers may lead in the next few years to many more applications of diamond films, especially in electronics. Perhaps the most likely applications, which would firmly establish diamond as a 21st century material par excellence, are in the area of specialized flat-panel displays and high-temperature electronics. Those CVD diamond methods that can relatively easily be scaled up to high area (MW plasma and HF) have low deposition rates. The methods allowing high deposition rates (oxygen– acetylene flame and arc jets) cannot be easily adapted to high-area deposition.
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In the low-temperature diamond deposition, which would allow considerable expansion of the range of its applications, a number of problems have been solved. The most important issues that remain to be solved in order to make the low-temperature (2008C) CVD diamond capable of winning the market competition are higher deposition rate and improved diamond quality. 2.11.
SUMMARY AND CONCLUSIONS
Exceptional properties of diamond, a number of which exceed properties of all other known materials, make its application for various purposes very attractive. It is not surprising therefore that the wish to synthesize diamond has existed since diamond has been known to man, about which the written documents touch the very beginnings of history. Such synthesis has been accomplished, however, only in the middle of 20th century, under conditions that are in agreement with the phase diagram of carbon—at high pressure and high temperature. By this rather complicated and expensive technology, which is today a major method to obtain diamond (a much greater quantity is produced by this process than by digging natural diamond), small diamond crystals are manufactured, more or less similar to the diamond found in nature. Synthesis of diamond at low pressure, the dream of many researchers in the past, is “forbidden” by the phase diagram of carbon. According to the phase diagram, diamond is stable only at very high pressure. Nevertheless, researchers have persistently endeavored to synthesize diamond at low pressure. In favor of such a synthesis is a small thermodynamic instability of diamond, which is evident from a slight difference in free energies of formation of diamond and graphite. In favor of the low-pressure synthesis is also a high kinetic barrier which prevents diamond, once formed, to revert to graphite. It is well known that diamond remains unchanged apparently forever under the ambient conditions and that high temperature is needed to transform it to graphite. Thus, diamond is “metastable”. After a long time and a great number of unsuccessful attempts, which resulted in a widely spread skepticism that diamond can be synthesized at low pressure, such a synthesis was in fact accomplished. First synthesis was made by Spitsyn with co-workers and then, independently, by Eversole. Both the Russians and the Americans used unstable carbon precursors which decomposed at high temperature and a natural diamond crystal as a substrate whose role was to “persuade” carbon atoms to order themselves in the way in which the substrate was ordered. Unfortunately, these first successful experiments, achieved at nearly the same time as the first successful high-pressure synthesis, were in fact not quite successful. The deposition rate was extremely low, and graphite was deposited together with diamond. The key to a really successful low-pressure diamond synthesis was the presence of an active gas phase, and especially of exceptionally reactive atomic hydrogen. This clue was discovered about 10 years later again by Spitsyn and
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co-workers. When, in the beginning of 1980s, Japanese researchers entered the game it was they who translated these results into a direct practical application. The whole world was then “infected” by CVD of diamond. It can be said that the “epidemic” continues. Meanwhile a number of different diamond deposition methods has been developed. Nevertheless, nearly all these methods (the exception is the recently found method of nanocrystalline diamond synthesis) have a lot in common. Perhaps this is not surprising, taking into account a very narrow range of conditions under which diamond can be deposited. For example, in the starting gas mixture composed of a carbon compound (usually methane) and hydrogen, a large excess of hydrogen must be present and, if oxygen is also present, the ratio of carbon to oxygen must be close to unity. On the other hand, the chemical form in which the starting gases are present is not important, because under the conditions suitable for diamond CVD the same reactive species composed of a small number of atoms are always formed. A majority of these methods operate at a pressure lower than atmospheric. By means of, say, an MW generator, plasma is formed in which an active gas mixture is generated from the starting gases, comprising predominantly radicals, certain molecular species, and atomic hydrogen. Instead of electrical activation, other means of activation can be used: thermal, in which the active mixture is obtained by virtue of high temperature, or chemical, as in the oxygen –acetylene flame. The substrate, made of a material that is stable under such conditions, and which satisfies other important requirements, must be heated to a temperature high enough (usually between 800 and 11008C) to ensure deposition of diamond. The rate of deposition in these methods substantially depends on the plasma temperature, which increases with the applied power density. Thus, the (isothermal) thermal plasma jet methods, especially DC arc plasma, allow deposition rates as high as 1 mm/h, which is more than two orders of magnitude higher than in the methods using nonisothermal plasma. What is the reason for such a large interest in diamond synthesis by CVD methods even though high-pressure synthesis is well established and provides by far the largest quantity of commercial diamond? The main reason is that CVD methods allow for the first time to obtain diamond coatings on various nondiamond materials, as well as self-standing diamond plates (by separating subsequently the diamond layer from the substrate). This substantially expands the horizon of diamond application. Another reason for the popularity of CVD methods is that they, unlike the high-pressure method, are comparatively simple, and in some cases extremely simple and accessible to a large number of researchers and potential manufacturers. The acetylene – oxygen flame CVD, making use of a commercial welding burner in the open atmosphere, is certainly the simplest and can be located even in a shed. Many researchers were engaged during the last 20 years in the development of diamond CVD primarily pursuing its applications. Diamond deposition technology has thus been ahead of the science. The science could not explain satisfactorily how it is possible, in spite of a thermodynamic “ban”, to obtain at low
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pressure a metastable diamond. In the first Russian method, this was accomplished starting from graphite heated to 20008C in a hydrogen atmosphere at a pressure considerably below atmospheric. Close to graphite was a diamond substrate at a much lower temperature. The active gas phase, formed around graphite owing to the high temperature, also existed in the vicinity of the diamond substrate because it was positioned very close to graphite. Thus, under these conditions (stable) graphite is consumed and (metastable) diamond is deposited! The explanation accepted today is that, because the deposition process takes place on the surface, and not in the bulk, thermodynamic conditions existing on the surface should be considered. In all probability, the conditions existing on the substrate surface are such that diamond is thermodynamically stable, not graphite. The decisive role is played by atomic hydrogen, which, by a sequence of gas-phase reactions, creates radicals necessary for diamond growth (such as CH3 and others), while stabilizing the deposited diamond at the surface and removing nondiamond phases formed, playing the role of also a reactive solvent that promotes conversion of graphitic nuclei to diamond. Naturally, in CVD diamond technology there also exist serious problems. One of the major issues is how to obtain a diamond single crystal by (hetero)epitaxy, because without it the use of diamond as a semiconductor would be difficult. Defect formation is also hardly avoidable. There are attempts to circumvent this problem by depositing highly oriented polycrystalline coatings, whereby a mosaic product is obtained. A very important issue is diamond doping, because diamond then becomes a high-temperature large-gap semiconductor. It is also not easy to obtain a homogeneous film of a polycrystalline diamond on a larger area. Finally, the high temperature of the substrate poses a large problem. That is, owing to a very low thermal expansion of diamond compared with the majority of materials that otherwise would be suitable as substrates, the choice of substrate is very limited. The point is that by cooling from the high deposition temperature large stresses arise, and the diamond film cracks or detaches from the substrate. The required high temperature of the substrate also prevents diamond deposition on low-temperature materials, such as polymers, thus further restricting the range of possible applications. Attempts to deposit diamond at low temperature have led to significant advances. Thus, deposition temperature can be lowered to 2008C. The problem remains, nevertheless, because deposition rate at low temperatures becomes extremely low, and the quality of the deposited diamond is unsatisfactory. A substantial factor on which commercial application of CVD diamond may hinge is its cost. A considerable advance has been achieved in this respect. The CVD diamond price of thousands dollars per carat (1 carat ¼ 0.2 g) a decade ago came down to about 1$/carat in the year 2000 for the first time. This was made possible by the introduction of higher-power reactors, as well as by research progress that allowed homogeneous deposition on large surfaces. Where is the application of CVD diamond today? This question can be answered by pointing out that it has already been a success and every day it
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fortifies its place among cutting tool technologies. Equally well placed are the wear-resistant coatings. Unlike the “active” ones, “passive” applications in electronics—coolers for high-power-density devices—are also entering the market, SAW filters are commercialized in the communication industry, windows for IR and detectors for UV radiation alike. However, all the existing applications are based on polycrystalline diamond. In the preparation and application of singlecrystal diamond, from which much more is expected, for the time being (technological) obstacles still exist. Summarizing, the application of CVD diamond is advancing, but not as fast as it was expected. Despite the rapid progress made lately in the science and technology of diamond film CVD, the commercialization of this amazing material is still in its infancy. Continued intensive research all over the world guarantees that we are approaching the time when CVD diamond will be firmly established as a 21st century material.
ACKNOWLEDGEMENT The author is indebted to the Ministry for Science, Technology, and Development of Serbia and to the Institute of Nuclear Sciences “Vincˇa” for their support in initiating and carrying out research on CVD diamond.
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13. Spitsyn, B.V.; Smol’yaninov, A.V. USSR Author’s Certificate No. 987912, filed April 21, 1971. 14. Angus, J.C.; Argoitia, A.; Gat, R.; Li, Z.; Sunkara, M.; Wang, L.; Wang, Y. Philos. Trans. R. Soc. Lond. A 1993, 342, 195– 208. 15. Butler, J.E.; Windischmann, H.J. MRS Bull. 1998, 23, 22 – 27. 16. Ashfold, M.N.R.; May, P.W.; Petherbridge, J.R.; Rosser, K.N.; Smith, J.A.; Mankelevich, Y.A.; Suetin, N.V. Phys. Chem. Chem. Phys. 2001, 3, 3471– 3485. 17. Chase, M.W., Jr. NIST-JANAF Thermochemical Tables 4th Edition. J. Phys. Chem. Ref. Data 1998, Monograph No 9 I-1951. 18. Goodwin, D.G.; Butler, J.E. In Handbook of Industrial Diamonds and Diamond Films; Prelas, M.A., Popovici, G., Bigelow, L.K., Eds.; Marcel Dekker: New York, 1998; 527– 581. 19. Vilotijevic´, M. Deposition of Diamond from Methane using Ar/H2 DC Arc Plasma (in Serbian). Faculty of Physical Chemistry, Belgrade University, 1998; MS Thesis. 20. Bachmann, P.K.; Leers, D.; Lydtin, H.; Wiechert, D.U. Diamond Rel. Mater. 1991, 1, 1 – 12. 21. Bachmann, P.K. In Handbook of Industrial Diamonds and Diamond Films; Prelas, M.A., Popovici, G., Bigelow, L.K., Eds.; Marcel Dekker: New York, 1998; 821 – 850. 22. Matsui, Y.; Yuuki, A.; Sahara, M.; Hirose, Y. Jpn. J. Appl. Phys. 1989, 28, 1718– 1724. 23. Petherbridge, J.R.; May, P.W.; Pearce, S.R.J.; Rosser, K.N.; Ashfold, M.N.R. J. Appl. Phys. 2001, 89, 1484– 1492. 24. Gruen, D.M. Annu. Rev. Mater. Sci. 1999, 29, 211 – 259. 25. Gruen, D.M. MRS Bull. 2001, 26, 771– 776. 26. Liu, H.; Dandy, D.S. Diamond Rel. Mater. 1995, 4, 1173– 1188. 27. Derjaguin, B.V.; Fedoseev, D.V. Sci. Am. 1975, 233, 102 – 109. 28. Matsumoto, S.; Matsui, Y. J. Mater. Sci. 1983, 18, 1785– 1793. 29. Ashfold, M.N.R.; May, P.W.; Rego, C.A.; Everitt, N.M. Chem. Soc. Rev. 1994, 23, 21 – 30. 30. Knuyt, G.; Vandierendonck, K.; Quaeyhaegens, C.; Vanstappen, M.; Stals, L.M. Thin Solid Films 1997, 300, 189–196. 31. Singh, J. J. Mater. Sci. 1994, 29, 2761– 2766. 32. Badzian, A.R.; Badzian, T. Surf. Coat. Technol. 1988, 36, 283 – 293. 33. Marinkovic´, S.; Zec, S. J. Serb. Chem. Soc. 1993, 58, 679 – 689. 34. Meilunas, R.; Wong, M.S.; Sheng, K.C.; Chang, R.P.H.; Van Duyne, R.P. Appl. Phys. Lett. 1989, 54, 2204 –2210. 35. Lux, B.; Haubner, R. In Diamond and Diamond Like Films and Coatings; Clausing, R.E., Horton, L.L., Angus, J.C., Koidl, P., Eds.; Plenum Press: New York, 1991; 579– 609. 36. Lambrecht, W.R.L.; Lee, C.H.; Segall, B.; Angus, J.C.; Li, Z.; Sunkara, M. Nature 1993, 364, 607– 610. 37. Yugo, S.; Semoto, K.; Kimura, T. Diamond Rel. Mater. 1996, 5, 25 – 28. 38. Arnault, J.C.; Demuynck, L.; Speisser, C.; Le Normand, F. Eur. Phys. J. 1999, B11, 327 – 343. 39. Marinkovic´, S.; Stankovic´, S.; Rakocevic, Z. Thin Solid Films 1999, 354, 118 – 128.
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40. Stankovic, S. A study of oxygen-acetylene flame CVD of diamond on tungsten carbide substrates (in Serbian). Faculty of Physical Chemistry, University of Belgrade, 1998; MS Thesis. 41. Lee, S.-T.; Lin, Z.; Jiang, X. Mater. Sci. Eng. 1999, 25, 123 – 154. 42. Klein-Douwel, R.J.H.; Spaanjaars, J.J.L.; ter Meulen, J.J. J. Appl. Phys. 1995, 78, 2086– 2096. 43. Butler, J.E.; Woodin, R.L. Philos. Trans. R. Soc. Lond. A 1993, 342, 209 – 224. 44. Matsui, Y.; Yabe, H.; Hirose, Y. Jpn. J. Appl. Phys. 1990, 29, 1552– 1560. 45. Harris, S.J. Appl. Phys. Lett. 1990, 56, 2298– 2300. 46. Goodwin, D.G. Appl. Phys. Lett. 1991, 59, 277 – 279. 47. Klein-Douwel, R.J.H.; ter Meulen, J.J. J. Appl. Phys. 1998, 83, 4734– 4745. 48. Wang, X.H.; Zhu, W.; von Windheim, J.; Glass, J.T. J. Cryst. Growth 1993, 129, 45 – 55. 49. May, P.W. Philos. Trans. R. Soc. Lond. A 2000, 358, 473 – 495. 50. Goodwin, D.G. J. Appl. Phys. 1993, 74, 6888– 6894. 51. Goodwin, D.G. J. Appl. Phys. 1993, 74, 6895– 6906. 52. Hatta, A.; Hiraki, A. In Handbook of Industrial Diamonds and Diamond Films; Prelas, M.A., Popovici, G., Bigelow, L.K., Eds.; Marcel Dekker: New York, 1998; 887 – 899. 53. Michler, J.; Stiegler, J.; von Kaenel, Y.; Moeckli, P.; Dorsch, W.; Stenkamp, D.; Blank, E. J. Cryst. Growth 1997, 172, 404 – 415. 54. Rudder, R.A.; Hudson, G.C.; Hendry, R.C.; Thomas, R.E.; Posthill, J.B.; Markunas, R.J. Surf. Coat. Technol. 1992, 54/55, 397 –402. 55. Yara, T.; Makita, H.; Hatta, A.; Ito, T.; Hiraki, A. Jpn. J. Appl. Phys. 1995, 34, L312– L315. 56. Kondoh, E.; Ohta, T.; Mitomo, T.; Ohtsura, K. J. Appl. Phys. 1993, 73, 3041– 3046. 57. Chu, C.J.; Hauge, R.H.; Margrave, J.L.; D’Evelyn, M.P. Appl. Phys. Lett. 1992, 61, 1393– 1395. 58. Maeda, H.; Ohtsubo, K.; Irie, M.; Ohya, N.; Kusakabe, K.; Morooka, S. J. Mater. Res. 1995, 10, 3115– 3123. 59. Suzuki, T.; Argoitia, A. Phys. Status Solidi A 1996, 154, 239 – 254. 60. Koizumi, S.; Inuzuka, T. Jpn. J. Appl. Phys. 1993, 32, 3920– 3927. 61. Jiang, X.; Klages, C.-P. Diamond Rel. Mater. 1993, 2, 1112– 1113. 62. Jiang, X.; Klages, C.-P.; Zachai, R.; Hartweg, M.; Fuesser, H.-J. Appl. Phys. Lett. 1993, 62, 3438– 3440. 63. Jiang, X.; Jia, C.L. Appl. Phys. Lett. 1995, 67, 1197– 1199. 64. Li, Z.; Wang, L.; Suzuki, T.; Argoitia, A.; Pirouz, P.; Angus, J.C. J. Appl. Phys. 1993, 73, 711– 715. 65. Argoitia, A.; Angus, J.C.; Wang, L., Ning, X.I.; Pirouz, P. J. Appl. Phys. 1993, 73, 4305– 4312. 66. Stoner, B.R.; Glass, J.T. Appl. Phys. Lett. 1992, 60, 698 – 700. 67. Yang, P.C.; Zhu, W.; Glass, J.T. J. Mater. Res. 1993, 8, 1773– 1776. 68. Saito, T.; Tsuruga, S.; Ohya, N.; Kusakabe, K.; Morooka, S.; Maeda, H.; Sawabe, A.; Suzuki, K. Diamond Rel. Mater. 1998, 7, 1381– 1384. 69. Schreck, M.; Roll, H.; Stritzker, B. Appl. Phys. Lett. 1999, 74, 650 – 652. 70. Wild, C.; Herres, N.; Koidl, P. J. Appl. Phys. 1990, 68, 973 – 978.
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71. Wild, C.; Kohl, R.; Herres, N.; Mueller-Sebert, W.; Koidl, P. Diamond Rel. Mater. 1994, 3, 373– 381. 72. Marinkovic´, S.; Zec, S. Diamond Rel. Mater. 1995, 4, 186 – 190. 73. Davidson, J.; Kang, W.; Holmes, K.; Wisitora-At, A.; Taylor, P.; Fulugurta, V.; Venkatasubramanian, R.; Wells, F. Diamond Rel. Mater. 2001, 10, 1736– 1742. 74. Jiang, W.; Ahn, J.; Chuen, C.Y.; Loy, L.Y. Rev. Sci. Instrum. 1999, 70, 1333– 1340. 75. Marinkovic´, S. In Chemistry and Physics of Carbon; Thrower, P.A., Ed.; Marcel Dekker: New York, 1984; Vol. 19, 1 – 64. 76. Brunet, F.; Germi, P.; Pernet, M.; Deneuville, A.; Gheeraert, E.; Lauiger, F.; Burdin, M.; Rolland, G. Diamond Rel. Mater. 1998, 7, 869 – 873. 77. Lagrange, J.-P.; Deneuville, A.; Gheeraert, E. Carbon 1999, 37, 807 – 810. 78. Gheeraert, E.; Koizumi, S.; Teraji, T.; Kanda, H.; Nesladek, M. Phys. Status Solidi A 1999, 174, 39– 51. 79. Polyakov, V.I.; Rukovishnikov, A.I.; Rossukanyi, N.M.; Ralchenko, V.G. Diamond Rel. Mater. 2001, 10, 593– 600. 80. Swain, G.M.; Anderson, A.B.; Angus, J.C. MRS Bull. 1998, 23, 56 – 60. 81. Marinkovic´, S.; Suzˇnjevic´, C.; Tukovic´, A.; Dezˇarov, I.; Cerovic´, D. Carbon 1973, 11, 217– 220. 82. Koizumi, S.; Teraji, T.; Kanda, H. Diamond Rel. Mater. 2000, 9, 935 – 940. 83. Kalish, R. Diamond Rel. Mater. 2001, 10, 1749– 1755. 84. Ristein, J.; Maier, F.; Riedel, M.; Cul, J.B.; Ley, L. Phys. Status Solidi A 2000, 181, 65 – 76. 85. Eccles, A.J.; Steele, T.A.; Afzal, A.; Rego, C.A.; Ahmed, W.; May, P.W.; Leeds, S.M. Thin Solid Films 1999, 343/344, 627 – 631. 86. Haubner, R.; Bohr, S.; Lux, B. Diamond Rel. Mater. 1999, 8, 171 – 178. 87. Argoitia, A.; Kovach, C.S.; Angus, J.C. In Handbook of Industrial Diamonds and Diamond Films; Prelas, M.A., Popovici, G., Bigelow, L.K., Eds.; Marcel Dekker: New York, 1998; 797– 819. 88. Cappelli, M.A. In Handbook of Industrial Diamonds and Diamond Films; Prelas, M.A., Popovici, G., Bigelow, L.K., Eds.; Marcel Dekker: New York, 1998; 865 – 886. 89. Kurihara, K.; Sasaki, K.; Kawarada, M.; Koshino, N. Appl. Phys. Lett. 1988, 52, 437 – 438. 90. Ohtake, N.; Yoshikawa, M. J. Electrochem. Soc. 1990, 137, 717 – 722. 91. Yu, B.N.; Girshick, S.L. J. Appl. Phys. 1994, 75, 3114– 3123. 92. Snail, K.A.; Marks, C.M.; Lu, Z.P.; Heberlein, J.; Pfender, E. Mater. Lett. 1991, 12, 301 – 305. 93. Girshick, S.L. In Handbook of Industrial Diamonds and Diamond Films; Prelas, M.A., Popovici, G., Bigelow, L.K., Eds.; Marcel Dekker: New York, 1998; 851 – 864. 94. Matsumoto, S. J. Mater. Sci. Lett. 1985, 4, 600 – 602. 95. Meyer, D.E.; Ianno, N.J.; Woollam, J.A.; Schwartzlander, A.B.; Nelson, A.J. J. Mater. Res. 1988, 3, 1397– 1403. 96. Matsumoto, S.; Hino, M.; Kobayashi, T. Appl. Phys. Lett. 1987, 51, 737 – 739. 97. Kohzaki, M.; Uchida, K.; Higuchi, K.; Noda, S. Jpn. J. Appl. Phys. 1993, 32, L438– 440. 98. Hirose, Y.; Amanuma, S.; Komaki, K. J. Appl. Phys. 1990, 68, 6401– 6405.
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3 Energetics of Physical Adsorption of Gases and Vapors on Carbons Eduardo J. Bottani Instituto de Investigaciones Fisicoquı´micas Teo´ricas y Aplicadas (INIFTA) La Plata, Argentina
Juan M.D. Tasco´n Instituto Nacional del Carbo´n, CSIC Oviedo, Spain
3.1.
INTRODUCTION
The gas adsorption process has been investigated since the time it was Þrst identiÞed by Scheele in 1773. Nowadays it is recognized that there is a large number of phenomena in which adsorption is involved. At the risk of being simplistic, there are two main interests that attract the attention of researchers to study adsorption. First we must mention the idea of characterizing the surface of solids through the behavior of the adsorbed phase. This goal represents the applied side of the issue. The second interest is a basic one since adsorption phenomena allow the investigation of interaction forces in a variety of systems and conditions, and to investigate new states of matter. It is well known that the behavior of adsorbed molecules depends on the properties of both the solid surface and the adsorbate itself. Among the most relevant characteristics of the solid are its chemical nature, its topography, and the presence of impurities. For the adsorbate, it is important to consider molecular
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size, shape, and electronic conÞguration. It has also been shown that temperature or, more precisely, the thermal energy of the adsorbate and the lateral interactions are factors from which a balance is established that deÞnes the thermodynamic properties of the adsorbed phase. Since the interactions determine the behavior of the adsorbed phase, the problem reduces itself to one single concept: energy. This is why we focus our attention on the energetic aspects of adsorption. Quite recently, Sircar[1] made a survey of the publications in adsorption science and technology. He begins with a brief summary of the reasons justifying the large bibliography existent on the subject. A series of tables condense the number of publications grouped by categories and languages covering the period between 1970 and 2000. Patents are analyzed in an independent section of the review. Sircar included a list of books and book chapters dealing with adsorption. There is a second review written by Daþ browski[2] that constitutes a general overview of almost all aspects of adsorption. This extensive review covers published material up to 1999. Historical aspects, the current state of physical adsorption, practical applications (industrial and environmental), and future trends in the Þeld are covered. Besides the classical text by Gregg and Sing,[3] we would like to mention the book recently published by Rouquerol et al.[4] that deals with adsorption by powders and porous solids. This book covers thermodynamic aspects of adsorption at the gas Ð solid and liquid Ðsolid interfaces, as well as an assessment of the surface area and porosity, areas in which the authors are very well known for their expertise. An entire chapter is devoted to adsorption on activated carbons. Our review is restricted to adsorption on carbonaceous materials. The importance of adsorption for different types of carbons and, conversely, the contribution of each class of carbons to the adsorption literature is extremely unequal, depending on the material. This reßects the wide variability in properties of solid carbons,[5,6] which makes their surface properties important in so very different Þelds. Thus, graphite, due to its relatively simple structure, has been used very often as a model material to simulate the adsorption of different molecules on its surface or to carry out adsorption measurements on a well-controlled surface. Likewise, carbon blacks, particularly those thermally treated, have been frequently used as reference nonporous adsorbents. The surface behavior of activated carbons deserves much interest because of their technological relevance. Among these technologies, we should mention pollution control, food processing, heterogeneous catalysis, and gas storage.[7] Therefore, it is not surprising to realize that a great majority of adsorption studies on carbons has been carried out using these materials as adsorbents. A corollary to this is the vast abundance of studies addressing the characterization of microporosity in these solids. On the opposite side of the spectrum of surface area development, carbon Þbers[8,9] are virtually a nonporous material and exhibit a surface area only slightly higher than their geometrical area. Since the surface characterization
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of carbon Þbers is important in Þelds such as the interfacial ÞberÐmatrix behavior in composites, researchers in this area have been obliged to adapt their methodologies, or to develop new ones, to study gas adsorption on these low surface area solids. This explains, for instance, the signiÞcant application of inverse gas chromatography (IGC) to this class of carbons (see Section 3.3.2.2). Even gas adsorption on novel carbon materials, such as fullerenes and carbon nanotubes, deserves interest in entirely different ways. In the area of fullerenes, the rather scarce number of studies has been focused mainly on the basic characterization of the surface energetics. In contrast, carbon nanotubes deserve great interest as possible materials for gas storage, to the point that there is at present a serious controversy about their adsorption capacity for hydrogen. This justiÞes why carbon nanotubes have been separated from the rest of carbon materials in every section of this review. This was done in an effort to put together the information relative to this fashionable form of carbon in the interest of readers speciÞcally concerned with it. In the words of the authors of a recent review on carbon materials as adsorbents in aqueous solutions,[10] ÒThe level of fundamental understanding of liquidphase adsorption is well below that of gas- or vapor-phase adsorptionÓ. This is an advantage not to be overlooked when purporting, as is the case of this review, to present a comprehensive overview of the energetics of gas and vapor adsorption on carbons. However, the task is made difÞcult by several factors. One of them is the aforementioned variability of carbon materials. Another is the large amount of published literature, produced over a long period and generated under very different environments and thus potentially very different conditions. This has prompted us to focus our analysis on more recent work, assuming that older studies may be outdated by the new ones, thanks to advances in instrumentation (for chießy experimental works) and to the logical progress of science (for works of theoretical nature). To this end, among the various books covering the Þeld of activated carbons we would like to draw the attention of readers to the one by Bansal et al.,[11] which reviews in commendable depth the literature on activated carbon prior to 1988, devoting speciÞc chapters to the characterization and the surface modiÞcation of activated carbons. Various techniques addressed in our review (e.g., immersion calorimetry) constitute entire sections of that book. Therefore, and taking into account that activated carbon is, by far, the principal contributor to the adsorption literature among all types of carbon materials, we have taken the date of publication of that book as an approximate starting point for the literature reviewed here, particularly for works of chießy experimental nature. In some cases, older references are given when they presented fundamental aspects or included data employed by other papers cited in this review. More recently, Derbyshire et al.[12] have put carbons in the perspective of their uses in environmental remediation. Gas-phase applications, which have a close relationship with the subject of this review, were focused on the removal of volatile organic compounds from air, ßue gas cleanup and other applications where elimination of undesired compounds is effected. Their review brießy
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addressed other important topics, such as adsorption from solution for water treatment, the use of carbons as supports in environmental catalysis and even medical applications of carbon. In the same volume of this series, Radovic et al.[10] have published a critical review of the behavior of activated carbons as adsorbents in aqueous solutions, with a focus on the relationship between the chemical nature of the activated carbon adsorbent and its adsorptive capacity for single solutes. The authors placed special emphasis in unraveling the role of surface chemistry in the adsorptive behavior of these materials, an issue that has been often neglected. Prior to this, Leo«n y Leo«n and Radovic[13] reviewed the interfacial chemistry and electrochemistry of carbon surfaces in an attempt to contribute to unify concepts providing a comprehensive review of carbon surface properties. Although the results analyzed in our review are very often discussed in connection with the porosity characteristics of the adsorbent (something unavoidable in the Þeld of adsorption on carbons), the characterization of porous texture based on adsorption results does not constitute the leitmotiv of this review. Therefore, for an assessment of the role of adsorption studies in characterizing the porous texture of carbons and other solids, the reader is referred to authoritative reviews by Rodrõ«guez-Reinoso and Linares-Solano[14] and Kaneko.[15] The book Porosity in Carbons, edited by Patrick,[16] contains relevant chapters related with, for example, gas physisorption,[17] and immersion calorimetry.[18] This book also contains a chapter[19] on carbon as catalyst support, another topic directly connected with gas adsorption studies but not speciÞcally dealt with in our review. Other thorough reviews on carbon dealing with heterogeneous catalysis have been published by Radovic and Rodrõ«guez-Reinoso,[20] Rodrõ«guezReinoso,[21] and Radovic and Sudhakar.[22] Very recently, Bandosz et al.[23] have reviewed the work done on the structure of carbonaceous materials in connection with their porosity. That review has examined in commendable depth the subject of structural models for pores, and its scope is wide enough to cover novel and even hypothetical carbon forms; only macroporous carbons were excluded explicitly. According to the authors, in order to interpret experimental results on carbons themselves and particularly as adsorbents, it is necessary to have structural models of both the pore morphology (geometrical shape, pore width, and pore volume) and topology (arrangement of the pores relative to each other, connectivity, and the macroscopic environment seen by adsorbates). The authors also indicated that the principal stumbling block is the development of more realistic models, although improvements in experimental techniques are also needed. In the same volume, Mowla et al.[24] have reviewed the (more speciÞc) topic of water adsorption on activated carbons. They concluded that micropore volume Þlling is the most accepted mechanism for water adsorption on these solids, but there is less agreement as to the state of the adsorbed molecules; they considered a rigid cluster structure as the most probable form. As for the terminology for solid carbons we have tried to follow, whenever possible, IUPAC recommendations.[25] Likewise, IUPAC terminology for physisorption[26] and porous solids and adsorption[27] has been adopted as well.
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This review is organized in a way that reßects, in a certain manner, our way of thinking. We begin by a brief description of the classical thermodynamic treatment of physical adsorption. Then we present the statistical thermodynamic approach to the problem under the form of a brief summary of the main equations. These aspects were selected as the starting point because they provide the basic knowledge necessary to design, understand, and interpret the experiments and the data derived from them. We complete this section with a brief description of the basic principles and applications that constitute the bridge between theory and experiments, at least with respect to the determination of the heat of adsorption. Then we review the techniques, more precisely the results obtained from them, which lead to a direct determination of the heat of adsorption and other thermodynamic quantities. It is necessary to point out that not all the experimental work is included in this section and the next one, which concerns the indirect methods. When we understand that a paper is providing direct experimental support to a theoretical interpretation, it is cited in another section. We would like to emphasize the synergy between theory and experiment, not always fully exploited. The experimental techniques included in Sections 3.3.1 and 3.3.2 are now considered as standard tools in physisorption research. We are conscious that other techniques exist but they do not lead to a direct determination of the heat of adsorption or they need a complicated and not yet fully understood theory. The next section (3.3.3) is devoted to studies of more theoretical nature. We begin with the virial treatment of adsorption, developed to a great extent by Steele and Halsey,[28] which proved to be a useful and practical approach to physisorption for both basic and applied research. In this section, we summarize the theoretical aspects as well as some of the experimental work connected with them. The research concerning, directly or indirectly, the heterogeneity of solid surfaces is by far the one that gathers the largest number of publications. Several papers that are not commented in this section are included in the subsequent ones. We have tried to summarize the most commonly employed methods to determine the adsorption energy distribution function, and have included papers where the integral adsorption equation is related to the pore size distribution. We left for the end the work done using computer simulation. We include together the Monte Carlo and molecular dynamics methods. In this section, several experimental papers are included because they are directly linked to the computer simulation results and this strengthens the relationship that must be preserved between simulations and experiments. Many of the systems reviewed concern the adsorption on homogeneous surfaces while others deal with adsorption on heterogeneous surfaces. The issues mentioned in previous sections have been most often studied empirically, theoretically, or by simulation for homogeneous solid surfaces such as the graphite basal plane or other perfect
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single crystal surfaces. However, there is similar work concerned with heterogeneous surfaces, which is mainly oriented toward measuring or assessing the nature of such heterogeneity. In all the sections, certain logical presentation order was maintained. We grouped the results obtained on homogeneous surfaces, followed by heterogeneous solids, and then the results concerning adsorption on novel carbon materials (mostly fullerenes and nanotubes). Each group begins with adsorption of simple gases and is followed by other adsorbates of increasing complexity. Then, papers dealing with adsorption of gas mixtures are included. Finally, we present a series of general conclusions that we could extract from the review and that, in our opinion, are most signiÞcant. 3.2.
THERMODYNAMIC ASPECTS OF GAS PHYSISORPTION
In this section, we shall brießy review the basic concepts of thermodynamics and statistical mechanics that are relevant to physical adsorption. After a very brief outline of classical thermodynamics (Section 3.2.1), we present a statistical mechanics approach, which is often used to compare model predictions with experimental thermodynamic quantities (Section 3.2.2). This will be followed by an analysis of the relationship between the various heats of adsorption and the experimental data (Section 3.2.3). The use of physical adsorption in refrigerator design is closely related to thermodynamics (see, e.g., Wu et al.[29 Ð 31]); nevertheless we will not deal with this subject. 3.2.1. Classical Thermodynamics Several formalisms have been developed leading to what can be called practical thermodynamics. Most of these treatments are quite old but nevertheless still valid (see, e.g., Refs.[32 Ð 35]). Among them can be mentioned the analog of solution thermodynamics where the adsorbent and the adsorbate are considered as components in a two-phase equilibrium.[36] The adsorbent with the adsorbate constitutes the condensed phase with variable volume and composition in equilibrium with the gas phase. Another way to study the system is to use the surface excess approach in which the properties of the adsorbed phase are determined in terms of the properties of the real two-phase multicomponent system and those of the same system without an interface (see, e.g., To«th[37]). This method could be considered an extension of solution thermodynamics.[38] Its main shortcoming is that speciÞcation of the reference system is not always easy. The most preferred approach to adsorption thermodynamics considers the adsorbed phase as a distinct phase located on the surface of the solid, which is considered to be inert. Here, the concept of solid inertness is two-fold: it indicates that no chemical reactions between the solid and the adsorbate are allowed, and that the structure of the solid is rigid. Thus, in this formalism the properties of the adsorbent and the gas phase are not explicitly included in the calculation. It is
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very well known that in certain adsorption systems some alterations are induced in the solid structure owing to the presence of the adsorbate (see, e.g., Refs.[39 Ð 42]). In these cases, the properties calculated from experimental data are very difÞcult to interpret because the structure of the solid is changing with the amount adsorbed. A reasonable estimation on how the isosteric adsorption heat changes when the solid structure is altered has been given by Yakovlev et al.[43] According to the law of conservation of energy, the total energy U is a constant with the condition that the system is isolated and its volume remains constant. Thus,
dUS,V,n ¼ 0
(3:1)
where V is the volume, n the amount of substance, and S the entropy. Equation (3.1) can be applied to the gas alone if the solid adsorbent is considered inert. Following the treatment developed by Hill[44] in his classical papers on thermodynamics of small systems, it is possible to divide the adsorption space (volume not occupied by the solid) in small elements. These elements are sufÞciently large to enable the characterization of the gas in them, and small enough to allow the thermodynamic properties inside them to be considered as local ones. Obviously, the elements close to the surface of the solid contain adsorbed gas and the ones that are far from the surface contain bulk gas. Since the Þrst law must be valid for each of the space elements, Eq. (3.1) takes the form: (a) (a) dU (a) ¼ T (a) dS(a) þ w(a) pV þ m dn
(3:2)
where the superscript identiÞes the space element and m is the chemical potential. For adsorption of gas mixtures the generalization of Eq. (3.2) is straightforward. Equation (3.2) represents the energy changes due to the reversible transfer of thermal energy between different space elements, the reversible work due to volume changes, and the energy due to the reversible transfer of gas molecules across the boundary of the space element. To derive a more useful form of Eq. (3.2), it can be assumed that the force per unit area normal to the surface of the solid, pzz, can be different from the force per unit area in the direction parallel to the surface, pk. If A(a) is the area of the space element in a plane parallel to the solid surface and z(a) its thickness (z is the coordinate normal to the surface) the pV work can be written as: (a) (a) (a) (a) (a) w(a) p(a) pV ¼ pk z dA zz A dz
The spreading pressure for each space element can be deÞned as: (a) (a) f(a) ¼ p(a) k pzz z
(3:3)
(3:4)
Replacing in Eq. (3.3): (a) (a) w(a) p(a) dV (a) pV ¼ f dA
(3:5)
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(a) where p(a) ; p(a) ¼ z(a) dA(a) þ A(a) dz(a). It is evident that the spreading zz and dV pressure will be zero for an isotropic phase, thus f(a) will be zero for all space elements containing bulk gas. Under these conditions, Eq. (3.1) will hold if the temperature, pressure, and chemical potential are the same in every space element. Moreover, it is possible to drop the superscripts on T, p, and m, and using Eq. (3.5), Eq. (3.2) can be written as:
dU (a) ¼ T dS (a) f(a) dA(a) p dV (a) þ m dn(a)
(3:6)
It must be pointed out that the size and location of the space elements remain unrestricted except that the solid adsorbent should not be included. The constraint of constant area A, which is the area of the adsorbate, needs to be clariÞed. In fact, A is the area of the adsorbate and it is not strictly equal to the area of the solid adsorbent although both are considered equal in practical applications. Any attempt to vary the two areas independently yields unnecessary complications.[38] To derive the expressions relating the experimental quantities like the amount adsorbed at a given temperature and pressure, we can use Eq. (3.6) written for the adsorbed phase. Since U(a) is of Þrst order in the extensive variables [e.g., the ones appearing as differentials on the right-hand side of Eq. (3.6)], integration of Eq. (3.6) is direct, leading to: U (a) ¼ TS (a) f(a) A(a) pV (a) þ m(a) n(a)
(3:7)
Again, the generalization of this equation to a multicomponent system is direct.[38] DeÞning the free energy, G(a), as G(a) ¼ U (a) TS (a) þ pV (a)
(3:8)
from Eqs. (3.7) and (3.8) it is evident that G(a) ¼ fA þ m(a) n(a)
(3:9)
Equation (3.8) can be differentiated and combined with Eq. (3.6) to give: dG(a) ¼ S(a) dT f dA þ V (a) dp þ m(a) n(a)
(3:10)
From Eqs. (3.9) and (3.10) an analog of the Gibbs Ð Duhem relation can be obtained if dG(a) is eliminated among them: n(a) dm(a) ¼ S(a) dT þ A df þ V (a) dp
(3:11)
This equation can be transformed into: dm(a) ¼
S (a) A V (a) dT þ d f þ dp n(a) n(a) n(a)
(3:12)
This expression can also be written in the following form: A (a) (a) dm(a) ¼ S~ dT þ (a) df þ V~ dp n
(3:13)
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217
where the tildes indicate a mean molar quantity. The equilibrium is maintained if the change in chemical potential of the adsorbed species equals the change in chemical potential of this species in the gas phase: dm(a) ¼ dm(g)
(3:14)
For an ideal gas phase the change in chemical potential is given by: (g) (g) dm(g) ¼ S~ dT þ V~ dp
From Eqs. (3.13) and (3.15), n (a) o n (a) o A (g) (g) S~ S~ dT ¼ V~ V~ dp þ (a) df n
(3:15)
(3:16)
where p is the vapor pressure of the adsorbed layer. From Eq. (3.16), it is possible to obtain Clausius Ð Clapeyron-type expressions. Moreover, if the spreading pressure is kept constant,
dp dT
¼ f
(a) (g) S~ S~ (a) (g) V~ V~
(3:17)
or, keeping the temperature constant, h (a) i (a) df (g) n ¼ V~ V~ dp T A
(3:18)
Several enthalpies can be obtained to describe the adsorption equilibrium. The Þrst one is the so-called equilibrium enthalpy, qeq: qeq ¼ U~
(a)
þ pV~
(a)
þ
fA ~ (g) (g) U pV~ (a) n
(3:19)
Rewriting Eq. (3.7) as follows,
fA (a) (a) (a) m(a) ¼ U~ T S~ þ (a) þ pV~ n
(3:20)
and for the ideal gas phase,
m(g) ¼ U~
(g)
(g) (g) T S~ þ pV~
and combining Eqs. (3.19) Ð(3.21), yields: (g) (a) qeq ¼ T S~ S~ Replacing into Eq. (3.17): qeq dp ¼ (g) dT f T V~ V~ (a)
(3:21)
(3:22)
(3:23)
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Since we have considered that the gas phase is ideal, its volume can be replaced by RT (g) V~ ¼ p
(3:24)
Further simpliÞcation of Eq. (3.23) can be achieved if the density of the adsorbed phase is close to the density of the bulk liquid since the volume of the gas phase (g) (a) will be much larger (V~ V~ ). Thus: qeq p dp ¼ (3:25a) dT f RT 2 or qeq d ln p ¼ dT f RT 2
(3:25b)
Equation (3.25) shows that the equilibrium enthalpy can be calculated from experimental data (i.e., if the temperature dependence of the isotherm at constant spreading pressure is known). However, the use of Eq. (3.25) is cumbersome because it requires the previous calculation of the spreading pressure instead of using the raw experimental data (i.e., n(a) vs. p). The spreading pressure can be determined with the Gibbs adsorption isotherm.[38] Furthermore, the molar quantities appearing in Eq. (3.20) are not the natural variables for adsorption systems. Instead of molar quantities it is generally preferred to use partial molar entropy and internal energy; these are deÞned for a one-component system by: (a) @U (a) (3:26) U ¼ @n(a) T,p,A and (a) @S (a) S ¼ @n(a) T,p,A
(3:27)
These quantities measure the changes in these properties when an inÞnitesimal change occurs in the number of adsorbed moles at constant temperature, pressure, and area. To be able to relate these quantities to experimental measurements, the differential of the chemical potential of the adsorbed phase [Eq. (3.20)] is necessary: @m @m @m ðdmÞn ¼ dT þ dp þ dA (3:28) @T T,A,n @p T,A,n @A T,A,n
Physical Adsorption of Gases and Vapors on Carbons
219
The deÞnition of the chemical potential can be used to proceed: (a) @2 G(a) @2 G(a) @2 G(a) dT þ dp þ dA dm n ¼ @T@n(a) @p@n(a) @A@n(a)
(3:29)
Now combining this with Eq. (3.10): (a) (a) @S @V @f dT þ dp dA dm(a) ¼ @n(a) T,p,A @n(a) T,p,A @n(a) T,p,A
(3:30)
which can be written as: (a)
dm
(a) (a) ¼ S dT þ V dp
@f @n(a)
dA
(3:31)
T,p,A
Using this equation together with Eq. (3.15) one obtains: (g) @f (g) (a) (a) S~ þ S dT ¼ V V~ dA dp @n(a) T,p,A
(3:32)
If the area is kept constant, this equation leads to: (g) (a) S~ S dp ¼ (g) dT V~ V (a)
(3:33)
The entropies can be eliminated from this expression with the aid of Eq. (3.8). In fact, @G(a) @U (a) @S(a) @V (a) ¼ (a) T (a) þ p (a) (a) @n @n @n @n
(3:34)
which can be written as: (a) (a) (a) m(a) ¼ U~ T S~ þ pV~
Combining this expression with Eq. (3.21) (a) (g) (a) (g) (a) (g) U~ U~ þ pV~ pV~ ¼ T S~ S~ ¼ qst
(3:35)
(3:36)
This expression gives the deÞnition of the enthalpy known as isosteric enthalpy of adsorption. Equation (3.36) can be simpliÞed to dp qst ¼ (g) (3:37) dT n(a) ,A T V~ V (a)
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Again, as in the case of Eq. (3.23), if the adsorbed phase is assumed liquid-like, Eq. (3.37) reduces to: d ln p qst ¼ dT n,A RT 2
(3:38)
There is at least one other enthalpy related to the experimental data. This enthalpy is obtained in a calorimetric experiment under adiabatic conditions. The experiment consists of the addition of gas, in a reversible manner, to the calorimeter containing the adsorbent. In what follows we assume that the mean (a) molar heat capacity of the adsorbed gas C~ p , the molar heat capacity of the non(g) adsorbed gas C~ p , the number of moles of adsorbed gas n(a), and the number of moles in the gas phase n(g) are known. An equivalent process could be considered to simplify the problem. Instead of adding gas to the system, it is possible to imagine that the adsorbed molecules are transferred from the gas phase to the adsorbed phase by action of a piston that changes the gas phase volume by an amount dV (g). Assuming that the area of the adsorbate is unchanged during the process, it is possible to write dU ¼ p dV (g) p dV (a)
(3:39)
where dU is the total energy change given by dU ¼ Cc dT þ dU (a) þ dU (g)
(3:40)
and Cc is the heat capacity of the calorimeter including the solid adsorbent. Since a temperature change and changes in the adsorbed, dn(a), and gas phase, dn(g), amounts are accompanied by a change in pressure dp, it is possible to write: dU (a) ¼
(g) (g) (g) @U @U @U dT þ dp þ dn(a) @T p,A,n(a) @p T,A,n(a) @n(a) p,A,T
(3:41)
The heat capacity of the adsorbate, Cp(a) , is given by: Cp(a)
(a) (a) @U @V (a) ~ ¼ n Cp ¼ þp @T p,A,n(a) @T p,A,n(a) (a)
(3:42)
Combining Eqs. (3.41) and (3.42) yields: (a)
dU (a) ¼ n(a) C~ p dT þ U
(a)
dn(a) þ
@U (a) @p
dp p p,A,n(a)
@V (a) @T
dT p,A,n(a)
(3:43)
Physical Adsorption of Gases and Vapors on Carbons
An analogous equation can be written for the gas phase: (g) (g) (g) @U @U @U dT þ dp þ dn(g) dU (g) ¼ @T p,n(g) @p T,n(g) @n(g) T,p
221
(3:44)
Assuming ideal behavior of the gas phase does not produce any loss of accuracy, so: (g) (g) dU (g) ¼ n(g) C~ p R dT þ U~ dn(g) (3:45) Since we have imagined the transfer of gas phase molecules to the adsorbed phase by means of a volume change, dn(g) ¼ 2dn(a). Using this relation together with Eqs. (3.39), (3.40), (3.43), and (3.45) results in: (a) n o n o @U (a) (g) (g) (a) dp Cc þ n(a) C~ p þ n(g) (C~ p R) dT þ U U~ dn(a) þ @p T,A,n(a) (a) @V p dT ¼ p dV (g) p dV (a) (3:46) @T p,A,n(a) The main term in this equation is related to the adiabatic enthalpy, qad, through the deÞning equation: [38] n o dT (a) (a) qad ¼ Cc þ n(a) C~ p þ n(g) C~ p (3:47) dn(a) ad Instead of deducing an exact equation, it is convenient to assume that the adsorbed phase is liquid-like and the gas phase is ideal. Under these conditions it is obtained that dp qad ¼ qst þ V (g) (3:48) dn(a) ad This relationship shows that it is possible to calculate the isosteric enthalpy of adsorption from calorimetric experiments. In summary, it has been shown how the adsorption enthalpies are obtained either calorimetrically or from the temperature dependence of the isotherms. Although the deÞnitions given for the different enthalpies are rigorous, it is necessary to show that they exhibit the same properties of the enthalpy of vaporization, which can be shown to be equal to the heat required to vaporize one mole of liquid at constant pressure and using a reversible and isothermal process. Moreover, only the isosteric enthalpy is simply related to the heat required in a reversible and isothermic process. We devote the next paragraphs to show this connection. Suppose that dn moles of adsorbate are transferred to the gas phase at constant temperature and pressure. The Þrst law of thermodynamics gives:
dQ ¼ dU (a) þ dU (g) þ fdA þ pdV (a) þ pdV (g)
(3:49)
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Bottani and Tasco´n
If the area of the solid is kept constant, this expression leads to: (a) (g) (a) dU dU dV (a) (g) (dQ)A ¼ d n þ d n þ p dn(a) dn(a) T,p,A dn(g) dn(a) T,p,A (g) dV þp dn(g) dn(g)
(3:50)
Using the deÞnitions of mean molar and partial molar quantities, Eq. (3.50) becomes: (g) (g) (a) (a) (dQ)A ¼ U þ pV dn(a) þ U~ þ V~ dn(g) (3:51) Since dn(g) ¼ 2 dn(a) ¼ dn, Eq. (3.51) can be written as: (g) dQ (g) (a) (a) ¼ U þ pV þ U~ þ V~ dn T,p,A
(3:52)
According to Eq. (3.36) this quantity is equal to the isosteric enthalpy, qst, which turns out to be equal to the heat per mole evolved in the reversible transfer of an inÞnitesimal amount of adsorbate from the adsorbed phase to the gas phase at constant temperature, pressure, and area. Up to this point the most important equations have been presented. Now, it is possible to analyze the work done in connection with the classical thermodynamic approach. In this sense, the Þrst systematic study of a thermodynamic adsorption quantity was perhaps the work done by de Boer[45] on the determination, interpretation, and signiÞcance of the enthalpy and entropy of adsorption. The papers by de Boer and Kruyer,[46 Ð 51] which were published in succession, analyzed almost all aspects of the experimental determination of the entropy and how to interpret the obtained values in terms of two extreme models, those of mobile and localized adsorption, which today have lost much of their usefulness. To catalog the behavior of the adsorbed Þlm as localized or mobile is a very simplistic solution and it has been demonstrated[44] that in most cases the adsorbed Þlm is neither completely localized nor completely mobile. This approach is also somewhat outdated because numerical simulations provide a better microscopic interpretation of the systemÕs behavior. A slightly different treatment has been recently reported by Fomkin et al.[52] in which they use Eq. (3.38) to calculate the isosteric heat of perßuoropropane adsorbed on a powdered activated carbon. In the same line of research, Agarwal et al.[53] reported the entropy of the adsorbed phase for a series of gases (methane, ethane, ethylene, propane, carbon dioxide, and nitrogen) adsorbed at high pressures on an activated carbon (labeled as G210). By comparing the entropy determined from the experimental data with the corresponding values for localized and mobile phases, they concluded that the adsorbed phase is localized. The classical approach to obtain the isosteric heat of adsorption [Eq. (3.25)] and the entropy of the adsorbed phase [Eq. (3.22)] was
Physical Adsorption of Gases and Vapors on Carbons
223
employed by Ban÷ares-Mun÷oz et al.[54] They studied nitrogen and argon adsorption on a pyrocarbon and employed the values obtained to infer that the surface of their sample was more heterogeneous than the surface of natural and artiÞcial graphites. Bottani et al.[55] also employed the classical approach to obtain the entropy of the adsorbed phase for N2 and CO2 adsorbed on graphitized carbon blacks. The authors discussed several problems affecting the precision of the obtained values using Eq. (3.38) or equivalents, and how they could be employed to characterize the surface of carbonaceous materials. Keller and Hardt[56] developed equations to describe the nonisothermal adsorption of a one-component ßuid. They used the entropy-free thermodynamic formalism [this formalism uses Eq. (3.10) as a starting point] and presented numerical results corresponding to a system constituted by an ideal gas phase and a ÒlangmuirianÓ adsorbent (an activated carbon, Aerosorb, from Degussa). More recently, Sircar et al.[57] have employed the Gibbsian surface excess model to describe multicomponent adsorption of gas mixtures. They also showed that this model could unambiguously deÞne the isosteric adsorption heats for components of a gas mixture. These variables can be experimentally determined using multicomponent differential calorimetry and in turn used to describe nonisothermal behavior of practical adsorbents. Even though they applied this approach to study nitrogen and carbon dioxide adsorption on silicalite, their model is general enough to be employed with other adsorption systems. Mezzasalma[58] employed a condition of maximum irreversible entropy production in the framework of a variational procedure where the isotherm equations are represented by a convergent sequence of ordinary functions. The transition from the ideal to real behavior was interpreted as a broadening process of a Dirac distribution driven by irreversibility. The proposed theory can be employed to describe any hysteresis loop where the expected extreme constraints can be formulated variationally. The Euler Ð Lagrange theorem yields a degenerate solution couple, which can be approximated to a new isotherm class provided that the adsorption and desorption curves are different, which means that this approach can be employed in all cases where hysteresis is present. The obtained equations describe the adsorption in several systems involving polar sorbates (e.g., benzene on steam-activated anthracite charcoal). Figure 3.1 compares predictions with isothermal adsorption data for this system (the experimental results were taken from the literature[59]), and the agreement is quite satisfactory. An equivalent system has been studied recently,[60] and the obtained results are equally good using the Dubinin Ð Radushkevich (DR) and the DubininÐ Stoeckli equations. Milewska-Duda et al.[61] employed the thermodynamic approach described earlier to derive an isotherm, similar to the BET equation, which can describe adsorption in microporous structures. The general thermodynamic approach, which has been discussed elsewhere,[62,63] is based on Eq. (3.9). They called the new equation LBET, where L stands for Langmuir, and applied it to analyze the isotherms of water and methanol on hard coal and of carbon dioxide on activated
224
Bottani and Tasco´n
Figure 3.1 Phenomenological description (solid line) of adsorption data for benzene on a steam-activated anthracite charcoal (data points); t, displacement from real to ideal adsorptions; c, gas concentration in the bulk phase. (Reproduced from Mezzasalma.[58] Copyright 1999 American Chemical Society.)
carbon. Their main conclusion is that the BET formalism is able to describe the adsorption process in microporous adsorbents provided that restrictions for pore capacity are taken into account. In the case of submicroporous and microporous solids, of low average pore size, an exponential distribution of pore capacity was assumed. They showed that the LBET equation gives a good representation of systems with moderate or high adsorptivity (Q/RT , 20.5) up to relative pressures close to 0.8. The adsorptivity is measured, in their approach, by Q, which is the main component of the molar adsorption energy. Nevertheless, they found that the total pore capacity estimation is rather poor. Asnin et al.[64] demonstrated that the classical thermodynamic approach does not contradict the molecular statistical theory and that it yields equations that are more general. Based on Eq. (3.16) and similar expressions for the internal energy, they analyzed the particular case of the Freundlich adsorption isotherm and concluded that its use in the region of very low coverage is incorrect. Jagiello et al.[65] presented a classical thermodynamic analysis of the process of gas liberation from a coal bed. They derived expressions to calculate the isosteric heat of adsorption and the desorption work. They could estimate the total work for a gas contained in coal at a given temperature and pressure, as well as the decrease in coal temperature during desorption. With data obtained from Kr adsorption on high-modulus carbon Þbers, Drzal et al.[66] determined the isosteric adsorption heat and the entropy of the adsorbed phase with the aim of characterizing the surface of this material. The authors demonstrated that such Þbers, which undergo a high-temperature graphitization treatment, possess a very homogeneous surface very similar to that of the basal plane of graphite. The same parameters were used to characterize the same material after exposure to an undeÞned (proprietary) surface treatment that added highly energetic sites at the surface making it more heterogeneous. Aranovich and Donohue[67] derived a new equation, based on the Ono ÐKondo model[68] for adsorption in slit-like
Physical Adsorption of Gases and Vapors on Carbons
225
pores, to describe the adsorption of vapors on microporous adsorbents. Their equation gives the correct limit of HenryÕs law at low concentrations and is more general than the DR equation because, according to the authors, it is valid for supercritical gas adsorption. This is possible since the equation does not explicitly depend on the vapor pressure of the adsorbate. Sircar[69,70] has presented a thermodynamic treatment of gas mixture adsorption on heterogeneous adsorbents with particular emphasis on the estimation of the isosteric adsorption heat. On an energetically heterogeneous adsorbent it could vary substantially depending on the fractional loading of the adsorbate, which, in turn, depends on the equilibrium gas-phase pressure, temperature, and composition. The nature and degree of adsorbent heterogeneity also play a very signiÞcant role. As an illustration, Fig. 3.2 shows the binary isosteric adsorption heats (solid lines) of ethylene and methane on Nuxit charcoal as a function of the gas-phase composition. The isosteric adsorption heat of ethylene from the mixture decreases with its increasing mole fraction in the gas phase, while the opposite occurs with methane. The values for both components vary signiÞcantly over the gas-phase composition range, reßecting the energetic heterogeneity of the adsorbent. The pure-gas isosteric adsorption heats for each component at the same coverage as for the mixture, at any given composition, are shown in Fig. 3.2 as dashed lines. The author highlighted the striking difference between continuous and dashed lines as indicative of the fact that the common assumption of equal isosteric adsorption heats for components from mixtures and pure gases at equal coverages can be extremely misleading.
Figure 3.2 Binary isosteric heats of ethylene and methane on Nuxit charcoal. (Reproduced from Sircar.[69] Copyright 1991 American Chemical Society.)
226
Bottani and Tasco´n
An alternative approach for thermodynamic treatment of gas mixture adsorption, developed by Nieszporek,[71] considers the adsorbed solution as non-ideal. The author presented theoretical expressions to calculate the isosteric adsorption heats of gas mixtures. This model only needs single-gas adsorption isotherms and the corresponding heats of adsorption to predict the isotherms and heats for the mixtures. The model was tested with data of adsorption on zeolites, not carbons. Myers[72] developed thermodynamic equations for adsorption of multicomponent gas mixtures in microporous adsorbents based on the principles of solution thermodynamics. He argued that the conventional spreading pressure and surface variables, which describe 2D Þlms, must be abandoned for adsorption in micropores, in which spreading pressure [Eq. (3.4)] cannot be measured experimentally or calculated from intermolecular forces. Instead, the adsorption process is divided into two steps: (a) isothermal compression of the gas and (b) isothermal immersion of clean adsorbent in the compressed gas. The author also described several practical applications, such as the characterization of adsorbents, gas storage at high pressure, mixture adsorption, enthalpy balances, molecular simulation, adsorption calorimetry, and shape selectivity in catalysis. Li et al.[73] recently reviewed the progress in predicting the equilibria of multicomponent mixture adsorption. They discussed the problems encountered in applying theories developed for subcritical mixtures to supercritical gases. In a recent paper, Chiang et al.[74] reported values of the free energy, enthalpy, and entropy of adsorption of volatile organic compounds (exempliÞed by benzene and methylethylketone) onto seven samples of activated carbon. The activated carbon samples were obtained by treatment of the original one with NaOH and ozone, combined in different amounts. The starting point for their development was Eq. (3.17) for the entropy of adsorption and Eq. (3.38) for the isosteric heat of adsorption. They also calculated the characteristic adsorption energy with the Dubinin ÐAstakhov (DA) equation and obtained values ranging from 17.1 to 36.9 kJ/mol for benzene and 14.5 to 32.3 kJ/mol for methylethylketone. Linders et al.[75] developed a new method, called Multitrack, to simultaneously determine the adsorption and diffusion parameters of gases in porous materials in a packed bed. They determined the heats of adsorption from the adsorption equilibrium constant, which are related through a Clausius Ð Clapeyron-type equation. They found that these values agree quite well with those obtained from uptake experiments using the integrated form of Eq. (3.38). They analyzed experimental data obtained for n-butane adsorbed on two commercial activated carbons (Kureha and Sorbonorit B3) and hexaßuoropropylene adsorbed on activated carbon. Recently, Park et al.[76] reported the isosteric heat [Eq. (3.38)] of adsorption of toluene, dichloromethane, and trichloroethylene onto activated carbon Þbers (ACFs); Shim et al.[77] reported the heat of adsorption of carbon tetrachloride and chloroform on Sorbonorit B4 activated carbon; and Choi et al.[78] reported the heat of adsorption of methane, ethane, ethylene, nitrogen, and hydrogen onto a Calgon activated carbon. These papers are mentioned here because the authors included the adsorption isotherms
Physical Adsorption of Gases and Vapors on Carbons
227
covering a wide temperature range and the calculated isosteric adsorption heats and all these data could be very useful to test theoretical models. To«th[79] demonstrated that the surface area of a solid can be calculated from any type I monolayer isotherm and from the monolayer domain of type II isotherms. The proposed method is based on the To«th equation,[80] which was shown to be thermodynamically consistent. Nitta et al.[81] determined the adsorption isotherms of acetone, diethyl-ether, methanol, and water on activated carbon. They calculated the isosteric adsorption heats using the Clausius Ð Clapeyron equation. In all cases they obtained proÞles that correspond to heterogeneous surfaces. Pribylov et al.[82] studied the thermodynamic parameters of excess and absolute adsorption of methane and SF6 on porous carbons with different pore size distributions. Their thermodynamic analysis started with an alternate form of Eqs. (3.46) and (3.47). For carbons with developed mesoporosity, they found that the isosteres of excess adsorption of SF6 were not linear due to changes in the ratio of the energies associated with gas Ð gas and gas Ð solid interactions. However, for a carbon molecular sieve the isosteres were linear in a wide temperature range. Isosteric heat of water adsorption on activated carbons obtained from food wastes has been reported by Nakanishi et al.; [83] however, the authors did not perform a deep analysis of the obtained data. 3.2.2. Statistical Mechanics The statistical mechanics formalism is probably the most efÞcient way to connect molecular models with experimental data. Thus, we shall present here a brief summary of the most important equations useful for numerical simulations that will be discussed later. Among all the statistical ensembles that can be employed, the canonical and grand canonical are the most popular. We also restrict our treatment to classical statistical thermodynamics; thus no quantum effects are taken into account. The probability that molecules 1, 2, 3, . . . , N are in volume elements dr1, dr2, . . . , drN located at r1, r2, . . . , rN is given by the Boltzmann expression: 1 U(r1 , r2 , . . . , rN ) P(a) ¼ exp (3:53) N kT ZN(a) where ZN(a) is the normalization factor given by ð ð U(r1 , r2 , . . . , rN ) (a) ZN ¼ exp dr1 dr1 drN kT V
(3:54)
Here V is the volume available to the gas molecules and U(r1, r2, . . . , rN) is the potential energy of the N molecules; thus U can be taken as the sum of two terms, gas Ð solid (Ugs) and gas Ð gas (Ugg) interaction energies: U(r1 , r2 , . . . , rN ) ¼
N X i¼1
Ugs (ri ) þ
X 1i,jN
Ugg (rij )
(3:55)
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It must be pointed out that this expression implicitly contains terms that depend on the orientation of the molecule with respect to the surface and the orientation of a given molecule with respect to its neighbors when the molecules are nonspherical. Equation (3.55) assumes that the potentials are additive and pairwise; since it does not include three-body or higher terms, this must be considered as an effective potential.[38] A system that is constrained to have a constant number of molecules, volume, and temperature constitutes a canonical ensemble. The thermodynamic properties of the system can be calculated from the corresponding partition function, Q(N, V, T).[84] For the adsorbed phase the partition function can be written as Q(N, V, T) ¼
ZN(a) N!L3N
(3:56)
where L is a factor that includes the kinetic properties of the molecule; for a monoatomic adsorbate it is given by h L ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2pmkT
(3:57)
If the adsorbate is polyatomic, the expression for L is more complex since it must include the inertia moments of the molecule, for a linear molecule, as well as the internal vibrational degrees of freedom. Equation (3.56) shows that the partition function can be written as the product of a conÞgurational factor and a kinetic or nonconÞgurational factor, L. This greatly simpliÞes the application of this approach to the theory of physical adsorption.[38] The main assumption implicitly contained in Eq. (3.56) is that the structural properties of the molecules are independent of the intermolecular interactions in all important conÞgurations of the system. Even though there is evidence that this is not correct, it is possible to derive the appropriate expressions to calculate the extent of the changes in those properties when the molecule is adsorbed. The thermodynamic properties of the system can be calculated from the following expressions: A ¼ kT ln Q @ ln Q U ¼ k @(1=T) N,V (a) ,A @ ln Q p ¼ kT @V (a) N,T,A @ ln Q f ¼ kT @A N,T,V (a)
(3:58) (3:59) (3:60) (3:61)
where A is the Helmholtz free energy, U the total energy, p the pressure, and f the spreading pressure. This set of equations constitutes the relationship between the
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229
theory and the experiments. It is interesting to note that the statistical mechanical formalism gives the isosteric enthalpy of adsorption, qst, as a conÞgurational property: this quantity is thus easy to calculate since it depends on the position of the molecules relative to each other and to the surface. The partition function for the gas phase is given by (g)
Q
¼
(V )N
(g)
N (g) !L3N
(3:62)
(g)
where V is the volume of the gas in its standard state, thus equal to NkT. Using Eqs. (3.56) and (3.59) gives: " # @ ln ZN(a) @ ln L3 (a) (3:63) kN (a) U ¼ k @(1=T) (a) (a) @(1=T) V ,A,N
Equations (3.56) and (3.62), for the gas phase, give: U (g) ¼ kN (g)
@ ln L3 @(1=T)
From Eqs. (3.63) and (3.64): " # (a) (a) 2 @U @ ln Z (a) N U ¼ (a) ¼ k @N @N @(1=T)
(3:64)
þk V (a) ,A,N (a)
@ ln L3 @(1=T)
(3:65)
and U (g) @ ln L3 (g) U~ ¼ (g) ¼ k N @(1=T)
(3:66)
Since the isosteric heat is given by qst ¼ U
(a)
þ U~
(g)
þ kT
replacing Eqs. (3.65) and (3.66) into (3.67) yields: " # @2 ln ZN(a) qst ¼ k þ kT @N @(1=T) (a) (a)
(3:67)
(3:68)
V ,A,N
In the canonical ensemble approach, the adsorbed phase is treated as a separate phase with known volume and containing a Þxed number of molecules at constant temperature. This approach is somewhat unrealistic even though the results obtained can be successfully correlated with experimental data.[38] If we consider that the gas Ð solid interactions induce a smooth gradient in the density of the gas as the surface is approached, another formalism is necessary. The solution is obtained by adopting the grand canonical ensemble in which the Þxed variables are the volume, temperature, and chemical potential.
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230
The unknown quantities are, for example, the number of molecules, energy, and pressure. The chemical potential of the adsorbed phase, once the equilibrium condition is achieved, is equal to the chemical potential of the gas phase, which is determined from the density at a point far from the surface. The amount adsorbed, N(a), can be deÞned as the difference between the total number of molecules in the system, N, and N , the number of molecules in a hypothetical system of equal volume but with no gas Ðsolid interactions. The grand partition function for the system with gas Ðsolid interactions is given by mN ¼ QN (V, T) exp kT N0 X
(3:69)
where QN is the canonical partition function and m is the chemical potential. If the gas phase is considered ideal, it is possible to write: exp
m kT
¼
L3 p kT
(3:70)
This result, together with Eqs. (3.56) and (3.69), leads to ¼
X Z (a) p N X Z (a) aN N N ¼ kT N! N! N0 N0
(3:71)
where a is the activity of the ideal gas. The thermodynamic properties of the system can then be obtained from the following set of equations: @ ln @ ln a T,V,A @ ln U ¼ k @(1=T) m,V,A
N ¼ kNl ¼
fA þ pV ¼ kT ln
(3:72) (3:73) (3:74)
To continue we write the corresponding equations for the hypothetical system we mentioned at the beginning of this section. The set of resulting equations is: @ ln N ¼ @ ln a T,V @ ln L3 U ¼ kN @(1=T)
pV ¼ kT ln
(3:75) (3:76) (3:77)
Physical Adsorption of Gases and Vapors on Carbons
Forming the differences to Þnd the adsorbed phase properties yields @ ln(= ) (a) () N ¼NN ¼ @ ln a T,V,A @ ln @ ln L3 (a) (a) U ¼ k þN k @(1=T) a,V,A @(1=T) fA ¼ kT ln
231
(3:78) (3:79) (3:80)
These expressions are particularly useful at high temperatures and low pressures where the adsorption is rather weak or diluted (small amount of gas is adsorbed even at high pressures). Introducing the necessary approximations, the very well known virial expansion is obtained.[85] As mentioned, the statistical mechanics approach is employed to connect molecular models with experimental data. It is also employed to give a theoretical basis to empirical models or to test other theoretical models. For example, an isotherm equation was derived for adsorption of gases and vapors on microporous and mesoporous solids from statistical mechanics principles by Chen and Yang.[86] The empirical DA and DR equations were then shown to be approximated forms of such isotherm equation. Another example is the isosteric heat of adsorption of simple ßuids onto ßat surfaces derived from a 2D equation of state. [86] As Table 3.1 shows, good agreement existed between calculated values (DHcal) and experimental results (DHexp) taken from the literature[87] for a wide set of adsorbateÐadsorbent systems. The fact that this comparison was satisfactory for a variety of systems was taken as an indication that molecules conÞned within micropores may be treated as 2D ßuids. Garbacz et al. [88] also derived an expression for the isosteric heat of a partially mobile monolayer of a single gas on a heterogeneous adsorbent surface. They optimized the model parameters to describe several sets of experimental data, especially the ones containing graphitized carbon black as an adsorbent. Floess and VanLishout[89] calculated the adsorption energy for different surfaces and pore conÞgurations summing the LennardÐJones potential for the gasÐsolid interaction of a molecule with a graphite Þnite-size basal plane surface. Their calculations showed that restricted diffusion occurs only for a small range of pore sizes between ca. 0.64 and 0.58 nm. In larger pores, the adsorbate is mobile, whereas pores ,0.58 nm are assumed to be largely inaccessible. Figure 3.3 illustrates the variation of the adsorption energy with pore width or spacing (i.e., the distance between the surface planes) for a slit-shaped pore. Adsorption energies are equal for two pore widths, one on each side of the width for which the adsorption energy is at a maximum (0.68 nm in Fig. 3.3). Patrykiejew et al.[90 Ð 92] discussed several theoretical problems of monolayer adsorption assuming that the adsorbed phase is neither completely mobile nor completely localized. They derived two adsorption equations and compared their model with experimental data for water and methanol adsorption
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232
Table 3.1 Comparison of Adsorption Heats, Experimental (DHexp) and Calculated from HenryÕs Constant (DHcal) Adsorbate H2S N2 O2 CH4 C2H2 C2H4
C2H6 C3H6
C3H8
n-C4H10 iso-C4H10
Adsorbent
DHcal (kJ/mol)
H-mordenite Activated carbon Zeolite Zeolite Activated carbon CMS Activated carbon Activated carbon Silica gel CMS Zeolite Activated carbon Activated carbon CMS Silica gel Activated carbon Silica gel H-mordenite Activated carbon CMS
39.1 22 19.9 16.1 24.4 23.0 29.3 31.5 25.3 35.8 36.4 32.7 39.9 39.6 28.9 34.9 25.7 35.1 38.6 41.3
DHexp (kJ/mol)
T (K)
37 Ð 45 16 Ð 18 8 Ð 19 12 Ð 15 18 Ð 23 25 Ð 27 26 Ð 35 23 Ð 33 25 Ð 32 37 Ð 39 33 27 Ð 32 37 Ð 39 37 Ð 58 23 Ð 30 30 Ð 37 19 Ð 23 40 Ð 63 33 Ð 50 66 Ð 82
368 273 273 273 422 303 394 422 313 373 423 422 323 323 313 333 313 303 477 373
Source: Reproduced from Chen and Yang.[86] Copyright 1994 American Chemical Society.
on an unidentiÞed carbon. In another paper of the series,[93] the authors applied their model to the adsorption of oxygen on graphite[94] to predict the temperature dependence of the adsorption isotherm. Murata and Kaneko[95] proposed a new equation of the absolute adsorption isotherm[96] for a supercritical gas to describe the adsorption of methane on activated carbons. The environmental aspects of supercritical gases conÞned in nanospaces have been reviewed by Kaneko.[97] Their model assumes that adsorption in micropores is slightly enhanced compared with that on a ßat surface. They supported this assumption based on comparison plots of experimental data obtained on activated carbons and ßat surfaces (e.g., nonporous carbon black). Several aspects of the adsorption of self-associating molecules in microporous structures have been developed by Talu and Meunier.[98] Their approach is similar to the chemical interpretation of nonideality of vapor and liquid phases. The theory leads to type V isotherm behavior and can explain the transition between types I and V. The data at one temperature are represented with three parameters: HenryÕs law constant, saturation capacity, and a reaction constant for cluster formation in the micropores. To describe a set of isotherms obtained over a temperature interval, the theory can be used with Þve temperature-independent
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233
Figure 3.3 Variation of adsorption energy (calculated by summing the Lennard-Jones potential for the gas Ð solid interaction of a molecule with a graphite Þnite-size basal plane surface) as a function of the pore width for a slit-shaped pore. (Reproduced from Floess and VanLishout,[89] with permission from Elsevier.)
parameters to determine the entire phase behavior, including the heat of adsorption. They tested their theory using water adsorption data from the literature measured on four very different types of activated carbons.[99 Ð 102] Besides a good agreement with experiments, they found that the dimerization enthalpy of water in the micropores is lower than that in the vapor phase. Rudzin«ski and Panczyk[103] have recently reviewed the classical theories of adsorption and desorption kinetics and concluded that models based on the absolute rate theory were challenged by new theories linking these rates with the chemical potentials of bulk and adsorbed molecules. Among the latter theories, the so-called statistical rate theory deserved the most advanced theoretical development. This model is based on both quantum mechanics and statistical thermodynamics; particularly it uses as a starting point both the Langmuir isotherm and the integral adsorption equations [see Eq. (3.141)]. The authors compared the theoretical predictions of the absolute rate theory with the statistical rate theory for a real adsorption system (carbon dioxide on scandium oxide[104]). They concluded that the parameters obtained with the statistical rate theory reproduced very well the behavior of both kinetic and equilibrium aspects of isothermal adsorption measurements and they also had a fully physical meaning. On the other hand, the absolute rate theory can Þt the kinetic adsorption measurements at constant temperature (kinetic adsorption isotherms) using many sets of parameters, but some of the determined parameters always lacked physical meaning. Pan et al.[105] used the nonlocal density functional theory (DFT)[106] and the three process Langmuir model (TPLM)[107] to predict the adsorption heats of
234
Bottani and Tasco´n
propane and butane on carbon and compared these results with experimental data determined from isotherms measured on a BAX (Westvaco) activated carbon at 297 Ð333 K. As an illustration, Fig. 3.4 shows the reasonable agreement between both sets of adsorption heats for propane over most of the loading (coverage) range, except at very low loadings. In contrast with this, adsorption heats for butane agreed well only at low loadings (Fig. 3.5). Figures 3.4 and 3.5 also show that the experimental and TPLM simulated isotherms for propane agree
Figure 3.4 (a) Isosteric adsorption heats of propane on BAX activated carbon at 313 K predicted by the three process Langmuir and the density functional theory and (b) the corresponding adsorption isotherms. (Reproduced from Pan et al.[105] Copyright 1998 American Chemical Society.)
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235
Figure 3.5 (a) Isosteric adsorption heats of n-butane on BAX activated carbon at 313 K predicted by the three process Langmuir and the density functional theory and (b) the corresponding adsorption isotherms. (Reproduced from Pan et al.[105] Copyright 1998 American Chemical Society.)
in the low-pressure range, but begin to deviate above 30 kPa (Fig. 3.4), while the opposite behavior was observed for butane (Fig. 3.5). Both models agreed in showing that the adsorption heat for butane was ca. 10 kJ/mol higher than that of propane at the same loading. The reasonable agreement found prompted the authors to propose the use of the DFT method as it requires only one experimental isotherm, in contrast with the numerous isotherms required by the classical technique (Clausius Ð Clapeyron equation, see Section 3.3.2.1). Following the same approach, Pan et al.[108] also predicted the adsorption heats of three binary gas mixtures (CO222C2H4, CH422C2H6, and CH422C3H8) on homogeneous (BPL-6) and heterogeneous (Westvaco BAX) carbons at
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350 K (here, homo/heterogeneity refers to the pore sizes). The isosteric heats showed complex behavior for the nonideal systems (CH422C2H6 and CH422C3H8 gas mixtures). Adsorbent heterogeneity played an important role in determining the behavior of the isosteric heats compared with the pure states. The authors attributed these differences to effects caused by the presence of the other (opposing) component of the mixture and to differences in the intermolecular forces between the adsorbate molecules. Myers[109] proposed an equation of state for adsorption of mixtures of gases in porous materials. Even though the examples shown in this paper concerned adsorption on zeolites, the results can be employed to explain adsorption on porous carbonaceous materials. The author introduced desorption quantities (enthalpy, entropy, and free energy) that have the advantage of being linearly correlated with the desorption properties of the pure components of the mixture. Bhatia[110] studied the transport of adsorbates in microporous random networks in the presence of an arbitrary nonlinear local isotherm. The transport model was developed by means of a correlated random walk theory, assuming pore mouth equilibrium at an intersection in the network and a local chemical potential gradient driving force. The author tested this model with experimental data of CO2 adsorption on a Carbolac carbon black.[111] He concluded that the experimental data are best predicted when adsorbate mobility, based on chemical potential gradient, is taken to have an activation energy equal to the isosteric heat of adsorption at low coverage, obtained from the HenryÕs law region. He also concluded that the choice of the local isotherm affects the predictions for the coverage dependence of the diffusivity, even among isotherms that Þt the equilibrium data equally well. Shekhovtsova and Fomkin[112] developed a discrete site model to describe the adsorption of methane on microporous adsorbents. The model was tested with adsorption on zeolite NaX and an activated carbon. A sharp decrease in the heats of adsorption was observed at high adsorbed amounts even in the supercritical temperature range. A multilayer adsorption theory was developed by Wang and Hwang[113] to describe the behavior of several adsorbates on activated carbons. The adsorbates employed included several alkanes, hydrogen sulÞde, and carbon monoxide. The isosteric heats of adsorption for all gases were determined using the Clausius ÐClapeyron equation. Cerofolini and Rudzin«ski[114] have reviewed the theoretical principles of single gas and mixture adsorption on heterogeneous surfaces. Their review is chronologically arranged from the early beginnings to the latest approaches. In the same book, Tovbin[115] reported the application of lattice-gas models to explain mixed-gas adsorption equilibria on heterogeneous surfaces; he also discussed[116] the kinetic aspects of adsorption Ð desorption on ßat heterogeneous surfaces. This book[117] contains other papers on different aspects of adsorption that deserve the attention of the reader interested in surface diffusion processes. It is accepted that the adsorption of binary and ternary vapor mixtures by activated carbon beds can be described successfully by combining the Dubinin
Physical Adsorption of Gases and Vapors on Carbons
237
equation with the theory of Myers and Prausnitz.[118] A major advantage of this approach lies in the simplicity of the parameters required to describe adsorption over a wide range of pressures and temperatures. Moreover, the combination of this method with computer simulation models developed by Ladugie et al.[119] extends the theory to the case of dynamic adsorption by activated carbons. Wintgens et al.[120] applied this approach to components that are immiscible in the liquid state. They concluded that it is also possible to predict the adsorption of such vapor mixtures if the variation of the characteristic energy of one component is taken into account. Riccardo and coworkers[121,122] reported the results of a statistical thermodynamic approach for linear adsorbates on heterogeneous surfaces based on Eqs. (3.71) and (3.75) Ð (3.77). In the Þrst paper, they dealt with low-dimensional systems (e.g., carbon nanotubes, pores of molecular dimensions, corners in steps found on ßat surfaces). In the second paper, they presented an improved solution for multilayer adsorption; they compared their results with the standard BET formalism and found that monolayer capacities could be up to 1.5 times larger than the one from the BET model. They argued that their model is simple and easy to apply in practice and leads to new values of surface area and adsorption heats. These advantages are a consequence of properly considering the conÞgurational entropy of the adsorbed phase. Rzysko et al.[123] presented a theoretical description of adsorption in a templated porous material. Their approach is based on the solution of the replica Ornstein Ð Zernike (ROZ) equations with PercusÐ Yevick and hypernetted chain closures. Their solution method uses expansions of size-dependent correlation functions into Fourier series. They tested it for model systems composed of hard spheres, speciÞcally a hard sphere ßuid in a polydisperse hard sphere disordered quench matrix, and the ROZ equations were extended to account for the effects of polydispersity of matrix and template particles. 3.2.3. Thermodynamic Quantities and Experimental Results The connection between experimental results and thermodynamic quantities presents different problems depending on the experimental design employed to obtain the data.[124 Ð 126] In what follows we analyze the relationship between the various heats of adsorption and the experimental data obtained under different conditions. To obtain enthalpy variations directly from experiments it is necessary to perform those experiments at constant pressure (or spreading pressure) but in general experiments are carried out in other conditions. This is the reason why Le«toquart et al.[127] recommend expressing the experimental data in terms of internal energy. In this way, it is straightforward to write the necessary expressions to calculate all the thermodynamic quantities. Another problem arises from the fact that most thermodynamic equations have been deduced for a closed system, which is often not the experimental situation.[127] As usual, we consider the solid adsorbent inert, in the sense that its internal energy is
Bottani and Tasco´n
238
constant at constant temperature and its total surface area is kept constant. For the gas phase, we assume ideal behavior. In any experimental setup that constitutes an open system, what is measured is the heat exchange with the surrounding media, which includes exchange of matter and eventually some work. In this case, one is tempted to introduce thermodynamic potentials (i.e., to introduce entropy). Nevertheless, we feel it is better to Þnd a way to relate the experimental data with the internal energy without introducing any additional hypotheses. The evaluation of internal energy change allows the direct use of the energy conservation law in two ways. We assume that our system contains c components distributed among w phases and during the adsorption process the system receives some work (W), heat (Q), and a certain amount of moles of the ith component (DNi) from the exterior, each one having a known molar internal energy, 1ie. Under these conditions the change in internal energy is given by DE ¼ W þ Q þ
i¼c X
1ie DNi
(3:81)
i¼1
Alternatively, if the ith component has a molar internal energy 1ij when it is in the jth phase (where Nij represents the number of moles of the ith component present in the jth phase), the internal energy change can be written as DE ¼
j¼w X i¼c X
D(Nij 1ij )
(3:82)
j¼1 i¼1
Using Eqs. (3.81) and (3.82) it is easy to obtain the expression that gives the experimentally determined thermal effect, Q, in terms of the internal energies. The result is: Q¼
j¼w X i¼c X j¼1 i¼1
D(Nij 1ij )
i¼c X
1ie DNi W
(3:83)
i¼1
Consider an inÞnitesimal transformation that takes the system from one equilibrium state to another one that is close to it. To calculate the amount of heat involved in the transformation it is necessary to derive Eq. (3.83), thus it is easily obtained that dQ ¼ d(Ng 1g þ Na 1a ) 1g (dNa þ dNg ) dW
(3:84)
where we have used the fact that dN ¼ dNa þ dNg. If we also use the fact that the gas admitted in the adsorption cell is at the same temperature (thus its internal energy does not change), it is possible to write Eq. (3.84) as follows: dQ ¼ (1a 1g )dNa þ Na d1a dW
(3:85)
Physical Adsorption of Gases and Vapors on Carbons
239
Now it is necessary to calculate the work involved, dW. Given that the gas is ideal, we can write: dW ¼ PdV
(3:86)
This equation is easily transformed into: PdV ¼ RT dN ¼ RT(dNa þ dNg )
(3:87)
Considering that the total volume of the system is constant, Vg, the change in the number of gas moles can be expressed in terms of the pressure. Thus Eq. (3.87) leads to: dW ¼ RT dNa þ Vg dP
(3:88)
Replacing in Eq. (3.85): dQ ¼ (1a 1g ) dNa þ Na d1a RT dNa Vg dP
(3:89)
This equation can be written in an equivalent form to show that it corresponds to a differential heat of adsorption. @Q @1a @P ¼ 1a 1g þ Na (3:90) RT Vg @Na T,A @Na T,A @Na This is in fact an isothermal heat of adsorption. The last term, which depends on the experimental setup, is obtained from the calibration of the equipment and the slope of the isotherm. We must consider now the fact that Eq. (3.90) is valid if the gas is reversibly admitted into the adsorption cell, a condition that is seldom obtained. We develop now the expressions corresponding to a Þnite addition of gas. The heat experimentally measured corresponds to a change in the number of adsorbed moles, DNa ¼ N2 ÐN1. Equation (3.90) must be integrated giving ð Na2 Q¼ dQ Na1
ð Na2 (1a dNa þ Na d1a 1g dNa RT dNa Vg dP)
¼
(3:91)
Na1
The result is: Q ¼ (1a2 1g )Na2 (1a1 1g )Na1 RT(Na2 Na1 ) Vg (P2 P1 ) (3:92) The Þrst and second terms of this equation are the integral heats of adsorption, Qint. Thus int Q ¼ Qint 2 Q1 RTDNa Vg (P2 P1 )
(3:93a)
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240
We have shown that the experimentally measured heat exchange is directly connected to the integral heat of adsorption at constant temperature. The experimental data needed to perform the calculation are Q, the number of moles adsorbed at two pressures, those pressures and the volume of the adsorption cell (the so-called Òdead spaceÓ). In a completely analogous way, it is possible to obtain an expression corresponding to the adiabatic heat of adsorption. The Þnal result is: int Qad ¼ Qint 2 Q1 RT(Na2 Na1 ) Vg (P2 P1 ) " # ð T2 @P P dT Vg @T Na,A T T1
(3:93b)
Now we can discuss a series of papers using classical thermodynamics, statistical thermodynamics, direct determination of adsorption heat, or a combination of these methods. The theory behind each paper has been sketched in the previous sections as well as in the current one. Della Gatta[128] has considered the energy changes occurring during adsorption in gas Ðsolid and solution Ðsolid systems in connection with the measurement of the adsorption enthalpies. He focused on the description of heat-ßow microcalorimeters and the calibration techniques. Piper et al. [129] have published a good description of an adiabatic calorimeter. Other types of calorimeters are the conduction calorimeter (the temperature of the sample is made equal to the temperature of the surroundings by simple conduction), compensation calorimeters (sample temperature is made equal to that of the surroundings by means of a power compensation), and ÔisoperibolÕ calorimeter (this is a conventional temperature rise calorimeter, also known as Thomsen or Berthelot calorimeter).[4] The determination of differential and integral heats and entropies of N2 adsorption on Grafoil illustrated its use. Groszek[130,131] studied the adsorption of simple gases (CO2, CH4, SO2, O2, He, and N2) on microporous carbons using ßow adsorption microcalorimetry. Shen and Bu¬low[132] demonstrated that the isosteric adsorption technique [Eqs. (3.38) or (3.68)] is a useful and effective tool to obtain highly accurate thermodynamic data for microporous adsorption systems like the heat of adsorption given by Eq. (3.92). They studied adsorption of CO2 and N2 ÐO2 mixtures on a superactivated, almost entirely microporous, carbon (M-30 from Osaka Gas) and three faujasite-type zeolites. They also quantiÞed the energetic heterogeneity of the solids due to speciÞc interactions between the adsorbate and the solid. As an illustration, Fig. 3.6 shows the dependence of the standard Gibbs free energy on CO2 concentration for the carbon (M-30) and two zeolites (FAU-I and FAU-II). This parameter, which accounts for the natural tendency of a system to spontaneous transformation, changes from negative values to zero as the CO2 concentration increases and exceeds saturation capacities, which was taken as proof of thermodynamic consistency of the experimental data.
Physical Adsorption of Gases and Vapors on Carbons
241
Figure 3.6 Standard Gibbs free adsorption energy of carbon dioxide on carbon M-30 and two zeolites, referred to 194.65 K. (Reproduced from Shen and Bu¬low,[132] with permission from Elsevier.)
Salem et al.[133] determined several thermodynamic functions from the excess and absolute adsorption isotherms for N2, Ar, and methane on an activated carbon (AS, used for respiratory protection) and a 13X zeolite. They concluded that for a consistent thermodynamic interpretation of high-pressure excess adsorption data it is necessary to consider the speciÞc adsorption quantities (these quantities are the ones that can be measured directly). However, they strongly depend on the initial values of adsorption (i.e., the HenryÕs law region). If this region is not included in the experimental data, the integral molar and speciÞc adsorption quantities are estimated with a systematic error of unknown magnitude. Another conclusion they reached is that a molecular interpretation of high-pressure data can be achieved only by using the absolute isosteric and differential molar adsorption quantities. In the case of microporous solids, this is relatively easy to do; however, it is a very difÞcult task in the case of macroporous and nonporous solids. Rychlicki and Terzyk[134] determined the heat of adsorption and the integral molar entropy of methane adsorbed on microporous carbons with different oxidation degrees. They found that oxidation of the micropore surface affected methane adsorption because of an endothermic effect, probably due to speciÞc adsorbateÐ adsorbent interactions. A similar effect was found in the case of CCl4 adsorption.[135,136] These authors also studied the adsorption of methanol, ethanol, and CCl4 on a series of microporous carbons[137] and compared the data obtained with the adsorption of the same
242
Bottani and Tasco´n
adsorbates on a graphitized carbon black. They concluded that their association in the micropores does not occur at low coverage. Adsorption of gas mixtures has been extensively studied. For example, Wendland et al.[138] applied the BornÐGreenÐYvon approach using a coarse grained density to study the adsorption of subcritical LennardÐJones ßuids. In a subsequent paper, they tested their equations with simulated adsorption isotherms of several model mixtures.[139] They compared the adsorption of model gases with equal molecular size but different adsorption potentials. They discussed the structure of the adsorbed phase, adsorption isotherms, and selectivity curves. Based on the vacancy solution theory, Nguyen and Do[140] developed a new technique for predicting multicomponent adsorption equilibria of supercritical ßuids in microporous carbons, based on the vacancy solution theory.[141] They concluded that the degree of adsorption enhancement, due to the proximity of the pore walls, is different for different adsorbates and it increases with a decrease in pore size. They found good agreement between model and experimental data. Do and Do[142] have reviewed very recently the adsorption of supercritical ßuids in porous and nonporous carbons. Ustinov and Do[143] proposed a model for binary mixture adsorption accounting for energetic heterogeneity and intermolecular interactions based on statistical thermodynamics. This model is able to describe molecular rearrangement of a mixture in a nonuniform adsorption Þeld inside a cavity. The Helmholtz free energy obtained has upper and lower limits, which deÞne a permissible range in which all possible solutions could be found. One limit corresponds to a completely chaotic distribution of molecules within a cavity, and the other to a maximum ordered molecular structure. Their model can also describe the negative deviations from RaoultÕs law exhibited by N2 ÐO2 mixtures. Bakaev and Steele[144] developed a lattice gas model of mixed adsorption on heterogeneous surfaces. The model considers an ideal mixture since it is assumed that the difference between the energies of the components on each adsorption site is the same. They showed that mixing at constant spreading pressure in this case is equivalent to that at constant coverage. The interaction between adsorbed molecules induces deviations from ideality, but the excess chemical potentials of the components calculated in the random mixing approximation depend linearly upon mole fractions, contrary to the regular bulk solutions, which in the same approximation have a quadratic dependence on mole fractions. Table 3.2 compares the experimental separation factors (selectivities) for methaneÐethane mixtures on an activated carbon, Sexp,[145] with those calculated according to the lattice gas model of mixed adsorption, S,[144] or by means of the the ideal adsorption solution theory (IAST), SIAST. The lattice gas model under discussion provided only rough evaluations of the selectivities in mixed adsorption but, unlike the IAST predictions, showed no dependence on the mole fraction in the gas phase yi or its total pressure P. (Notice that SIAST shows a dependence upon the composition of the gas phase opposite to that of the experimental data.) According to the authors, the main limitation of the lattice gas model is that of the Langmuir model as a whole; namely, the requirement that the adsorption capacities of all the components in a mixture be equal.
Physical Adsorption of Gases and Vapors on Carbons
243
Table 3.2 Selectivity of Methane Ð Ethane Mixtures on Activated Carbon y1
Sexp
S
SIAST
P ¼ 5 bar 0.981 0.945 0.827
15.1 16.4 17.1
11.1 11.1 11.1
21.1 18.9 17.1
P ¼ 20 bar 0.980 0.916 0.699
16.4 13.5 13.5
11.1 11.1 11.1
Note: y, Mole fraction; symbols for selectivity, see text. Source: Reproduced from Bakaev and Steele.[144] Copyright 1996 American Chemical Society.
Recently, Ustinov and coworkers[146,147] developed a thermodynamic approach based on an equation of state to model adsorption over a wide range of pressure. Their model is based on the virial-like Bender equation of state, with temperature-dependent parameters based on the Benedict ÐWebb ÐRubin equation of state.[148] They employed the model[149,150] to describe supercritical gas adsorption on activated carbon (Norit R1) at high temperature, and extended this treatment to subcritical ßuid adsorption taking into account the phase transition in elements of the adsorption volume. They argued that parameters such as pore volume and skeleton density can be determined directly from adsorption measurements, while the conventional approach of He expansion at room temperature can lead to erroneous results due to the adsorption of He in narrow micropores of activated carbon. Li et al.[151] have reviewed recently the thermodynamic basis of a novel model of the combined cycle of a solar-powered adsorption Ð ejection refrigeration system. They described the adsorption isotherms with a virial-like equation and adsorption heats were calculated with expressions derived from Eq. (3.93a).
3.3.
METHODS AND TECHNIQUES OF ANALYSIS
3.3.1. Direct Methods 3.3.1.1.
Adsorption Calorimetry
According to GravelleÕs classical review on the determination of heats of adsorption,[152] Òthe most straightforward method to determine heats of adsorption is to measure them in a calorimeterÓ. However, the nontrivial nature of
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the measurements and the lack of availability of commercial instruments have restricted this technique to a relatively small number of specialized research groups. More recently, the construction of suitable microcalorimeters has been facilitated by the advent of low-cost, high-sensitivity, heat-ßux sensors and low-cost computer data-acquisition systems. Condon[153] recently pointed out the necessity of simultaneous determination of the adsorption isotherm and the heat of adsorption to use his model (chi theory). As concerns instrumentation, Parrillo and Gorte[154] have recently analyzed some important parameters for the construction and operation of heat-ßow calorimeters used in the measurement of adsorption heats. Since calorimetric measurements can be signiÞcantly inßuenced by the design and operation of the instrument, the authors highlighted the importance of careful consideration of certain design parameters such as length scales for adsorption and heat transfer, and recommended the use of complementary techniques such as temperatureprogrammed desorption (TPD). To obtain the differential heat of adsorption as a function of coverage, equipment for simultaneous measurements of adsorbed amounts and heats evolved is needed; suitable microcalorimeters coupled to adsorption apparatuses have been described in detail by Rouquerol et al.,[155] Guil et al.,[156] and OÕNeil et al.[125] A number of reviews such as those from Gravelle,[152] Wedler,[157] or Cardona-Martõ«nez and Dumesic[158] have addressed the application of adsorption calorimetry to catalysts. More recently, Cÿerny[159,160] has reviewed in commendable depth the application of this technique to well-deÞned metal surfaces, in the form of Þlaments, vacuum-evaporated Þlms, or single crystals. Extensive work by Dunne et al.[161,162] on the application of adsorption calorimetry to zeolites can provide useful information for other types of microporous solids such as activated carbons. Recently, Mene«ndez[163] has reviewed the application of calorimetric (immersion, ßow adsorption, and gas adsorption) techniques to different carbon materials, with a focus on assessing the surface chemical properties of carbons such as nature of surface groups, hydrophobic/hydrophilic character, and acid/basic behavior; a brief section was devoted to the application of calorimetry in determining pore structure parameters. Dallos et al.[164] showed how the heat of adsorption, equilibrium, and kinetics of adsorption can be simultaneously determined using a reaction calorimeter. They studied the system 1-ethoxy-2-propanol adsorbed on granular activated carbon (AP4-60, Chemviron) at 298.2 K. As Fig. 3.7 shows, the heat of adsorption decreased with increasing equilibrium pressure as could be expected for a heterogeneous surface. As indicated in Section 1, here we review papers of chießy experimental nature. We follow a sequence that begins with adsorption of simple gases and continues with increasingly complex molecules. Several experimental papers are not cited in this section because they are included as support of theoretical or computer simulation results and are referenced together (see Section 3.3.3.3). Although this review is mainly concerned with physical adsorption studies, we Þnd it justiÞed to start with a brief reference to work by OÕNeal et al.[125] on
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245
Figure 3.7 Heat of adsorption of 1-ethoxy-2-propanol adsorbed on a granular activated carbon (AP4-60 from Chemviron Carbon) at 298.2 K. The solid line is a least squares Þt to Freundlich adsorption equation. (Adapted from Dallos et al.[164] Copyright 2002 Kluwer Academic Publishers.)
oxygen adsorption on high-surface-area carbons using a calorimeter of original design. Oxygen is known to form strongly bound complexes on carbon; indeed, at low coverage the heats of adsorption of this gas on a high surface area polymer-derived carbon[165] and on demineralized coal chars[166] exhibited values typical for a chemisorption process involving the formation of CO2- and CO-desorbing groups. Adsorption calorimetry of oxygen has also allowed to explain the differences between N2- and H2-treated carbons.[167,168] The use of this calorimeter allowed the measurement of adsorption heats at higher temperature[169] and provided unique and unexpected insights into the chemistry of carbon surfaces. Berger et al.[170] compared CO2 adsorption enthalpies measured directly by adsorption calorimetry with isosteric adsorption heats calculated from adsorption isotherms on an activated carbon and a silica gel. Good agreement was found between results from both types of measurements for the nonpolar activated carbon, but differences were found in the case of silica. The distinct behavior of silica was attributed to its polar character. A similar methodology based on the joint use of adsorption calorimetry and adsorption isotherms has been used by Cao and Sircar[171] to study sulfur hexaßuoride adsorption on two activated carbons (PCB and BPL Calgon), two zeolites, and an alumina. The adsorption heat of SF6 on the two activated carbons decreased with increasing adsorbate loading before leveling off in the high-coverage region; qualitatively similar pathways were followed by the two carbons, as Fig. 3.8 shows. This behavior is typical for heterogeneous surfaces, while the proÞles obtained for silicalite,
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Figure 3.8 Isosteric adsorption heats of SF6 on various adsorbents at 305 K: (a) silicalite, NaX zeolite; (b) alumina; and (c) BPL and PCB carbons. (Reproduced from Cao and Sircar.[171] Copyright 2002 Kluwer Academic Publishers.)
NaX zeolite, and alumina showed a constant or even increasing heat of adsorption with increasing adsorbate loading (see Fig. 3.8). The HenryÕs law constant [see Eq. (3.123)] showed the expected behavior for a highly heterogeneous surface in the case of the PCB carbon. Ammonia, a molecule typically used to study the acidity of solid surfaces, has been used by Xie et al.[172] to characterize acid/base sites on activated carbons treated with acid or ammonia. The authors argued this to be the Þrst use of microcalorimetry to probe the acid site distribution on carbons. Calorimetry proved to be a valuable addition to the set of techniques currently used for this purpose. However, ammonia calorimetry showed some limitations and the authors proposed that it should be used in conjunction with other techniques such as TPD, Boehm titration, and/or X-ray photoelectron spectroscopy (XPS).
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Duisterwinkel and van Bokhoven[173] described the development of a calorimetric method adapted to adsorbates that are liquid at room temperature, and applied it to study water adsorption on activated carbons. The authors indicated that the accuracy in the measurements was limited, in part, by the small net adsorption enthalpy for water on activated carbons; the effects of the presence of residual surfactants loaded on carbon were also addressed. More recently, Phillips et al.[174] have used adsorption calorimetry of water to further probe the effects of various types of surface modiÞcation treatments on the surface chemistry of activated carbons.[167,169,172] For this, an extensive matrix of treatments and carbons was selected. The authors differentiated three adsorption mechanisms, namely, chemical adsorption, condensation, and physical adsorption, and their relative preponderance was a function of surface chemistry. Figure 3.9 illustrates the variation of the heat of adsorption for water as a function of coverage for samples of a high-purity carbon (Norit-C) prepared by H3PO4 activation of wood. The adsorbent was subjected to treatments at 1223 K in H2 or N2 followed by exposure to O2 at 423 K. Chemisorption is the predominant
Figure 3.9 Variation of the heat of adsorption for water as a function of uptake for samples of a high-purity carbon submitted to various treatments. The horizontal dashed line corresponds to the heat of condensation, and error bars are approximately given by the size of the symbols. (Adapted from Phillips et al.[174] Copyright 2000 American Chemical Society.)
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mechanism in N2-treated carbon, whereas treatment in H2 at the same temperature renders the carbon hydrophobic and physical adsorption becomes the predominant mechanism. Further treatments in oxygen enhanced the capacity for water adsorption, with increases attributable to physical adsorption. To explain the Þnding that heats of adsorption are lower than the heat of condensation (datapoints below the dashed line in Fig. 3.9), the authors postulated the formation of a weakly bound 2D water monolayer that is not conducive to further adsorption. Calorimetric studies of a series of hydrocarbons (n-hexane, n-octane, cyclohexane, neopentane, and benzene) on pitch-based activated carbon Þbers (ACFs) were conducted in parallel with isotherm measurements by Matsumoto et al.[175] The differential adsorption heats, as well as the integral heats on ACFs with narrower pores, tended to become higher than those in ACFs with wider pores; this was ascribed to micropore Þlling and it has been reported for other systems, as discussed subsequently. These experimental results were compared with the theoretical proÞle of intermolecular interactions between adsorbates and adsorbents but, as the authors themselves recognized, further reÞnements should be made in the calculations, perhaps by using data for the bulk liquid for the interaction parameters. Rychlicki and Terzyk[176] reviewed the role of calorimetry in adsorption, and emphasized the differences between calorimetric heats and those calculated from the Clausius Ð Clapeyron equation for the adsorption of ethanol on activated carbons. They concluded that calorimetry is an indispensable tool to get a real thermodynamic description of adsorption in these systems. They also compared results of adsorption Ð desorption and calorimetric techniques for methane and CCl4 adsorption on microporous activated carbons,[177,178] which led them to an explanation for the origin of adsorption Ð desorption hysteresis and the adsorption mechanism. Kowalczyk et al.[179] reported data on the adsorption of pyrrolidine, cyclopentane, and tetrahydrofuran on a carbon black (Sterling MT) obtained using classical volumetry combined with calorimetry. The obtained data were employed to report a thermodynamic veriÞcation of NonakaÕs gradient method[180] for determining the surface area of solids. Terzyk and Rychlicki[181] also presented the results of a comprehensive study on the adsorption of these and other molecules (methanol and dichloromethane) on two polymer-derived activated carbons. An overall view on the adsorption mechanism in carbon micropores emerged, with emphasis on the role of carbon surface oxidation state. The authors concluded that the isosteric enthalpy alone does not provide a correct description of the adsorption energetics in these systems. Fiani et al.[182] have found similar discrepancies between adsorption heats determined from calorimetric measurements and from adsorption isotherms for n-butane on an unidentiÞed granular activated carbon. These authors attributed the differences to the lack of applicability of equations (e.g., the Langmuir equation) rather than experimental errors. This is expected given that the assumptions of Langmuir theory (a perfect mixture of free and occupied adsorption sites, and a homogeneous site distribution) are hardly met in real systems. Thus, the
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Freundlich equation, although not being more theoretically justiÞed than the Langmuir equation, is more widely obeyed as it assumes an exponential distribution of adsorption sites with respect to the energy of adsorption (see, e.g., Martõ«n et al.[183]). Nevertheless, the heats showed a parallelism in their variation with surface coverage, determined from calorimetric measurements or adsorption isotherms, which led the authors[182] to propose a single type of adsorption site for n-butane adsorption on the studied activated carbon. More recently, Terzyk et al.[184] compared a number of techniques, including benzene adsorption calorimetry, for characterizing the microporosity of cellulose-derived carbonaceous Þlms where the majority of micropores possessed the same diameter. The determination of pore size, based on the enhancement of potential energy in micropores in comparison to the energy of adsorption on a ßat surface,[185] agreed well with results obtained by DFT analysis of nitrogen adsorption data. Figure 3.10 shows the experimental results (which are Þtted better by the DA equation than by the DR equation) as well as enthalpies measured by adsorption calorimetry or calculated[186] from equilibrium data by
Figure 3.10 Experimental data (crosses) measured for benzene and Cox carbon (T ¼ 313.15 K). Adsorption isotherm: solid line, DA equation; dashed line, DR equation. Entropy: solid line and dashed line as above; crosses, differential molar entropy of adsorbed benzene; squares, integral molar entropy; horizontal dashed lines, values of the entropy of liquid [Sliq ¼ 179.89 J/(K mol)] and solid [Ssol ¼ 136.50 J/(K mol)] benzene. Enthalpy: line and dashed line as above; crosses, differential molar enthalpy measured calorimetrically; horizontal dashed line, value of the enthalpy of condensation (L ¼ 33.042 kJ/mol). (Adapted from Terzyk et al.,[184] with permission from Elsevier.)
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applying the formalism of DubininÕs theory of volume Þlling of micropores. Also included in Fig. 3.10 are experimental adsorption entropies calculated from the isotherm and the differential molar heat of adsorption; the constancy of the integral molar entropy was attributed to pore size homogeneity. Comparison with entropies calculated from theoretical models suggested that all three traslational degrees of freedom were almost lost by the adsorbed benzene molecules. Although the use of immersion calorimetry as an indirect source of information on the energetics of gas Ð carbon interactions is discussed in Section 3.3.1.4, some papers addressing combined use of adsorption and immersion calorimetric techniques merit discussion at this point. Besides their wellknown work on immersion calorimetry, Stoeckli et al.[187,188] have used adsorption calorimetry to characterize carbon blacks, activated carbons, and ACFs. Dichloromethane was the probe molecule they used in gas adsorption calorimetry of carbon blacks. A coincidence was found between a decrease in the differential heat of adsorption and Þlling of the larger micropores, as deduced from CH2Cl2 isotherms and heats of immersion (in the same liquid). The authors suggested that the combined use of adsorption and calorimetric techniques provides complementary information leading to unambiguous characterization of carbon blacks. More recently, working with activated carbons CAF-B, AGB, ACF KF1500, and nonporous carbon black Vulcan 3 used as reference, Guillot et al.[189] have performed in parallel direct measurements of the differential heats of adsorption of CO2 and high-pressure CO2 adsorption isotherms; complementary measurements were made at low pressures by coupled thermogravimetry (TG)Ð differential scanning calorimetry (DSC). The proposed combination of techniques applied to a single adsorbate was useful to characterize the whole range of porosity in the studied adsorbents. Kowalczyk and Karpinski[190] investigated the adsorption of mixtures of methanol and tetrahydrofuran, methanol and cyclopentane, and tetrahydrofuran and cyclopentane on a graphitized carbon black (Sterling MT). They established the dependence of the intermolecular interactions on the composition of the adsorbed layer; they also proposed a mechanism to explain the adsorption of the equimolar methanol Ð tetrahydrofuran mixture, which takes into account both homo- and heteromolecular association. Using the same approach, Kowalczyk[191] studied the adsorption of binary mixtures of tetrahydropyrrol with methanol and cyclopentane on a homogeneous graphitized carbon black. Some recent work on carbon nanotubes illustrates the application of adsorption calorimetry to this new class of materials. Muris et al.[192] have applied isothermal microcalorimetry in quasi-equilibrium (carried out by introducing the adsorbate at an extremely slow constant rate; see Grillet et al.[193]) to study methane physisorption on single-wall carbon nanotubes (SWNT) arranged in bundles. The isosteric adsorption heat at 77.3 K obtained in this way agreed very well with that obtained from isotherms measured at several temperatures between 78 and 110 K. The existence of two different types of quasi-uniform surface patches was inferred; one of them is more attractive than the graphite
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surface and the other less attractive. Bienfait et al.[194] have complemented this work using quasi-elastic neutron scattering to characterize the diffusivity of methane molecules condensed in single-wall carbon nanotubes. The two adsorption sites were shown to correspond to two types of adsorbed species: a solid phase for the more strongly bound one at temperatures below 120 K, and a viscous liquid for the more weakly bound species between 70 and 120 K. 3.3.1.2.
Flow Calorimetry
Flow adsorption techniques are widely recognized as important methods to study adsorptionÐ desorption phenomena at solid Ð ßuid interfaces. The most important characteristics of these techniques have been reviewed by Groszek.[195] According to the author, ßow adsorption microcalorimetry has now been developed to a point where it provides accurate and reliable adsorption and desorption data for events occurring at the solid Ðliquid[196] or gas Ðsolid interface over a wide range of temperatures, pressures, and solution concentrations. Indeed, the energetic heterogeneity of acid and basic sites on carbon adsorbents has been reported, at least partially, by Groszek.[197,198] He concluded that cyclic ßow adsorption microcalorimetry could be employed to provide differential molar heats of irreversible adsorption of acidic or basic probes. Changes in the values of adsorption heats with the amount adsorbed are characteristic of each carbon adsorbent and can be employed to predict its catalytic activity. The adsorption of fatty acids, alcohols, and aromatic compounds on carbon black pigments has been investigated by Pen÷a et al.[199] using ßow microcalorimetry in combination with other techniques, for example, IR spectroscopy, XPS, and N2 adsorption. Reucroft and Rivin[200] reported the adsorption heats of toluene on a microporous carbon determined by ßow microcalorimetry. They pointed out that a consistent determination of the integral molar adsorption heat requires an independent measurement of the equilibrium adsorption isotherm. Phenol adsorption on a series of materials, including a commerical activated carbon from J.T. Baker Co. (catalog E345-07), was studied by Xing et al.[201] They determined, among other parameters, the molar heat of adsorption. The values obtained varied with the amount adsorbed in the way expected for a heterogeneous surface. The heat of adsorption at very low coverage was ca. 30 kJ/mol; closer to saturation, it was ca. 16 kJ/mol. The Þrst value agrees with the one calculated by Bertoncini et al.[202] for a phenol molecule adsorbed in a ßat position on the surface of the basal plane of graphite. The value obtained at saturation is indicating that phenol molecules are adsorbed in a vertical position with respect to the surface. The value corresponding to the OH group close to the surface calculated by Bertoncini et al. was 16.6 kJ/mol, and for the OH group away from the surface it was 15.8 kJ/mol. Nevertheless, the experimental value obtained for an activated carbon near the saturation pressure is quite low compared to the results obtained by Bertoncini et al.[203] from computer simulations and the experimental values obtained by Teng and Hsieh[204] and Vinod and Anirudhan.[205]
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A very complete investigation of the factors affecting the adsorption of stabilizers and antioxidants on carbon blacks, using ßow microcalorimetry and IR spectroscopy, has been published by Pen÷a and coworkers.[206 Ð 209] The studied antioxidants were phenolic, aryl phosphates, and phosphonites, and the stabilizer used was a piperidine-based one. Reucroft and Rivin[210] reported a mechanism for the adsorption of toluene on microporous and mesoporous carbons using ßow calorimetric data. Their main conclusion, not completely unexpected, is that toluene is adsorbed within the mesopores and then it migrates into the micropores where it is stabilized by the enhancement of the adorption potential. 3.3.1.3.
Differential Scanning Calorimetry
The information produced by DSC is useful to characterize certain aspects of the energetics of adsorption or desorption. The application of this technique to adsorption studies essentially consists in adsorbing a substance on a solid and then performing a TPD analysis. A complete description of instrumentation has been reviewed by Gill.[211] Baudu et al.[212] employed DSC to study adsorption of water vapor and several organic molecules (benzene, chlorobenzene, toluene, benzaldehyde, phenol, naphthalene, methanol, n-butanol, and dichloromethane) on different activated carbons. Their main goal was to determine the adsorption and desorption heats. They concluded that DSC is an effective direct method for determining desorption energies. They also argued that it is possible to infer the adsorption mechanisms (i.e., the modes of interactions between the adsorbate and the solid surface and between the adsorbate molecules). Their results suggested that the adsorption energy can be correlated with the molar refraction or with the dipolar moment and the molar volume of the adsorbate. They obtained linear relationships for families of compounds, in agreement with previous work done by Wood,[213] who found direct correlations of experimental afÞnity coefÞcients with molecular parachor, molar polarization, and molar volume. Hickey and Sharma[214] studied the selective adsorption of several organic compounds on different solids of high surface area, including a wellcharacterized carbon molecular sieve. They employed several techniques including DSC to calculate the adsorption energy. They concluded that intermolecular forces dominate desorption of molecules with characteristic sizes similar to the pore dimensions. Popescu et al.[215] studied the adsorption of butanol, toluene, and butyl acetate on activated carbons from Romcarbon and CECA (R-CAFS and AC40) using DSC and TPD. They found that the heats of adsorption (desorption) for butanol, toluene, and butylacetate were 98.8, 38.6, and 48.4 kJ/mol, respectively. From the data presented, it could be inferred that the heat of adsorption exhibits the expected behavior for a heterogeneous surface (continuous decrease with amount adsorbed). Unfortunately, the authors did not include enough data to conÞrm this.
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The DSC technique combined with incoherent elastic neutron scattering has been employed by Castro et al.[216] to investigate the competitive adsorption of simple linear alkanes (n-hexane, n-octane, n-nonane, and n-decane) and their binary mixtures on recompressed exfoliated graphite (Papyex, from Le Carbone Lorraine). They conÞrmed the formation of single solid monolayers adsorbed from liquid alkanes above the bulk melting point. They also found that the enthalpy of the monolayer transition at higher coverage is much smaller than the bulk enthalpy of fusion for all the alkanes investigated. In the case of mixtures, they found that the longer alkane is always preferentially adsorbed, even when it is present as the minor component of the mixture. This fact suggests that the adsorption energy and the entropic change are the properties that control the adsorption process. Another application of DSC has been shown by Watanabe et al.[217] They measured the melting temperature elevation of benzene conÞned in micropores of pitch-based ACFs (P5, P10, P15, and P20 from Osaka Gas, and KAC31 from Kansai Coke). They identiÞed the melting temperature of conÞned benzene, which was 16 Ð20 K higher than that of bulk benzene. Moreover, they could estimate the enthalpy of fusion of conÞned benzene, which was in the range of 4 Ð 5 J/mol (Table 3.3). This value is much smaller than that of bulk benzene (10.7 kJ/mol), indicating that the structure of the adsorbed phase in the pores is different from the bulk solid. The authors conÞrmed a suggestion made by Miyahara and Gubbins[218] about the increase in melting temperature with decreasing pore width when the interaction potential energy of a molecule with the pore wall is greater than that with the pore wall consisting of adsorbate molecules. Water vapor adsorption on activated carbons has been studied by Staszczuk,[219] who combined controlled-rate thermal analysis with DSC and obtained the pore size distribution and several characteristics of the solid surface. Kirsh et al.[220] investigated the association of water molecules in a nanoporous carbon material using DSC. They concluded that the association Table 3.3
Amounts of Benzene Adsorbed in Carbon Micropores and DSC Data
Sample P5 P10 P15 P20 KAC31 Bulk solid benzene
Benzene uptake (mg/g)
Melting temp. (K)
Enthalpy of fusion (kJ/mol)
335 350 583 744 1190 Ñ
294 295 295 298 298 278
0.003 0.004 0.005 0.005 0.005 10.7
Note: Sample codes, see text. Source: Reproduced from Watanabe et al.,[217] with permission from Elsevier.
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mechanism and the properties of water are controlled by nanopore size and morphology. They identiÞed three coexisting states of water molecules, and found that water molecules enclosed in nanopores are unable to crystallize at temperatures from 273 to 203 K. These pores are Þlled with water molecules due to the presence of graphite-like conjugated structures whose p systems are assumed to be capable of forming hydrogen bonds with the adsorbed molecules. Pre« et al.[221] employed DSC to determine the heats of adsorption of 40 volatile organic compounds adsorbed on an activated carbon (Picactif NC60). With these results they performed a quantitative structure Ð activity relationship (QSAR) analysis. Figures 3.11 and 3.12 show the correlations found between computed energies (from physicochemical variables, Fig. 3.11; or from molecular connectivity indices, Fig. 3.12) and measured energies. The measured adsorption Ð desorption energies were linearly correlated with the polarizability of the adsorbate and with the reciprocal of the ionization potential. The authors showed that the molecular size, its branching, and steric hindrance also have a certain effect, which is not easy to elucidate: while bulky molecules present a wider contact surface, this beneÞt may be compensated by a difÞcult access of branched molecules to the adsorption sites. 3.3.1.4.
Immersion Calorimetry
The heat of immersion is a parameter that is measured directly in a calorimeter, while the surface energy of a solid is not easily measured. Indeed, the heat of immersion provides an indirect measure of the surface energy; it also provides information on the surface heterogeneity of carbonaceous solids. Early work
Figure 3.11 Predictive ability for adsorption Ð desorption energies of quantitative structure Ð activity relationships found from physicochemical variables. (Reproduced from Pre« et al.,[221] with permission from Elsevier.)
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Figure 3.12 Predictive ability for adsorption Ð desorption energies of quantitative structure Ð activity relationships found from molecular connectivity indices. (Reproduced from Pre« et al.,[221] with permission from Elsevier.)
on this subject, partially connected with our objectives, has been reviewed by Zettlemoyer and Narayan.[222] The heat of immersion is a function of the differential heat of adsorption, q, the heat of liquefaction, q1 , and the surface enthalpy of the liquid, h1 ð 1 (q ql )dn þ hl hl ¼ (3:94) A Here A is the speciÞc surface area of the solid and n is the adsorbed amount, usually expressed per unit mass of adsorbent. The heat of immersion provides valuable information on the average surface polarity and the surface heterogeneity of carbonaceous materials. Surface heterogeneity can be determined from measurements of the variation of immersion heat with coverage. Stoeckli and Kraehenbuehl[223] discussed the derivation of an exact expression for the enthalpy of immersion of activated carbons using DubininÕs theory as a starting point. They tested this expression with experimental data for 10 different carbons immersed in benzene and n-heptane. In a subsequent paper, Kraehenbuehl et al.[224] reported the use of immersion calorimetry to determine the micropore size distribution of carbons in the course of their activation. The fundamental and theoretical aspects of this technique have been reviewed by Terzyk et al.[225] In this paper, the authors pointed out an error found in the DS equation modiÞed by Stoeckli and Kraehenbuehl. The reason for the error was that their equation neglected the temperature dependence of the maximum adsorption uptake. If this is taken into account, it leads to a decrease in adsorption enthalpy with coverage. Prior to this, Partyka et al.[226] developed the immersion microcalorimetric version of the Harkins Ð Jura[227] procedure for determining speciÞc surface areas.
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The heat released during the loss of the liquid Þlm saturating the solid Ð vapor interface is related to the surface area through the basic equation,[226] @g l,g jDH imm j ¼ A g l,g T @T
(3:95)
where g l,g is the interfacial tension at the liquid Ð vapor interface. The authorsÕ success in the application of this method was based on the use of a very sensitive differential microcalorimeter. Denoyel et al.[228] derived the pore size distributions of two sets of activated carbons (one activated in water vapor and the other activated with phosphoric acid) using immersion calorimetric data. They concluded that immersion calorimetry could be considered a convenient technique to assess the total surface area available for a given molecule and the micropore size distribution. Though this technique is not directly related to gas adsorption, there are several results obtained from immersion in pure liquids that have certain common features with adsorption from the vapor phase. Therefore, only immersion in pure liquids or mixtures of immiscible liquids is reviewed in this section. A comparison of several calorimetric techniques has been made by Mene«ndez.[163] The use of immersion calorimetry to characterize the textural and surface chemical nature of activated carbons has been reviewed by Rodrõ«guez-Reinoso and coworkers.[229,230] Immersion calorimetry is mostly employed to characterize the porous structure of different adsorbents. For example, Stoeckli et al.[231] used physical adsorption of CH2Cl2 and N2O combined with immersion microcalorimetry into liquids of different molecular sizes to analyze the porous structure of activated carbon Þbers prepared from poly( p-phenylene terephthalamide) (Kevlar) and poly(m-phenylene isophthalamide) (Nomex). They based their analysis of the experimental data on the DR equation for the micropore volume Þlling and its extension to immersion calorimetry data. The authors pointed out that immersion calorimetry alone can provide a reasonable assessment of micropore accessibility. By comparing the proÞles for access to the micropores of liquids with different molecular sizes it was possible to follow the evolution of the microporosity with the burn-off degree. However, the determination of absolute pore volumes requires at least one isotherm for each sample studied. Using a similar approach, Rebstein and Stoeckli[232] characterized a sulfur-impregnated activated carbon. The porous texture of a series of Nomex-derived carbon Þbers activated to different burn-offs has been characterized by Villar-Rodil et al.[233,234] by immersion calorimetry into liquids with different molecular dimensions and from N2 and CO2 adsorption isotherms. Table 3.4 includes the immersion enthalpies and the corresponding surface areas. The authors paid special attention to the choice of the reference material (they used Vulcan 3G, Vulcan 3, and Spheron 6 carbon blacks), and found that this choice strongly affects the value obtained
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Table 3.4 Experimental Enthalpies of Immersion at 298 K into Different Liquids of Nomex-Derived Carbon Fibers Steam-Activated to Different Burn-offs. Surface Areas Derived From Them, and From N2 Adsorption at 77 K (SBET) Burn-off (%) 0 10 21 42
Surface areas (m2/g)
2DHimm (J/g) CH2Cl2
C6H6
C6H12
CH2Cl2
C6H6
C6H12
SBET (m2/g)
45.3 92.1 123.1 138.1
11.0 65.9 122.4 146.7
10.0 47.6 81.6 107.6
338 687 918 1029
100 600 1116 1337
96 460 787 1038
Ña 560 936 1329
a
Only geometric area. Source: Reproduced from Villar-Rodil et al.,[234] with permission from Elsevier.
for the speciÞc surface area, and that this effect should be taken into account when comparing these values with the ones obtained by other methods. Similar increases in the immersion heat in benzene with increasing activation degree have been found by Carrott et al.[235] for a variety of activated carbons (Carbosieve, from Supelco; MSC-3A, MSC-4A, and MSC-30, from Takeda; and Maxsorb MSC-25 and MSC-30, from Kansai Coke), by Rodrõ«guezReinoso and coworkers while investigating activated carbons from olive stones[236] and activated carbon cloths from viscous rayon,[237,238] and by Albiniak et al.[239] working with chars from a high Ð volatile bituminous coal. On the other hand, Rodrõ«guez-Reinoso et al.[240] reported an almost constant heat of immersion of benzene on carbon samples with different surface chemical structures obtained by oxidative (HNO3) and thermal treatments of an activated carbon prepared from olive stones. It should be kept in mind that benzene, though a nonpolar molecule, possesses a large quadrupole moment, which could account for large electrostatic interactions, and it may still be sensitive to the presence of oxygenated surface groups. Nonpolar molecules with smaller quadrupole moment like n-heptane should be still less sensitive.[241] Immersion calorimetry can also be employed to characterize the surface of carbon-supported catalysts. For example, Dõ«az-Aun÷o«n et al.[242] investigated the activity of [Rh(m-Cl)(COD)]2 supported on activated carbons (ROX-0.8 carbon from Norit, either fresh or HNO3-oxidized) toward the hydroformylation of 1-octene, in connection with the support surface chemistry. The authors were able to identify differences in the surface chemical composition through the analysis of adsorption heats for several molecules (n-hexane, acetone, and methanol). For example, they found that a nonpolar solvent like n-hexane showed the highest heat of adsorption for the original untreated activated carbon, which had the lowest surface polarity. Analogously, methanol exhibited the lowest heat of adsorption on this material. The carbon oxidized with HNO3, containing a large amount of surface oxygen complexes, showed a more or less reverse tendency with respect to the heats of adsorption of the different solvents.
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Stoeckli and Kraehenbuehl[243] determined the external surface area of microporous carbons, that is, the area of the solid excluding the micropores, using immersion calorimetry with benzene, n-heptane, and n-hexadecane. They compared these results with the areas obtained from gas-phase adsorption (nitrogen and benzene) and found good agreement. Moreno and Giraldo[244,245] employed immersion calorimetry with CCl4 to determine the total surface area of a series of activated carbons from different precursors and different porosity characteristics. The results were interpreted with the Stoeckli Ð Bansal ÐDonnet equation[11] and reßected signiÞcant differences in surface characteristics of the analyzed samples. Water adsorption has been studied extensively using immersion calorimetry. The early knowledge on this subject has been summarized by Kinoshita.[246] The results obtained on carbon blacks containing surface oxygen show a linear correlation between the heat of immersion and oxygen concentration. The same linear correlation has been reported by Szymanski et al.[247] Stoeckli et al.[248] conÞrmed that water adsorption isotherms on a number of carbons, near room temperature, are of type IV in IUPAC classiÞcation. Those isotherms could be decomposed into two contributions of types I and IV isotherms and the DA equation accounted for the main features of the isotherms. The initial segment of the isotherm suggested the presence of sites with characteristic energies in the range of 5 Ð8 kJ/mol and similar contributions to the molar enthalpy of immersion of the carbons into water. The second part of the isotherm was compatible with the earlier model of Dubinin and Serpinski.[249] Bradley et al.[250] used immersion calorimetry to study water adsorption on samples of a carbon black (N330 from Cabot) oxidized with ozone and nitric acid to different extents. Figure 3.13 shows the correlation they found between the immersion
Figure 3.13 Correlation between the enthalpy of immersion of activated carbons into water and the total surface oxygen concentration measured by XPS for ozone- and nitric acid-oxidized carbon blacks and native materials. Refs.[6] and[7] in the Þgure are, respectively, Refs.[251] and[252] in this work. (Reproduced from Bradley et al.,[250] with permission from Elsevier.)
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enthalpy into water and the oxygen surface concentration as measured by XPS; this Þgure also includes results taken from the literature.[251,252] The authors estimated the enthalpy of polar interaction for water to be 17 kJ/mol; with this value, they could predict the immersion enthalpy in water with reasonable accuracy. The data corresponding to samples oxidized with nitric acid in Fig. 3.13 do not align with the native and ozone oxidized surfaces. Regression analysis of these points led, however, to an intercept (which was interpreted as the characteristic energy for immersion of the pure carbon surface, with no oxygen chemisorbed) of 40 mJ/m2, similar to the one obtained with the other family of data points (35 mJ/m2). Barton et al.[253] studied water and cyclohexane adsorption on oxidized porous carbons. They employed the DS equation to interpret the experimental data. For adsorption of nonpolar organics, the pore Þlling itself produces the major enthalpy change. The magnitude of the change was found to depend, to some extent, on the hydrophilic or hydrophobic nature of the surface. Stoeckli and Centeno[254] pointed out that immersion calorimetry is a useful tool for characterizing solid surfaces in general, but in the case of microporous solids it usually requires complementary information obtained from the adsorption isotherms. They also discussed the limitations and possibilities of the technique and recommended that at least one adsorption isotherm from the vapor phase (e.g., CH2Cl2 or C6H6) is necessary to remove all the uncertainties. Another example where a series of techniques, including water adsorption, are employed to characterize activated carbons with different degrees of oxidation is a study of Carrasco-Marõ«n et al.[255] The authors combined water vapor adsorption, immersion calorimetry, acid Ð base titration, and TPD of CO2 and CO. They related the number of carboxyl, lactone, phenol, and basic groups with the parameters obtained from the DA equation and with the immersion enthalpy in water. They found good agreement between experimental data and the calculations based on the DA equation. A review concerning DubininÕs theory and its extension to immersion calorimetry has been published by Stoeckli.[256] The author concluded that DubininÕs approach provides a satisfactory description of the adsorption equilibrium of single vapors, and that it has now been extended to describe their removal from air under dynamic conditions. SpeciÞc and nonspeciÞc interactions of methanol and ethanol with a large series of activated carbons have been investigated by Lo«pez-Ramo«n et al.[257] They described the adsorption isotherms using the DA equation and immersion calorimetry data and used benzene vapor adsorption as reference. They concluded that activated carbons containing oxygenated surface groups experienced speciÞc interactions with those alcohols and argued that these interactions mainly depend on the total amount of oxygen rather than on the chemical nature of the groups. Lo«pez-Ramo«n et al.[258] have also addressed the problem of speciÞc and nonspeciÞc interactions of water with carbon surfaces as inferred from immersion calorimetry. For a variety of 27 activated carbons oxidized to different degrees, they obtained a correlation between the enthalpy of immersion into water and a function accounting for the total oxygen content of the surface, the
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basic groups, the micropore Þlling, and the wetting of the external (nonmicroporous) surface, which is shown in Fig. 3.14. The authors followed a similar approach for Cabot Black Pearls 570 carbon black and found that the enthalpy of immersion into water correlated with the surface oxygen and the wetting of the surface (here, micropore Þlling no longer occurs). A similar, but less comprehensive study has been reported by Gonza«lez-Martõ«n et al.,[259] who used the immersion enthalpies into water and benzene to quantify the modiÞcations in hydrophobicity of a set of Darco (Aldrich) activated carbons subjected to wet air regeneration following saturation with phenolic compounds. Guillot and Stoeckli[260] proposed the use of CO2 adsorption isotherms at 273 K as reference for both porous and nonporous carbons. The results obtained for the external surface area determined with immersion calorimetry of benzene at 293 K were in good agreement with those of N2 at 77 K. Immersion calorimetry has also been employed to characterize carbonaceous materials exhibiting molecular sieving behavior.[261 Ð 263] For example, de Salazar et al.[264] studied the ability of carbon molecular sieves to separate gas mixtures as a function of their molecular size. They found, as could be expected, that the accessible surface area decreases as the molecular size of the immersion liquid increases. The enthalpy of immersion for a given liquid increased with the activation degree for each series of materials. Stoeckli et al.[265] characterized a series of carbon molecular sieves using the previously described methodology[260] developed by the authors. Combining CO2 adsorption isotherms at 273 K with immersion calorimetry at 293 K and model isotherms, the authors were able to assess gate effects created by constrictions in the micropore system. In this and previous work,[266] Stoeckli and coworkers
Figure 3.14 Overall correlation between the enthalpy of immersion of activated carbons into water and the total surface oxygen, the basic groups titrated with HCl, the micropore Þlling and the wetting of the nonporous surface area. (Reproduced from Lo«pez-Ramo«n et al.,[258] with permission from Elsevier.)
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have combined immersion calorimetric techniques with scanning tunneling microscopy (STM) for the characterization of porosity in activated carbons. In connection with the adsorption of gas mixtures, the molecular sieving properties of ACFs have been characterized using immersion calorimetry combined with other techniques.[231,267] ACFs prepared from similar precursors and subjected to chemical vapor deposition of carbon to induce molecular sieve behavior have been studied by Villar-Rodil et al.[234] using a methodology equivalent to that alluded to before. As immersion liquids, dichloromethane, benzene, and cyclohexane were used.[267] The calorimetric results were consistent with Þndings about the ability of these carbon molecular sieves to separate the CO2 ÐCH4 and O2 Ð N2 gas mixtures. Nevskaia et al.[268] used immersion calorimetry on n-nonane, water, and phenol to characterize activated carbons used in nonylphenol adsorption from aqueous solutions. It is interesting to note that two-step isotherms were obtained for all carbons investigated. The Þrst plateau was attributed to the adsorbentÕs mean pore width. Adsorption in this region was monomolecular and exhibited the characteristics of vapor adsorption, suggesting that the process is very similar to adsorption from the vapor phase and that solvent effects, if existent, are negligible. The second plateau was attributed to the presence of an inorganic impurity. 3.3.2. Indirect Methods The calorimetric methods described in Section 3.3.1 provide direct measurements of thermodynamic properties, namely, adsorption heats. In this section, we will describe results obtained with indirect methods, basically from the variation of adsorbed amount with temperature (Section 3.3.2.1), or from IGC (Section 3.3.2.2) (particularly under inÞnite dilution conditions). Finally, the use of miscellaneous techniques to measure adsorption and comparisons of several different methods will be addressed (Section 3.3.2.3). 3.3.2.1.
Adsorption Isotherms
In this section, we shall review the results obtained through the determination of the adsorption isotherms. Some experimental results have been included in other sections when they are related to other papers, and they will not be repeated here. The major interest in determining the adsorption isotherms, within the context of this review, is to characterize the adsorbent in an indirect way: indeed, the characteristics of the solid surface are inferred from the behavior of the adsorbed phase. In the case of carbons, the most important practical issue is probably the determination of the pore size distributions. Since this review is intended to be focused on the energetic aspects of physisorption, we will include studies on the determination of pore size distributions if they deal also with other fundamental
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issues of adsorption thermodynamics (e.g., the characteristic adsorption energy or the use of pore models connected with adsorption energetics). This section is organized as follows. We begin with several general papers, mostly devoted to the analysis of porous solids, then a series of papers studying the adsorption of different gases on carbons. At this point, we cannot avoid mentioning DubininÕs contributions in this area, for which we selected only one of his classical articles[269] from his vast production. The same criterion applies to KiselevÕs contributions. The review article we have chosen[270] is one where many adsorption isotherms are reported in tabular form, including the isosteric heats of adsorption. Carbon nanotubes have acquired importance in recent years; thus a series of papers dealing with them are grouped together. Finally, we summarize studies on adsorption of gas mixtures. Rozwadowski and Wojsz[271] studied the mechanism of adsorption of light aliphatic alcohols and amines on activated carbons using a modiÞed Polanyi Ð Dubinin potential theory. The authors found that the degree of association of alcohols is lower in the adsorbed phase than in the pure liquid, whereas the reverse is observed for amines. They derived this conclusion from the analysis of entropy, enthalpy, and free energy changes. They also found that, within the low relative pressure range, molecules of polar adsorbates undergo chemisorption or strong speciÞc adsorption. The energy of these interactions is much greater than that of dispersive interactions and it is responsible for the low initial values of the activity coefÞcients. Marsh[272] presented a critique of the methods currently employed to study the adsorption in coals and carbons. He described several problems associated with the use of polar adsorbates, made an appeal for the understanding of limitations, and discussed the value of theoretical adsorption equations. He also discussed activated diffusion, molecular sieve effects, and cooperative adsorption effects. His main conclusion is that coals and carbons are extremely difÞcult materials to characterize in terms of structure of porosity: each adsorbate provides unique but partial information and thus the adsorption equations must be understood at the fundamental level and be employed judiciously. He also recommended the use of equivalent surface area instead of real or true physical area of microporous solids. McEnaney[273] analyzed in detail the use of the DR equation to estimate the dimensions of micropores in activated carbons. He correlated the decrease in the characteristic energy of the DR equation with the increase in the micropore size determined using molecular probes. He proposed a new method to relate the characteristic energy to the micropore size calculated from adsorption potentials in slit-shaped model pores. He tested the method with experimental data for Ar adsorption at 77 K on a series of steam-activated carbons. Dubinin and Kadlec[274] developed a general equation to describe the physisorption of vapors on nonhomogeneous microporous solids. In their model, the adsorption energy increases because of the effect of superposition of dispersion force Þelds of the opposite micropore walls. The heterogeneity of the microporous structure is described in terms of a Gaussian distribution of
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micropore volumes with respect to the reciprocal value of the characteristic adsorption energy. The model contains three parameters: the total micropore volume, the characteristic energy at the maximum of the distribution curve, and the dispersion. If the dispersion term is set to zero, the DR equation is obtained. The model was tested using benzene adsorption data for several activated carbons and porous silica. This method has been also employed, among others, by Bradley and Rand.[275] On the other hand, Kruk et al.[276,277] have questioned the procedure since the DA (or DR) equation does not adequately represent the volume Þlling of uniform pores. (It predicts a rather gradual increase in the adsorbed amount, spread over several orders of magnitude of the relative pressure; however, in actual dispersed homogeneous pores a rather steep increase will occur at pressures of the monolayer formation or condensation inside a given pore.) They recommended the use of the Horvath ÐKawazoe method, and concluded that numerical methods employing local isotherms, obtained from computer simulations or nonlocal DFT,[278] are better for calculations of micropore size distributions. Li and Jaroniec[279] employed the thermodesorption technique to characterize the surface energetics of different carbon blacks (Cabot Corp.). The adsorbates employed were water, n-butanol, and n-heptane. The authors showed that the polarity of the adsorbate is essential to control thermodesorption from low-surface-area carbon blacks, while this factor seems to be less important in the case of high-surface-area samples. They argued that the relative thermodesorption plot introduced in this study provided information about surface heterogeneity equivalent to the one obtained from the comparative adsorption plot. In 1989, Dubinin[280] reviewed the fundamental aspects of the theory of adsorption of vapors in micropores. He argued that it is possible to predict the uptake of different vapors and the adsorption vs. temperature relationships based on the DS equation. This equation has three parameters: the micropore volume, the characteristic adsorption energy, and the variance (plus the speciÞc surface area of the mesopores, if important). He concluded that benzene and nitrogen, two commonly accepted reference adsorbates, are not equivalent to each other, and that benzene is more appropriate to obtain a comprehensive characteristic of both the adsorption properties and the microporous structure. Puziy[281] employed benzene adsorption data at 298 K to characterize the surface heterogeneity of a series of activated carbons. Figure 3.15 compares the usefulness of various equations for determining the adsorption potential distribution in micropores of a synthetic carbon prepared by steam activation of a styrene Ðdivinylbenzene copolymer. The DA equation (with an exponentn of 3.05) Þts the experimental points well. The DS and JaroniecÐ Choma[282] equations give distributions similar to each other, but in bad agreement with experimental data. The author argued that these two equations are derived from the generalized adsorption isotherm with the classical DR equation as a core, and therefore they are designed for adsorption on heterogeneous microporous solids. The studied carbons were, however, relatively homogeneous
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Figure 3.15 Adsorption potential distribution in micropores of synthetic activated carbon calculated from experimental data (symbols) and from the Dubinin Ð Astakhov (DA), Dubinin Ð Stoeckli (DS), and JaroniecÐ Choma (JC) equations. (Reproduced from Puziy.[281] Copyright 1995 American Chemical Society.)
(the DA equation gave an exponent n . 3 for most of them) and the extent of homogeneity was outside the capabilities of the two equations based on the DR equation. Kaneko et al.[283] developed a method known as the subtracting pore effect to determine the speciÞc surface area of high-surface-area activated carbons. Their method includes a model representation of the structure of microporous carbons: a stack of graphitic crystallites with slit-shaped pores. The authors supported their models by comparing them with experimental results. The adsorption of gases as a means to store them implies the study of physical adsorption at supercritical temperatures. This problem has been of interest since a long time ago, but there are still several unresolved questions, both theoretical and practical. For example, Jurewicz et al.[284] reported the electrochemical storage of hydrogen in activated carbons and concluded that this method could be better than the classical cryogenic storage. Zhou et al.[285] determined the adsorption isotherms of nitrogen and methane on several activated carbons at supercritical and subcritical temperatures, and calculated the isosteric heats of adsorption using the Clausius Ð Clapeyron equation. Zhou and Zhou[286,287] reported a method for linearizing the adsorption isotherm for high-pressure applications, based on a modiÞcation of the DA equation, the identiÞcation of the effect of adsorbate volume on the isotherm, and the evaluation of the isosteric heats of adsorption. They tested their method with experimental data for hydrogen
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on AX-21 activated carbon at 77 Ð298 K and up to 7 MPa. Their method consists in representing the isotherms in the coordinates of ln ln(n) vs. 1/ln P, where n is the amount adsorbed and P is pressure. The linear expression employed is: ln ln(10n) ¼ a þ
b ln P
(3:96)
This equation has two parameters that are linear functions of temperature. The relationships obtained from the isotherms are: a ¼ 1:0411 þ 0:009684T
(3:97)
b ¼ 7:848 0:10595T
(3:98)
and
The authors showed that linearization is possible, at least for hydrogen adsorption, over a wide range of conditions. The method provides a physically reasonable reference state for the supercritical adsorbate, and this information could be employed to modify the DA equation. From Eq. (3.96) it is possible to calculate the isosteric heat of adsorption and to compare it with the experimental value [determined using the Clausius Ð Clapeyron equation (3.38)] and with the value derived from the DA equation. Figure 3.16 shows the values obtained using the numerical values given in Eqs. (3.97) and (3.98). Data calculated from the linearized model are much closer to the experimental results than those from the DA equation. The authors also concluded that their proposed method can identify the effect of adsorbate volume, which is responsible for the alteration of the isotherm shape at low temperatures and high pressures.
Figure 3.16 Isosteric adsorption heat of hydrogen on activated carbon AX-21. exp: experimental values obtained from Eq. (3.38); model: analytical solution of Eq. (3.96); DA: analytical solution of Dubinin Ð Astakhov equation. (Adapted from Zhou and Zhou,[287] with permission from Elsevier.)
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Another example of the use of Eq. (3.96) has been reported by Zhan et al.,[288] concerning the study of supercritical hydrogen adsorption on a superactivated carbon (3886 m2/g, 1.8 mL/g). An adsorption limit for supercritical H2 on porous carbon of 23.764 wt.% at a pressure of 80 MPa was thus deduced. Manzi et al.[289] characterized a series of Maxsorb superactivated carbons and evaluated them as potential materials for gas storage, particularly CH4. They calculated nitrogen isosteric heats of adsorption using the Clausius ÐClapeyron equation as part of the characterization procedure; they also found that these activated carbons can adsorb up to 150 volumes of gas at STP per container volume at 3.5 MPa. Supercritical adsorption of Xe on ACFs has been studied by Aoshima et al.[290] The authors compared N2 adsorption isotherms with the isotherms obtained for Xe, both vapor and supercritical. They showed that the Dubinin micropore Þlling mechanism adequately describes Xe adsorption when it is a vapor. The isotherms of supercritical Xe conformed to the Langmuir equation. They also found that the isosteric adsorption heat for Xe was greater than the vaporization enthalpy by more than 12 kJ/mol, suggesting that Xe atoms are stabilized in the form of a cluster in micropores even at 300 K. Carbon aerogels prepared by pyrolysis of organic aerogels have attracted attention recently for their structural properties. The aerogel consists of a 3D structure made of interconnected uniform carbon particles predominantly containing mesopores. Hanzawa et al.[291] analyzed N2 adsorption isotherms obtained on such aerogels, mainly based on the use of high-resolution as plots. They also analyzed the isotherm hysteresis using the Saam ÐCole theory, which produced a reasonable average pore size while the conventional pore analysis method led to unsatisfactory results. Recently, Wu et al.[292] reported an evaluation of predictive models for the afÞnity coefÞcient in the DR equation. Their proposed method is based on a QSAR model. As a Þrst step in the analysis, they deÞned a training set, which consists of a minimum number of adsorbates necessary to perform the evaluation (eight compounds covering Þve compound classes). In the second step, the afÞnity coefÞcients are determined from experimental isotherms on Norit R1 activated carbon. The next step is the assemblage of 45 physicochemical properties of the adsorbates in the training set. Finally, the model correlates these properties with their afÞnity coefÞcient. The authors validated the model using data from other sources for 40 compounds. They concluded that the predictive power of this model (M2 in Fig. 3.17) is better than the use of traditional methods based on parachors, molar polarizabilities, or molar volumes. They proposed the use of three parameters: molecular weight, van der Waals volume, and the calculated gas Ð solid interaction energy for a graphite model surface. Kaneko et al.[293] measured N2, NH3, H2O, and SO2 uptakes at different temperatures to characterize ACFs (PIT, from Osaka Gas Co.) subjected to air oxidation. They reported the isosteric adsorption heat for SO2 as a function of the oxidation temperature. The values obtained were between 34 and 36 kJ/mol and reached a maximum for a sample oxidized at ca. 600 K. More recently, authors
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Figure 3.17 Comparison between observed and predicted afÞnity coefÞcient (beta) by four methods. M2 is a reduced model based on molecular weight, van der Waals volume, and gas Ð solid interaction energy. (Reproduced from Wu et al.,[292] with permission from Elsevier.)
from the same group[294] proposed a new method to determine the absolute adsorbed amount for high-pressure gas adsorption that can also be employed to determine the isosteric adsorption heat. They called this the buoyancy-mediated method and argued that it is simpler than the adsorbed volume mapping method.[295] As an illustration, Fig. 3.18 shows the isosteric adsorption heat for methane on a pitch-based ACF with a micropore width of 0.7 nm. The values obtained range from 19 to 25 kJ/mol and almost coincide with results obtained from Monte Carlo computer simulations.[296] As the vaporization enthalpy for methane is 8.17 kJ/mol at the boiling point, the methane molecules conÞned in micropores are stabilized by 11Ð17 kJ/mol. The authors argued that this method can be applied to volumetric data if the density of the adsorbent is known.
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Figure 3.18 Isosteric adsorption heat of methane on an activated carbon Þber determined from the temperature dependence of the absolute adsorbed amount isotherm determined by the buoyancy-mediated method. (Reproduced from Murata et al.,[294] with permission from Elsevier.)
Knowledge of the porous structure of coal is important for understanding and optimizing practically all coal utilization processes. It is thus expected that a large amount of work has been done to elucidate this issue. Apparently, this is not the case. Radovic et al.[297] reported experimental and theoretical studies of adsorption and diffusion of CO2 and methane in coals of widely varying rank and concluded that many problems remain unresolved. They employed DubininÕs theory of volume Þlling of micropores to analyze the low-pressure CO2 adsorption isotherms. Tracer pulse chromatography in conjunction with an appropriate adsorption Ð diffusion model and129Xe NMR were also employed. No clear trends in surface area with coal rank were found, and no correlation appears to exist between coal rank and the average size of the slit-shaped micropores. They also found that the existence of an interconnected but highly constricted pore system imposes severe limitations on the use of quasi-equilibrium adsorption data to predict coalbed methane content and recovery rates. The authors found that neither a static volumetric technique nor a dynamic perturbation chromatography method allowed the achievement of true adsorption equilibrium using ordinary procedures. Clearly, a reliable practical method must be developed to overcome, or analyze, the activated diffusion problems. Gil and coworkers[298,299] employed the DR and DA equations to characterize the microporous properties of several materials, including activated carbons, using N2 adsorption at 77 K. They also reported the adsorption energy distribution functions obtained from the employed equations (a more detailed
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study using this approach has been reported recently by Terzyk et al.[300]). They found that the pore size distributions obtained with their method exhibit the same maxima as those based on the Horvath ÐKawazoe model; however, the distributions have different shapes. This could be due, according to the authors, to the fact that the HorvathÐ Kawazoe model is based on the adsorption energy thus giving more importance to smaller pores. Nitrogen adsorption data were employed by Carrott and Carrott[301] to evaluate the method developed by Stoeckli to estimate the micropore size distribution.[302] This method uses the DA equation with experimental data that involve the calculation of the characteristic energy. They investigated the porosity of a series of activated charcoal cloths, and concluded that StoeckliÕs method gives reasonable and internally consistent semiquantitative micropore size distributions. Floess et al.[303] determined the surface area, micropore volume, and isosteric heat of N2 adsorption on microporous carbons at different burn-off levels. They calculated the isosteric heat using a virial expansion of the isotherm, and then derived the isosteric heat from the HenryÕs law constant. The results obtained correspond to adsorption on heterogeneous surfaces. At high surface coverage, the adsorption heat approached the enthalpy of vaporization, as could be expected. High-temperature isotherms of CF4 and SF6 have been employed by Jagiello et al.[304] to characterize two commercial microporous carbons: Carbosieve G (Supelco) and Maxsorb (Kansai Coke and Chemicals Inc.). They extracted the information based on three levels of analysis with increasing number of assumptions. The Þrst level begins with the isosteric adsorption heat obtained from the isotherm temperature dependence. Figure 3.19 illustrates the dependence of the obtained adsorption heats on the adsorbed amount; it indicates that the average gas Ðsolid potential is higher for Carbosieve G. The heats obtained allow a qualitative comparison of adsorption energetics by means of detailed adsorption energy distribution functions for different carbons. The micropore size distributions are then calculated from the energy distributions assuming that the adsorption energy of molecules conÞned in micropores is determined by their size and geometry. The authors also showed that the results obtained depend on the gas Ð solid interaction parameters and pore wall thickness. They supported their analysis using independent data obtained from a chromatographic method based on the size exclusion effect. Cao and Sircar[171] also measured SF6 adsorption on both microporous and mesoporous adsorbents including two activated carbons, but only calorimetric heats were reported; these results have been discussed in Section 3.3.1.1. Adsorption of different probes to characterize activated carbons has also been employed by Molina-Sabio et al.[305]: N2 at 77 K, CO2 at 251, 273, and 298 K, and SO2 at 262 and 273 K. They interpreted their results based on the assumption that the gas Ðsolid interactions in the case of SO2 are weaker (as could be inferred from the lower adsorbed amounts at the same relative pressure)
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Figure 3.19 Isosteric adsorption heats of CF4 and SF6 on two activated carbons (G, Carbosieve G; M, Maxsorb) calculated from an adsorption model (solid lines) and from nonparametric regression (dotted lines). Error bars represent standard deviations of the calculated values. (Reproduced from Jagie··o et al. [304] Copyright 1996 American Chemical Society.)
than those of N2 and CO2 because of the strong gas Ð gas interactions in SO2 bulk gas phase. Mangun et al.[306] studied the adsorption of SO2 on ammonia-treated ACFs. They calculated the adsorption energies from the DR equation and found that they increase linearly with the nitrogen content of the Þbers. Water and methanol adsorption at ambient temperature were employed by Salame and Bandosz[307,308] to characterize some wood-based activated carbons (WVA and UMC, both from Westvaco) and their oxidized counterparts. Using the virial expansion formalism, the authors calculated the isosteric heats of adsorption and showed that the values obtained are affected by surface chemical heterogeneity only at low surface coverage. They also found that, at high surface coverage, the heat of water adsorption was equal to the heat of condensation (45 kJ/mol), while for methanol the isosteric heat was always greater than the heat of condensation. They concluded that the differences in uptake of water and methanol at low relative pressures are related to different adsorption mechanisms. The effects of pore size and volume are more pronounced in the case of methanol, whereas water adsorption is mainly governed by surface chemistry at low relative pressure. In fact, when methanol is adsorbed in pores of small diameter, the density of surface groups is reduced and the adsorption is governed by dispersive interactions and the heat of adsorption is larger, up to 10%, than the
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271
condensation heat of pure methanol. On the contrary, water molecules tend to form small clusters acting as nucleation centers and the water Ðwater interactions dominate the process producing a heat of adsorption equal to the condensation heat of pure water. When the pore size increases, there are more surface groups and methanol shows a monotonically decreasing heat of adsorption, as for any heterogeneous surface. Similar results, with respect to water adsorption, have been obtained by Qi et al.[309] using BPL-activated carbon (Calgon Carbon Corp). The isosteric heats obtained as a function of surface coverage were characteristic of adsorption on heterogeneous surfaces and all the proÞles approached the heat of condensation at the saturation limit. Miura and Morimoto[310] employed water adsorption to characterize the effect of O3 treatment on a hydrogenated surface of natural (Sri Lanka) graphite. They measured both the water adsorption isotherm and the amount of gas desorbed on heating the sample. In agreement with results from several other studies[311 Ð 317] they concluded, based on the analysis of the adsorption isotherms and the heat of adsorption proÞles, that water adsorption is governed by the surface chemistry of the adsorbent. The isosteric adsorption heat of water as a function of surface coverage showed a minimum (Fig. 3.20); when the monolayer is almost completed it became constant and equal to the heat of condensation. This proÞle is characteristic of adsorption on a ßat surface. The ozone-treated sample
Figure 3.20 Isosteric adsorption heats of water on graphite, hydrogenated at 1273 K (dotted circles) and then ozone-treated and degassed at 298 K (open circles), 773 K (half-solid circles), or 1273 K (solid circles). Arrows indicate the monolayer capacity, Vm (solid line), H2O content (dashed line), and CO2 content (dotted line). (Reproduced from Miura and Morimoto.[310] Copyright 1994 American Chemical Society.)
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degassed at the lowest temperature (298 K) was an exception (open circles in Fig. 3.20); the proÞle was identical to that obtained for a heterogeneous surface (monotonic decrease until the heat of condensation is reached). The authors explained the observed effects based on the presence of different oxygenated species on the adsorbent surface. Jagiello et al.[318] studied the adsorption, at temperatures near ambient, of CH4, CF4, and SF6 on three CECAs: Carbosieve G (Supelco), Maxsorb (Kansai Coke and Chemicals, Ltd.) and a Westvaco carbon identiÞed as W. The isotherms were reduced using a virial-type equation. Table 3.5 gives the isosteric adsorption heats obtained for all the systems studied, which show the behavior expected for heterogeneous surfaces. Westvaco and Maxsorb carbons exhibit similar isosteric heats for each adsorbate, while Carbosieve has the largest heats for each adsorbate because it has smaller pores than the other solids. The authors concluded that the isosteric heats provide an important basis for differentiating between the micropore structures of different carbon samples. Their analysis is based on the adsorption potential enhancement within a pore, which will produce increasing isosteric heats as the pore size approaches the molecular size thus introducing a difference between solids of the same chemical nature but with different pore size distribution. Simpson et al.[319] studied the adsorption properties of a new type of polymer (modiÞed polystyrene) using nitrogen and 11 volatile organic compounds (VOCs). The work included an activated carbon sample (ACF400, from Calgon). They obtained isotherms from the gas and vapor phase and, in some cases, they studied adsorption from aqueous solution. An interesting result concerns the comparison of results from gas, vapor, and liquid phases based on PolanyiÕs adsorption potential analysis. When the curves for gas- or vapor-phase adsorption did not coincide with that obtained for the liquid phase, the authors assigned the difference to a competitive (soluteÐ solvent) adsorption process. Figure 3.21 shows the Polanyi potential characteristic
Table 3.5 Isosteric Adsorption Heats (qst) of CH4, CF4, and SF6 on Several Activated Carbons qst (kJ/mol)
Activated carbon
CH4
CF4
SF6
Vmic (cm3/g)
Westvaco W Carbosieve G Maxsorb
19.5 23.5 18.2
21.1 28.3 21.9
30.5 41.5 31.8
0.47 0.56 0.76
Note: Vmic is the micropore volume calculated from N2 adsorption using the DR method. Source: Adapted from Jagie··o et al. [318] Copyright 1995 American Chemical Society.
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Figure 3.21 Comparative Polanyi potential characteristic curves for aqueous and vapor phases, including data for nitrogen adsorption at 77 K and vapor phase 100% relative humidity (RH) prediction for activated carbon ACF400. (Reproduced from Simpson et al.[319] Copyright 1996 American Chemical Society.)
curves for aqueous and vapor phases from the regression of data for all (11) sorbates studied in each individual phase for activated carbon ACF400; this Þgure also includes data for nitrogen adsorption at 77 K and for the vapor phase at 100% relative humidity predicted for the same sorbent. The authors calculated the isosteric heats using the Clausius Ð Clapeyron equation, and found that the values obtained corresponded to adsorption on a heterogeneous surface. At the saturation limit, however, they obtained values that were lower than the heat of condensation. They hypothesized that a certain amount of energy is needed to produce a ÒholeÓ in the polymer matrix for the entrant molecule to become absorbed. If this energy is not available, the adsorbate Ðadsorbent interaction is weak resulting in a lower adsorption heat. Choung et al.[320] have reported adsorption data for toluene on polymeric adsorbents. Their results show a contrasting behavior of the isosteric adsorption heat of carbon adsorbents: the calculated values (using the Clausius Ð Clapeyron equation) increased continuously with surface coverage. In fact, even at low surface coverage the isosteric heat was twice the enthalpy of vaporization (33.18 kJ/mol at the boiling point or 38.01 kJ/mol at 298 K). Unfortunately, the authors did not study further this intriguing behavior and simply attributed these results to surface heterogeneity, which is doubtful. Adsorption of halogenated organic compounds on carbonaceous materials has been studied on several occasions,[321 Ð 324] mostly by determining the isosteric heat of adsorption using the Clausius Ð Clapeyron equation. Yun et al.[325] studied the adsorption equilibrium of chlorinated hydrocarbons (dichloromethane, 1,1,1-trichloroethane, and trichloroethylene) onto an activated carbon
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(Xtrusorb-600 in pellets, from Calgon Carbon Co.). They employed classical static adsorption volumetry as the experimental technique to obtain the data. They calculated the isosteric adsorption heats using the Clausius ÐClapeyron equation, and the values obtained were twice the enthalpy of condensation, in agreement with the behavior previously mentioned for other adsorbates. The HenryÕs law constants obtained from the experimental data showed a good linear correlation with reciprocal temperature, and they were employed to determine the adsorption afÞnity of the adsorbates. The isosteric heats extrapolated at zero coverage, obtained from HenryÕs law constants, were 25.13 kJ/mol for dichloromethane, 61.17 kJ/mol for 1,1,1-trichloroethane, and 39.21 kJ/mol for trichloroethylene. Mariwala et al.[326] reported the isotherms of 16 halocarbons to characterize the surface of a carbon molecular sieve using standard procedures. From a comparison with N2 adsorption results it was concluded that the state of adsorbed C1 halocarbons is bulk liquid-like. Moon et al.[327] studied the adsorption of CFC-115 on a powdered activated carbon (Aldrich) impregnated with Pd or not impregnated. They calculated the isosteric adsorption heat (using the Clausius ÐClapeyron equation) and found that it increased with surface coverage, at least up to the highest coverage obtained (80% of a monolayer). They also found that the isosteric heat was of the same order of magnitude as the condensation heat, and that the experimental isotherms could be represented well using the BET model. The same behavior has been reported [328] for several chloroßuorocarbons adsorbed on zeolites NaY, KY, and CsY. The explanation given by the authors is the obvious one, since an increasing isosteric heat proÞle is indicating that lateral interactions are repulsive. Akkimaradi et al.[329] studied the adsorption of 1,1,1,2-tetraßuoroethane on three commercial activated carbons (Chemviron, Fluka, and Maxsorb). They found a linear concentration dependence of the adsorption enthalpy, obtained with the Clausius ÐClapeyron equation, (Fig. 3.22); the isosteric adsorption heat was higher than the vaporization enthalpy. Notice in Fig. 3.22 the monotonically increasing trend for Maxsorb,
Figure 3.22 Loading dependence of enthalpy of adsorption. Squares, Chemviron; solid circles, Maxsorb; triangles, Fluka. (Reproduced from Akkimaradi et al.[329] Copyright 2001 American Chemical Society.)
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which the authors associated with heterogeneous molecular interactions due to a large micropore area. The conclusion was that Maxsorb carbon is energetically more heterogeneous than the other two. Moon et al.[330] reported on the adsorption of chloropentaßuoroethane and pentaßuoroethane on activated carbon pellets (Norit B4). The calculated isosteric heats (using the Clausius ÐClapeyron equation) were approximately twice the heat of condensation in agreement with the behavior found for other similar systems.[327 Ð 330] Ritter and coworkers[331,332] studied the adsorption of the n-alkane series C1 to C7 on a commercial activated carbons (BAX-1100 from Westvaco). They employed wide temperature (293 Ð 393 K) and pressure ranges and found that the experimental data could be represented by a single characteristic curve. They developed a new potential theory approach, based on a multisegment Gaussian distribution, to calculate the total pore volume and the pore size distribution. The isosteric adsorption heats were calculated using the Clausius Ð Clapeyron equation and a stepwise regression model. Based on a statistical analysis of the experimental data, they concluded that the use of the Clausius Ð Claperyon equation could overlook the temperature dependence of the isosteric heats. This method provides an alternative for the indirect estimation of the isosteric heat from the statistically smoothed dependence of the logarithm of the pressure on the temperature at Þxed adsorbed amounts. Prasad et al.[333] reported adsorption data of diethylsulÞde on activated carbons of different grades (40, 50, 60, and 70 CTC) and a coconut shellderived carbon. They mainly studied the adsorption kinetics and determined the gas Ðsolid interaction coefÞcient from an empirical relationship between the amount adsorbed and time.[334,335] Their results showed no differences between the activated carbons, fresh or impregnated with different metal compounds, the value of the interaction parameter being equal to 0.76 + 0.05. They found that chemisorption, even though it was present, was not important. In what follows we shall summarize selected experimental studies done using adsorption of different gases on carbon nanotubes, with special emphasis on adsorption energetics. Jagtoyen et al.[336,337] employed standard techniques of N2 adsorption to characterize the porosity of carbon nanotubes. Yang et al.[338] also employed N2 adsorption to characterize the porosity of carbon nanotubes, and when comparing these papers a very different conclusion with respect to the size of the pores can be drawn. The latter authors recognized that these differences are due to problems in the puriÞcation of the samples and to the presence of impurities. He adsorption results at low temperature (2 Ð 14 K), which have been reported quite recently,[339] show a proÞle of the isosteric adsorption heat as a function of the amount adsorbed very similar to the one obtained for a heterogeneous surface (this means a steady decreasing heat tending to the bulk vaporization heat). Carbon nanotubes have attracted the attention of many adsorption researchers due to their potential use for hydrogen storage. For example, Tibbetts et al.[340] compared the hydrogen storage capacity of carbon nanotubes with that of carbon
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Þlaments and vapor-grown carbon Þbers. They concluded that a maximum capacity of 1% by weight, at ambient temperature, cannot be improved and, if reported, it should be due to experimental errors. Dillon and Heben[341] have reviewed much of the work done on hydrogen storage using all types of carbon adsorbents and concluded that, due to the low interaction energy and the lack of very narrow micropores where the interaction potential is enhanced, these materials do not seem to be suitable for hydrogen storage, and that much research is needed to overcome this limitation. Studies of hydrogen adsorption on carbon nanotubes have also been performed by Hirscher et al.,[342] Pradhan et al.,[343,344] and Bernier et al.[345] Yang and Yang[346] performed ab initio calculations of mostly chemisorption of atomic hydrogen on graphite (see also Lu and Sun[347]) with the aim to relate such results with the hydrogen storage capacity of carbon nanotubes. These results will be further discussed in ÒResultsÓ in Section 3.3.3.3. Wilson et al.[348] reported experimental isotherms of H2 and D2 on carbon nanotube bundles. They studied physisorption above 77 K to investigate the high-energy binding sites, and below 45 K to characterize the adsorption on the outside surface of the bundles. They also obtained N2 and Ar isotherms as references.[349] They calculated the isosteric adsorption heats (using the Clausius Ð Clapeyron equation) corresponding to grooves between the tubes (9 kJ/mol for D2 and 7 kJ/mol for H2) and on the bundle external surface. They found that the adsorption energy in the grooves is approximately twice the value at the outer surface. In contrast, Kostov et al.[350] reported a value of 18.9 kJ/mol for the adsorption heat of hydrogen on the external surface of single-wall carbon nanotubes (SWNT). It is evident that when using ab initio methods very different results are obtained depending on the way the calculations are performed. The cohesive energy of SWNT has been studied in relation to H2 adsorption by Ye et al.[351] They employed crystalline ropes of SWNT and found that the uptake exceeded 8% by weight, which is the highest capacity of any carbon material. They concluded that H2 is Þrst adsorbed on the outer surfaces of the ropes; then at pressures ca. 40 bar at 80 K a phase transition occurs where there is a separation of the individual SWNT, and hydrogen is physisorbed on their exposed surfaces. The pressure at which this phase transition occurs allowed them to estimate the cohesive energy of the material (ca. 0.5 kJ mol21/C atom) from the chemical potential associated to the phase transition, since it is closely related to a larger separation between the tubes in an individual rope. Cao et al.[352] demonstrated that the intertube space between densely aligned carbon nanotubes largely contributes to the H2 adsorption capacity. They estimated the maximum capacity at 2.4% by weight. As can be appreciated, the question of H2 uptake in SWNT remains unanswered and there continues to be no agreement among the different authors. The isosteric heat of N2 adsorption on closed nanotubes has been determined by Yoo et al.[353,354] over a wide temperature range from the Clausius Ð Clapeyron equation. It initially increases with surface coverage, passes through a maximum (ca. 9 kJ/mol) and then steadily decreases. Nevertheless, this
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277
maximum value seems to be rather low when compared with estimates from computer simulations,[355] 17Ð 18 kJ/mol, and from experiments,[356] 19.6 kJ/mol. One reason for this could be the small separation between the isotherms employed to calculate the isosteric heat, which increases the uncertainty of the calculation.[55] Yang et al.[357] reported the pore size distributions of multiwall carbon nanotube samples determined with N2 adsorption using standard techniques. Nevertheless, the observed porosity must be taken with caution because it can be due to impurities present in the sample.[355] One important aspect in the use of carbon nanotubes concerns the purity degree of the samples employed. Since it is not an easy task to obtain puriÞed samples without a great loss of material and/or without opening the tubes, the puriÞcation method has become a critical point when comparing experimental data. For example, Bougrine et al.[358] claimed that carbon nanotubes could be puriÞed by simply heating the sample in Ar atmosphere at 1873 K. They followed the puriÞcation process by determining very precise Kr adsorption isotherms combined with other techniques. Unfortunately, such results have not been reproduced yet in other laboratories.[355] According to a recent review of the potential applications of carbon nanotubes in hydrogen storage,[359] puriÞcation is nowadays the bottleneck for practical application of nanotubes, especially when large amounts of material are required. Nisha et al.[360] reported data on ethanol adsorption on single-wall carbon nanohorns (horn-shaped, single-wall graphene sheets, in the form of sheath aggregates). The adsorption capacity was larger than that of activated carbons. They also found that the nanohorns catalyze the decomposition of ethanol into acetaldehyde and that this material could also be very useful as a carbon support to achieve high metal dispersions. Peng et al.[361] reported the isosteric adsorption heat for 1,2-dichlorobenzene on carbon nanotubes from aqueous solutions. The value obtained for the as-grown nanotubes was 16.4 kJ/mol, and 5.9 kJ/mol for a sample heated for 2 h in N2 atmosphere at 2473 K. Weber et al.[362] studied methane adsorption on SWNT bundles over a 40 K range. They employed the Clausius Ð Clapeyron equation. The calculated binding energy was 21.4 kJ/mol, which is larger than the corresponding value for methane adsorbed on a planar graphite surface (12.1 kJ/mol). The same difference was found[363] for Xe adsorption on carbon nanotube bundles compared with adsorption on graphite. In a subsequent paper, Talapatra and Migone[364] reported a more detailed analysis of the isosteric heat of methane adsorbed in carbon nanotube bundles. The heat decreased with increasing surface coverage like in the case of heterogeneous materials. Bienfait et al.[194] studied the mobility of methane adsorbed on carbon nanotubes using quasi-elastic neutron scattering. They characterized the state of the adsorbed Þlm on two types of sites having different adsorption energy:[192] 18.3 and 11.2 kJ/mol. They concluded that the strongly bound molecules are immobile below 120 K, whereas the ones adsorbed on the weaker sites are in a viscous liquid state between 70 and 120 K. Below 90 K the mobile component progressively solidiÞes, and it completely disappears
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at 50 K. Muris et al.[365] completed the characterization of the adsorption process for Xe, CF4, and SF6 on SWNT, and the dependence of the adsorption properties on the nanotube morphology was reported by Masenelli-Varlot et al.[366] The former authors[365] reported the isosteric heats for all the gases studied, plus methane. Their results are summarized in Table 3.6. A comparison with the respective isosteric heats for graphite, also shown in Table 3.6, indicated that this magnitude is systematically smaller for all the adsorbates. As the nanotubes were closed on both ends, this was attributed to the convex external nanotube surface and to the fact that only one graphene plane would be involved in the interaction (instead of several in the case of graphite). Adsorption of binary or more complex gas mixtures on carbons has deserved much attention because of the potential applications to gas separation, particularly when using activated carbons as adsorbents. (A general basic introduction to the study of adsorption separation processes can be found in RuthvenÕs book.[367]) Thus, Costa et al.[368] reported the calculation and prediction of activity coefÞcients for mixtures of several hydrocarbons (methane, ethane, ethylene, and propylene) adsorbed on an activated carbon (AC-40, Compan÷«õa Espan÷ola de Carbones Activos). Van der Vaart et al.[369] studied the adsorption of mixtures of CO2 and CH4 on a commercial microporous activated carbon (Norit RB1). They analyzed the experimental data using the IAST and found only moderate agreement. They concluded that new solution models including nonideal behavior and surface heterogeneity should be developed. Siperstein et al.[370] found that the mixture of ethylene and ethane shows a nearly ideal behavior when adsorbed on carbon, and it exhibits moderate negative deviations from ideality on a zeolite. They explained the deviations by a difference in the quadrupole moments of the molecules (ethane lacks a quadrupole moment). The diffusion process of gases in molecular sieve carbons was reviewed long ago by Walker et al.[371] The authors focused their investigation on activated diffusion with brief comments on bulk and Knudsen diffusions. They also presented a theoretical analysis of the problem including the calculation of gas Ð solid interaction energies.
Table 3.6 Isosteric Adsorption Heats (qst) of Several Gases on Single-Wall Carbon Nanotube Bundles Adsorbate CH4 Xe CF4 SF6
Temperature range (K)
qst (nanotubes) (kJ/mol)
qst (graphite) (kJ/mol)
95Ð 110 90Ð 130 92Ð 103 130Ð 150
11.1 15.7 15.3 17.2
14.9 21.5 19 22.6
Source: Adapted from Muris et al.[365] with permission from Elsevier.
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The kinetic aspects of adsorption of single gases or multicomponent mixtures have been addressed as well; for example, Rege and Yang[372] studied the kinetic separation of oxygen and argon using a carbon molecular sieve (BergbauForschung). Reid et al.[373] studied the kinetic selectivity of a commercial carbon molecular sieve (Air Products and Chemicals) for air separation. They determined the isotherms for N2, O2, neon, argon, and krypton at different temperatures to calculate the HenryÕs constant at each temperature and then calculate the isosteric heat of adsorption from the constantÕs variation with temperature. The resulting values were 23.9, 18.6, and 18.3 kJ/mol for N2, O2, and argon, respectively. They also included a complete set of tables summarizing the virial analysis done. In a subsequent paper, Reid and Thomas[374] employed the same method to study the size exclusion properties of probe molecules for the selective porosity of a carbon molecular sieve used in air separation. Again, they included complete sets of tables summarizing the virial analysis. The isosteric heats obtained for the adsorption of methane, ethylene, chloroform, carbon tetrachloride, pyridine, and benzene are summarized in Table 3.7. It can be noticed that the values obtained are systematically larger than the vaporization enthalpies. In some instances commented upon earlier, the same effect was observed, even though in this case it is more marked for methane and ethylene. 3.3.2.2.
Inverse Gas Chromatography (IGC)
IGC is an extension of traditional gas chromatography in which the material to be investigated is packed into a gas chromatographic column. The technique involves injecting a series of volatile probes and measuring their retention volumes. Retention volume is related to the interaction between the probe and the solid and it can be converted into a number of surface thermodynamic properties. Through an adequate choice of the probe molecules to be adsorbed,
Table 3.7 Isosteric Adsorption Heats (qst) Measured for Several Gases and Vapors on a Carbon Molecular Sieve Employed in Air Separation Adsorbate
qst (kJ/mol)
DHvap (kJ/mol)
Methane Ethylene Chloroform Carbon tetrachloride Pyridine Benzene
23.8 + 1.1 50.1 + 1.5 44.7 + 1.6 44.1 + 2.8 47.6 + 0.9 41.8 + 1.5
8.19 13.53 31.28 32.43 40.21 33.83
Note: The vaporization enthalpies are included for comparison (see text). Source: Adapted from Reid and Thomas.[374] Copyright 2001 American Chemical Society.
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it is possible to obtain information about the surface structure and/or surface chemical functionality of carbon adsorbents. This technique is applicable to a wide variety of materials.[375 Ð 377] In this section, we discuss results as closely as possible connected with the fundamental aspects of the energetics of physical adsorption on carbons. The basic principles of IGC have been described by several authors.[378 Ð 381] The isosteric adsorption heat and the integral adsorption entropy are derived from the retention volume. Both quantities are given by the following expressions: VN qst ln þ ln R þ ln A þ Ks,o ¼ T RT
(3:99)
and DS o ¼
0 qst p VN þ R þ R ln þ R ln T P A
(3:100)
Here A is the adsorbent surface area and the term including p0 and P is related to the reference standard state; thus p0 ¼ 101 kN/m (1 atm) and P ¼ 0.338 mN/m (arbitrarily proposed by de Boer[45]). Replacing these values in Eq. (3.100), it takes the Þnal form: DS o ¼
qst cal VN þ 31:61 þ R ln mol deg T A
(3:101)
Equations (3.99) and (3.101) can be employed to calculate the isosteric heat and entropy of adsorption if the retention volumes are independent of the injection amount, because this behavior is a condition for linear chromatography.[382] This condition is identiÞed by performing injections with different amounts of adsorbate and verifying that the maxima of the obtained peaks are located in the same position. It is recommended that peaks without tails should be employed to perform the calculations. It is also necessary to verify that the retention volume is not a function of the ßow rate. When this condition is achieved, the system is in thermodynamic equilibrium.[383] The high sensitivity of chromatographic detectors makes it possible to work under inÞnite dilution conditions (zero surface coverage); this means that very small amounts of adsorbate are injected and the adsorption data obtained are in the HenryÕs law regime. This is the condition at which IGC is most often employed and where it is a technique of choice to determine trueadsorption-equilibrium thermodynamic magnitudes; however, one must keep in mind that, in the frequent case of heterogeneous solids, the information obtained will be restricted to the most energetic sites. Grajek and coworkers have recently contributed to improvements in heat of adsorption determination[384] and porosity characterization[385,386] by IGC. Sun and Berg[387] have recently addressed the
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determination of surface energy of heterogeneous solids by IGC, and concluded that both high-energy and low-energy patches are sampled even at inÞnite dilution. Alternatively, working under Þnite concentration it is possible to obtain the entire adsorption isotherm by IGC. Bogillo et al.[388] have discussed the calculation of adsorption free energy and adsorption energy distribution functions for heterogeneous solids from IGC data at Þnite concentration. For the evaluation of speciÞc adsorbate Ðadsorbent interactions from IGC data using polar probe molecules, various methods based on partial pressures,[389,390] London dispersive components,[391] heats of vaporization[392] or Ko«vats indices[393] of the probes have been proposed. The method developed by Donnet et al.,[394] based on the polarizability of the probes, seems to be the most widely accepted to date. The versatility of IGC for very different types of adsorbates facilitates comparisons of the interactions of a material with very different probe molecules, often in the same paper. Therefore, unlike other sections of this review where the nature of the adsorbate deÞnes the sequence followed to present the results, this section will be arranged according only to the type of carbon adsorbent of concern, from more homogeneous to more heterogeneous (i.e., in approximately decreasing degree of structural order). Natural graphite (from Madagascar) was the substrate used by Donnet et al.[394] to develop their method for evaluation of speciÞc adsorbateÐ adsorbent interactions alluded to earlier. Prior to this, Donnet et al.[395] studied by IGC the effect of plasma treatment on natural (Madagascar and Kropfmu¬hl) graphites. Microwave plasma treatments signiÞcantly increased both the dispersive component of surface energy and/or the acid Ðbase character of this material, depending on the nature of the vapors used to generate the plasma. More recently, Thielmann and Pearse[396] have determined surface heterogeneity proÞles from isotherms measured at Þnite concentration on synthetic graphites (E-graphite, Richard Anton; Thermocarb TC-300, Conoco). Molecules with different acid Ð base character (hexane, acetone, and ethanol) were used, allowing discrete energy levels to be distinguished. The IGC technique has been employed extensively to characterize different aspects of the surface structure and chemistry of carbon Þbers, either fresh[397] or after surface modiÞcation treatments aimed at improving their adhesion to polymeric matrices in composites.[398,399] Vukov and Gray[400] studied the adsorption at zero surface coverage of n-alkanes on high-modulus (P-55) and high-strength (T-300) carbon Þbers (both from Union Carbide Co.). Their results indicated that both types of Òas receivedÓ Þber are low-energy surfaces for the adsorption of n-alkanes. Desorption of physically adsorbed species, like CO2 and H2O, resulted in signiÞcant increases in adsorption heat and in the London component of the surface free energy. This shows that the high-energy sites were occupied by physically adsorbed gases and emphasizes the importance of properly cleaning the Þber surface prior to IGC characterization. Nardin et al.[401] used IGC to
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compare the characteristics of carbonized and stabilized carbon Þbers (Ashland Petroleum Company). The dispersive component of the surface energy was independent of the nature of the Þbers. However, they differed in surface acid Ðbase character, as the carbonized Þbers exhibited basic character whereas the ones stabilized (which contained 14 wt.% oxygen, vs. only 1 wt.% for the carbonized Þbres) were more amphoteric. This higher oxygen (and also hydrogen) content was ascribed to hydroxyl groups, which would be responsible for the increased acceptor character of the stabilized Þbre surface. Pogue et al.[402] investigated the surface energy of vapor-grown carbon Þbers following solvent washing, air oxidation, and sililation treatments. The Þbers modiÞed by oxidation exhibited a decrease in the dispersive surface energy component, as expected, as well as an increase in the acidity of the surface. Industrial carbon Þbers (Tenax, Akzo Nobel) have been characterized by van Asten et al.[403] These authors questioned the validity of results for the dispersive component of the surface energy when the adsorption area for the adsorbed n-alkane molecule was estimated from parameters of the corresponding liquid. They argued that meaningful Gibbs energy values for the acid Ðbase interaction were obtained only with the polarizability concept of Donnet et al.[394] They obtained accurate enthalpy data from the temperature dependence of the Gibbs acidÐ base interaction energy; however, no clear relationship between this enthalpy and the acceptor and donor numbers[404] of the probes could be established. Montes-Mora«n et al.[405] investigated the effects of oxygen plasma treatment of ultrahigh-modulus, pitch-based, and high-strength, PAN-based carbon Þbers on their surface chemical characteristics and the mechanical properties of their composites. Figure 3.23 shows the relationship between the interfacial shear strength in composites with a polycarbonate matrix and the adsorption enthalpy of three polar probes on fresh and plasma-treated carbon Þbers. Acceptable correlations were found only for the interactions with diethyl ether (basic) and acetone (amphoteric), in good agreement with the basic character of the polycarbonate matrix. It was therefore concluded that the increase in concentration of acidic Ð amphoteric surface functional groups induced by plasma treatment is the main reason for the improvement of Þber Ð matrix adhesion. Interfacial characterization of carbon Ð epoxy composites prepared from the same Þbers[406] conÞrmed the beneÞcial effect of plasma treatment. The same group investigated in greater detail the degree of heterogeneity brought about by different extents of oxygen plasma treatment onto highstrength, PAN-based carbon Þbers. The differential adsorption heats for n-alkanes[407] on fresh and plasma-treated samples exhibited values typical for n-alkanes adsorbed on the basal plane of graphite. However, the dispersive component of the surface tension systematically increased upon plasma oxidation; this effect was attributed to generation of high surface energy sites responsible for trapping of n-alkane molecules. The authors ruled out any effect of textural changes, which did not take place during the oxidation process as revealed by
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Figure 3.23 Relationship between the interfacial shear strength (t) in carbon Þber Ð polycarbonate composites and the enthalpies of adsorption of (a) nitromethane, (b) diethyl ether, and (c) acetone on the corresponding carbon Þbers, fresh and plasmatreated. (Reproduced from Montes-Mora«n et al.,[405] with permission from Elsevier.)
CO2 adsorption isotherms. Adsorption of polar probes with different acid Ð base characteristics on the same materials[408] showed increases in the speciÞc free energy of adsorption of acidic, basic, or amphoteric probe molecules, indicative of creation, upon plasma treatment, of surface functionalities with various acid Ð base strengths. The effects of sizing agents on the surface properties of carbon Þbers have also been investigated by IGC. Rubio et al.[409] found no differences in the dispersive component of surface free energy when different types of sizings were applied to the same type of carbon Þber. In contrast, Montes-Mora«n et al.[410] compared the surface properties of PAN-based carbon Þbers covered or not covered with different amounts of an unknown sizing agent and reported that the presence of the sizing strongly reduced the surface energy of the Þbers as measured by adsorption of n-alkanes. Both studies agreed in showing that sized carbon Þbers had a clearly basic character.[409,410] Nevertheless, the surface properties of sized Þbers are expected to be dominated by the properties of the sizing material itself (usually a polymer), and this falls ouside the scope of this review. Also outside our scope are high-performance polymeric Þbers such as aramid Þbers, which are mentioned here only because of their close parallelism with carbon Þbers. The effects of sizings/plasma treatment on the surface of poly( p-phenylene terephthalamide) (Kevlar 29, Du Pont)[411] and poly( p-phenylene benzobisoxazole) (PBO, Toyobo)[412] or the effect of
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crystallinity degree on the surface energetics of poly(m-phenylene isophthalamide) (Nomex, Du Pont)[413] have been investigated by IGC, and the interested reader is referred to the respective papers. Carbon black is the next type of carbon material to be considered. Wang et al.[381] reviewed in 1993 the work carried out on surface energy of carbon blacks as characterized by IGC. Papirer et al.[414] determined the adsorption energy distribution function for several commercial carbon blacks (Spheron 6 and N347 from Cabot; N110 and N326 from Degussa) from data obtained by IGC at Þnite concentration. The adsorbates employed were n-alkanes and benzene. The isosteric heat proÞle as a function of surface coverage was characteristic of a heterogeneous surface; nevertheless, it did not approach the vaporization enthalpy value in a monotonic manner. From the isotherms they calculated the adsorption energy distribution function and their main conclusion was that a single-peak distribution seemed inadequate to describe the heterogeneity of the studied materials. More recently, Donnet et al.[415] have used IGC at Þnite concentration to get an overall description of the surface energy sites distribution in a series of carbon blacks. Changing the nature of the probe molecules (n-hexane, n-pentanol, and n-pentylamine), different interaction behaviors with the carbon blacks were found, accounting for the evolution of the surface microstructure and/or chemical functions. Wang et al.[416] examined the effect of plasma treatments on the surface characteristics and activity of a graphitized carbon black using IGC at inÞnite dilution for a series of polar and nonpolar probes. They evaluated several thermodynamic properties including the adsorption energy distribution function; the surface chemistry of the samples was investigated using XPS. Papirer et al.[417] followed by IGC the chemical modiÞcations and surface properties of a series of carbon blacks (Degussa). The samples were subjected to different chemical treatments: moderate oxidation with potassium persulfate, severe air oxidation, halogenation, and grafting of short or long alkyl chains. They found that, under similar reaction conditions, these carbons exhibit different behaviors depending on their mode of preparation. However, as expected, they have in common the reactivity dependence on their peculiar surface structure, being very heterogeneous as far as the distribution of active sites is concerned. IGC detected the most active sites and allowed to monitor the variation of surface properties upon chemical modiÞcation of the blacks. Mastrogiacomo and Pierini[418,419] have characterized graphitized carbon blacks (Carbograph 4 and Carbograph 5, from LARA) using IGC of a series of n-alkanes and benzene. The obtained isosteric heats and entropies of adsorption were interpreted in connection with the use of these materials in analytical separations. The variations in surface area and surface heterogeneity of graphitized carbon blacks activated with air were also followed by IGC by Moreno-Castilla et al.[420] The temperature dependence of the HenryÕs law constant has been used to calculate the adsorption heat of nitrogen-containing heterocycles on graphitized
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carbon black[421] using IGC data and Eqs. (3.122)Ð (3.124). The value found for pyridine was 38.9 kJ/mol and the experimental value from other sources was 41.0 kJ/mol. The agreement was also very good in the case of pyrazine (37.0 kJ/mol) and 1,3,5-triazine (33.3 kJ/mol obtained by the authors and 35.0 kJ/mol from the literature). Papirer et al.[422] have comparatively studied the surface energetics of graphite, carbon black, and fullerene samples as measured by IGC at inÞnite and Þnite concentration conditions. Figure 3.24 compares the adsorption energy distribution curves for heptane on carbon blacks A and B (two different batches of FEF 550, from Columbian Carbon USA), graphite A (natural, from Madagascar), graphite B (KS250, Lonza), and C60 (Technocarbo). Carbon blacks and graphites show some similarity, with maxima at 18 Ð 19 kJ/mol (assigned to graphene layers) and 33Ð 34 kJ/mol (assigned to adsorption sites located on prismatic planes). For the fullerene, the maximum on the lowerenergy side (ca. 20 kJ/mol) was assigned to graphene-like structures and the second one to oxygenated surface sites (originating from oxidation of fullerene, as demonstrated by XPS). This result will be dealt with again in ÒAdsorption on fullerenes and carbon nanotubesÓ in Section 3.3.3.3 when discussing results of numeric simulations for adsorption on fullerenes. We shall now discuss papers on activated carbons. Carrott and Sing[423] used IGC to determine the heats of adsorption of C1 ÐC6 n-alkanes on microporous activated carbons. The maximum enhancement in adsorption energy, which was approximately twice that on nonporous carbons, corresponded to
Figure 3.24 Comparison of n-heptane adsorption energy distribution curves determined on different carbon materials. (Reproduced from Papirer et al.,[422] with permission from Elsevier.)
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samples with a homogeneous micropore structure (slit-shaped pores of ca. 0.43Ð 0.50 nm width). Later, the same authors[424] studied the adsorption of several hydrocarbons on a pitch-based superactivated carbon (AX21); their Þndings indicated a very high degree of interconnectivity of the micropore structure. Cao[425] investigated the adsorption of several n-alkanes and n-alkenes on microporous carbons (Carbosieve B and two charcoal cloths) with different porous structures. He found a decrease in adsorption heat as the pore size distribution of the adsorbent became broader. This trend was not observed with branched hydrocarbons because wider pores may be preferentially adsorbing bulkier molecules and the enhancement in the isosteric heat depends on the ratio of micropore width to adsorbate molecular diameter.[185] Jagiello et al.[426,427] and Bandosz et al.[428] used IGC to determine the dispersive component of surface energy and the adsorption enthalpies of n-alkenes on activated carbons from different sources oxidized with nitric acid. They established a correlation between the acidity of carbons and the energy of the speciÞc interactions with unsaturated hydrocarbons and argued that increasing surface acidity is reßected by an increase in the energy of the speciÞc interactions with p-electrons in n-alkenes. The authors concluded that this method probes the donor Ð acceptor nature of the surface of carbons and provides information complementary to that supplied by other methods (point of zero charge and Boehm titration), having less limitations.[428] The good correlation with Boehm titration prompted the authors to propose the usefulness of this procedure to characterize carbon surface chemistry for aqueous applications. Jagiello et al.[429] studied adsorption of several n-alkanes, 2-methylalkanes, and 2,2-dimethylalkanes on three microporous carbons of different origins and determined thermodynamic quantities by IGC at inÞnite dilution and Þnite concentrations. The enthalpy and free energy of adsorption were dependent on the carbon micropore structure. Bandosz et al.[430] studied the sieving properties of carbons obtained by template carbonization of polyfurfuryl alcohol within intercalated clay matrices.[431] They combined N2 adsorption with IGC (using probes of different molecular size) to characterize the textural and energetic heterogeneities, and concluded that the microporous texture is dependent on the size and structure of pillars, the water content, and the thermal stability of the matrix. The materials obtained exhibit interesting sieving effects for molecular sizes between 0.36 and 0.6 nm and can separate molecules with small differences in size such as methane, carbon tetraßuoride, and sulfur hexaßuoride, as well as normal and branched hydrocarbons. Salame et al.[432] used IGC and other techniques to analyze several problems concerning the adsorption of water on activated carbons (WVA 1100 from Westvaco, oxidized with ammonium persulfate or not oxidized) washed with methanol. They pointed out that, when certain chemical reactions are present (mostly ester hydrolysis), the isotherms cannot be employed to determine the isosteric adsorption heats due to irreversibility, non-equilibrium conditions, and the presence and adsorption of a second component (methanol).
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Bagreev and Bandosz[433] reported the determination of thermodynamic functions for H2S adsorption on a number of activated carbons (RB3 from Norit America; S208c from Waterlink Barnebey Sutcliffe; BAX 1500, WVA900, WVA-1100, and UMC from Westvaco; and two ÒcatalyticÓ carbons designed for H2S removal: Centaur from Calgon Carbon, and ROZ3 from Norit). The isosteric adsorption heats were close to or slightly higher than twice the values obtained on a ßat carbon black surface (20.9 kJ/mol). This fact was interpreted as indicative that adsorption is taking place in very small pores. Indeed, Fig. 3.25 shows the dependence of isosteric adsorption heat on average micropore size, Lmic , calculated using the approach of Stoeckli et al.[434] The isosteric heat was expected to be at a maximum for pores equal in size to the H2S molecule (0.42 nm), and then decrease as a result of a decrease in the adsorption potential[185] to a limiting value of 20 Ð25 kJ/ mol.[435] As Fig. 3.25 shows, Þtting of the experimental points follows the expected trend although the pores in the studied carbons cover only a limited range of sizes. Some of the carbons were modiÞed by treatment with urea and, in these cases, occurrence of stronger adsorbent Ðadsorbate interactions was attributed to incorporated basic nitrogen groups. The same group[436] further used IGC to study H2S interaction with nitrogen-containing activated carbons prepared by treatment of a wood-based carbon with urea. Evidence for H2S reaction with the carbon surface was inferred from the IGC peak characteristics (high retention time, asymmetry). The important role played by small micropores and basic nitrogen groups in H2S adsorption was conÞrmed. El-Sayed and Bandosz[437,438] have investigated the features of activated carbon surfaces that are important for adsorption of acetaldehyde using IGC combined with other techniques. Acetaldehyde adsorption on activated carbons (BPL from Calgon, MVP from Norit, BAX 1500 from Westvaco) strongly depended not only on the pore size distribution but also on the adsorbent surface chemistry.
Figure 3.25 Dependence of the isosteric adsorption heat of H2S on the average width of micropores in several activated carbons. (Reproduced from Bagreev and Bandosz.[433] Copyright 2000 American Chemical Society.)
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The maximum heat of adsorption was obtained when the pore size closely matched the size of the adsorbate and oxygenated surface groups were present. A low density of surface groups can enhance the adsorption heat, whereas extensive oxidation causes a decrease in the strength of adsorption forces due to blocking of pore entrances by the functional groups. Salame and Bandosz[439,440] studied the effects of oxygenated surface groups and pore sizes on the adsorption of diethyl ether on two activated carbons of wood origin (WVA1100 and UMC, from Westvaco). The pore size distribution was the predominant factor here. Hydrogen bonding was found to be weaker than other energetic factors such as the gas Ð pore wall interactions. Again, the authors found that adsorption in very small pores has a heat of adsorption that is close to double of the corresponding value obtained on ßat surfaces. Very recently, GunÕko and Bandosz [441] have analyzed the effect of surface heterogeneity on adsorption energy of water, methanol, and diethyl ether on two activated carbons (WVA-1100 and UMC, Westvaco). IGC was used to obtain the ethyl ether adsorption data. As they corresponded to relatively high temperature, the adsorption energy distributions were broad with only one peak. For the diethyl ether molecule dispersive interactions of the hydrocarbon moiety with the carbon surface were much stronger than hydrogen bonding, suggesting adsorption on one, heterogeneous group of adsorption centers. Domingo-Garcõ«a et al.[442] used IGC, among other techniques, to assess the effects of oxidation with ammonium persulfate, hydrogen peroxide, and oxygen plasma of a commercial activated carbon. The connection between thermodynamic parameters obtained at inÞnite dilution and pore sizes involved was discussed. From these results it was concluded that the two oxidation treatments in solution produced the opening of very small micropores (0.43 Ð 0.60 nm). The same authors[443] found two linear regimes in plots of the log of the retention volume (Vs) vs. reciprocal temperature for the adsorption of formaldehyde on a suite of activated carbons and carbon blacks. They explained this behavior based on the assumption of two temperature-dependent mechanisms allowing the adsorption to occur in smaller pores at lower temperatures and in larger ones at higher temperatures. These results have the important consequence that it is not possible to predict the adsorption uptake and heat for this adsorbate (HCHO) by linear extrapolation of Vs vs. 1/T over a wide range of temperatures. This effect has been reported for other systems.[433] Adsorption of a series of methylamines on a suite of activated and oxidized activated carbons has been investigated by Pe«rez-Mendoza et al.[444] using IGC and other techniques. They concluded that the standard heat of adsorption alone cannot discriminate between speciÞc and nonspeciÞc interactions in methylamine adsorption. Bardina et al.[445] have recently used IGC to follow changes in the surface properties of carbonized cellulose subjected to different thermal and CO2 activation treatments. They reported that the sequence of values of the speciÞc retention volume and the initial adsorption heat for different adsorbates on the
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carbonized cellulose Þbers is basically determined by the polarizability of their molecules. Much recent IGC work on porous carbons is connected with their environmental applications. Burg et al.[446] employed IGC and the linear solvation energy relationship (LSER) approach to determine the selectivity of a commercial activated carbon toward the adsorption of 14 VOCs. They concluded that the main interactions involved are dispersion and hydrogen-bond interactions. The obtained LSER coefÞcients were useful for characterizing the adsorbent and predicting its selectivity toward pairs of VOCs. Cossarutto et al.[447] determined the dispersive component of the surface free energy for several commercial activated carbons from wood and coconut shell. The authors employed IGC at inÞnite dilution and, not unexpectedly, they found that this technique globally characterizes the most energetic micropores. From the values of the dispersive component of the surface energy, they concluded that IGC discriminates between activated carbons from different origins produced by either physical or chemical activation. Also in the environmental Þeld, Baikova et al.[448] reported that the isosteric adsorption heats of Freon 13B1 on several activated carbons change very little among different activated carbons and attributed this to the fact that adsorbateÐ adsorbent interaction occurs in pores whose sizes are comparable to those of the adsorbed molecules. Prado et al.[449] measured by IGC the isosteric adsorption heats for benzene and n-hexane on various adsorbents including an olive stone-based activated carbon and combined these measurements with immersion calorimetry. Results conÞrmed the close connection between micropore volumes and adsorbate Ðadsorbent interactions. Hrouzkova et al.[450] compared the isosteric adsorption heats of a variety of organic compounds on a number of carbon molecular sieves, activated carbons, and graphitized carbon blacks in connection with preconcentration of volatile organic compounds for environmental analysis. Lo«pez-Garzo«n et al.[451] have extensively investigated by IGC a suite of glassy carbons prepared by slow carbonization of poly(furfuryl alcohol). These materials exhibit moderate surface areas (24 Ð475 m2/g from N2 at 77 K; 257 Ð 468 m2/g from CO2 at 273 K, see Table 3.8). Using these materials, the authors developed a new approach by considering the effect of surface curvature in pores on the dispersive component of the surface free energy. As Table 3.8 shows, when this effect was taken into account, the surface free energy values (gds ) were dramatically reduced as the dimensions of the adsorbate became similar to the pore size; the new values (gds (o)) became comparable to results obtained by contact angle measurements and therefore seem more realistic. Conversely, the authors proposed that a textural analysis of porous solids by IGC at inÞnite dilution can be made for a given radius of the adsorbate if the dispersive component of the surface free energy can be conÞrmed by another method. The glassy carbons studied have some features in common with conventional activated carbons, and the information obtained should be capable of being extrapolated to other microporous carbons. Later, Domingo-Garcõ«a et al.[452] used nine
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Table 3.8 Values of the Dispersive Component of Surface Free Energy of Four Glassy Carbon Samples (P1 ÐP4), Calculated Taking [gds (o)] or not Taking (gds ) Into Account the Effect of Surface Curvature in Pores Adsorbent P1 P2 P3 P4
SN2 (m2/g)
SCO2 (m2/g)
Equation
475 24 398 458
408 257 344 468
gds ¼ 606.15 2 1.83t gds ¼ 499.41 2 2.03t gds ¼ 435.51 2 1.21t gds ¼ 462.53 2 1.72t
a
gds at 298 K (mJ/m2)
gds (o) (mJ/m2)
560.5 + 2.4 448.7 + 1.6 405.4 + 6.5 419.5 + 2.1
47.4 + 0.2 37.9 + 0.1 34.3 + 0.5 35.5 + 0.2
a t ¼ Temperature (8C). Source: Adapted from Lo«pez-Garzo«n et al.[451] Copyright 1993 American Chemical Society.
different organic probe molecules to characterize the same materials. They concluded that the standard adsorption enthalpy at zero coverage of n-alkenes, benzene, and cyclohexane (for which the adsorption is nonspeciÞc although the adsorption heats are very high) is not a proper criterion to distinguish between speciÞc and nonspeciÞc interactions when microporous adsorbents are studied and when the adsorption is carried out at zero surface coverage. Complementary characterization of glassy carbons by conventional adsorption isotherms has been reported.[453] The same team has also investigated the effects of several treatments of glassy carbon surface. Thus, these materials were modiÞed by impregnation with KI in connection with enhancement of their capacity for removal of radioactive iodine-131.[454] Thermodynamic data for methyl iodide at zero surface coverage were determined by IGC. The reported adsorption heats were greater than the liquefaction heat of pure CH3I (27.6 kJ/mol), and the difference increased as the pore size approached the adsorbate molecular size. The same type of behavior was found in studying glassy carbons modiÞed by oxygen plasma treatment.[455,456] Pe«rez-Mendoza et al.[457] have characterized in detail the modiÞcations produced by plasma treatments of one of the aformentioned glassy carbons, which exhibited molecular sieving behavior for the N2/CO2 couple. Exposure to O2 plasma only induced minor textural changes in comparison with CO2 plasma, which created microporosity to a large extent. Lo«pezGarzo«n et al.[458] have reviewed the applicability of IGC to assess adsorption of different vapor pollutants on nonporous and porous carbon materials. The authors highlighted the relevance of these results for improving the performance of carbonaceous adsorbents in very diluted atmospheres. Early IGC work with bituminous coking coal[459] already pointed out the inßuence of both porous texture and surface chemistry on adsorption of organic molecules. Larsen et al.[460] studied the interaction of a variety of organic molecules (26 species of different polarities) with a high-rank coal and addressed the roles of speciÞc and nonspeciÞc interaction forces. Similar work
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was done by Guha and Roy in their IGC studies of bituminous coals and anthracite[461] and lignites.[462] These authors found that the selectivity toward carbon dioxide, at ambient temperature, and the retentions of water and methanol at 448 K, are dependent on coal rank. This dependence was found to be similar to the porosity Ðrank relationship of coal. Later, coal surface properties were extensively studied by Glass and Larsen using IGC of nonpolar[380] and polar[463] molecules. Working with hydrocarbons, they found that adsorption heats on Illinois No. 6 coal were higher than heats reported for graphitized carbon.[37,270] However, when the coal was extracted with tetrahydrofuran (THF), the adsorption heats became similar to those on graphitized carbon. Figure 3.26 shows the dependence of adsorption heat on the electronic polarizability (a) of n-alkanes for the original, demineralized, and THF-extracted coal samples. Heating to 523 K had the same effect as extraction in THF, and these changes in adsorption heat were irreversible. All of this indicates that heating to 523 K or extraction with THF causes an irreversible structural relaxation of coal that causes a decrease in surface energy; the surface interactions become less exothermic, consistent with a rearrangement of the coal to give a lower surface energy. Glass and Larsen[464] also studied by IGC the adsorption of polar molecules on Illinois No. 6 coal in order to gain information on the speciÞc acid Ð base interactions of adsorbates with coal surfaces. Pyridine, alcohols and amines interacted preferentially with carbonate and/or ion-exchangeable mineral matter, while aprotic, oxygen-containing bases interacted more strongly with the organic
Figure 3.26 Adsorption heat versus electronic polarizability, a, for Illinois No. 6 coal samples. Lines are drawn through points for the n-alkanes and inert gases. Hollow circles, original coal; triangles, demineralized; solid circles, THF-extracted. All coal samples were heated to 423 K. (Reproduced from Glass and Larsen.[380] Copyright 1993 American Chemical Society.)
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component of the coal surface. The same authors[465] found that the speciÞc interactions of organic bases with coal were analogous to their hydrogen-bond strengths with p-ßuorophenol, and proposed that these bases hydrogen-bond to pendant phenol groups on the coal surface. Glass and coworkers have further studied by IGC the surface thermodynamics of hydrocarbons[466] and polar adsorbates[467] on a Wyodak subbituminous coal. Unlike the behavior of alkanes, unsaturated hydrocarbons interacted speciÞcally with the coal surface, most likely because of interaction between the unsaturated portion of the hydrocarbon and polar or ionic groups on coal. Alkylating the coal resulted in a coal surface having similar nonspeciÞc interactions with saturated and unsaturated hydrocarbons.[466] The work with polar adsorbates (organic bases and 1-propanol)[467] showed that alkylation of Wyodak coal removes the nonspeciÞc dipole Ðdipole interactions but does not remove the speciÞc hydrogen-bond interaction with 1-propanol, the opposite behavior being found for organic bases. The authors concluded that different modes exist in Wyodak coal for hydrogen bonding to these reagents. Huang et al.[468] have discussed the types of interactions existing between coal surfaces and a number of gases as probed by IGC. Baquero et al.[469,470] used IGC to study the adsorption of n-alkanes and polar molecules on several Colombian coals and their chars prepared at 773 K. The coals exhibited higher surface energies than the chars, and the highest difference between coal and char corresponded to the lowest-rank coal studied (Cerrejo«n). Very recently, Starck et al.[471] have investigated the effects of demineralization with HCl and HF on the surface chemistry of a Polish (Lubsto«w) lignite. LSER modeling of IGC results indicated a strong interaction of the demineralized coal with compounds of basic character, and they were in agreement with Boehm titration results evidencing an increase of the acidic character of the lignite surface following the demineralization treatment. Burg et al.[472] have recently reviewed in detail the use of the LSER approach to determine polar and nonpolar sites on carbon surfaces. The authors argued that this method provides a more detailed understanding of the interaction factors than other existing methods, as the LSER separates not only polar and nonpolar interactions but also the polar interaction into the sum of a number of separate interactions. Before closing this section, brief reference will be made to some recent developments in IGC methodology. One is a method of measuring surface heterogeneity of nonporous adsorbents by working in the area of linear chromatography (HenryÕs law). This method is based on the variation of adsorption kinetics on different sites of a heterogeneous surface and has been applied to glass Þbers by Bakaev et al.[473] This method is an alternative to conventional method of studying surface heterogeneity by IGC based on nonlinear chromatography (see, e.g., Stanley and Guiochon[474]). The other method is reversed-ßow gas chromatography (RF-GC), which is a time-resolved method whereby the carrier gas ßow is reversed during a certain time in the course of the experiment. This is a differential method that is not
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affected by some limitations of nonlinear isotherms and requires minimal modiÞcations of a conventional gas chromatograph. Katsanos has recently reviewed the applications of RF-CG to physicochemical measurements[475] and catalyst characterization.[476] 3.3.2.3.
Miscellaneous Techniques
In this section we will review several papers in which miscellaneous techniques have been employed to obtain information concerning the energetics of adsorption. Shen et al.[477] compared three methods to obtain the heat of adsorption: differentiation of the adsorption isotherm at constant surface coverage, measurement of the adsorption isosteres, and adsorption calorimetry. Although they made the comparison for data obtained on zeolites, their results are general enough to be of interest in the study of carbon adsorbents. The adsorbates employed were N2 , O2 , and CO2 . They concluded that the isosteric method and calorimetry are in reasonable overall agreement. In some cases they found differences but were not able to explain them and left the question open. Papers involving the use of adsorption thermogravimetry have been mentioned in all the previous sections; nevertheless, one that combines this technique with immersion calorimetry to characterize steam gasiÞed humic acids from brown coal[478] deserves special attention. The authors concluded that the micropore volume and the integral immersion enthalpy are closely related to the porous structure of the chars studied. These conclusions were obtained for micro- and mesoporous carbonaceous materials and so should be applicable to the evaluation of adsorption data for other activated carbons with similar porous textures. Finally, we must mention NMR as another useful technique, although it has not yet been sufÞciently exploited. It has been recently thoroughly reviewed by Turov and Leboda,[479] and the reader is referred to that publication for further information. 3.3.3. Theoretical Methods 3.3.3.1.
Henry’s Law Constant and Virial Coefficients
In this section we will summarize the studies concerning low coverage region of the adsorption isotherm in which HenryÕs law reproduces the experimental data. It must be pointed out that deviations from HenryÕs law also provide useful information. The statistical mechanics treatment of low coverage adsorption is based on the grand partition function (i.e., the grand canonical ensemble) and it is an exact approach.[480] The experimental data can be interpreted based on a virial expansion in the pressure or activity of the adsorbate. To obtain the adsorption isotherm in terms of the virial expansion, we start by considering the conÞguration integrals given by Eq. (3.54) and the expression of the potential energy of a molecule in terms of gas Ðgas and gas Ð solid interaction energies [Eq. (3.55)]. Introducing Eq. (3.55) into (3.54), the following
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expressions are obtained: ð ð Ugs (r1 ) Z1 ¼ exp dr1 ¼ (1 þ f1 )dr1 kT V V ðð Ugs (r1 ) þ Ugs (r2 ) þ Ugg (r1 , r2 ) exp Z2 ¼ dr1 dr2 kT V ðð ¼ (1 þ f1 )(1 þ f2 )f12 dr1 dr2
(3:103)
(3:104)
V
Here Ugs (ri ) fi ¼ exp 1 kT
(3:105)
and f12
Ugg (r1 , r2 ) ¼ exp 1 kT
(3:106)
In the grand canonical ensemble it is possible to obtain the average density of a system, r , in terms of the fugacity or activity of the gas. The corresponding expression is X X f i i r ¼ ibi z ¼ ibi (3:107) kT i1 i1 where bi ¼ bi/V, z is the activity, f the fugacity, and bi are expressions involving the conÞguration integrals:
b1 ¼ Z1 b2 ¼
(3:108)
1 (Z2 Z12 ) 2!
(3:109)
Now consider two systems each of volume V and at temperature T. One system contains a gas interacting with an external Þeld and the second one contains only the gas. At the same value of the activity the difference in the average number of gas molecules between both systems is given as X N ad ¼ V(r r 0 ) ¼ i(bi b0i )zi (3:110) i
where Eq. (3.107) was employed to derive this expression. Equation (3.110) can be rewritten to give X N ad ¼ (Z1 Z10 )z þ Z2 Z20 Z12 þ (Z10 )2 z2 þ ¼ Biþ1,a zi d
i
(3:111)
e
Physical Adsorption of Gases and Vapors on Carbons
where the coefÞcients Biþ1,a are given by: ð B2a ¼ f1 dr1
295
(3:112)
V
ðð B3a ¼ V
0 ½(1 þ f1 )(1 þ f2 )f12 f12 dr1 dr2
(3:113)
If the ideal gas standard state is taken as reference then z ¼ f/kT, and at low densities the fugacity is approximately equal to the gas pressure. From Eq. (3.111) we Þnd: N ad ¼ B2a
2 i X p p p þ ¼ Biþ1,a þ B3a kT kT kT i
(3:114)
If the external Þeld introduced in one of the systems is due to the presence of an inert solid, the coefÞcients Bia are called the gas Ðsolid virial coefÞcients and Eq. (3.114) is an adsorption isotherm valid at low surface coverage. It must be pointed out that this treatment is exact; nevertheless, approximations are needed to attempt the evaluation of the conÞguration integrals. From an experimental point of view, the amount adsorbed is determined by Þrst measuring the geometric volume of the system. This task is often accomplished using helium since it is considered that no adsorption of this gas occurs at moderately low temperatures. The calibration procedure involves the determination of the system volume, with the adsorbent present, by simply expanding the gas from a known volume. The amount adsorbed is deÞned as the difference between the actual number of molecules present in the system and the number that would be present in the geometric volume at the same activity but in the absence of gas Ð solid interactions. The adsorbed quantity can be expressed as a number of molecules, N ad , or number of moles, nad , in both cases referred to the mass of the adsorbent. According to Eq. (3.114), nad ¼
i N ad X f ¼ Biþ1,a RT N0 i1
(3:115)
where N0 is AvogadroÕs number and f is the fugacity. In the experiments the pressure rather than the fugacity is measured, so it is convenient to rewrite Eq. (3.115) in terms of pressure. Fugacity can be written as a power series in pressure, ! ! B02g 2 B03g f ¼pþ p3 þ p þ RT 2(RT)2
(3:116)
where B02g and B03g are the second and third virial coefÞcients of the bulk gas in the absence of adsorbent. Replacing Eq. (3.116) into (3.115) and rearranging the terms
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of the power series in the pressure gives: p p 2 nad ¼ B2a þ (B3a þ B2a B02g ) RT RT 1 p 3 0 0 þ B4a þ 2B3a B2g þ B2a B3g þ 2 RT
(3:117)
The gasÐsolid virial coefÞcients can be determined from experimental data in the same way as gas-phase virial coefÞcients. B2a and B3a can be obtained easily from the low-pressure part of the adsorption isotherm: nad RT lim (3:118) ¼ B2a p!0 p and (nad RT=p) B2a lim ¼ B3a þ B2a B02g p!0 p=RT
(3:119)
If B3a and higher coefÞcients are zero or negligible, a plot of nadRT/p vs. p will give a straight line with B2a as the intercept and (B3a þ B2a B02g )=RT as the slope. The virial coefÞcients are related, as has been shown, to the conÞguration integrals, which in turn depend on the intermolecular forces. Thus, it is possible to calculate them based on a given model for the intermolecular forces. As previously stated, at this moment it is necessary to introduce approximations depending on the adopted model. It is interesting to note that the conÞguration integrals are also related to the thermodynamic properties of the system. For example, the isosteric adsorption heat is given by: [481] 2 @ ln p qst ¼ RT (3:120) @T nad Inverting Eq. (3.117) and replacing into (3.120) gives: ( ) 0 2 d½(B þ B B )=B d ln B 3a 2a 2g 2a 2a qst ¼ RT RT 2 nad þ RT 2 dT dT (3:121) This expression, extrapolated to the limit of zero coverage, gives the isosteric heat at zero coverage: 0 2 d ln B2a qst ¼ lim qst ¼ RT RT (3:122) nad!0 dT In the same way, other thermodynamic properties can be obtained in terms of the virial coefÞcients.
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The second virial coefÞcient is by far the easiest of the gas Ðsolid virial coefÞcients to measure and interpret because it is related to the HenryÕs law constant. One expression of the HenryÕs law is: nad lim (3:123) ¼ Kh1 p!0 p The constant Kh is related to the second virial coefÞcient through Eq. (3.118): B2a ¼
RT Kh
(3:124)
According to this equation, the HenryÕs law constant is directly related to the interaction of a single adsorbate molecule with the solid adsorbent. The second virial coefÞcient can be calculated using Eq. (3.112). To perform this task it is necessary to assume a form for the gas Ð solid interaction energy. Using a LennardÐ Jones (m, n) potential the following general expression is obtained: ð n n m=(nm) 1gs hsgs n sgs m i B2a ¼ exp 1 dr nm m kT r r V (3:125) Here 1gs is the minimum in the potential energy and sgs is the distance at which the potential energy is zero. In the case of a heterogeneous surface the integrand in Eq. (3.125) is a function of all the coordinates, x, y, and z, but for a homogeneous ßat surface the interaction energy of an isolated adsorbed molecule is a function of the distance to the surface. In this case the integral over x and y gives the surface area of the adsorbent and the obtained expression is 1 X n n m=(nm) 1gs ½t(nm)þ1=n tm 1 1 B2a ¼ Asgs (nt!) G nm m n kT t¼0 (3:126) where G is the gamma function and A is the area of the adsorbent. Figure 3.27 shows a series of plots of B2a/Asgs vs. 1gs/kT and, as can be seen, this virial coefÞcient shows a linear dependence with 1gs/kT. This kind of plot is often employed to determine the interaction parameters as was established by Steele and Halsey.[28] It is interesting to note that, according to the results plotted in Fig. 3.27, the difference between the potentials is quite small particularly for 1gs/kT . 3. In this region, the attractive part of the potential dominates, so changing the exponent of the repulsive part of the potential will not alter the linear dependence. Figure 3.28 shows a plot of the Lennard Ð Jones (12, 6) potential together with the corresponding Mayer function [Eq. (3.105)]. It is clear that the negative values of the Mayer function are originated in the region where the repulsive part of the potential dominates. Thus to obtain more information concerning
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Figure 3.27 Second virial coefÞcient [Eq. (3.126)] calculated for different (m, n) potential functions.
the repulsive component of the potential it is necessary to determine B2a at high temperatures. The Mayer function calculated at different temperatures is represented in Fig. (3.29) where it can be seen that as temperature increases the large peak due to attractive interaction decreases until it disappears for T ¼ kT/1gs 10. This creates an experimental problem because it establishes that adsorption isotherms should be determined at temperatures where adsorption itself is feeble and B2a is very small.
Figure 3.28 Lennard-Jones (12, 6) potential, U/1gs , plotted together with the corresponding Mayer function, f [Eq. (3.105)].
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Figure 3.29 Mayer function, f [Eq. (3.105)] calculated at different temperatures for the Lennard-Jones (12, 6) potential.
If the adsorbate is a diatomic or polyatomic molecule, the expression for B2a also contains a dependence on the relative orientation of the molecule with respect to the surface. Using a (12, 6) Lennard Ð Jones potential function to describe the gas Ðsolid interaction, the resulting expression is: 1 B2a ¼ 4p
ð ð
ugs (r, V) exp 1 dr dV kT
(3:127)
Here ugs(r, V) is the gas Ð solid interaction energy of the molecule at position r with orientation V relative to the adsorbent surface. Steele and Halsey[28] developed a method by which the values of 1gs and sgs can be obtained from experimental data. Moreover, this method provides a way to obtain the surface area of the adsorbent without needing to estimate the monolayer capacity and not depending on multilayer formation. The method basically takes advantage of the linear dependence of ln(B2a) on 1/T for both the experimental and theoretical values of B2a obtained from Eq. (3.127). Figure 3.30 shows the line obtained for CO2, N2, and O2 adsorbed on a series of carbonaceous materials. Steele and HalseyÕs method has been recently employed by Bottani and coworkers[482,483] to calculate the interaction parameters of CO2 adsorbed on graphitized carbon blacks, and N2, O2, and CO2 adsorbed on graphite, amorphous carbons, Al2O3, and TiO2. For the particular case of carbonaceous materials, the obtained values for nitrogen and oxygen are shown in Table 3.9 and the corresponding values for carbon dioxide are shown in Table 3.10. Carbon dioxide could be employed as example of one problem that arises in the calculations when the molecular complexity is increased.[482] Since the
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Figure 3.30 Experimental reduced virial coefÞcients vs. reduced temperature for CO2, N2, and O2 adsorbed on carbonaceous materials (samples: National graphite, JM-3, and JM-4; see Tables 3.9 and 3.10). (Adapted from Cascarini de Torre et al.[483] Copyright 1995 American Chemical Society.)
number of Þtting parameters in the potential function is quite large, there is a certain degree of ambiguity in the selection of the best set of parameters and there is no clear criterion for choosing one set over another. This situation is aggravated by the fact that under these conditions the experimental error increases, producing a quite large scatter of the data. This point becomes critical when using this method to estimate the area of the adsorbent.[482] Bojan and Steele[484] also studied the adsorption of N2 and CO on the graphite basal plane using this approach. They showed that Lorentz ÐBerthelot combining rules give good estimates of the interaction parameters for N2 adsorbed on
Table 3.9 N2 and O2 Interaction Parameters Obtained From Experimental Data Adsorbent
Gas
sgs (nm)
1gs (K)
Sterling MT-FF
N2 O2 N2 O2
0.336 0.338 0.336 0.319
31.63 34.16 34.65 41.52
National graphite
Note: National graphite was obtained by grinding a graphite bar; the sample consists of particles exhibiting a large proportion of edges and cracks. Source: Adapted from Cascarini de Torre et al.[483] Copyright 1995 American Chemical Society.
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301
Table 3.10 Interaction Parameters for CO2 Adsorbed on a Series of Carbonaceous Materials Solid
sgs1 (nm)
sgs2 (nm)
1gs1 (K)
1gs2 (K)
JM-3 JM-7
0.33 0.33
0.314 0.314
40.49 43.56
23.96 25.76
Note: JM-7 is a carbon black, and JM-3 is an activated synthetic graphite used as a catalyst support. The subscript 1 refers to the O(CO2) surface site and 2 refers to the C(CO2) surface site. Source: Adapted from Cascarini de Torre et al.[483] Copyright 1995 American Chemical Society.
exfoliated graphite. A detailed discussion of Lorentz Ð Berthelot rules has been published by Delhommelle and Millie«.[485] In the case of CO, Bojan and Steele[484] found that a considerably large reduction in the quadrupole moment of the molecule is needed to make the calculations coincide with the experimental data. A possible mechanism for this reduction in the effective electrostatic interactions between molecules adsorbed on a dielectric solid comes from the image charge deÞned in classical electrostatics. They concluded that there was one unresolved problem: a reduction of 20% in quadrupole moment, with respect to the bulk gas, for adsorbed N2 gives agreement between experiments and theoretical calculations, but the image charge arguments suggest that the change should be considerably larger than 20%. Bojan and Steele[486] also found that, for both gases adsorbed on graphite, a reduction in the interactions must be assumed in both the well depths and the effective quadrupole moments. They calculated that this effect is of the magnitude predicted for substrate-mediated changes in the intermolecular interactions. Representing the quadrupole moment of the adsorbate as a set of discrete charges, conveniently located on the molecule, would generate a resulting image of the quadrupole in the solid. This image interacts with the real quadrupole moment to produce an extra attractive term that is proportional to the quadrupole moment and, thus, is largest for CO. In addition, the images interact with the quadrupoles of neighboring adsorbed molecules to give an effective repulsion term. The resulting effect on the total electrostatic interaction depends on the molecular size, which determines the distance between the quadrupole and the solid and, through this distance, the magnitude of the image charge. Finally, the estimated reduction of the site Ð site well depth due to substrate mediation includes the nonquadrupolar O2 data, and the calculated B2a are much more sensitive to this part of the interaction than to the electrostatic terms. Very recently, Do et al.[487] reported a comprehensive analysis of gas and vapor (including many VOCs) adsorption on nonporous graphitized thermal carbon black. Their analysis is very exhaustive with respect to the number of adsorbates and adsorbents included. However, the model is quite simplistic as it does not take into account the internal structure
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of the adsorbate because the molecules are considered as spherical. This can explain why the authors found that Lorentz Ð Berthelot rules give a good estimate of the interaction parameters; this is illustrated in Table 3.11, which gives a comparison of the optimal Þtted values for the vertical interaction energies (1sf (opt)/k) and the values calculated by the Lorentz Ð Berthelot rule (1sf (theor)/k). Several attempts have been made to modify the potentials to reproduce better the available experimental data. Pierotti and Thomas[480] have presented quite a complete discussion of this subject. They concluded that one way to avoid several problems in a study of the interaction potentials is to use the isosteric heat extrapolated to zero coverage calculated with Eq. (3.122). This, according to Pierotti and Thomas, is better because to calculate the isosteric
Table 3.11 Comparison Between Vertical Interaction Energies in the Adsorbed Layer and in the Gaseous Phase Adsorbate Helium Neon Argon Krypton Xenon Ammonia Water Nitrogen Carbon dioxide Sulfur hexaßuoride Methane Ethane Propane n-Butane Isobutene n-Pentane Neopentane n-Hexane Ethylene Cyclohexane Benzene Methanol Ethanol Diethyl ether Tetraßuoromethane Chloroform Tetrachloromethane
1sf (theor)/k (K)
1sf (opt)/k (K)
1sf (opt)/1sf (theor)
16.92 30.31 50.11 70.78 80.42 125.03 150.52 44.71 73.93 78.86 64.50 77.71 81.48 121.98 96.14 97.73 73.59 105.74 79.32 91.21 107.44 116.15 100.76 93.74 63.28 104.24 95.06
8.95 17.35 54.03 59.47 80.12 107.73 163.37 51.78 66.72 62.12 64.01 79.24 77.07 94.53 82.89 95.07 69.47 110.04 80.05 95.69 120.01 121.08 116.75 77.1 62.29 100.3 92.88
0.53 0.57 1.08 0.84 1.00 0.86 1.09 1.16 0.90 0.79 0.99 1.02 0.95 0.77 0.86 0.97 0.94 1.04 1.01 1.05 1.12 1.04 1.16 0.82 0.98 0.96 0.98
Source: Reproduced from Do et al.[487] Copyright 2003 American Chemical Society.
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303
heat only the temperature dependence of B2a is needed. The calculated isosteric heat can be compared with experimental values and the surface area of the adsorbent does not enter the calculations. Maurer et al.[488] have followed a different approach, which involved the use of the Hamaker constant of the solid to calculate the HenryÕs law constant. The authors applied their method to predict the HenryÕs constant of gases and vapors adsorbed on graphites/graphitized carbon blacks and activated carbons. This is illustrated in Fig. 3.31, which shows the excellent agreement existing between predicted and experimental Henry coefÞcients for 21 gases and vapors on 18 activated carbons (the four adsorbates indicated are highlighted as representative examples). The accuracy was similar in the case of graphites/graphitized carbon blacks; the only exception was found to be water, which was attributed to its special interactions with these adsorbents. Barker and Everett[489] developed an alternative method to determine the area of the adsorbent using high-temperature adsorption data. Their proposed theory is similar to the one developed by Steele and Halsey[28] but using a Gibbs deÞnition of adsorption. This approach needs the introduction in the calculations of the dividing surface concept. Barker and Everett placed this plane at z ¼ sgs since the number of adsorbed molecules below this plane is negligible, at least for the case where 1gs/kT . 3. They arrived at the expression nad ¼ Kh Ap
(3:128)
Figure 3.31 Comparison of experimental and predicted Henry coefÞcients of different gases and vapors on activated carbons at 300 K. (Reproduced from Maurer et al.,[488] with permission from Elsevier.)
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where A is the area of the adsorbent and Kh is the HenryÕs law constant given by: ð i 1 1 h ugs Kh ¼ exp 1 dz (3:129) RT sgs kT This expression shows that, if ugs is known, Kh can be calculated and then the surface area of the adsorbent is obtained from Eq. (3.128). Barker and Everett used this method to calculate the surface area of carbon black Black Pearls 71 (Cabot), a pelleted form of Monarch 71. Their results agreed quite well with the values obtained from electron microscopy but neither of them is even close to the BET value. Barker and Everett concluded that either BET or their theory, or both, are inapplicable to a heterogeneous surface. Recently, the adsorption equilibrium for Type V isotherms has been analyzed to calculate the HenryÕs law constant and to derive the heat of adsorption.[490] Cochrane et al.[491] studied Xe adsorption on graphitized carbon blacks using a radioactive tracer method based on 133Xe, along with a conventional volumetric technique. They determined the HenryÕs law constant using data at low fractional surface coverage (u ¼ 10210 Ð 1026) and with these values they calculated the activity coefÞcient, f (u), proposed by Steele:[492] f ( u) ¼
p Na Kh
(3:130)
According to Steele, deviations in f (u) from its limiting value of unity are due to interactions between adsorbed molecules. The experimental data obtained by Cochrane et al. at 195.2 K show signiÞcant deviations in f (u) for surface coverages larger than 3.1 1025 in the case of Sterling MT-3100, and coverages larger than 2.7 1028 in the case of Graphon. Morrison and Ross[493] calculated the second and third virial coefÞcients for a 2D gas to describe Ar adsorption on a graphitized carbon black at high temperature. They presented a series of numerical values for the reduced virial coefÞcients and discussed the effect of adding more terms to the virial series. When compared with the experimental data, their calculated isotherms show the same discrepancies as other methods as the surface coverage departs from the HenryÕs law region. Pierotti and Thomas[494] applied the general treatment of McMillan Ð Mayer theory of solutions to low-coverage adsorption data on heterogeneous surfaces. The statistical thermodynamic treatment is based upon the grand canonical ensemble. This approach makes clear that the experimentally determined virial coefÞcients in physical adsorption are virial coefÞcients of a potential of average force (i.e., they are virial coefÞcients of a free energy function and not of an ordinary potential energy function).[495] In the Pierotti ÐThomas approach two partition functions are needed, one corresponding to the system where gas Ð solid interactions are present and another for a system where these interactions are absent. This last system is the so-called calibration condition in
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305
adsorption studies. The adsorption isotherm for a system with one adsorbate is obtained from @ ln(= ) (3:131) kNad l ¼ z @z T,V where kNadl is the average of the amount of gas adsorbed, z is the activity of the adsorbate, and are the partition functions for the system with gas Ðsolid interactions and the calibration condition, respectively. Expanding the logarithm of / in a power series in z and applying Eq. (3.131) term by term yields X i(bi bi )zi (3:132) kNad l ¼ i1
where the b values are Mayer-type cluster integrals. Operating in a conventional way, the Þnal expressions for the second and third virial coefÞcients are ð B2a ¼ g1 dr (3:133) VV
and ðð B3a ¼ VV
0 ½(1 þ g1 )(1 þ g2 )g12 f12 dr1 dr2
(3:134)
where the g values are related to potentials of average force for single and pairs of adsorbate molecules. These expressions are identical in form to those obtained for an adsorbate in an external Þeld [Eq. (3.112) and (3.113)] except that they contain the potentials of average forces and adsorbent structure and hence adsorbent heterogeneity is included. This approach can be employed to determine the surface area of the adsorbent and the interaction parameters of the potential functions as in the previously reviewed methods. Nevertheless, in this case a third adjustable parameter (the most probable adsorption energy) appears if a Gaussian heterogeneous surface is assumed. Pierotti and Thomas proposed to select a value of the most probable adsorption energy and calculated an effective virial coefÞcient from each experimental value of B2a using the expression ( ) 1 gU 2 u (3:135) B2a ¼ B2a exp 2 kT where B2a is the experimental value of the second virial coefÞcient, Bu2a is the second virial coefÞcient calculated for a uniform adsorbent, g is an adjustable parameter, and U2 is the variance of the energy distribution. Ross and Olivier,[496] Steele,[497] and Hoory and Prausnitz[498] have employed expressions similar to Eq. (3.135) with g ¼ 1. Among the conclusions presented by Pierotti and Thomas,[494] one that must be pointed out is that they found the log-normal, exponential, and Maxwell ÐBoltzmann distributions inadequate to
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represent the site-energy distribution function for the virial analysis, whereas the Gaussian distribution gave suitable expressions. One consequence of the introduction of surface heterogeneity in the analysis is that it usually improves the agreement between the calculated and experimental (BET) surface areas of the adsorbent. On the other hand, the method applied to the analysis of experimental data obtained for a number of porous solids showed no improvement in the Þt. Analysis of the values of the third virial coefÞcient indicated that surface heterogeneity has a pronounced effect on this coefÞcient. Pierotti and Thomas employed the Gaussian site-energy distribution combined with a patchwise and a random pair distribution function. They concluded that the random pair distribution gave more realistic best-Þt parameters although the experimental data employed could be questioned concerning its extensiveness and precision. Ross et al.[499] reviewed various approaches to the derivation of HenryÕs law constant of an adsorbed gas using statistical mechanics. They disentangled implicit assumptions to show what is required to reconcile differences between them. Classical and quantum mechanical treatments were compared for the motion of adsorbed molecules normal to the substrate. They argued that data conÞned to the HenryÕs law region are susceptible to more than one interpretation in terms of substrate characteristics. Their main argument is that high-temperature adsorption data contain no useful information concerning surface heterogeneity because in this condition those effects are minimized. They added that data inaccuracy also conspires against the reliability of such analysis. Smith and Wells[500] developed a method to achieve the formal inversion of gas Ð solid second virial coefÞcient. This method is an analog of the one employed for the inversion of the gas Ð gas second virial coefÞcients. They argued that ßexible inversion procedures enable the characterization of the full potential function. Moreover, they demonstrated that, although those procedures cannot formally determine the potential uniquely, they are nevertheless found in practice to lead to a deÞnition of the complete potential function for systems in which the potential energy function is subject to certain constraints of shape and continuity. From the practical point of view, the method is of little use because, as the authors themselves calculated, to obtain a full description of the Ar/graphite potential without resorting to additional data, experimental isotherms in the low-pressure region would be needed for temperatures as high as 1500 K. Stecki and Soko·owski [501] calculated the second virial coefÞcient for a homogeneous solid. They analyzed the Lennard-Jones (12, 6), (9, 3), and square-well potential functions with different energies for the gas Ð solid and gas Ð gas interactions. Their main conclusion is that the residual spreading pressure and residual adsorption uptake are better than the HenryÕs law constant and adsorption uptake itself because the former do not depend on the exact location of the Gibbs dividing surface between the solid and the gas. Nevertheless, they did not compare their model results with experimental data. Peters et al.[502] have studied the adsorption process on homogeneous surfaces. The system they analyzed is acetylene on exfoliated graphite in a
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307
wide temperature range. They determined the HenryÕs law constants to reÞne the interaction parameters that were used in computer simulations to identify the structure of the adsorbed phase (this paper will be further discussed subsequently). Blu¬mel et al.[503] studied the supercritical adsorption isotherms of Kr on graphite. To compare with the adsorption of other gases, they presented a way to choose suitable reduced variables. They found good agreement between their calculations and experimental data for noble gases (Ar and Kr) but systematic deviations for nonspherical molecules (e.g., methane). The deviations became more pronounced as the ratios of the gas Ð solid and gas Ðgas well depth of the gases differed from each other and as the temperature was lowered toward the critical temperature. Cuadros and Mulero[504,505] have recently analyzed the validity of analytical equations for 2D ßuids in the prediction of monolayer adsorption isotherms and spreading pressures of noble gases on graphite. They compared the Reddy Ð OÕShea (RO) equation,[506] based on the Þt of pressure and potential energy computer simulated results, with an equation that they derived (Cuadros ÐMulero equation, CM),[507,508] based on the Þt of the Helmholtz free energy calculated from computer simulated results of the radial distribution function. Figure 3.32 shows that the isosteric adsorption heats of Kr on Sterling FT graphitized carbon black at 104.49 K predicted by the CM equation match the experimental results much better than the RO equation except at the lowest or highest surface coverages, where predictions from both equations tend to converge, or the data Þt better the RO equation, respectively. Rudzin«ski et al.[509] studied the adsorption of single gases at very low pressures on strongly heterogeneous surfaces. They argued that for such surfaces
Figure 3.32 Isosteric adsorption heat of Kr on Sterling FT carbon black at 104.49 K. Squares, experimental data; continuous line, CM theoretical values; dashed line, RO theoretical values. (Reproduced from Cuadros et al.[505] Copyright 2001 American Chemical Society.)
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the true HenryÕs law region might appear at so low adsorbate pressures that they could not be experimentally achieved. At the same time, an apparent HenryÕs law region could be found in a wide range of adsorbate pressures. This argument was used to explain certain difÞculties in using the virial analysis for adsorption systems with heterogeneous solids. These authors showed that the large dispersion of adsorption energy, combined with the appearance of Þnite physical energy limits, is responsible for the special behavior of the adsorbate at very low pressures. Thus, the temperature dependence of gas Ðsolid virial coefÞcients cannot be practically employed as the source of information about the energetic heterogeneity of the solid surface. Bakaev and Chelnokova[510] calculated for the Þrst time the HenryÕs law constant for a surface with an assumed irregular atomic structure. Although they simulated an oxide surface using BernalÕs model,[511] their method is general enough to be applied to other systems, including amorphous carbonaceous materials.[512] Bakaev and Chelnokova studied the adsorption of Ar and Xe on the surface of two oxides, one with a regular arrangement of atoms and the second with an amorphous structure. They concluded that their model agrees with the accepted idea that the dependence of the HenryÕs law constant on reciprocal temperature should not be linear for a heterogeneous surface. Nevertheless, they found an asymptotically linear dependence at high and low temperatures. Jaroniec et al.[513] derived an expression for the second gas Ðsolid virial coefÞcient on a heterogeneous surface characterized by a gamma distribution of adsorption energies. They concluded that the inßuence of the adsorbent energetic heterogeneity on this virial coefÞcient is signiÞcant, particularly in the low-temperature region. Kaminsky and Monson[514,515] published a theoretical study of the inßuence of the microstructure of a porous adsorbent upon its adsorption behavior. They developed a model that describes the interaction of adsorbed molecules with an adsorbent treated as a matrix of particles. Each particle is considered as a continuum of interaction centers. They calculated the HenryÕs law constant using Monte Carlo integration for a series of microstructures, including a variety of crystal lattices as well as structures derived from equilibrium conÞgurations of hard spheres. They concluded that changes in the microstructure, even at constant porosity, can cause big changes in the potential energy distribution. These changes lead to either enhanced or decreased HenryÕs constant behavior for different temperature regimes. Figure 3.33 illustrates the temperature dependence of the HenryÕs constants (KH) for different adsorbent hard-core volume fractions (h) in an equilibrium hard sphere (EHS) system [Fig. 3.33(a)] and a face centered cubic (fcc) structure [Fig. 3.33(b)]. As the matrix density increases (porosity decreases), KH increases due to the increased overlap of the low-energy regions of the potential Þelds emanating from the adsorbent particles. However, the effect of temperature is different for both systems: KH changes nearly in proportion to h for the EHS system whereas a distinct sharp increase
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Figure 3.33 Temperature dependence of the HenryÕs constants (KH) for different matrix hard-core volume fractions (h) in (a) an equilibrium hard sphere system and (b) a face centered cubic structure. (Reproduced from Kaminsky and Monson.[514] Copyright 1991 American Institute of Physics.)
occurs for the fcc structure. The authors discussed[514] the origin of these and other features of the curves such as their parallelism at low temperatures or the crossover region appearing near KH ¼ 1. Finally, they found that it is possible to deÞne three adsorption regimes in the microstructure dependence of the adsorption isotherms. Carrott and Sing[516] employed the virial analysis of experimental data to calculate the limiting isosteric heats of adsorption for methane on microporous carbons. They found good agreement with gas chromatographic measurements. They also analyzed adsorption on zeolites and found a discrepancy that they attributed to speciÞc adsorbateÐ adsorbent interactions. Another conclusion of their study is that the virial analysis can provide useful information about the nature of the adsorbent pore structure and the mechanism of pore Þlling. Another use of virial analysis was made by Nodzen«ski[517] in studying methane and carbon dioxide adsorption on hard coal samples from the Lower Silesia Coal Basin. A thermal sorption equation in the virial form[65,518] was used to calculate the isosteric heat. Values of the isosteric heat and their trends as a function of coverage were indicative of an adsorption Ðabsorption mechanism. Indeed, the isosteric heat was at a maximum for a coal with a fairly loose structure, which can be expected to facilitate penetration of the sorbate molecules into the bulk of the coal matrix. Studies of nonisothermal desorption led to similar conclusions. Rybolt and coworkers[519,520] studied the correlations of HenryÕs law and gas Ð solid virial coefÞcients with chromatographic retention times. For adsorption of 17 species (mainly hydrocarbons and alkyl halides) on Carbopack C, they found that the second virial coefÞcient and gas Ð solid interaction energies are correlated with molar refractivity of the adsorbate. They also calculated the surface area of Carbopack and obtained good agreement with the BET value even though they included in their determination all the adsorbates studied. Finally, they argued that their investigation of the gas Ðsolid interactions not
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only provides a method to measure the area of a solid but also uses surface area consistency with the adsorbate as a means of testing the validity of the parameters chosen to predict gas Ð solid interactions. These studies were closely related to another report by Meeks and Rybolt[521] in which the authors studied 63 gases adsorbed on different solids (zeolite, silica gel, carbon blacks, and microporous carbons). They correlated the adsorption energies with molecular parameters such as the boiling point and a critical constant ratio involving critical temperature and critical pressure. Okambawa et al.[522] carried out a virial analysis of methane adsorption isotherms determined on samples of a commercial coconut char (CNS 201, Carbon Canada Inc.) steam-activated for different periods. Figure 3.34 shows the obtained B2a values as a function of the activation time. B2a initially decreases, corresponding to a decrease in the cumulative pore volume for pore widths between 1.20 and 1.93 nm. Then B2a increases passing through a maximum and then it decreases again. This Þnal step corresponds to a widening of the pores with widths between 1.20 and 1.93 nm. The maximum in the B2a vs. activation time curve indicates the existence of an optimum activation period, as expected and as established, for example, by Alcan÷iz-Monge et al.,[523] MolinaSabio et al.,[524] and Walker.[525] Finally, the authors proposed that this gas Ð solid virial coefÞcient approach can provide a systematic tool for optimizing the activation process. The second virial coefÞcients for Ne, Ar, Kr, and Xe adsorbed on a graphitized carbon black have been calculated in a pioneering study of Sams et al.[526]
Figure 3.34 Experimental second gas Ð solid virial coefÞcient for methane adsorption on a coconut char steam-activated for different times. (Adapted from Okambawa et al.[522] Copyright 2000 American Chemical Society.)
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They determined the adsorption isotherms of these gases in a wide temperature range with the aim of calculating their interaction parameters with the surface of graphite employing the method developed by Steele and Halsey.[28] They studied a large number of interaction potentials and calculated the corresponding parameters. Finally, they tried to choose one among the whole set using the surface area of the adsorbent as a decisive factor. They concluded that they could not settle for a reasonable one due to experimental error, and thus suggested that the use of a higher surface area adsorbent as homogeneous as graphite is necessary to overcome this problem. In another paper, Sams et al.[527] presented additional experimental data for Ar adsorption on a graphitized carbon black covering a larger surface coverage range. They applied the virial equation of state including the third virial coefÞcient. They were able to determine the gas Ðsolid interaction parameters from the second virial coefÞcient and the gas Ð gas interaction parameters from the third virial coefÞcient. The area of the ¬ller adsorbent, used as the selection criterion, indicated that the KirkwoodÐ Mu formula for second-order interaction was the best. Johnson and Klein[528] calculated the second virial coefÞcient using two forms for the interaction energy between adatoms. They found that the Sinanogùlu and Pitzer potential,[529] which assumes a triple dipole force, gives rise to a repulsion term between adatoms that is proportional to r23. This potential gave the best agreement between experimental and calculated surface areas of the adsorbent. Johnson and Klein[530] also studied the interactions between adsorbed molecules for the system Ar/graphite. They calculated the second virial coefÞcient using the McLachlan approximation[531] of the adsorbent to obtain the gas Ð solid potential. From a comparison of their results and the available experimental data, they concluded that there could be other contributions to the lateral interactions not allowed for in McLachlan theory (e.g., noncontinuum effects such as an inhomogeneous electric Þeld at the graphite surface). One of the rare occasions in which higher gas Ðgas virial coefÞcients have been calculated was in a paper by Ree and Hoover.[532] They presented a calculation of the Þfth and sixth virial coefÞcients for hard spheres and hard disks. They obtained these coefÞcients as sums of modiÞed star integrals containing Mayer f and ( f þ 1) functions and demonstrated that the number of topologically distinguishable graphs occurring in the new expressions was about half the number required in previous expressions. Later, Wolfe and Sams[533] discussed the use of the method developed by Barker and Everett to determine the surface area of the adsorbent. Their conclusions can be summarized in three statements: (i) the results depend slightly on the exact form of the function chosen to represent the interaction potential; (ii) there is also a dependency on the nature of the adsorbate; and (iii) the area obtained depends markedly on the equation used to evaluate the dispersion energy constant. Moreover, they employed four noble gases and the obtained areas did not differ by more than 5%. They pointed out that larger variations were observed when dealing with heterogeneous surfaces.
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Soko·owski [534] derived the expressions for calculating the virial coefÞcients using the graph theory. His analysis showed that the gas Ð solid virial theory is imprecise and leads to an erroneous deÞnition of higher virial coefÞcients. However, he found that the deÞnition of the HenryÕs law constant is the same in both formulations. In a later paper, Soko·owski and Stecki [535] calculated the 3D pseudo-planar virial coefÞcients and compared the Þrst two 3D pseudoplanar ones with 2D coefÞcients. Their calculations show that the third 2D and 3D pseudo-planar coefÞcients exhibit similar behaviors. However, the differences between the 2D and 3D pseudo-planar coefÞcients are larger for the third coefÞcients than for the second ones. Soko·owski [536] also investigated the effect of nonsphericity and quadrupole moment of the adsorbed molecules on the 3D second virial coefÞcient for nitrogen adsorption on graphite. Krizan[537] has also calculated the 3D virial coefÞcients using a Lennard-Jones potential plus the three-body force derived by Sinanogùlu and Pitzer.[529] He concluded that for the particular case of Ar/carbon black the 2D approximation is very good. Al-Muhtaseb and Ritter[538,539] derived a new virial isotherm for single and multicomponent gas adsorption equilibria to predict the isosteric heat of adsorption. They considered virial coefÞcients with two different orders of temperature dependencies. The coefÞcients with a Þrst-order dependence on reciprocal temperature showed that the single-component isosteric adsorption heat is temperature-independent. However, those coefÞcients with a second-order dependence on reciprocal temperature indicated that the single-component isosteric heat could signiÞcantly change with temperature. Both types of coefÞcients showed signiÞcant temperature dependence for the multicomponent isosteric heat of adsorption. Ahmadpour et al.[540] studied the adsorption equilibrium of methane, ethane, propane, and CO2 as well as the binary mixtures of methane with the other three gases on commercial activated carbon Ajax and three activated carbons prepared by KOH activation of macadamia nutshells (NSK25, NSK100, and NSK500). Data from the literature[87] for Nuxit-al activated carbon were used as well. The authors employed six models to analyze the experimental data: IAST, loading-dependent isosteric heat (IHFL), micropore size distribution (MPSD), adsorption energy distribution function (ED), extended Sips model (ES), and extended Langmuir isotherm (EL). The results are summarized in Table 3.12, which shows that all the models describe the experimental data for the commercial activated carbons with reasonable accuracy, but only the model based on the isosteric heat as a function of loading, which takes into account the heterogeneity of carbons through the adsorbate Ðadsorbent interactions, could reasonably predict the data for the three KOH chemically activated carbons (NSK25, NSK100, and NSK500). Afzal et al. studied the adsorption at different temperatures of methanol[541] and acetone[542] on an activated carbon (Merck 2184) and metal (Cd, Cu, Ni, or Zn)-doped carbons. Adsorption free energies, enthalpies, and entropies were
Physical Adsorption of Gases and Vapors on Carbons
Table 3.12
313
Comparison of Model Performance for Binary Gas Adsorption Data
Prediction Models Carbons
System
IAST
IHFL
MPSD
ED
ES
EL
Nuxit-al Ajax
CH4 ÐC2H6 CH4 ÐCO2 CH4 ÐC2H6 CH4 ÐC3H8 CH4 ÐCO2 CH4 Ð C2H6 CH4 Ð C3H8 CH4 ÐCO2 CH4 Ð C2H6 CH4 Ð C3H8 CH4 ÐCO2 CH4 Ð C2H6 CH4 Ð C3H8
G G B B A A B B B B A B B
G A G G B G B B G B A A B
G A G G G A B B B B B B B
G G G G B A B B B B B B B
G G G A A A B B B B B B B
G G G A A A B B B B B B B
NSK25
NSK100
NSK500
Note: G, good; A, acceptable; B, bad. Model reference codes: see text. Source: Reproduced from Ahmadpour et al.,[540] with permission from the American Institute of Chemical Engineers.
calculated using the virial and Langmuir isotherm expressions. Values of these magnitudes indicated that interactions of methanol or acetone were stronger with the metal-doped carbons, probably due to methanol or acetone chemisorption on metallic sites. A positive correlation was found between adsorption enthalpy and electronegativity of the metals, suggesting that the adsorbates, which are polar in nature, interact strongly with metal sites (e.g., by inductive or speciÞc interactions which depend on the electronegativity of the metal). Gusev et al.[543] reported N2 and argon adsorption on the fullerene C60 (quoted purity of 99.5%, from Dynamic Enterprises, Ltd.) and a mixture (76% C60/22% C70, from PINP). They analyzed their experimental data using a virial expansion in the HenryÕs law region and found that, in the low-pressure limit where the ßuid Ðßuid interactions are negligible, the N2 interaction with the fullerene surface is macroscopically similar to that with graphite, whereas in the major part of the monolayer the N2 and Ar afÞnity for the fullerenes is weaker than for graphite. Based on the virial isotherm, Bottani and Steele[544,545] proposed a new approach to the theory of adsorption isotherms on heterogeneous surfaces. Theoretical descriptions of adsorption on heterogeneous surfaces are often based on the idea that the surface can be represented by a lattice of sites with different adsorption energies. These sites are taken to be independent from each other except possibly for mean Þeld interaction energies with neighboring adsorbed molecules. It is generally assumed that each site is capable of holding one adsorbed
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molecule in the monolayer. The adsorptive properties of such a surface are then characterized by a distribution of these sites over their adsorption energies. This model has several drawbacks: it does not lend itself to treatment of adsorption of mixtures of molecules with different sizes, since a site area chosen to accommodate one size will not give a good Þt to other molecular sizes. Moreover, it appears that the Þnal monolayer capacities for different physically adsorbed molecules often do not correspond to adsorption on a Þxed number of sites but rather to nearly close-packed arrays of adsorbate molecules. Furthermore, models of the surface of amorphous materials yield complex adsorption energy surfaces for which the concept of adsorption sites as a regular array of points is found to be a gross oversimpliÞcation. The actual energy surfaces exhibit large regions of high adsorption energy corresponding to nanovalleys. These surfaces also show ÒpartialÓ sites, where shallow minima occur in an otherwise rapid monotonic energy variation; and Þnally, there are regions of relatively small minimum energy that take up signiÞcant fractions of the total surface area and thus are hard to account for in the usual sitewise models. In the new approach, it is suggested that one replace the idea of an adsorption site with what the authors called a ÒsupersiteÓ. These supersites are obtained by dividing the surface into a regular lattice of elements that are sufÞciently large to hold several adsorbed molecules (on the order of four to six). Within each supersite, the energy will vary from point to point so that surface heterogeneity is maintained. The local isotherm concept is retained, but in a form which allows more than one molecule per site. It must be pointed out that the patchwise approach is an example of the supersite model in which each supersite is homotactic. The authors tested this theory with computer simulation results obtained for N2 adsorption on amorphous carbonaceous solids, and concluded that one advantage of the supersite approach is that it allows one to better deal with the effects of lateral interaction. It is possible to evaluate the mutual interactions between the small numbers of molecules on a supersite to good precision, as in virial coefÞcient calculations, and then append a mean Þeld estimate of the interactions between molecules on neighboring supersites. In this way, at least part of this energy could be accurately calculated and the effects of variations in the spatial distributions of sites over the surface will be minimized. 3.3.3.2.
Integral Adsorption Equation
This section is devoted to the study of surface heterogeneity as inferred from the adsorption isotherm. This subject has deserved the attention of many researchers since a long time ago.[546 Ð 552] Once the experimental data showed that the accepted models, assuming uniform homogeneous surfaces, were inadequate for certain systems, the concept of surface heterogeneity became the focus of many studies. Langmuir himself had recognized that his assumption of a uniform surface must be the reason why his model could not account for certain experimental facts. The heterogeneity of a surface has at least two origins: surface
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315
imperfections and chemisorbed species on the surface or substitution of surface atoms. The Þrst is usually known as structural or geometric heterogeneity and the second is called energetic heterogeneity. Everett[553] has discussed some problems in the study of surface heterogeneity concerning the uniqueness of the description obtained. Several methods have been proposed to characterize the surface heterogeneity of adsorbents.[554 Ð 568] Terzyk and Rychlicki[569] have discussed several empirical relationships that correlate the adsorption energy with physicochemical parameters of the adsorbate. They studied the adsorption of CH2Cl2, CHCl3, C2H6, C3H7Cl, CH2Cl2, and iso-C3H7OH. They determined the adsorption enthalpy and the entropy at zero surface coverage and then correlated these quantities with molecular parameters of the adsorbed molecules. They argued that the derived relationships could be employed to determine the porosity of the adsorbent. Wang and Hwang[570] derived a general isotherm to describe multilayer adsorption on heterogeneous surfaces. They investigated the effects of the polarity and molecular weight on the gas Ð solid and gas Ð gas interactions. They argued that their model Þtted the experimental data better than the model previously developed by Do and Do.[571] This last model was based on the analysis of the dependence of the isosteric adsorption heat on the surface coverage for adsorption on a heterogeneous surface. Daþbrowski et al.[572] have compared the energy distributions obtained from gas Ð solid and liquid Ðsolid adsorption data. They found good agreement between both distributions provided a regularization procedure is employed to solve the integral equation. We begin by showing the derivation of the integral adsorption equation. Consider the surface of an adsorbent having L types of adsorption sites and let nL be the amount adsorbed on adsorption sites of the Lth type. Each site is characterized by an adsorption energy 1L. Thus the total amount adsorbed on the entire surface, called the overall adsorbed amount, must be the sum of the local adsorbed amounts, nL, comprising all the Lth type adsorption sites. In mathematical terms this is expressed as nt ¼
L X
nL
(3:136)
i¼1
where nt is the overall adsorbed amount. The fraction of adsorption sites of the Lth type, fL, is given by fL ¼
noL no
(3:137)
where noL and no are the number of Lth type sites and the total number of adsorption sites, respectively. Substituting Eq. (3.137) into (3.136) and introducing the overall (ut) and local (uL) surface coverages gives:
ut ¼
L X i¼1
fL u L
(3:138)
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The overall surface coverage is a function of equilibrium pressure, p, and temperature, T. The local surface coverage is a function of pressure, temperature, and adsorption energy of the given adsorption site. These quantities, ut(p, T) and uL(p, T, 1L), are called the overall and the local isotherm, respectively. Equation (3.138) deÞnes the overall adsorption isotherm for surfaces with a discrete distribution of adsorption energies. This distribution may be expressed as F(1) ¼
L X
fL d(1 1L )
(3:139)
i¼1
where d(1 2 1L) is DiracÕs delta function. The normalization condition requires that L X
F(1) ¼ 1
(3:140)
i¼1
If the number of adsorption sites approaches inÞnity, the summation in Eq. (3.138) can be replaced by integration: ð u( p, T) ¼ u(p, T, 1)F(1)d1 (3:141) V
If the temperature is kept constant, it can be removed from the equation and, if the adsorbed quantity is explicitly introduced instead of surface coverage, Eq. (3.141) can be written as ð v( p) ¼ vm u( p, 1)F(1)d1 (3:142) V
where v(p) is the overall amount adsorbed expressed as the equivalent of gas volume per gram of adsorbent, and vm is the monolayer capacity in the same units. The integration is performed over the entire range of adsorption energies, V. Later we will discuss this point; thus for the moment it is left undeÞned. The normalization condition now takes the form: ð F(1) ¼ 1 (3:143) V
Equation (3.142) is the fundamental equation in the theory of adsorption on heterogeneous surfaces and is sometimes called the integral adsorption equation. It can be analytically solved for different cases but it is necessary to deÞne a priori the local isotherm equation and the energy distribution function. In this way, it is possible to obtain most of the empirical adsorption isotherms. Even though this could lead to useful results, it is seldom used because one is interested in obtaining the true distribution function for adsorption energies. From a physical point of view, however, Eq. (3.142) is not correct since the adsorption energy
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317
must be a discrete magnitude. Nevertheless the energy spectrum is so dense that considering F(1) a continuous function introduces negligible error. The next question to be solved before using the integral equation concerns what is called the topography of the surface. In the beginning, the adsorption sites with equal adsorption energy were grouped in surface regions called patches. These patches could be considered as independent adsorption systems. Each patch is large enough to ensure that border effects are negligible and no interactions between adsorbed molecules on different patches are included. Since each patch is characterized by constant adsorption energy it is possible to use, as a local isotherm, all the empirical equations obtained for homogeneous surfaces. The other topography commonly employed is the one that assumes a random distribution of adsorption sites on the surface.[573] Steele[497] published a general approach to the theory of physically adsorbed monolayers on heterogeneous surfaces. He developed the equations to describe adsorption properties in terms of the distribution function for single sites, pairs of sites and similar higher order functions. Rudzin«sky and Baszyn«ska[574] studied the inßuence of the topography of adsorption sites on calorimetric effects in adsorption. They employed the Bragg Ð Williams lattice gas using both patchwise and random topographies, and a quasi-Gaussian distribution was employed to represent the adsorption energy distribution function. Energetic heterogeneity and molecular size effects in physical adsorption have been studied by Marczewski et al.,[575] particularly the relationship between the energy distribution function and the molecular size of the adsorbate. They proposed equations that could be employed to describe adsorption from gas as well as liquid phases. Cascarini de Torre and Bottani[576] have modiÞed the BET equation to introduce the heterogeneity of the adsorbent. They assumed several adsorption energy distribution functions: Gaussian, Weibull, and double Gaussian. Although the heterogeneity introduced in the model produces changes in the Þrst layer only, these are enough to explain several experimental facts, such as the surface coverage dependence of the BETC parameter and the inversion of the adsorption isotherms determined at temperatures very close to each other.[577] Having in mind that the main goal pursued with Eq. (3.142) is to obtain the adsorption energy distribution function from the overall adsorption isotherm, this equation could be employed in different ways. For example, it is possible to try to obtain F(1) by direct inversion of Eq. (3.142). From the mathematical point of view, Eq. (3.142) is a Fredholm Þrst kind integral equation.[578] Equation 3.142 can be written in matrix notation, Ax ¼ b
(3:144)
where A is the matrix of the local isotherm multiplied by the quadrature coefÞcients, x is the vector representing the adsorption energy distribution, and b is the vector containing the overall isotherm. Several authors have described the mathematical problems found to solve the Fredholm integral equation; see,
318
Bottani and Tasco´n
for example, Hagin[579] and Varah.[580,581] To use Eq. (3.144) it is necessary to assume or select a local isotherm among all the classical equations (e.g., Langmuir, van der Waals, and BET). Once this selection is made it is possible to try a direct inversion of Eq. (3.144) using conventional matrix inversion procedures. After the inversion is done, one obtains the F(1) and can calculate the overall isotherm to compare with the experimental one. Figure 3.35 shows the adsorption isotherm obtained for the system N2/Carbopack B experimentally and the one calculated with Eq. (3.144). Both isotherms are virtually identical (the average deviation between experimental and calculated values is less than 1026 mL/g). Figure 3.36 displays the corresponding distribution function where it can be seen that the obtained distribution lacks any physical meaning since it oscillates between negative and positive values. These oscillations are due to the ill-posed nature of the problem. In fact, in Eq. (3.144) the matrix of the local isotherm, A, has its rows that are not absolutely linearly independent. The oscillations are also ampliÞed by the fact that the inversion procedure tends to magnify the errors in the experimental points.[582] The Þrst and probably the most naõ¬ve way to overcome this problem is to restrict the solutions to positive values. This option only yields distributions that have larger positive peaks to compensate for the negative ones previously obtained. In summary, another kind of mathematical procedure must be employed if a realistic and meaningful solution to Eq. (3.142) is the desired goal. Assuming a local isotherm, Adamson and Ling[583,584] developed a graphical method to obtain F(1) from an experimental isotherm. They obtained reasonable results for certain systems but the procedure is lengthy and somewhat inaccurate. This method has been recently employed by Schro¬der et al.[585,586]
Figure 3.35 Eq. (3.144).
N2 adsorption isotherm on Carbopack B at 80.2 K. Calculated points with
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319
Figure 3.36 Adsorption energy distribution function obtained by direct inversion of Eq. (3.144) for the experimental isotherm shown in Fig. 3.35.
to determine the surface heterogeneity of carbon blacks using ethene adsorption (some results will be dealt with later in this same section). Returning to Adamson and LingÕs method, the problems posed by the graphical method impose the necessity of seeking another solution to the problem. Thus, a numerical method that complies with several conditions must be developed. First, it should be a fast converging one; second, the loss of information must be minimum; and third, it must be reproducible and not depend on arbitrarily chosen parameters. The problem is not an easy one as could be deduced from certain special characteristics of the equation, as has been pointed out by Guy et al.[587] Several methods have been proposed and we will summarize them in the following paragraphs. The Þrst method is known as HILDA (heterogeneity investigated at Loughborough by distribution analysis), and was developed by House and Jaycock.[588] In principle the method is a modiÞcation of the one developed by Adamson and Ling.[583] The Þrst approximation to F(1) is obtained as in Adamson and LingÕs method using the condensation approximation (CA) for the local isotherm (on the use of the CA, see, e.g., Hsieh and Chen[589]). The procedure is iterative, and, once the minimum in the deviation between experimental and calculated data is reached, the obtained distribution is numerically derived to obtain the correct function. Unfortunately, numerical derivation is not a very precise and reliable method. The second method is known as computed adsorption energy distribution in the monolayer (CAEDMON) and has been developed by Ross and Morrison.[590] This method takes as starting point the ideas originally published by Ross and Olivier.[496] The main idea is that the distribution function of adsorption energies
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320
is generally a Gaussian one. The CAEDMON method is iterative based on the assumption of patchwise heterogeneity and virial series as local isotherms. The integral equation is written as nt ( p) ¼
L X
Ai ui (p=ki )
(3:145)
i¼1
where Ai and ki are, respectively, the area and the HenryÕs constant for the ith patch. Equation (3.145) deÞnes a set of equations that is solved by choosing a set of ki values between predetermined limits that are obtained from the upper and lower pressures of the experimental isotherm. Once the limits are deÞned, the procedure continues with the deÞnition of an initial distribution of the areas of the patches, Ai. Usually an equal area is Þrst assigned to all patches. Then a systematic serial adjustment of the areas is performed until an absolute minimum is reached. If in the adjustment process an Ai becomes negative, it is set equal to zero and the process continues, so any unreal solution is avoided. The method was tested with the system Ar/carbon blacks with different degrees of graphitization. Figure 3.37 shows the distribution functions obtained, which make it clear how surface homogeneity increases with increasing graphitization temperature. Wesson et al.[591] compared the speciÞc areas obtained from mercury porosimetry, BET method, and using the CAEDMON analysis for argon and nitrogen adsorption data on pristine glass Þlaments. They found
Figure 3.37 Adsorption energy distribution functions obtained with CAEDMON for Ar adsorption on graphitized carbon blacks (T: heat treatment temperature). (Adapted from Ross and Morrison,[590] with permission from Elsevier.)
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321
good agreement between the methods involving gas adsorption and the geometric value of the Þbers. Sacher and Morrison[592] improved CAEDMON by incorporating other optimization techniques for which uniqueness and convergence criteria exist. They discussed several methods and Þnally concluded that, if the criterion of minimizing the sum of squared relative deviations is chosen, a nonnegatively constrained linear least squares method is the best for the minimization problem. In other cases, they could not make a clear choice due to problems in the implementation of the simplex method. House[593] has analyzed the consequences of the ill-posed nature of the system of Eq. (3.144) on the solution of Fredholm integral equations of the Þrst kind. Equation (3.144) can be written as v( pj ) ¼
t X
wi uij ( pj , 1i )F(1i )
for j ¼ 1, 2, . . . , s
(3:146)
i¼0
where t is the number of intervals taken in the integration according to SimpsonÕs rule, wi are the quadrature weighing coefÞcients, and s the number of experimental points. Small perturbations in v( p) lead to large variations in F(1).[594] The magnitude of the perturbations depends on the experimental accuracy and the form of the local isotherm chosen. The solution to this problem could be found, at least theoretically, using a regularization[595] procedure to perform the inversion of Eq. (3.142). The method incorporates the experimental error in the matrix Eq. (3.144); thus b þ e ¼ Ax
(3:147)
where e is the vector of the absolute experimental errors affecting the experimental data b. As has been previously said, if the system is solved with e ¼ 0, large oscillations between negative and positive values are obtained, and the solution is physically meaningless. The way in which the errors are treated leads to variations of the regularization method. A general application program (CONTIN) to solve Fredholm integral equations of the Þrst kind has been developed by Provencher.[596,597] The program, which uses a cubic spline smoothing process, is available from the author (S.W. Provencher) upon request and a good user guide and the corresponding mathematical background as well as test data is provided. Merz[598] employed a generalized cross-validation technique to solve the problem. He also presented a concavity criterion to choose among the different local isotherms that can be employed. According to Merz, the most serious problem with the general adsorption equation is model correctness rather than the ill-posed character of the problem. That is why he proposed the concavity criterion. Very recently, Gauden et al.[599] developed a new procedure called adsorption stochastic algorithm (ASA) to solve the Fredholm equation and tested it with N2 adsorption data on activated carbon Norit Row 0.8 Supra. Recently, Puziy et al.[600] employed the program CONTIN to calculate the pore size distribution of a series of synthetic carbons activated with phosphoric
322
Bottani and Tasco´n
acid. The authors compared the results obtained using several methods to determine the pore size distribution and found good agreement. A good example on how structural and chemical characteristics of activated carbon of wood origin can be obtained using N2 adsorption has been reported very recently.[426] Szombathely et al.[601] used the regularization procedure to argue that the information provided by the distribution function strongly depends on the experimental errors and on the range of the measured isotherm. Brown and Travis[602] analyzed the problem of optimal smoothing of the site-energy distribution functions obtained from the isotherms. They studied the accepted smoothing criterion proposed by Butler et al.[603] and demonstrated that this criterion is too conservative (i.e., it will never introduce non-existent features in the distribution but signiÞcant information could be lost). Bereznitski et al.[604] also studied the inßuence of the analysis conditions on low-pressure adsorption measurements and its consequences on the characterization of energetic and structural (geometric) heterogeneities of microporous carbons. Heuchel et al.[605] published a systematic study of the energetic heterogeneity of a wide set of graphitized and nongraphitized reference carbonaceous materials using several standard adsorption isotherms. The adsorption energy distribution functions were calculated with an algorithm based on the regularization method. They employed adsorbates of very different chemical nature and molecular complexity like Ar, N2, n-butane, neopentane, and benzene. As an example, Fig. 3.38 compares the distribution functions of N2, argon, and n-butane on an activated carbon (Ap) from olive stones heat-treated to 2073 K to obtain a nonporous reference material similar in surface chemical nature to
Figure 3.38 Distribution functions of nitrogen, argon, and n-butane on an activated carbon (Ap) heat-treated to 2073 K to eliminate micropores. (Reproduced from Heuchel et al.[605] Copyright 1993 American Chemical Society.)
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323
conventional activated carbons.[606,607] The functions for N2 and Ar have sharp peaks, whereas the one for n-butane is a broader distribution with two maxima at higher energies (28 and 37 kJ/mol). The authors attributed the splitting into two peaks to structural differences between the adsorbate molecules; this was supported by the fact that spherical neopentane gave only a single peak. The main conclusions of their detailed comparison of the energy distribution functions were that strong differences exist among the studied reference materials (nonporous carbons), and that the use of several adsorbates provides additional information about the energetic heterogeneity of the adsorbent. The regularization method has been employed by Kruk et al.[608] to calculate the adsorption energy distribution function for a series of commercial carbon blacks using N2 adsorption. Ryu et al.[609] demonstrated that the DFT, employing the regularization procedure, provides profound insight into the structural heterogeneity of carbonaceous adsorbents. Vos and Koopal[610 Ð 612] developed a method known as CAESAR (computed adsorption energies, SVD analysis result), based on the singular value decomposition technique,[613] to control the ill-posed character of the integral adsorption equation. They argued that an advantage of CAESAR over other methods is that the errors owing to experimental inaccuracy and the approximate nature of the local isotherm are explicitly taken into account in the calculations. As a result, the distribution function shows the maximum amount of relevant detail. Jagie··o and Schwarz [614] analyzed adsorption data based on local analytical exact and approximate solutions of the integral equation. The local exact solution implies the use of Langmuir equation as local isotherm, thus accepting the localized adsorption model with no lateral interactions between adsorbed molecules. In this method, the accuracy of the calculated distribution can be improved by lowering the adsorption temperature and the experimental pressure range covered by the isotherm determines the range of adsorption energies. Bra¬uer et al.[615] developed the program EDCAIS (energy distribution computation from adsorption isotherm utilizing the smoothing spline functions), which uses quasi-Langmuir local isotherms involving multilayer corrections. This method leads to a solution through an integral transform method when the experimental error is non-existent. In other cases, a smoothing process must be applied to the experimental data. The authors recommended the use of cubic splines for the smoothing. Jagie··o [616] has extensively analyzed the stability of the solutions obtained using B-splines to smooth the distribution; he also discussed the accuracy of the solution in relation to the experimental error in the data and the complexity of the true distribution function. He proposed the use of a comprehensive analysis of the variance of the solution, and of the effective bias introduced by the regularization method, to facilitate the optimal smoothing degree choice. Mehrotra[617] developed a method to solve the integral equation based on the use of LobattoÕs quadrature formula and a previous transformation of the
324
Bottani and Tasco´n
integrand. The parameter evaluation is made through a nonlinear optimization technique. He also indicated that with this method the monolayer capacity could be estimated. Langmuir equation is employed as local isotherm. Hocker et al.[618] proposed the method of projections onto convex sets (POCS) to calculate the adsorption energy distribution function from the integral adsorption equation using the Langmuir equation as local isotherm. This method allows the incorporation, into an iteration scheme, of available information about the experimental data and the measurement error as well as a priori constraints, such as nonnegativity, based on physical reasoning. They tested the method by recovering the distribution functions of simulated data. Cerofolini[619] showed that replacing the local isotherm by a kernel, which considered as a function of the pressure contains a discontinuity or an angular point (i.e., a point where the Þrst derivative is discontinuous), transforms the Fredholm integral equation into a Volterra integral equation whose solutions are very well known. Cerofolini[620] also indicated that, for a Fredholm integral equation of the Þrst kind, the problem of existence and of uniqueness of the solution had been resolved by Sips[621,622] in 1950, using the theory of Stieltjes transforms to Þnd a closed solution, and by Landmann and Montroll[623] in 1976 using a Wiener ÐHopf technique. Cerofolini also analyzed the problem of existence, uniqueness, and stability of the solution. He concluded that the exact method gives the distribution function for the whole energy range but this requires the knowledge of the overall isotherm outside the physical region. The approximate local methods require the knowledge of the overall isotherm only in the experimental region but give an approximate estimate of the distribution function in a restricted energy range. The Stieltjes transform has also been employed by Prasad and Doraiswamy[624] to derive a limiting isotherm similar to the Fowler Ð Guggenheim equation. One question always present concerns the choice of local isotherm and its inßuence on the adsorption energy distribution function. Bra¬uer and Jaroniec[625] have discussed this problem and considered several criteria for simplifying the choice. Their discussion was mainly centered on the concavity criterion. They pointed out that any selection criterion could be complicated if, in the calculation of the distribution function, constraints are imposed to avoid negative values of the distribution function. Equation (3.142) has been employed by Silva da Rocha et al.,[626] who derived an expression for the adsorption isotherm as an extension of the Freundlich isotherm, using the Langmuir isotherm as local isotherm. Later, the same authors[627] studied the inßuence of the temperature on the parameters of the extended Freundlich isotherm. A different approach to calculate the distribution function, which exploits the Fourier convolution nature of the Þrst-kind Fredholm integral equation, has been proposed by LumWan and White.[628] A local isotherm is assumed and the method can handle a wide variety of local isotherm types including both patchwise and random distributions, as well as the effects of lateral interactions.
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OÕBrien and Myers[629] have analyzed the effect of lateral interactions using numerically simulated data. They concluded that large deviations from the true adsorption energy distribution function occur when relatively small lateral interaction effects are ignored. They also studied[630] an alternative way to solve the integral equation by reformulating the right-hand side of Eq. (3.141) as an inÞnite series whose terms involve derivatives of the local isotherm with respect to the energy and the central moments of the distribution. With their approach, no integration is needed. In addition, if the inÞnite series converges rapidly it is possible to evaluate the local isotherm with knowledge of only the Þrst few central moments of the energy distribution. Unfortunately, they tested their model mostly with simulated data and only one experimental data set,[631] namely CO2 adsorption on an activated carbon at three temperatures. Cascarini de Torre and Bottani[632] calculated the distribution function assuming both the local isotherm and the distribution function. The problem is reduced to a least squares search of the minimum in an i-dimensional hypersurface where i is the number of adjustable parameters included in the local isotherm and the distribution function. The minimization condition is ) (X s @s 2 @ 2 ¼ ½v( pi ) vc ( pi ) ¼ 0 for j ¼ 1, 2, . . . , n (3:148) @aj @aj i¼1 where s 2 is the square of the deviation between experimental and calculated values of the adsorbed amount, v(p), and n is the number of experimental points. The aj are adjustable parameters determined when the minimum in the deviation is achieved. Finding the absolute minimum of a hypersurface is complicated by the existence of an unknown number of local minima. The program developed uses two algorithms to search for the minimum. When the solution is far from the suspected minimum, a grid method is employed. As the solution approaches the minimum, the search method is changed to a gradient[633] search. The accuracy required in the parameters is limited by the experimental error in the overall isotherm; thus, it is unnecessary to use other sophisticated mathematical methods.[613] The computer code automatically switches between searching methods making the program very efÞcient. Since the method cannot guarantee that the absolute minimum has been found, it is necessary to use another criterion to choose the correct solution. If the integral equation is written as Eq. (3.142), the monolayer capacity is the normalization parameter of the integral. Since the monolayer capacity is known from the overall isotherm, through BET or any other model, it is possible to perform the minimization process several times and to choose the solution that better reproduces the experimental monolayer capacity. Cascarini de Torre and Bottani[632] have carried out computer simulations on model heterogeneous solids (amor1, amor2) in order to obtain the overall adsorption isotherm. Then the obtained isotherm is processed with the proposed algorithm and the best solution is obtained. Figure 3.39 shows the simulated and calculated adsorption isotherms. For example, one of the
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Figure 3.39 Computer simulated nitrogen adsorption isotherms (empty symbols) obtained for two model amorphous solids (amor1 and amor2), compared with the isotherms calculated solving Eq. (3.142) (symbols containing plus signs). (Adapted from Cascarini de Torre and Bottani,[632] with permission from Elsevier.)
simulated isotherms shown gives a BET monolayer Vm ¼ 116.52 molecules, while the best solution gives Vm ¼ 114.6 molecules, and the overall deviation is 5.2 1024. Since the model surface is known, it is possible to calculate the true adsorption energy distribution function and then to compare it with the solution obtained for Eq. (3.142). The results are shown in Fig. 3.40. The solution is in excellent agreement with the true distribution function, and the agreement can be improved if a distribution more ßexible than Gaussian is employed. Sircar[634] described an analytical method to solve the integral equation assuming both the local isotherm (Jovanovic model) and a gamma probability density function for the distribution function. He tested the method using literature data for several adsorbed gases on BPL[635] and MSC V[636] microporous heterogeneous activated carbons. He compared the Jovanovic model[637] as local isotherm with the Langmuir isotherm and concluded, intriguingly, that both models are capable of describing the experimental data but produced very different distribution functions. Figure 3.41 compares the energy probability density functions calculated from the two models. The Jovanovic-local model indicates larger heterogeneity of the carbon surface than the Langmuir-local model for all systems. The author argued that, despite this dependence of the calculated energy distribution function for a heterogeneous adsorbent on the choice of the local isotherm equation, these results may be useful for comparative evaluation of surface heterogeneities for adsorption of different gases on the same adsorbent or those of the same gas on different adsorbents.
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Figure 3.40 True energy distribution function (histogram) and solution obtained for Eq. (3.142) (Gaussian distribution) with the proposed method applied to isotherms from Fig. 3.39: (a) N2/amor1 and (b) N2/amor2. (Adapted from Cascarini de Torre and Bottani,[632] with permission from Elsevier.)
Casquero Ruiz et al.[638] used an exponential distribution function for the energy of the adsorption sites to obtain a multilayer adsorption equation. Their «s and Araya[639] model is based on the Frenkel Ð HalseyÐ Hill model. Corte derived the relationship between KaganerÕs model and the energy distribution function. They employed simulated data to test their conclusions and the condensation approximation for the local isotherm. They concluded that, since KaganerÕs model implicitly assumes a Rayleigh distribution, the usual criteria of the experimentalists, such as the adaptation of the model to the experimental data or independence of the recovered parameters with the pressure range are not sufÞcient. It would also be necessary to check the distribution curve, thereby making subsequent use of the Dubinin ÐRadushkevichÐ Kaganer equation less meaningful. Rudzin«ski et al.[640] developed a method to determine the adsorption energy distribution function using experimental isotherms and heats of adsorption. They tested the distributions corresponding to both random and patchwise topographies. The distributions obtained from the isotherm are identical to the
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Figure 3.41 Comparison of energy probability density functions derived from the Jovanovic and Langmuir-local isotherm models for CH4 and CO2 adsorption on two activated carbons. (Reproduced from Sircar,[634] with permission from Elsevier.)
ones obtained from the isosteric heats. The same behavior was observed for both topographies. Nieszporek and Rudzin«ski[641] studied the enthalpic effects accompanying the mixed gas adsorption on heterogeneous surfaces using the integral equation approach. They developed an extension of Langmuir Ð Freundlich equation for the case of gas mixtures and presented the expressions to calculate the isosteric adsorption heats. Their model requires data corresponding to pure adsorbates to calculate the properties of the mixture. Nieszporek[642] discussed the possibilities of the integral equation approach to study the adsorption of gaseous mixtures. He developed a generalization of the DA equation for the case of mixed-gas adsorption and compared it with experimental results from the literature for adsorption on zeolites. The main advantage of this study is that to predict isosteric heats of gas mixture components only the knowledge of isotherms and isosteric heats of single gases is required. Thus far, we have presented various methods developed to calculate adsorption energy distribution functions. In what follows, we will summarize a series of papers dealing with the applications of these methods or their modiÞcations to different systems involving carbon surfaces. In the particular area of microporous carbons, McEnaney[643] published a review that presents the most signiÞcant aspects of the subject prior to 1988 and includes sections on the generalized adsorption isotherm and estimations of micropore sizes. Jaroniec and Choma[644,645] characterized the heterogeneity of activated carbons using benzene adsorption data. Their method employed the exponential
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equation of the isotherm combined with a gamma-type distribution to obtain the adsorption energy distribution function. The micropore dimensions were extracted from the distribution function. Ethene adsorption has been investigated by Schro¬der et al.[586] to determine the energy distribution function of a series of commercial and experimental carbon blacks. They employed classical adsorption volumetry to obtain the isotherms from 0.001 to monolayer coverage, and identiÞed four discrete sites: graphitic planes (site I, 16 kJ/mol), amorphous sp3 carbon (site II, 20 kJ/mol), crystallite edges (site III, 25 kJ/mol), and slitshaped cavities (site IV, 30 kJ/mol). Table 3.13 shows the distribution of these four adsorption sites in the studied carbon blacks, which was discussed and found to depend signiÞcantly on the microstructure and primary particle size, manufacturing conditions and surface treatment (graphitization). Despite the signiÞcant difference in energy distribution functions, it seems worth mentioning that all four discrete types of sites were found in practically all carbons irrespective of morphology. Jaroniec et al.[646] developed an equation for the total retention volume obtained in gasÐsolid chromatography that can be related to the distribution function. Although they tested their method for the adsorption of cyclohexene and cyclohexane on porous silica, it is general enough to be used with other systems. The total net retention volume can be represented by the integral equation ð1 VN,t ( p) ¼ VN ( p, 1)Fo (1)d1 (3:149) 1m
where VN,t is the total retention volume and VN the local retention volume, given by @u VN ¼ jRT (3:150) @p T Table 3.13
Fractions of Energy Sites in Different Carbon Blacks
Sample Dgb (Degussa gas black) N115 EB1 (Degussa experimental black) N220 N550 N220g Pb2 (Plasma black) N990
SN2 (m2/g)
I (%)
II (%)
III (%)
IV (%)
267 143 121 118 44 88 107 9
71 77 81 84 93 99 99 96
5 10 7 7 6 Ñ Ñ Ñ
8 10 10 7 1 ,1 1 3
16 3 2 2 ,1 ,1 ,1 1
Note: Sites I, II, III and IV: see text. Source: Adapted from Schro¬der et al.,[586] with permission from Elsevier.
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They arrived at an expression that allows the calculation of the distribution function that is associated with the gamma function. This equation was found to yield a good description of the experimental data for different systems. Roles and Guiochon[647] employed IGC data to calculate the distribution function. They argued that their method, based on Stieltjes transform and using an iterative approach to Þnd the Þnal distribution function, is robust with respect to quasi-Langmuir isotherms. Donnet et al.[415] also employed IGC at Þnite concentration to determine the energy distribution for a series of carbon blacks using different probes. El-Sayed and Bandosz[438] employed IGC at inÞnite dilution to study acetaldehyde adsorption on nitrogen-containing activated carbons. They estimated the heats of adsorption from values of retention volumes. After modiÞcation with urea (which resulted in an increase in the total number of surface groups and a decrease in the surface area and the micropore volume), the interaction strength of acetaldehyde with the carbon surface was found to decrease. Jaroniec et al.[648] characterized oxidized activated carbon Þbers using a distribution function determined from low-temperature N2 adsorption isotherms. Employing the condensation approximation method, they concluded that a distribution showing two peaks could be associated with a bimodal porous structure of the carbon Þbers. They also reported changes in the distribution function with oxidation temperature. Jagie··o et al. [649] studied the effects of oxidation of activated carbons by means of high-pressure methane adsorption. They calculated the energy distributions and found that they are shifted to lower adsorption energies for oxidized carbons. The mean energy decreased, indicating that oxidized carbons have lower afÞnity for methane adsorption. To solve the integral equation they employed the local solution method,[650] which yields the distribution function directly from the isotherm as the series
F(1c ) ¼
r X n¼0
(1)nþ1
ðpRT Þ2n @2nþ1 V (2n þ 1)! @12nþ1 c
(3:151)
where r is the order of the approximation and 1c is the so-called condensation energy. They concluded that changes in the distribution function that occur as a result of surface oxidation are predominantly due to the presence of surface chemical groups. These groups may hinder the most favorable geometrical arrangement of adsorbed molecules and thus cause the observed decrease in the adsorption energy. Jagie··o et al. [651] studied the adsorption of linear and branched alkanes on several homemade, non-commercial and commercial activated carbons at supercritical temperatures. They obtained the adsorption energy distributions using methane and related them with the pore size distributions. From the temperature dependence of the isotherm, the isosteric heats were calculated and used to verify the model of the pore geometry assumed.
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Tsutsumi et al.[652] studied the oxidation and reduction conditions to control the number of functional groups in activated carbons. Through the analysis of the adsorption energy distribution function, they concluded that oxidation made them more energetically heterogeneous, but more homogeneous with respect to surface geometry. Jaroniec and coworkers[653,654] employed a model-independent analysis of low-temperature N2 isotherms to characterize oxidized activated carbons. The authors oxidized a series of commercial activated carbons in the liquid phase using several oxidizing agents such as H2O2 , HClO4 , and HNO3 . They could evaluate the distribution function, the surface area, and the micropore volume, which were subsequently employed to estimate the average micropore width. They found that the chemical treatment with those agents, at room temperature, did not cause a substantial change in the adsorption energy distribution function. On the other hand, oxidation with nitric acid at boiling temperature produced signiÞcant deterioration of the porous structure of the activated carbons in addition to different changes in their surface functionality, which was evidenced by the adsorption energy distribution. Kruk et al.[655] reported the preparation of novel synthetic activated carbons that they characterized, among other techniques, by calculating the distribution function from N2 isotherms.[656] Villie«ras et al.[657] calculated the energy distribution function using a method based on the summation of derivative local isotherms. Each local isotherm is described by three parameters: gasÐsolid interaction, lateral interactions, and the amount adsorbed on each surface patch. The relationship among these parameters and the position of a maximum of a local derivative isotherm is obtained using second-order derivative equations of the fundamental equation of gas adsorption on a homogeneous surface. The authors tested their method with quasi-equilibrium experimental data on two clay minerals (kaolinite and sepiolite). Hu and Do[658] postulated that the surface heterogeneity of activated carbons can be viewed as being induced by either a micropore size distribution or an energy distribution. The pore size distribution was related to an energy distribution using the LennardÐ Jones potential function. It must be pointed out that they focused their study on the kinetics of adsorption and desorption. In the description of adsorption kinetics, the model using a gamma pore size distribution can adequately represent the concentration and temperature dependency of the rate, as a uniform energy distribution does. Heuchel and Jaroniec[659] compared the distribution functions obtained from adsorption data of benzene from both gas phase and aqueous solutions. They employed as local adsorption isotherm the Fowler Ð Guggenheim equation given by
u( p, U) ¼
KL p exp(wu=kT) 1 þ KL p exp(wu=kT)
where KL is the Langmuir constant given by: U o KL ¼ KL (T) exp kT
(3:152)
(3:153)
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To calculate the pore size distribution they employed the DFT.[660] They concluded that the energy distributions obtained from data for dilute aqueous solutions can be interpreted by assuming strong adsorption of benzene inside small pores and on the external surface, and extremely weak interactions of water molecules with carbon. Consequently, the distributions obtained from liquid Ð solid adsorption exhibit slightly higher resolution than those obtained from gas Ð solid adsorption. Mamleev and Bekturov[661] developed a different algorithm to solve the adsorption integral equation, but this is recommended for investigation of crystalline surfaces when the number of distinguishable adsorption sites is not too large (between 1 and 5). Unfortunately, they only tested their method with data obtained for nitrogen adsorption on hydroxylated silica. Nevertheless, it may be suitable for other solids where the number of distinguishable sites is not too large (1 Ð5). Pan and Jaroniec[662] studied the applicability of high-resolution thermogravimetry to monitor changes in the surface of three commercial activated carbons upon treatment with nitric acid. This aggressive chemical treatment affects not only the surface chemistry of the carbons but also their porous structure. To test this method they employed adsorbates of different polarity, namely water, 1-butanol, and hydrocarbons. The distribution functions obtained from N2 adsorption at 77.7 K were employed to characterize the surface. The integral adsorption equation was solved using the Fowler Ð Guggenheim equation as local isotherm and a patchwise distribution for the adsorption sites. Their main conclusion concerning the energy distribution function was that small differences between treated an untreated samples could be detected by N2 adsorption. This is the expected result since a N2 molecule interacts with the surface via dispersive forces. As an illustration, Fig. 3.42 compares the adsorption energy distributions before and after HNO3 oxidation for the activated carbon that underwent the greatest energy changes upon oxidation (Filtrasorb 200, from Calgon Carbon Co.). The proÞles reßect substantial changes in the micropore region. The authors also concluded that the best probe is water due to its smaller size than the hydrocarbons (particularly 1-butanol) and its polarity. Choma and Jaroniec[656] characterized a series of synthetic microporous carbons through the pore size and adsorption energy distributions functions. They employed N2 adsorption data obtained over the entire pressure range with special emphasis on the very low-pressure region. They found that the adsorption energy distribution and pore size distribution of Ambersorb 563, 575, and 572 synthetic carbons were of a bimodal type and that the distribution functions were relatively narrow in comparison to those of a conventional activated carbon (CAL, Calgon Carbon Corp.), indicating that the studied synthetic carbons possessed smaller energetic heterogeneity. Tsutsumi et al.[663] derived the equations to calculate the isosteric heat of adsorption from the distribution function. They demonstrated that the differential adsorption heat could be calculated at different temperatures in either reversible
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333
Figure 3.42 Comparison of the adsorption energy distributions for unmodiÞed and HNO3-modiÞed Filtrasorb 200 activated carbon. (Reproduced from Pan and Jaroniec.[662] Copyright 1996 American Chemical Society.)
or irreversible adsorption provided that a real energy distribution function is known. Dondur and Fidler[664] studied the inßuence of the energy distribution function on thermodesorption. They considered the distribution function as a kinetic parameter and showed that the shape and position of the thermodesorption peaks depend on the type of energy distribution adopted. They showed that the differential adsorption heat also depends on the energy distribution. Rudzin«ski et al.[665] calculated the adsorption energy distribution function from experimental TPD. They developed an improved version of the condensation approximation applicable to thermodesorption kinetics. The statistical rate theory of interfacial transport[666,667] offers the possibility of describing thermodesorption kinetics by using the same thermodynamic quantities that appear in theories of adsorption equilibria. This new approach solves the problem of taking into account the kinetics of simultaneous readsorption. The method based on the Wigner ÐPolanyi equation is the most commonly employed to interpret the experimental TPD peaks. The authors demonstrated that the Wigner ÐPolanyi equation shows the surface as more energetically heterogeneous than their method. The overestimation of the heterogeneity increases as the re-adsorption process becomes more important. Sircar[668] developed a model to describe adsorbent heterogeneity assuming that the solid surface consists of a distribution of energetically different sites, the local isotherm on a site is of the Langmuir type and the energy distribution on the surface has the gamma probability density form. He tested the
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model with experimental data for several gases (N2 , CH4 , CO2 , and C2H4) on Calgon BPL activated carbon (ca. 60% of pores with size smaller than 3 nm) over large ranges of pressure and temperature. He found that the variance of surface energy is the same for all gases although the isosteric heats of adsorption in the HenryÕs law region are very different (they decrease in the order: C2H4 CO2 . CH4 . N2). Another interesting result was that this carbon appears to be more homogeneous for CO2 adsorption than for the other gases. Choma and Jaroniec[669] reported a new method for determining the surface areas of nonporous and macroporous carbons from gas adsorption isotherms. They argued that the method has rigorous foundations since it employs the adsorption energy distribution, which is a unique thermodynamic characteristic for a given adsorption system. They analyzed N2 isotherms at 77 K for a series of low-surface area graphitized and nongraphitized carbons and compared it with the BET method. They additionally tested their method with Ar, N2 , and Kr adsorption at 87 K on a highly graphitized carbon black. They concluded that the surface area analysis based on adsorption energy distribution is very promising for determining the amount adsorbed corresponding to the monolayer capacity of carbon surfaces of different types. Corte«s[670] analyzed the effect of surface heterogeneity on the vibrational adsorption motion, which he illustrated for cases of mobile physisorption. His main conclusion was that the heterogeneity effect is rather small, with a greater relative incidence on the entropy than on the vibrational energy. Jaroniec and Madey[671] analyzed the characterization of heterogeneous microporous solids in terms of a gamma-type distribution describing surface heterogeneity. They illustrated the utility of this approach using benzene adsorption on type RKD-4 (Norit Co.) activated carbon at 293 K.[672] They argued that one important advantage of the proposed description is its association with the aS-method in order to extract the amounts adsorbed in the micropores and on the mesopore surface. Al-Muhtaseb and Ritter[673] developed analytical expressions for singlecomponent adsorption systems to predict the isosteric adsorption heat and the differential phase heat capacity as a function of temperature, surface coverage, lateral interactions, and surface heterogeneity. They showed that the temperature dependence of the isosteric heat is always related to the adsorbent heterogeneity. They also concluded, as could be expected, that the isosteric heat extrapolated at zero-coverage increases with increasing surface heterogeneity and is not affected by lateral interactions. They also studied complex binary and multicomponent adsorption equilibria.[674] OÕBrien[675] analyzed the effect of lateral interactions and energetic heterogeneity on gas Ðmixture adsorption on activated carbons. He showed a higher selectivity for the patchwise case, at least with the set of parameters employed in his calculations. He also concluded that there is progress to be made by going beyond the model-less thermodynamic approach through consideration of the physical mechanism of the adsorption process.
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In a recent paper, Gardner et al.[676] employed the adsorption energy distribution function to select two carbons (Black Pearls, nongraphitized carbon black; and Carbopack F, graphitized carbon black) as reference adsorbents for argon adsorption[677] on nongraphitized carbons, such as activated carbons, as well as graphitized carbons. Quin÷ones et al.[678] presented a method to estimate the adsorption energy distribution function for the Jovanovic Ð Freundlich isotherm model using the Jovanovic equation as local adsorption isotherm. They compared their method with the results obtained with an established expectation Ð maximization procedure that does not assume any particular model for the overall isotherm. They found good agreement between the two methods. Bereznitski et al.[679] used the adsorption energy distribution function to characterize the surface of activated carbons (Ambersorb 573, Rohm and Haas Co.; CAL, Calgon Carbon Corp.) modiÞed by a multicycle deposition of silica. They employed N2 as probe to determine the distribution functions of several composite adsorbents modiÞed with different amounts of deposited silica. Silica deposition caused a gradual decrease in energetic heterogeneity and inßuenced mainly the low-energy part of the distributions due to a gradual Þlling of the mesopores. GunÕko et al.[680] studied related systems obtained by pyrolysis of methylene chloride on silica gel at ca. 820 K (carbon Ðsilica gels, or carbosils). They obtained N2 isotherms and calculated the adsorption energy distribution functions using a constrained regularization procedure with several adsorption equations. They found that the structural characteristics of carbosils depend markedly on the amount of carbon deposited, and that changes in the pore size distribution with increasing carbon concentration suggest its grafting mainly into pores, resulting in a diminution of pore volume, surface area and average mesopore size. Figure 3.43 shows N2 adsorption energy distributions for the starting mesoporous silica gel (Si-60) and carbosil samples with increasing carbon contents (CS-1 through CS-6). With increasing amounts of carbon deposited the energy distribution slightly shifts toward higher energies, as narrower micropores appear in samples due to carbon grafting as silica mesopores are Þlled with tiny carbon particles. Recently, Villie«ras and coworkers[681,682] studied the adsorption on a heterogeneous surface within the framework of the lattice model, taking into account a correlation in arrangement of nearest adsorption sites. The mean Þeld approximation was employed to derive the expression for the adsorption isotherm. From an experimental isotherm, the proposed algorithm computes fractions of different sites, reduced adsorption energies and a matrix expressing conditional probabilities of detection of different sites in a neighborhood of sites of a chosen kind. The elements of that matrix are supposed to be expressed through the fractions of sites. For the particular case of the patchwise topography, this matrix is diagonal. In this case, the proposed algorithm allows the estimation of lateral interaction energies for admolecules localized on different patches. They applied this model to adsorption of Ar on muscovite but the results have a rather general interest. Katsanos et al.[683] employed IGC to estimate
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Figure 3.43 N2 adsorption energy distributions for a mesoporous silica gel (Si-60) and carbosil samples with increasing carbon contents following the CS-1 through CS-6 sequence. Data correspond to relative pressures in the range 1028 , p/p0 , 0.2. (Reproduced from GunÕko et al.,[680] with permission from Elsevier.)
the differential energy of adsorption due to lateral interactions of adsorbed molecules on heterogeneous solids. They interpreted their data based on the model proposed by Bakaev and Steele.[684] Frere et al.[685,686] studied a method to determine the micropore volume distribution function of activated carbons based on the integral adsorption equation concept. They assumed that the pore size distribution is a Gaussian whose parameters are unknown. The determination of the parameters is accomplished using CO2 isotherms at 278 Ð 328 K. They discussed the inßuence of the choice of the local adsorption isotherm on the results, and concluded that the Hillde Boer and Langmuir local isotherms are the most efÞcient. A similar approach has been reported by Cazorla-Amoro«s et al.,[687] who concluded that CO2 adsorption at 273 K can be employed to characterize the whole range of porosity. The results obtained agreed with the distributions for N2 adsorption. Ravikovitch et al.[688] reported a uniÞed approach to pore size characterization of microporous carbonaceous materials (e.g., activated carbons and ACFs with different degrees of activation) using N2 and Ar at 77 K and CO2 at 273 K. They calculated isotherms for N2 , Ar, and CO2 for model slit-shaped pores with widths ranging
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from 0.3 to 36 nm using nonlocal DF T. The pore size distribution is calculated with an adaptable procedure of deconvolution of the integral adsorption equation using regularization methods. The deconvolution procedure employs the same grid of pore sizes and relative pressures for all adsorbates and an intelligent choice of regularization parameters. They demonstrated the consistency of the approach using examples of pore structure characterization of activated carbons. 3.3.3.3.
Numeric Simulations
The increasing availability of well-characterized and homogeneous adsorbents, as well as the highly accurate results gained with the traditional techniques in the last 30 years, have attracted the attention of scientists from other disciplines, particularly physics and mathematics. Along with new experimental techniques, these researchers have introduced theoretical approaches that have contributed greatly to our understanding of the adsorption process. Computer simulations could not be absent in this Þeld. The method, including the simulations it provided, has served to increase the gap between the old theories and new approaches. Since the classical studies of the liquid state by Wood[689] using Monte Carlo methods and by Alder and Wainwright[690] using molecular dynamics, it has been recognized that computer simulation could be a very powerful tool to study natural phenomena. Computer simulation is a very interesting tool since it provides a method in which the researcher is in complete control of all the variables of the system. At least ideally, it is possible to solve the statistical mechanical problem exactly. The only unknown that stands between computer simulations and experimental data is the nature of the intermolecular forces in the system of interest. Moreover, these forces are exactly known in the simulation; thus, the approximations necessary in statistical mechanical theory can be reÞned by reference to the data resulting from computer simulations. Obviously, the experimental data prevail over any theoretical result that is in contradiction with the experiment. Computer simulations applied to physical adsorption have started with the simplest systems that could be found (e.g., ßat, homogeneous surfaces and atomic adsorbates). In the real world, the surface that is the closest to an ideal one is the graphite basal plane (or graphene sheet). Thus the large amount of work published employing graphite as the adsorbent is not surprising. We begin this section with a brief introduction to the basics of computer simulation in its two most commonly employed forms: Monte Carlo (MC) and molecular dynamics (MD). Then we present the results covering different aspects of physical adsorption from the gas phase on carbonaceous materials. Sometimes, as in previous sections, we are tempted to make reference to papers dealing with adsorption from solution or using other adsorbents because new methods, or variations of the older ones, are presented that we feel are general enough to be applicable to other systems. At the end of this section, we include a brief description of other simulation methods.
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There are excellent books that could be considered as necessary reading when using computer simulation to study physisorption phenomena. Nicholson and ParsonageÕs book[691] deals with computer simulation, MC and MD, and statistical mechanics. HaileÕs book[692] is devoted to MD and has a complete set of exercises and the computer code necessary to assemble a MD simulation program. If one is interested in how things are done in computer simulations, the book that must be considered is that of Allen and Tildesley.[693] The authors also provide a complete set of computer code to perform from simple to very complicated tasks in simulations. Ciccotti et al.[694] have published an excellent collection of basic papers. This book groups the papers according to the subject and the editors have included comments and notes on most of them. Other preliminary papers have been presented at international meetings in the series Fundamentals of Adsorption (e.g., Refs.[695 Ð 697]). MC techniques: The MC method was developed by Metropolis et al.[698] In their classical paper, they presented the method applied to the determination of the equation of state for any substance in a 2D system. The simulation cell was a square that contained N molecules (generally up to several hundred). The equations we present here are for a 3D system. The potential energy of the system is given by: E¼
N X N 1X e(rij ) 2 i¼1 j¼1
for i = j
(3:154)
To calculate the properties of the system they employed the canonical ensemble. Thus, the equilibrium value of any quantity of interest, kF l, is given by Ð F exp(E=kT)d3N p d3N q kFl ¼ Ð (3:155) exp(E=kT)d3N p d3N q where d3Np d3Nq is the volume element in the 6N-dimensional phase space. Since forces between particles are independent of their velocity, it is possible to separate the momentum integrals and perform integration over the 3N-dimensional conÞguration space. To perform the integration, Metropolis et al. employed the MC method, which has been proposed independently by J.E. Mayer and by S. Ulam. The MC method for many-dimensional integrals consists simply of integrating over a random sampling of points instead of over a regular array of points. Thus, the integration is done by placing each of the N particles at random positions in the simulation cell. This deÞnes a random point in the 3N-dimensional conÞguration space. Once the conÞguration is obtained, the total energy is calculated and the conÞguration is assigned a weight given by the Boltzmann factor: E g ¼ exp (3:156) kT
Physical Adsorption of Gases and Vapors on Carbons
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This method, however, is not practical for systems with relatively high density since there is a high probability of choosing a conÞguration with very small weight. At this point is where Metropolis et al. modiÞed the MC scheme by choosing conÞgurations with probability given by Eq. (3.156) and weighed them evenly. To do this they proposed to place the N particles in any conÞguration, and then move each particle in succession according to the following prescription: X ! X þ az1 Y ! Y þ az2
(3:157)
Z ! Z þ az3 Here a is the maximum allowed displacement that is arbitrary, and zi are random numbers between 21 and þ1. Then, after a particle is moved, it is equally likely to be anywhere within a cube of side 2a centered about its original position. If a particle leaves the cell due to the imposed displacement, it re-enters the cell through the opposite side. Once a particle has been placed in its new position the change in energy of the system, DE, is calculated. If DE , 0, that is, if the move brings the system to a state of lower energy, the move is accepted and the particle is conÞrmed in its new position. If DE . 0 the movement is accepted with the probability given by Eq. (3.156), that is, a random number, z4 , is generated between 0 and 1, and if z4 , g the particle is moved to its new position. If z4 . g the particle is returned to its previous position. Then, whether the move has been allowed or not, the conÞguration is considered as a new one for taking averages. So kFl ¼
M 1X Fi M i¼1
(3:158)
where Fi is the value of the property F of the system after the ith move is carried out according to the complete prescription given earlier. Having attempted to move a particle the procedure continues with the next one. One condition that any sampling method in the conÞguration space must fulÞll is that it must be ergodic (i.e., all possible points in the space should be reachable). Next, consider a very large ensemble of systems. Assume for simplicity that there are only a Þnite number of states, and that nr is the number of systems in state r. It is necessary to prove that after a certain number of moves the ensemble tends to a distribution given by Er nr / exp (3:159) kT If a move in all the systems of the ensemble is carried out, let the probability that the move will carry a system in state r to state s be Prs . First, it is clear that Prs ¼ Psr since, according to the way the movement is done, a particle is
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equally likely to be moved anywhere within a cube of side 2a centered about its original position. Thus, if states r and s differ from each other only by the position of the particle moved and if these positions are within each otherÕs cubes, the transition probabilities are equal; otherwise they are zero. Assume Er , Es , then the number of systems moving from state r to state s will be simply ns Psr exp(2DE/kT). Thus the net number of systems moving from s to r is ð Er Es Þ Prs ns exp (3:160) nr kT This results in that on average more systems move from state r to state s if nr exp (Er =kT) . (3:161) exp (Es =kT) ns The ergodicity of the system together with this last consequence ensures that the ensemble must approach the canonical distribution. It is clear from the above discussion that after a forbidden move the initial conÞguration must be counted again. Not to do this would correspond, in the above case, to removing from the ensemble those systems that try to move from s to r, and were forbidden. These arguments do not specify how fast the canonical distribution is approached. It must be mentioned that the maximum displacement must be chosen with some care; if too large, most moves will be forbidden, and if too small, the conÞguration will not change enough. In either case, it will then take longer to come to equilibrium. Computer simulations are usually performed on a small number of molecules. The size of the system is limited by the available storage on the host computer, and more crucially by the speed of execution of the program. Nowadays this last condition is the limiting factor since memory capacity has been increased in large amounts. It must be remembered that the number of calculations needed only to evaluate the potential energy of a conÞguration is proportional to N 2. The other problem concerns the size of the simulation cell; in fact, results obtained with small cells will be seriously affected by border effects. A particle located near the boundary of the cell will experience different interactions with respect to one in the interior of the cell. This problem can be overcome by implementing periodic boundary conditions.[699] The cubic simulation cell is replicated throughout space to form an inÞnite lattice. In the course of the simulation, as a molecule moves in the original box, its periodic image in each of the neighboring boxes moves in exactly the same way. Thus, as a molecule leaves the central cell, one of its images will enter through the opposite face. In consequence, there are no walls at the boundary of the central cell and no surface particles. This scheme is represented in Fig. 3.44 for a 2D periodic system. With periodic boundary conditions, the number of particles in the central cell remains constant during the simulation. Now it is necessary to ask if the properties of a small system, although it is inÞnitely periodic, and the
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Figure 3.44 Scheme showing the structure of the simulation cell and its replicated images (L is the side of the box).
macroscopic system that it represents, are the same. This will depend on both the range of the intermolecular potential and the phenomenon under study. For a Lennard-Jones ßuid, it is possible to perform a simulation in a cubic box of side L ¼ 6s without a particle being able to ÒsenseÓ the symmetry of the periodic lattice. If the potential is long ranged there will be a substantial interaction between a particle and its own images in neighboring boxes, and consequently the symmetry of the cell structure is imposed on a ßuid, which is in reality isotropic. The example of periodic boundary conditions shown here is the simplest case; moreover, periodic conditions have been developed for noncubic simulation boxes. In adsorption studies, the simulation box usually is replicated in the x and y directions; in the z direction, the box is closed on one side by the solid adsorbent, and on the other side by a reßecting plane that keeps the gas-phase molecules in a predeÞned volume. In MC simulations, the most common ensembles employed are the canonical (CEMC) and the grand canonical (GCMC) ones. The average value of a property, kAlNPT , is given in the canonical ensemble by kAlNPT ¼
1 ZNPT
ð
ð PV N U(s) dV exp dsA(s) exp V kT kT
(CEMC) (3:162)
where ZNPT is the appropriate conÞgurational integral [Eq. (3.54)], V is the volume of the system, and U(s) is the potential energy, which depends on the molecular coordinates, s. And in the grand canonical ensemble, kAlmVT ¼
1 QmVT
ð
ð 1 U(s) N N V z ds AðsÞ exp N! kT
(GCMC)
(3:163)
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342
where QmVT has been deÞned in Eq. (3.69), and z is the activity given by z¼
exp(m=kT) L3
(3:164)
and L has been deÞned in Eq. (3.57). The GCMC procedure is equivalent to that previously described for CEMC except that an additional kind of ÒmovementÓ needs to be introduced to generate a new conÞguration. To the normal displacements, it is necessary to add the possibility of creating and destroying molecules. Obviously, the Þrst increases the number of particles in the system while the second one decreases it. There are several recipes proposed to carry out the creation or destruction step but the most common consists in an attempt at particle creation in a random location within the simulation box. The destruction is also done by randomly selecting an existing particle and deleting it. In both cases, the rules for acceptance or rejection of the new conÞguration are the same as in particle displacement. To satisfy the microscopic reversibility condition, the probability of an attempted creation must be set equal to the probability of an attempted destruction. Norman and Filinov[700] found that the method convergence is the fastest when the stochastic matrix, often called the underlying matrix of the Markov chain, is symmetric and its elements equal to 1/3. Thus, moves, destructions and creations are selected at random, with equal probability. GCMC simulations are more complicated to program than CEMC. The advantage of the method is that it provides a direct route to the statistical properties of the ßuid. GCMC is particularly useful for studying inhomogeneous systems such as monolayer and multilayer adsorption.[701] It is possible to use other ensembles in MC simulations (e.g., the Gibbs ensemble that we will discuss in Òother ensemblesÓ). Molecular dynamics simulations: Molecular dynamics simulations compute the motions of individual molecules in models of solids, liquids, and gases. This is the modern realization of an essentially old-fashioned idea in science; namely, that the behavior of a system can be computed if we have, for the systemÕs parts, a set of initial conditions plus the forces of interaction. The MD method encompasses two general forms: one for systems at equilibrium, another for systems away from equilibrium. Equilibrium MD is typically applied to an isolated system containing a Þxed number of molecules in a Þxed volume. Because the system is isolated, the total energy (deÞned as the sum of the molecular kinetic and potential energies) is also constant. Thus, the variables N, V, and E determine the thermodynamic state of the system. In NVE-MD molecular positions r N are obtained by solving NewtonÕs equations of motion Fi (t) ¼ m
@2 ri (t) @U(r N ) ¼ 2 @t @ri
(3:165)
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where Fi is the total force on the ith particle caused by the N 2 1 other particles, and m is the mass of the particle. Integrating Eq. (3.165) once produces the particle momenta; integrating a second time yields the particle positions. Repeatedly integrating, for several thousand times, produces individual particle trajectories from which time averages kAl can be computed for macroscopic properties: 1 t!1 t
ð t0 þt
kAl ¼ lim
A(t)dt
(3:166)
t0
At equilibrium, this average cannot depend on the initial time t0 . Since positions and momenta are obtained, the time average represents both static properties, such as thermodynamics, and dynamic properties such as transport coefÞcients. In MD simulations, periodic boundary conditions are employed as in MC simulations. In dynamic systems, conservation laws are consequences of inherent symmetries. Thus, if it is possible to identify symmetries, the corresponding conservation laws can be deduced. For N-body isolated systems the conserved quantities are mass, energy, linear momentum, and angular momentum. However, periodic boundary conditions could disrupt the symmetries and prevent those quantities from being conserved. According to the ergodic hypothesis, the time average Eq. (3.166) provided by molecular dynamics should be the same as the ensemble average obtained with MC. Although a rigorous proof of the ergodic hypothesis exists only for the hard-sphere gas[702], it can be tested by comparing results from MC with MD. MD simulations are limited largely by the speed and storage constraints of available computers. As in the case of MC, speed is now the limiting factor. Because of the speed limitation, simulations are conÞned to studies of relatively short-lived phenomena, roughly, those occurring in less that 100 Ð 1000 ps. The characteristic relaxation time for the phenomenon must be small enough so that one simulation generates several relaxation times. Non-equilibrium methods have been developed in the early 1970s,[703 Ð 705] initially as an alternative to equilibrium simulations for computing transport coefÞcients. In these methods, an external force is applied to the system to establish the nonequilibrium situation of interest, and the systemÕs response to the force is then determined from the simulation. Non-equilibrium MD has been used to obtain the shear viscosity, bulk viscosity, thermal conductivity, and diffusion coefÞcients. Although the physical and mathematical basis of MC may be more obscure than that of MD, MC is usually much easier to code in a high-level computer language. MC is also easier to implement for systems in which it is difÞcult to extract the intermolecular force law from the potential function. To determine simple equilibrium properties such as the pressure in atomic ßuids, both methods are equally effective (both require approximately the same amount of computer time). However, MD more efÞciently evaluates properties such as the heat capacity, compressibility, and interfacial properties in general. Besides conÞgurational properties, MD also gives access to dynamic quantities such as
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transport coefÞcients, and time correlation functions. Such dynamic quantities cannot generally be extracted from MC simulations, although certain kinds of dynamic behavior may be deduced.[706,707] Results: This section is organized as follows. We begin with general papers dealing with computer simulations, and then we continue with papers containing results obtained for systems in which graphite is the adsorbent. Then we summarize papers dealing with adsorption on porous carbonaceous materials, Þrst in slit-shaped pores and then in fullerenes, carbon nanotubes, and model porous carbons with cylindrical pores. General studies on simulation. Abraham[708] presented a great variety of MC computer experiments, which have established the important features of the phase diagram for a 2D Lennard ÐJones ßuid. He also outlined the main features of the dynamics of the melting process through the implementation of a new isobaric Ð isothermal MD method. Abraham[709] also surveyed some computer simulations, MC and MD, relating to the statistical physics of surface phenomena. The examples he analyzed concern the structure and thermodynamics of microclusters, liquid Ð vapor and liquid Ðsolid interfaces, and 2D simple Þlms. Computer simulations could be employed, in connection with adsorption, to study not only the adsorption process but also the structure of the adsorbent itself.[710 Ð 722] Chemical reactions such as coke formation in zeolites have been studied by Nelson et al.[723] Finn and Monson[724] presented results of MC simulations using an isobaric Ðisothermal ensemble. They studied 1D systems and compared their results with the exact solutions known for these systems. Then they applied their method to simulate the Ar/graphite interface and compared their results with GCMC simulations. They concluded that the two methods agree; however, the adsorption excess at multilayer conditions can be obtained with signiÞcantly greater precision via the isobaric method. Markovic« et al.[725] studied water scattering from graphite combining simulations and experiments. They tested several models of gas Ð solid interaction and simulated angular distributions for different translational energies, incident angles, and surface temperatures. They found good agreement between simulations and experiments. In a general paper, Ferrenberg et al.[726] analyzed the statistical and systematic errors in MC sampling, focusing particularly on the error dependence on the size of the system when a Þxed amount of computer time is used. They concluded that, depending on the degree of self-averaging exhibited by the quantities measured, the statistical errors can decrease, increase, or stay the same as the system size is increased. They developed a scaling formalism to describe the size dependence of those errors. Myers et al.[727] clariÞed several concepts that must be taken into account when comparing computer simulation results with experimental data. Marx et al.[728] developed the equations needed to calculate the heat capacity using path integral MC simulations. They showed that the standard relation linking heat capacity to energy ßuctuations, which is useful in standard
Physical Adsorption of Gases and Vapors on Carbons
345
classical problems with temperature-independent Hamiltonian, becomes invalid. They proposed a new equation to perform the calculation. Fodi and Hentschke[729] presented a good description of MD simulations of adsorption of linear alkanes and benzene on graphite. They obtained reasonable agreement between simulations and experimental data. Figure 3.45 compares experimental (hollow circles)[730,731] and simulated (solid circles and solid squares) isosteric adsorption heats on graphite at 300 K in the limit of zero coverage (q0st) as a function of the number of methylene units (n), from ethane through n-decane. The solid circles and solid squares correspond to different calculations made by changing several parameters of the n-alkane Ðgraphite interaction; the crosses are q0st/n values corresponding to the q0st solid circles. Whichever the parameters used, the scatter is within the range of the experimental error. Finn and Monson[732] employed isobaric MC simulations to study the selective adsorption of gas mixtures (Ar/CH4). They compared their results with the predictions obtained from HenryÕs law, ideal adsorption solution theory, and 2D equation of state theory. They concluded that at low pressures the relationship between the adsorbed and bulk phase compositions is described quite well by HenryÕs law, although the composition dependence of adsorbed phase density, which depends more strongly upon the adsorbate Ð adsorbate interaction, is not. They argued that such results illustrate the important role of the relative strengths of gas Ðsolid interactions in determining selective adsorption. Kierlik and Rosinberg[733] studied the adsorption of gas mixtures using the nonlocal DFT for hard spheres. They analyzed the structure and thermodynamics of several binary mixtures: (i) Lennard Ð Jones ßuids in slit-shaped pores; (ii) selective adsorption of Ar/CH4 mixtures on graphite; and (iii) density proÞles of charged spheres in the vicinity of a highly charged hard wall. They compared model calculations with MC computer simulation results and concluded that
Figure 3.45 Isosteric adsorption heats of n-alkanes on graphite at 300 K in the limit of zero coverage (q0st) as a function of the number of methylene units (n). Hollow circles, experimental results; solid circles and squares, simulations (see text). (Reproduced from Fodi and Hentschke.[729] Copyright 1998 American Chemical Society.)
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their theory leads to similar or slightly better results than earlier models while requiring a signiÞcantly lower computational effort. According to these authors, density functional methods coupled to computer simulations provide a much more detailed insight of adsorption phenomena than the classical thermodynamic description currently in use. Cracknell and Nicholson[734] developed a 3D thermodynamic treatment to describe the adsorption of gas mixtures. Their approach generates an additional term that has signiÞcant consequences for the derivation of adsorbed solution theories. They tested their theory with GCMC computer simulations-generated data of mixtures of CH4/C2H6 adsorbed in slit-shaped graphitic pores. They concluded from their analysis that an ideal solution will not have a constant spreading pressure, but rather that it is a related thermodynamic parameter which must be constant. In practice, this means that it is the total adsorption isotherm and not the excess that is required for calculations using the ideal adsorbed solution theory. Quantum MC simulations have been employed to study He adsorption on graphite;[735] particularly the authors focused their attention on the phase diagram that is a very rich one. The purpose of using quantum simulations was to obtain information on the microstructure of the adsorbed phase. This study is a continuation of a previously published one using Feynman path integral MC simulations.[736] Vives and Lindgaûrd[737] investigated the adsorption of deuterium on corrugated surfaces using MC simulations. They focused their study on the phase transitions as a function of the surface coverage and temperature. They identiÞed an intermediate g-phase between the commensurate and incommensurate phases that is stabilized by defects. Krypton adsorption on graphite has been extensively studied using computer simulations. Jensen[738] employed MD simulations to identify two phases: a low-temperature incommensurate phase and a high-temperature ßuid phase. The transition between the two phases proceeds via a Þrst-order transition. The reported simulations did not show a commensurate phase in contrast with what is observed in real systems. One possible reason for the discrepancy is that in this study Kr atoms are not allowed to move in a direction normal to the surface. Abraham and coworkers[739,740] studied the incommensurate phase of Kr adsorbed on graphite in more detail, using MD with more than 100,000 atoms. They found honeycomb networks of domain walls at low temperature and for all coverages. With increasing temperature, distortion from perfect honeycomb structure becomes prevalent, characterized by signiÞcant ßuctuations from the symmetry directions, wall thickening, and wall roughening. Their simulation results agree with experimental results.[741] Bhethanabotla and Steele[742] analyzed two models to describe Kr adsorption on graphite at 100 K. The two models differ in the gas Ð gas interaction potentials. The Þrst is characterized by parameters derived from bulk Kr properties and from pairwise sum over the Kr Ð C site potentials. In the second model, Kr ÐKr interaction well depth was reduced by ca. 15% to allow for the substratemediated effect, and the periodic part of the gas Ðsolid potential was doubled
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to allow for the anisotropy of the C sites. They calculated the potential energy and chemical potentials of the adsorbed Þlm at coverages ranging from the commensurate density up to two commensurate layers. By comparing their results with experimental data, they concluded that the second model is in good but not perfect agreement with the data. Shrimpton and Steele[743] studied the corrugation effects on the adsorption of Kr on graphite. They argued that the best information about corrugation effects could be obtained from inelastic scattering studies such as those performed for N2 adsorbed on graphite[744] and Kr on graphite.[745] In inelastic scattering, the dynamic information obtained can be factored from the scattering cross-section information. This factored term is the dynamic structure factor. The authors calculated the dynamic structure factor from MD simulations at several temperatures to assess the thermal variation of this factor. From comparisons with experimental data, they concluded that the substrate potential is well described with their model using a corrugation factor slightly less than 1.5. The vibrational motion can be described in terms of normal modes with frequencies that are shifted and broadened by temperature. Steele and Bojan[746] analyzed the heats of adsorption of simple gases (N2 and Kr) on the basal plane of graphite using MD computer simulations. They focused their attention on studying nitrogen orientation changes as a function of surface coverage. They found that close to the monolayer coverage more molecules are standing in vertical position on the surface. A detailed study of Ar adsorbed on graphite has been performed by Cheng and Steele[747] using MD. Their simulations covered a wide temperature range, 50Ð 112 K, and surface coverages up to three layers. They found a layer-by-layer melting for each of the three layers in the multilayer system, and for the single layer system simulated. The transitions observed are Þrst order and continuous and the roughening of the trilayer Þlm occurs gradually as the temperature increases. Ar adsorption on graphite has also been studied by Nicholson and Parsonage[748] using GCMC method with two models to describe the surface of graphite. The Þrst one represents the solid as a continuum and the second uses a periodic potential with barrier heights artiÞcially raised by a factor of three compared with those which would be obtained with conventional 12 Ð6 potentials. They concluded that the characteristic shape of the experimental heat of adsorption curves is essentially a 3D phenomenon in which lateral periodicity is of minor importance. On the other hand, the pressure at which the transition from a ßuid to a solid occurs is greatly affected by the substrate periodicity, although this pressure is lower in the simulations than in the real system. They also found rather strong localization effects through the analysis of the lateral distributions for molecules close to the surface in the ßuid phase when the periodic adsorbent is used. Kr adsorption on model heterogeneous surfaces has been investigated by Bojan and Steele[749 Ð 752] using MD computer simulations. The model surface was a graphitic surface with parallel, straight-wall grooves, as shown in Fig. 3.46. The gas Ð solid energy, represented in Fig. 3.47, shows the values of the minima in the Kr Ðsolid interaction energy. A deep minimum is observed
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Figure 3.46 Grooved surface constructed by adding two extra planes to the graphite basal plane. The additional planes are spaced by the interplanar distance in graphite. (From Bojan and Steele.[751] Copyright 1989 American Chemical Society.)
when the adsorbed atom is near the edges of the groove, and a strong maximum occurs when the adatom is near the edges of the step. The results also show how the large adsorption energy decreases the mobility of the edge atoms, how the large barrier suppresses step-to-groove transfers in the monolayer, and how interlayer changes assist the diffusional motion in this system. The authors also found that both diffusion parallel to the surface and Òvertical transportÓ such as step-togroove changes or desorption, are greatly enhanced by a small amount of second layer adsorption. Adsorption on graphite. In the previous section we have presented general studies on simulation, some of which concerned the development of methods using graphite as a model substrate. In this section we summarize the work done on graphite, going from simple to more complex adsorbates. Beginning with N2 adsorption, Talbot et al.[753] used MD to study a submonolayer of ßuid N 2 Þlm adsorbed on the basal plane of graphite. They modeled the surface as a continuous external Þeld using a Fourier expansion in the reciprocal lattice vectors of the basal plane. They compared their simulations with experimental results, particularly the isosteric heat of adsorption. They found that the surface lattice modiÞes the structure of the adsorbed liquid and there is signiÞcant out-of-plane orientational ordering at all surface coverages studied.
Figure 3.47 GasÐ solid interaction energy for Kr adsorbed on the model surface shown in Fig. 3.46. (Adapted from Bojan and Steele.[751] Copyright 1989 American Chemical Society.)
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They found that the isosteric heat variation with surface density is linear up to the density corresponding to the commensurate phase. A least squares Þt to a straight line of the obtained values yields qst (kJ=mol) ¼ RT 103 þ 9:29 þ 50:93r
(3:167)
û 22. Piper et al.[129] determined the heat of adsorption using an adiawith r in A batic calorimeter and obtained, for nitrogen adsorbed on Graphoil: qst (kJ=mol) ¼ RT 103 þ 9:34(+0:2) þ 48:7(+3)r
(3:168)
Equations (3.167) and (3.168) reßect the excellent agreement achieved between simulations and experiments. Joshi and Tildesley[754] used the MD technique to analyze the patches of solid N2 adsorbed on the basal plane of graphite. A model of gas Ðsolid interaction involving an isotropic site Ð site interaction predicts a melting transition 9 K below the experimentally observed temperature. They used a potential that included the anisotropy (actually the anisotropic polarizability of the graphite surface) in the site Ð site interaction that produces an increment in the lateral surface barriers; thus the experimental transition temperature is reproduced. In their calculation they included adsorbate Ðadsorbate quadrupolar interaction. As experimental data concerning the structure of the adsorbed phase[755 Ð 759] became available, more reÞned simulations were needed to account for all the experimental features. Patrykiejew et al.[760] studied the orientational effects in monolayers of diatomic adsorbates using MC simulation. They studied systems of adsorbed molecules with different elongation on the (100) plane of an fcc crystal. They found that for molecules with small elongations the adsorbed monolayer orders into a simple (1 1) structure. On the other hand, for larger elongations the Þlm orders into structures which are more complex. Vernov and Steele[761,762] studied the structure of physisorbed nitrogen on the basal plane of graphite using MD simulations. They found that the behavior of nitrogen Þlms could be due to the effect of the periodic term in the gas Ð solid potential and that this effect is reinforced by the inherent tendency of these molecules to pack with spacing close to that of a commensurate lattice. Thus, the observed solid-like behavior of the Þrst layer of nitrogen at high coverage must be the result of a combination of substrate periodicity and a fortunate match with molecular size parameters. They also found a coupling between orientation and maximum Þrst-layer coverage. The out-of-plane motions of the adsorbed molecules are oscillatory and librational in both the Þrst and second layers, the in-plane reorientations are relatively free, and the in-plane translations are highly hindered. Tildesley and Lynden-Bell[763] studied the motion in surface layers of nitrogen on graphite, particularly the commensurate-ordered, uniaxial, and commensurate-disordered phases. They concluded that the MD technique is not a natural tool for studying phase transitions unless an adequate intermolecular
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potential is employed. They showed that there is clear evidence of coupling between librational and traslational phonons, which is responsible for the structure in the librational density of states. The simulation shows the longitudinal phonons inducing rotational ordering in the high-temperature phase. The uniaxial phase of nitrogen adsorbed on graphite has been studied by Talbot et al.[764] using MD in the region of the monolayer at low temperatures. They found that the adsorbed phase is slightly compressed relative to the comp p mensurate 3 3 phase. The compression is taken to be uniaxial (i.e., a 5% change in the large intermolecular spacing along a glide line of the oriented herringbone structure). The compression necessary to form this phase from the commensurate one does not produce a signiÞcant change in the out-of-plane ordering, at least at the lower temperature studied (15 K). On the other hand, it brings about changes in the in-plane ordering of the adsorbed molecules. Kuchta and Etters[765,766] studied the properties of nitrogen mono- and multilayers on graphite using pattern optimization of the total lattice energy and MC simulations with continuously deformable periodic boundary conditions. Their main conclusions were: (i) the Þrst layer of the bilayer forms a somewhat distorted out-of-plane herringbone arrangement and the second layer is a pinwheel structure, much like the (111) plane of bulk a-N2; (ii) the bilayer, trilayer, and bulk a-N2 are virtually in coexistence with one another, which indicates that bulk formation occurs at densities above bilayer completion, as suggested by the experimental data available; and (iii) following the changes in the order parameter an order Ð disorder phase transition takes place at 25+ 2 K, in excellent agreement with experiments.[767] Opitz et al.[768] studied the herringbone transition in full monolayers of nitrogen adsorbed on graphite in the registered commensurate phase. These authors determined, for the Þrst time, that the transition is a weak Þrst-order one. The rotations of N2 and H2 adsorbed on graphite have been studied by Marx et al.[769] using path-integral MC simulations. They found that the quasiharmonic treatment yields the correct order parameter suppression and the quasi-classical simulation of the lowering of the transition temperature, but only the full quantum path-integral MC simulations describe the entire temperature range of interest correctly. Bottani and Bakaev[770] studied the adsorption of nitrogen on the basal plane of graphite using CEMC and GCMC computer simulations. They could reproduce the dependence of the average adsorption energy on coverage obtained by independent MD simulations; the adsorption isotherm obtained with GCMC reproduced the experimental data. The authors found small deviations of the simulated isotherm from the experiment in the submonolayer region, which could be explained by the residual heterogeneity of the real graphite surface. A deviation in the region of the second layer was attributed to the many-body interactions that are not properly taken into account in the simulations. Finkelstein and coworkers[771,772] studied nitrogen monolayers on Papyex (a graphite in form of sheets, from Deutsche Carbone AG) using
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nuclear resonance photon scattering (NRPS) to measure the out-of-plane tilt angle of physisorbed 15N2 relative to the graphite surface, between 80 and 297 K. They found a disagreement between experimental and GCMC simulations.[770] Figure 3.48 compares average tilt angles (kul) of the N2 molecular axis with respect to the graphite planes as a function of coverage at 80 and 140 K, corresponding to the liquid and vapor phases, respectively. The disagreement between experimental results and GCMC simulations in Fig. 3.48(b) was attributed to the fact that the GCMC simulations neglect the surface corrugations of graphite and assume a geometrically ßat surface. In fact, the MD simulations, which account for the corrugations (constituting a more realistic physical description of the surface), yield persistently larger angles that are in excellent agreement with the experimental results at 80 K [Fig. 3.48(a)]. Recently, Hansen and Bruch[773] reported MD simulations of the diffusion in adsorbed nitrogen Þlms on graphite, both in the monolayer and submonolayer regimes. They included McLachlan substrate-mediated interaction and surface corrugation effects.[531,774] Hansen[775] also studied the effects on the structure
Figure 3.48 Average tilt angles (kul) of the N2 molecular axis with respect to the graphite planes as a function of coverage at (a) 80 and (b) 140 K. Solid lines are second-order polynomial Þts, which were passed through the measured data points (open circles with error bars) to lead the eye. Triangles and squares, MD simulations; asterisks, GCMC simulations. The inset in the right bottom corner deÞnes the out-of-plane tilt angle, u, of N2 relative to the graphite planes. (Reproduced from Finkelstein et al.,[771] with permission from Elsevier.)
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of ßuid nitrogen Þlms by the corrugation in the gas Ð solid potential. He obtained generally good agreement between experimental and calculated isosteric adsorption heats. Nevertheless, to match the slope in the experimental data it is necessary to reduce the magnitude of the McLachlan term from 15% to 3Ð 4%. The corrugation in the gas Ð solid potential induces some hexagonal structure in the ßuid, not seen on a model uncorrugated graphite surface, at temperatures as high as 60 K, approximately 30 K above the melting point and about twice the height of the potential barrier in the corrugation. In another recent paper, Lushington and Chabalowski[776] reported ab initio simulations of N2 physisorption on pregraphitic clusters. They estimated effective adsorption diameters and sticking coefÞcients for nitrogen adsorbed on ßat graphitic surfaces as reference. They found that the mean adsorption diameter exhibits very little dependence on the adsorbent model, but binding energy increases consistently with increasing size of the model adsorbent, as could be expected (at least until a certain limit determined by the interaction potentials is reached). Results from ab initio calculations were reported earlier by Sordo et al.,[777] who calculated adsorption energies of methane, ethane, propane, n-butane, ethylene, propene, 1-butene, 1,3-butadiene, acetylene, benzene, toluene, naphthalene, anthracene, and pyrene on the basal plane of graphite. They found good agreement between their calculations and the experimental results available in the literature. In addition, these calculations yielded the most favorable orientation of the adsorbate on the surface, which was also in agreement with experimental evidence.[778] Oxygen adsorption on the basal plane of graphite has also been studied with computer simulations. Although oxygen quadrupole moment is very small, Joshi and Tildesley[779] argued that it strongly affects the orientational correlation between neighboring molecules in the adsorbed solid phase. They combined MD and energy minimization techniques to perform their study. Energy minimization shows the existence of two non-equivalent competing structures with nearest neighbors arranged parallel and at an angle of 608. The quadrupolar interaction stabilizes one structure with respect to the other. Moreover, to achieve the structure observed in experiments, the quadrupole moment must be set equal to zero. Patrykiejew and Soko·owski [780] presented a van der Waals-like theory to describe submonolayer oxygen adsorption on graphite. They compared their results with GCMC simulation data. They found that their theory is suitable for describing adsorption of diatomic molecules on solid surfaces. The main source of discrepancy between theory and simulations seems to be numerical simpliÞcation in the model rather than the model itself. Bhethanabotla and Steele[781] studied the thermodynamic, structural, and dynamical properties of dense oxygen layers on graphite between 30 and 70 K using MD simulations. They located the temperature for the Þrst-layer melting between 55 and 60 K and determined that it was not much dependent upon total coverage. This melting transition appeared to be sharp for most cases studied. On the other hand, the melting of the second layer depends strongly on the layer density,
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and compound liquid Ð solid layers are observed. The authors also demonstrated the importance of orientational changes in determining the properties of these systems. Marx et al.[782,783] studied the structure of CO monolayers adsorbed on graphite. They employed different simulation techniques (e.g., purely classical MC, full quantum mechanical and path-integral MC simulations). They focused their attention on the ordering transition of a full monolayer of CO. This transition is roughly located at 5 K and is attributed to a head Ðtail ordering of the molecules. They concluded that the transition has 2D Ising character,[784,785] in agreement with experimental evidence. Furthermore, by switching off the dipole moment they found that the head Ð tail ordering is not induced by electrostatic dipole forces but by the shape asymmetry of the molecule. Quantum effects concerning this transition were found to be rather small. Hammonds et al.[786] performed MD simulations of CO2 adsorbed on the graphite basal plane between 100 and 130 K. They focused their attention in the submonolayer and monolayer coverages. Gas Ðsolid interactions were calculated using the method developed by Steele,[787] and the interaction parameters were calculated using the Lorentz ÐBerthelot combining rules.[485] To calculate the lateral interactions three models (2CLJ, MOM, and PRC1) for the carbon dioxide molecule were tested. Model 2CLJ is a two-center Lennard-Jones potential previously employed to describe the properties of liquid CO2; in this model, the two centers are located on the oxygen atoms. Models MOM and PRC1 are more realistic because both allow electrostatic interactions between the molecules. In the MOM model, the quadrupole moment is represented by a set of Þve fractional point charges on each molecule. The partial charges were calculated using ab initio methods. This calculation was needed because the potential was originally parameterized to reproduce the experimental quadrupole moment and higher electrostatic moments. Reducing the number of charges to three did not affect the calculations since higher moments contributed negligibly to the total interaction energy. The non-electrostatic van der Waals contributions were also represented by three interaction sites. These interaction parameters produced isosteric heats that were close to experimental values. Bottani et al.[788] employed the MOM model to describe the CO2 molecule but with the size parameter for O Ð O interactions reduced by 3% with respect to the value employed by Hammonds et al.[786] This set of parameters produced isosteric heats in very good agreement with experimental data (see discussion in Section 3.3.3.1 and the data published by Bottani and Cascarini de Torre[789]). Moreover, the parameters used in GCMC and CEMC simulations[788] gave thermodynamic properties in excellent agreement with data published by other authors. Terlain and Larher[790] reported a 2D triple point at 122 K, a 2D gas Ð liquid critical point at 126 K and, by interpolation, a pressure of 0.024 torr for the step in the isotherm at 120 K. Figure 3.49 shows a detail of the simulated isotherm, which clearly exhibits the step in the isotherm at the same pressure experimentally determined by Terlain and Larher. Bottani et al.[788] pointed out two features of the
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Figure 3.49 CO2 GCMC adsorption isotherm on the basal plane of graphite at 120 K. (Adapted from Terlain and Larher,[790] with permission from Elsevier.)
simulations. The Þrst is the variable average tilt angle for molecules in the monolayer and the concomitant variable effective molecular size as measured by the area projected onto the surface. This is a complication not adequately dealt with in adsorption theories, even though it may be encountered often when the adsorbate molecules are signiÞcantly nonspherical. The second was the importance of the quadrupolar energy in determining the thermodynamic properties of this system even at high temperatures where thermal averaging might be expected to minimize its magnitude. Bottani et al.[788] have estimated the quadrupole contribution to the total lateral interaction to be roughly 50% in the monolayer. Phillips and Hruska[791] employed CEMC simulations to study CH4 adsorption on graphite Þlms, particularly the multilayer growth at low temperature. Their results at 25 K showed that the Þrst and second methane layers are not mutually commensurate for all but the highest coverage studied. Even though they did not employ MD, the system is sampling phase space for the intermediate conÞgurations in an approach to equilibrium. Based on this, they presented snapshots of unequilibrated conÞgurations suggesting a microscopic mechanism for the transport of molecules within the Þlm as could be appreciated in Fig. 3.50. Phillips[792] compared simulations of several systems: methane/graphite, methane/Au(111), and Ar/graphite at 25 and 100 K. He concluded that methane and Ar Þlms on graphite appear to be solid-like and are virtually internally commensurate. At lower coverages, the Þrst and second layers of methane on graphite are incommensurate, which is the case for methane on Au(111) at all coverages. At 100 K, the growth characteristics of all the systems studied are experimentally found to be the same, namely, complete wetting. Phillips and Shrimpton[793] performed MD simulations of a bilayer of methane on graphite. They predicted that the commensurateÐincommensurate transitions between the Þrst two layers in a multilayer agreed with the results obtained with neutron diffraction experiments.[794]
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Figure 3.50 Snapshot of an unequilibrated conÞguration generated in CEMC simulations of methane adsorbed on graphite at 25 K. The arrows indicate the recent history for the particles. (Adapted from Phillips and Hruska.[791] Copyright 1989 from the American Physical Society)
Kim and Steele[795] also studied the adsorption of methane on graphite. They focused their study on the effect of corrugation in the graphite surface potential, on the thermodynamic quantities, the commensurate Ðincommensurate, and melting transitions. Simulations with a corrugation magnitude 50% larger than that given by the pairwise spherical-site summation approximation to the potential gave good agreement with experimental data. Pinches and Tildesley[796] performed MD simulations of the melting of CF4 adsorbed on graphite. To avoid typical problems in simulating commensurate Ð incommensurate phase transitions, they studied a patch of 400 molecules in the center of a periodically replicated box at a total coverage of 0.5. Their model patch melted at temperatures close to the experimentally observed one. They also performed energy minimization, which showed an important characteristic of this system: the low translation barrier for tripod-down molecules between bridge and atop sites on the graphite surface. Another Þnding was orientational order both in the plane and out of the plane of the surface; molecules prefer to be tripod-down and there is a preferred direction in the plane of the surface for the CF bonds pointing toward the surface. Energy minimization indicated that the low-temperature structure for the model employed is an incommensurate, hexagonally close-packed structure with the molecules in the tripod-down orientation. Nevertheless, the simulations did not show any evidence of phase transitions below 73 K observed in calorimetric studies.[797] Acetylene adsorption on graphite has been studied by Peters et al.[502] using experimental data in the HenryÕs law region and MC computer simulations. HenryÕs constants were used to determine the interaction parameters. Possible structures of the solid phases were discussed in light of simulation results using several intermolecular potential models, and complete sets of the interaction parameters were included. The conclusion was that the potential functions
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commonly employed for other systems are inadequate in this case. The authors attributed this to the large quadrupole moment of the adsorbate and the inability to treat the induction energy for C2H2/graphite with the usual image plane model. From experimental isotherms, they found some evidence for the existence of two solid surface phases with monolayer densities of 0.189 and 0.157 nm2/molecule. MC simulations also predicted both solid phases in agreement with their data and some limited neutron diffraction results.[798] One of the Þrst computer simulations of hydrocarbons adsorbed on graphite was the one performed by Nose« and Klein.[799] They studied the structural and dynamical behaviors of overlayers of ethylene adsorbed on the basal plane of graphite using MD. They tested the parameters employed in their calculations by studying the structure of bulk monoclinic ethylene, which they could reproduce very accurately. They estimated the isosteric adsorption heat (20 kJ/mol), which was in good agreement with available experimental data[800] (19.2 kJ/mol). One important conclusion is that they predicted higher densities than experimental values for all the phases studied. This was attributed to the absence of quadrupole interaction terms and surface corrugation effects in their intermolecular potential and gas Ð solid potential. Bottani[801] performed GCMC simulations of ethylene adsorption on the basal plane of graphite, analyzed in detail the lateral interaction potential and tested several models to describe the adsorbate molecule. The interaction potentials employed take into account the quadrupoleÐ quadrupole interactions between adsorbed molecules. The results agreed very well with experimental data, for example, the adsorption isotherms at several temperatures (Fig. 3.51) are reproduced quite well. The temperature range studied was 120 Ð 173 K. The
Figure 3.51 Ethylene adsorption isotherms on the basal plane of graphite at several temperatures: circles, 173.2 K; squares, 163.2 K; triangles, 153.2 K. Open symbols: experimental data; Þlled symbols: GCMC simulations. (Adapted from Bottani.[801] Copyright 1999 American Chemical Society.)
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quadrupolar contribution to lateral interactions was found to be quite important. Small changes in quadrupole moment produced large effects on the isotherm shape, especially on the condensation pressure. The isosteric adsorption heat estimated from the simulations, 18.52 kJ/mol, agreed very well with values previously reported in the literature and the ones mentioned earlier: Kalashnikova et al.[802] reported 17.99 kJ/mol, and Battezzati et al.[803] 20.2 kJ/mol. The estimated cross-sectional area (0.202 + 0.01 nm2) is the same as the one obtained from the van der Waals constant (0.201 nm2).[804] Adsorption of alkanes on graphite has also been studied by Vidal-Madjar and Minot;[805] in particular they analyzed the gas Ðsolid interaction potential. They employed band structure calculations in the framework of extended Hu¬ckel theory. They calculated the second gas Ð solid virial coefÞcient and thermodynamic characteristic functions for methane, ethane and propane adsorbed on the basal plane. Leggetter and Tildesley[806] published a very complete paper dealing with the simulation (MC and MD) of adsorbed hydrocarbons on graphite. They discussed the interaction potentials in detail and showed a complete set of expressions needed to perform such calculations. They also analyzed the structures of adsorbed hydrocarbons on graphite at different surface coverages. Hentschke et al.[807] reported MD simulations of ordered alkane chains physisorbed on graphite and compared the results with STM images. Zhao et al.[808] reported the isosteric heats of adsorption of propane on graphite. They compared the value obtained from optical differential reßectance experiments (23 + 2 kJ/mol) with the one obtained from GCMC and CEMC simulations (24 + 1 kJ/mol) and studied the layering behavior of propane on graphite. Meyer et al.[809] have studied neopentane adsorption on Sterling FT carbon black. They reproduced experimental isotherms obtained at Þve temperatures using the van der Waals and Steele models. They also compared their results with chromatographic data. The estimated isosteric heats of adsorption (34 Ð 44 kJ/mol) are in good agreement with the experimental values. Vernov and Steele[810] reported simulations of benzene adsorbed on the graphite basal plane at 298 K. They studied the structures and energies of the adsorbed Þlms and found a nearly constant heat of adsorption in the submonolayer region because of a cancellation of increasing average benzene Ð benzene interaction energy by the decreasing average benzene Ðgraphite energy. The observed decrease in gas Ð solid energy was due to a change in the orientation of the adsorbed molecules with respect to the solid surface. Bertoncini et al.[202] performed GCMC and CEMC simulations of phenol adsorption on the graphite basal plane. The phenol molecule was modeled as a rigid set of 13 Lennard-Jones interaction sites located on each atom. The dipole moment was simulated by placing partial charges on each atom, which were calculated with the AM1 standard method.[811] Gas Ðsolid energy was calculated using SteeleÕs potential with corrugation s ¼ 1.5 and the set of parameters obtained using the Lorentz ÐBerthelot combining rules. Figure 3.52 shows a map of the surface of the basal plane of graphite as ÒseenÓ by a phenol molecule lying ßat on the
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Figure 3.52 Energy of a phenol molecule sweeping the surface of the basal plane of graphite. The molecule is ßat on the surface and a0 ¼ 0.246 nm is the graphite unit cell length. (Adapted from Bertoncini et al.[202] Copyright 2000 American Chemical Society.)
surface, sweeping several surface unit cells. The periodic variation of the adsorption potential is clearly seen. The gas Ð solid potential presents three minima (see Fig. 3.53), one corresponding to the molecule lying ßat on the surface and the two others when the molecule is standing vertical on the surface, one of these corresponding to the molecule with the OH group pointing toward the surface.
Figure 3.53 GasÐ solid interaction potential for phenol on the basal plane of graphite for the molecule lying ßat and in vertical position with the OH group pointing toward and away from the surface. (From Bertoncini et al.[202])
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Gas Ðsolid and gas Ð gas potentials were extensively analyzed. The authors concluded that the graphite surface offers two main adsorption sites located at the center of the carbon hexagon (center site) and between two carbon atoms (saddle site). Gas Ðsolid energy ßuctuations are mainly due to the oxygen Ð carbon (graphite) contribution. Lateral interaction is attractive due to the electrostatic component of O Ð H and C ÐH pair interactions. Moreover, C Ð H almost compensates H Ð H repulsive interaction. The authors also estimated the crosssectional area of the adsorbate and two values were proposed, one corresponding to the strict deÞnition of cross-section equal to 0.408 nm2, as well as an effective cross-section, based on the effective area occupied by a molecule, equal to 0.485 nm2. No order was found in the adsorbed Þlm even at the lowest temperature studied, and the layer thickness was estimated at 0.744 nm. Peters and Tildesley[812] reported MD simulations of the melting of an n-hexane monolayer on graphite. They adopted an adsorbate model that contains intramolecular and intermolecular terms, including bond-length extension, bondangle distortion, torsional, Lennard-Jones, and molecule Ð surface energies. They centered their study on the effect of the isotropy of the force Þeld on melting behavior. The methyl and methylene segments of the skeletal chains were modeled by using either the Òunited atomÓ or Òanisotropic united atomÓ potential model. Both models gave good agreement with the experimental melting temperature and the observed phases. At low temperature, the monolayer of n-hexane exhibited a commensurate herringbone structure, which on heating melts in two stages. First, at monolayer coverage the solid undergoes an orientational phase transition to form a rectangular centered phase in coexistence with an isotropic ßuid. This solid is incommensurate and is simultaneously expanded with respect to the herringbone structure. The coherence length of the nematic patches decreases and the solid Þnally melts to an isotropic liquid phase. Guo et al.[813] reported MD simulations of a single long chain polyethylene adsorbed on a solid surface. They modeled the hydrocarbon chain as a single long ßexible chain with more than 200 CH 2 units, each one treated as a united atom. The conÞgurational energy of the chain is given as a sum of the intrachain interaction energy and the polymer-solid van der Waals energy calculated using the Dreiding II force Þeld. They found that, as the surface-carbon-atom number density increases, the intermolecular energy decreases but the intramolecular energy increases. For a high intermolecular interaction force, the chain adsorbs onto the solid surface and develops into a stretched monolayer-like structure. However, for low surface afÞnities, segments of the chain avoid the surface and fold into a compact lamella-like structure. On the other hand, for a moderate surface afÞnity the chain forms a poly-layer-like structure at the surface. They also found that the intramolecular van der Waals force, rather than any other intramolecular interactions, drives the chain to fold into a compact, ordered, lamella-like structure. Kwon et al.[814] reported the results of a combined experimental and theoretical study of acetone adsorption Ð desorption on graphite. The experimental data
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were obtained using optical differential reßectance and temperature programmed desorption under high vacuum conditions. They performed molecular simulations of acetone on planar graphite to compute the geometry and coverage of acetone up to three layers. They found that acetone molecules tend to lie parallel to the surface in the submonolayer region. The relative orientation between the adsorbed molecules is determined by dipole Ð dipole interactions. The upper layers are more disordered than the monolayer. Second layer formation starts when the coverage in the Þrst one is ca. 75%, and the third layer formation begins when the coverage in the Þrst one is ca. 90%. Turner and Quirke[815] employed GCMC simulations to study the adsorption of nitrogen on graphitic surfaces containing pit defects, which were created by simply deleting surface atoms according to certain patterns. Their simulations indicate that, while adsorption is enhanced at low pressure, the high-pressure adsorption is reduced. In contrast to adsorption at 77 K on nondefective surfaces, nitrogen molecules are ordered in the pits. Adsorption on amorphous carbon surfaces has been studied by Cascarini de Torre and Bottani[512] using BernalÕs model[511] to describe the adsorbent structure. They tested the model by comparing GCMC nitrogen isotherms with experimental data obtained for several nonporous carbonaceous materials (e.g., carbon Þbers, synthetic graphites, mesocarbon microbeads, carbon blacks, and cokes). The main criticism of BernalÕs model is that it does not take into account the chemical structure of the solid; however, it is capable of reproducing the adsorption properties of these materials, as can be judged from the good agreement between simulated and experimental isotherms shown in Fig. 3.54. The solid line is a single curve that was obtained when plotting all experimental isotherms
Figure 3.54 Experimental (solid line) and GCMC (amorphous and Bernal models) nitrogen adsorption isotherms at 80.2 K on several carbonaceous materials (including Sterling 10R carbon black). (Adapted from Cascarini de Torre and Bottani.[512] Copyright 1995 American Chemical Society.)
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as surface coverage (N/Nm) vs. the equilibrium pressure (some experimental points for a nongraphitized carbon black, Sterling 10R, are shown as an example for the Þtting). Using the Bernal model to describe the amorphous carbon solid, Cascarini de Torre et al.[816] studied the adsorption of nitrogen, oxygen, and carbon dioxide at several temperatures and surface coverages. The isotherms for these systems increase smoothly with coverage, as expected for a heterogeneous surface. CO2 molecules are shown to be closer to the surface than the other adsorbates studied, which could be a consequence of the tendency of this molecule to lie ßat on the surface in the monolayer. It was also shown that the very different values of cross-sectional area proposed by other workers for these gases might be a consequence of the changes in packing due to the variable molecular orientation in the monolayer region. The authors concluded that there is a large number of probable conÞgurations of the adsorbed molecules involving very different orientations with respect to the surface. Furthermore, this is a consequence of the atomic roughness of the model heterogeneous surface employed in the simulations. Cascarini de Torre and Bottani[817] also studied the adsorption of ethylene on amorphous carbon in a wide temperature range using GCMC simulations. The solid was generated using the Bernal model and then its heterogeneity was increased by deleting atoms until a large valley was formed. This valley presented almost vertical walls with rough surfaces. Their main conclusions were that the structure of adsorbed ethylene Þlm seems to be determined by the topography of the solid surface at all temperatures studied. No preferential orientations were observed and the cross-sectional area of the adsorbate was in agreement with the molecular dimensions. The BET method, applied to the simulated isotherms, gave an area in perfect match with the geometric areas of the simulation cell. Finally, they showed that the number of neighbors in the adsorbed phase could be correlated with the spatial distribution of equivalent surface points. BernalÕs model has been employed also by Sasloglou et al.[818] in a very similar way to model the surface of alumina and to study its adsorption properties. Gargiulo et al.[819] characterized the energetic topography of heterogeneous surfaces using MC simulations of TPD spectra. The surface was modeled according to the dual-site-bond model,[820] where the adsorptive energy topography is described in terms of a correlation length. The authors argued that this kind of analysis is better than the normal analysis of the adsorption isotherm, because in this case adsorbate Ðadsorbate interactions do not compete with topography effects. Adsorption in slit-shaped pores. In this section we review computer simulation studies concerning the adsorption of different gases on carbonaceous solids with slit-shaped pores. Much work has been done in this area: modeling the adsorbate, the adsorbent pore network, and/or the structure of the pore itself. Both MC and MD simulations have been more or less equally employed depending on the kind of study performed. When they deserve general interest, we occasionally include papers concerning other adsorbents or pore shapes.
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It must be pointed out that Olivier[821] has criticized the currently widely used model of semi-inÞnite rigid slits. He observed that model isotherms calculated by MD for this model surface exhibit abrupt increases near 0.6 and 1.0 nm and attributed them to artifacts from the model (packing effects). Figure 3.55 is a plot of the mean pore ßuid density at saturation as a function of available pore width, where these effects are seen through four adsorbed layers. Based on these results, Olivier questioned the validity of computer simulation results obtained with this model, which are frequently utilized to analyze micropore size distributions. This conclusion seems not to be shared by other researchers, as may be seen in what follows. Samios and coworkers[822 Ð 824] developed a method to determine the micropore size distribution based on GCMC simulations and experimental results. They tested their method with CO2 adsorption data on a microporous carbon membrane at 195.5 K. They employed slit-shaped graphitic pores of different widths. Their method consists of simulating several isotherms on solids with a single pore and different sizes, then to construct the total isotherm using a size distribution assumed a priori, and Þnally to compare the obtained isotherm with the experimental one. The isotherm that best Þts the experimental data is the one that represents the closest pore size distribution to the real one. Their results agreed quite well with standard methods such as mercury porosimetry and the DR approach. Gusev and OÕBrien[825] demonstrated that GCMC simulations could be employed to predict adsorption on activated carbons. They tested their model with experimental data obtained for ethane on an industrial activated carbon. The pore size distribution was determined from the adsorption of methane at a
Figure 3.55 Mean pore ßuid density based on amount adsorbed plotted as a function of pore width to evidence the occurrence of packing effects. (Reproduced from Olivier,[821] with permission from Elsevier.)
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single temperature. The model solid was a slit-shaped graphitic pore, and the gas Ð solid potential was the one proposed by Steele[38] for the basal plane of graphite. They also showed that a spherical model of ethane was not adequate to predict adsorption in the real system. The phase behavior of a ßuid in mesopores just below the critical temperature using MD and experimental data has been studied by de Keizer et al.[826] Although the authors studied adsorption of SF6 on controlled-pore size glass, their presentation is general enough to be reviewed here. They concluded that the isotherms for this adsorbate change phenomenologically from subcritical behavior, with the appearance of pore condensation and hysteresis, to a supercritical behavior without these features. MD results qualitatively agree with the experimental results except in the width of the hysteresis loop. The pore model employed was that of an inÞnite cylindrical pore with uniform walls and, according to the authors, this could be the reason for the discrepancy between simulations and experiments. The simulations show that a decreasing strength of the ßuidÐßuid pair interaction causes a pronounced shift of pore condensation toward higher relative pressures. Sarkisov and Monson[827] used MD simulations at Þxed chemical potential to study the stability of states associated with hysteresis obtained in GCMC simulations. For a model of a simple ßuid, the hysteresis loops found with MD were essentially identical to those obtained in GCMC simulations of the same system. They concluded that GCMC hysteresis could reßect the experimental behavior more closely than has been previously appreciated. The hysteresis has its origin in thermodynamic metastability. Neimark et al.[828] studied the capillary condensation hysteresis in nanopores using MC simulations and the nonlocal DFT. They analyzed argon and nitrogen adsorption data and identiÞed several regimes as the pore size increases at a given temperature, or as the temperature decreases at a given pore size: volume Þlling without phase separation, reversible stepwise capillary condensation, irreversible capillary condensation with developing hysteresis, and capillary condensation with developed hysteresis. They found good agreement between simulations and experimental data. The latter correspond to MCM-41 silica but the results deserve general interest. Giona and Giustiniani[829] studied the clustering effects of admolecules driven by surface diffusion in a heterogeneous energy landscape as a mechanism for Freundlich-type behavior at low temperatures. They proposed an idealized preferential adsorption model and tested it with MC simulations. They also analyzed the effects of temperature and of patchwise distributions of adsorption energies. Their model is based on the idea that the adsorbate can diffuse on the surface until it Þnds the most favorable adsorption site. Bojan et al.[830] reported MD simulations of methane adsorption, at 300 K and pressures up to 70 atm, on rough-wall cylindrical pores as an approximation to the system methane/coal. They employed a model pore generated using BernalÕs model[511] and based on an idea Þrst published by Bakaev.[831] BakaevÕs idea was that it is possible to generate a random heterogeneous surface with the sequential addition algorithm reviewed by Finney,[832] which produces
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an amorphous, close-packed hard-sphere solid. Since the energetic heterogeneity that this algorithm can produce is somewhat limited, deletion of atoms from the solid will generate a hole that increases the geometric heterogeneity of the solid. Bojan et al.[830] simulated several pores with radii ranging from 0.65 to 1.34 nm, and as reference they employed a ßat surface of the same material. One interesting result is that at high temperatures a signiÞcant fraction of the methane in the pore is unadsorbed gas. The authors proved this through analysis of adsorbateÕs local density, r(r). Thus, Fig. 3.56 shows three curves of r(r) computed for different
Figure 3.56 Dependence of the local density of methane upon distance from the pore axis for adsorption at 300 K in cylindrical pores with radii equal to (a) 0.65, (b) 1.00, and (c) 1.34 nm. The hatching scheme subdivides the total density curve into unadsorbed gas ( ), monolayer adsorption ( ), and multilayer adsorption ( ). (Reproduced from Bojan et al.[830] Copyright 1992 American Chemical Society.)
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pore Þllings and pore radii. The unadsorbed gas density is indicated, as are the densities associated with monolayer formation on the pore wall and multilayer formation in the interior region. Another interesting idea developed in this paper concerns the estimation of the pore radius. The authors performed this estimation during the calculation of HenryÕs law constants by calculating the average distance at which the potential energy of a molecule is zero (i.e., the Boltzmann factor exp[2U/kT] , 1). They found that pore radii determined in this way are always smaller than the geometric value. Using a similar approach to generate a heterogeneous porous solid, Cascarini de Torre and Bottani[833] reported GCMC simulation results for nitrogen adsorption at 77.5 K. They compared the adsorptionÐdesorption isotherms on a series of solids differing in the number and geometry of pores. Well-deÞned hysteresis loops were obtained for all solids studied. The results obtained clearly showed that the adsorbate is in a liquid-like state within the pores; moreover, the total pore volume estimated by integration of the density proÞles agreed with the theoretical pore volume calculated from geometric considerations. The pore size distributions obtained from the adsorption branch were meaningless, probably due to the metastable character of this branch of the isotherm. Another interesting Þnding was that the adsorbed molecules were not desorbed, at least down to pressures where the observed hysteresis loop was closed. Papadopoulos et al.[834] employed MD simulations to study methane diffusion in model cylindrical pores at very low densities and ambient temperature. The cylinders were modeled as a continuum solid that interacts with methane in the radial direction only. The self-diffusion coefÞcient was calculated using both integration of the velocity auto-correlation function (VACF) and the time-evolution of the mean squared displacement (MSD) method.[693] They found that the VACF method does not yield reliable values of the self-diffusion coefÞcient, but a suitable choice of time step and run length enables values of the diffusion coefÞcient to be found from MSD plots that are below the classical Knudsen diffusion coefÞcients. Hysteresis in the proximity of the capillary condensation transition was made evident by ßuctuations between liquid and vapor phases as the length of the Markov chain increases. The authors argued that the degree of hysteresis reßecting the non-ergodic behavior of the Markov chain could be diminished by increasing the area of the pore wall and by extending the Markov chain. Papadopoulos[835] completed the study with analysis of orientational ordering transition upon diffusion of supercritical carbon dioxide in the nanopores. He found good agreement between simulations and experimental data obtained for CO2 adsorption in nanoporous carbon membranes. Schoen et al.[836] studied the manifestations of hysteresis using GCMC simulations of noble gas adsorption in slit-shaped pores. Soko·owski[837] reported extended GCMC simulations of oxygen adsorption in slit-like pores. He calculated the isotherms for several pore widths and two temperatures (100 and 200 K). At the lower temperature and for wider pores the phenomenon of capillary condensation was observed. For pores with diameters equivalent to ca. 5 molecular diameters, he found that the critical temperature inside the pore was slightly below 100 K. He also found that orientational effects were visible only within the two Þrst layers
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adjacent to the pore walls. Matranga et al.[838] studied the adsorption of natural gas (as a Þrst approximation they assumed it to be pure methane) on activated carbon using GCMC simulations. They modeled the porous structure as a collection of inÞnite graphite planes arranged parallel to each other. Through a comparison of the simulations with experimental data, they demonstrated that their model solid represents an upper bound for equilibrium capacity above 10 atm. One interesting result is that their simulations predict that fast adiabatic Þlling is accompanied by a temperature rise of 87 K and a 48% loss in storage capacity. Cracknell et al.[839] studied the adsorption of mixtures of Lennard-Jones ßuids (methane Ðethane) in slit-shaped pores (with graphitic walls) using GCMC. They introduced a modiÞcation in the GCMC algorithm to improve the efÞciency of the method. The modiÞcation consisted in allowing attempts to change the particle identity. They found qualitative agreement with DFT and IAST. Adsorption selectivity depends on packing considerations as well as the relative potential well depths of the gas Ð solid interaction potentials. Valladares et al.[840] analyzed several methods for porosity characterization in activated carbons. They employed MC simulations to generate N2 isotherms on different model solids composed of slit-shaped pores with graphitic walls. Figure 3.57 compares the values of the peak positions of the input distributions
Figure 3.57 Position of the peak of the pore size distribution function prediction by means of the DubininÐ Stoeckli method (triangles). The circles are mean values of the input distribution functions (Gaussian, dispersion of 0.30 nm). (Reproduced from Valladares et al.,[840] with permission from Elsevier.)
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for many ideal isotherms with those of the distributions predicted by the DS equation (vertical bars represent the dispersion of these distributions). As the mean input pore size increases, the dispersion of the predicted distribution increases and the deviation of its peak goes through a maximum at 0.15 nm. The authors associated the failure of this method to predict the correct pore size distribution of ideal isotherms with the fact that Dubinin-type behavior was not observed in their simulations. The consequence is that the DubininStoeckli method will not be adequate for a microporous solid composed by ideal slit-shaped pores. Vishnyakov et al.[841] studied the critical properties of a Lennard-Jones ßuid conÞned in slit-shaped graphitic pores using the Gibbs ensemble MC method (see Òother ensemblesÓ in Section 3.3.3.3) and the lattice gas model. They found a linear dependence of the critical temperature on the inverse pore width. They also demonstrated that the critical temperature might depend strongly on the strength of the solid Ðßuid interactions. Aydt and Hentschke[842] performed MD simulations of high-pressure adsorption of methane in slit-shaped graphitic pores. They found good agreement between simulations and experiments, at least with respect to the excess adsorption isotherms. Van Slooten et al.[843] studied room-temperature methane adsorption in slit-shaped graphitic pores that were made chemically heterogeneous by introducing sulfur atoms into the graphite basal planes. Sulfur atoms were introduced in a regular array with two levels of substitution. The authors showed that the uptake and the heat of adsorption increased with respect to the unsubstituted pore. However, they also found that the most energetic sites were the remaining exposed carbon atoms and not the incorporated sulfur atoms. Through analysis of the distribution of adsorption energies they found that adsorption does not occur by occupation Þrst of the most active sites followed by coverage of the weaker parts of the surface. Kaneko et al.[844] studied N2 adsorption at 303 K in slit-shaped pores and compared simulation results with experimental data. They employed GCMC simulations where the pores had parallel smooth graphite surfaces separated by 0.75 or 1.45 nm. They discussed alternative methods to calculate the pore width, and showed that calculation of the pore width based on the spacing between graphite planes is less satisfactory than the one based on the adsorbateÐ adsorbate potential. Brodskaya and Piotrovskaya[845] studied nitrogen adsorption in slit-shaped graphitic micropores at 77 and 195 K. They calculated the isotherms using GCMC and found that the degree of pore Þlling and the character of the distribution of molecules inside the pore is substantially dependent on the model employed to describe the adsorbate. Cracknell et al.[846] performed MD simulations of methane adsorption in slit-shaped graphitic micropores and calculated the diffusion coefÞcients in the pores. They also modeled two types of wall reßection for adsorbed molecules and found signiÞcant differences between them. This result suggests that the wall structure must be carefully designed. Similar conclusions have been
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derived by Chen et al.,[847] who found that variations in the density of carbon atoms in the pore wall have a signiÞcant inßuence on adsorbed methane density. They calculated the inßuence of pore wall thickness on stored methane capacity, and the results were in reasonable agreement with experimental data. Piotrovskaya and Brodskaya[848] have also studied methane adsorption in slit-like pores at 111.1 K using GCMC simulations. They focused their study on the two-phase equilibrium in narrow pores with wetted walls. The pore widths were changed from 4 up to 12 molecular diameters. The authors showed that the vapor Ð liquid coexistence at the concave meniscus existed for pore widths larger than 10 molecular diameters. They studied a weaker adsorbent and found that the coexistence between vapor and liquid could be found for smaller pore widths than when simulating the stronger attractive surface. In a subsequent paper, Vanin et al.[849] studied methane adsorption in pores of different geometries. They simulated pores with rectangular, square, and circular cross-sections. They found that, for square and rectangular pores, the adsorbate does not wet the surface, in contrast to what was observed for circular pores. Sliwinska-Bartkowiak et al.[850] studied the effect of conÞnement in slit-shaped pores on the melting of aniline. They simulated the system aniline-activated carbon Þbers and compared their results with experimental data obtained by dielectric relaxation spectroscopy. Simulations were carried out using GCMC together with the Landau free energy calculations, and phase transitions were located as points where the grand free energies of two conÞned phases are equal. They determined the nature of those phases through analysis of in-plane pair positional and orientational correlation functions. The transitions found were from 2D hexagonal crystal to hexatic phase at 296 K, and from hexatic to liquid-like phase at 336 K. They concluded that conÞnement within slit-shaped pores stabilizes the hexatic phase, which is the stable phase over a wide temperature range for quasi-2D liquid Þlms. Kim and Kim[851] studied N2 adsorption in micropores using the density functional perturbation approximation, which is based on the second-order perturbation theory of the liquid and on the pore-averaged density. For a wide slit-shaped pore, the mean Þeld approximation with empirical parameters seems to yield reasonably good results for adsorption hysteresis. However, agreement is not as good when slit width is decreased. For a narrow pore, the density functional perturbation method compared fairly well with computer simulation. A non-equilibrium MD simulation technique has been proposed by Cracknell et al.[852] The method uses both stochastic and dynamic steps and describes the ßux of particles ßowing between deÞned regions of different chemical potential. For methane adsorption in carbonaceous slit micropores, they found that the ßux is linearly dependent on the concentration gradient (i.e., FickÕs law is obeyed). Sowers and Gubbins[853] reported calculations based on DFT[854] and computer simulations for the adsorption of trace contaminants (CCl4, CF4, and SO2) carried in nitrogen streams at 300 K. The pores had slit-shaped graphitic walls of
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different widths. For different concentrations of the trace pollutant they found that there is an optimal pore width for which the selectivity is greatly enhanced. Pressure has a similar but much less marked effect. Balbuena and Gubbins[855] employed the nonlocal DFT to interpret and classify the adsorption behavior of simple ßuids in model materials having slit-shaped pores. They determined the adsorption isotherms, isosteric heat of adsorption and phase diagrams, and identiÞed a seventh type of adsorption isotherm that may have to be added to IUPAC 1985 classiÞcation. This new type of isotherm corresponds to capillary evaporation. Kaneko and coworkers[856 Ð 858] have reviewed micropore-Þlling mechanisms. The authors mentioned studies on SO2 adsorption in slit-shaped graphitic pores: as could be expected, this molecule, with its high dipole moment, presents a 2D preferential orientation in a micropore. They also found that formation of dipole-oriented structure of SO2 is mediated by interaction of the permanent dipole with the induced dipole in the graphitic wall. They also employed calorimetric data to support their conclusions. Klochko et al.[859] reported the results of MD and MC simulations of the thermodynamic, structural, and kinetic properties of bulk and adsorbed ArÐ Kr mixtures in slit-like graphitic pores at 88 K. The dependence of the diffusion coefÞcient on the pore width was mainly deÞned by the behavior of local density in pores. They also found that increasing Kr concentration decreased the diffusion coefÞcients of both components. Cracknell et al.[860] studied adsorption of CO2 mixtures with methane and nitrogen in slit-shaped graphitic micropores. They compared GCMC simulations with experimental data at ambient temperature. Simulations predict that CO2 is preferentially adsorbed from both mixtures. In their GCMC algorithm they included the possibility of particle identity exchange. This probability is given by
Pi!j
zj DE exp ¼ min 1, kT zi (Nj þ 1)
(3:169)
Microscopic reversibility requires that Pi!j ¼ Pj!i. The effective pore width was calculated using the gas Ðsolid potential size parameter. The authors found that in very small pores with a physical width below 0.7 nm, which corresponds to an internal width of less than 0.5 nm, methane and nitrogen are virtually excluded compared to carbon dioxide. This sieving effect is highly dependent on the molecular models employed in the simulations and may not be realizable in practice. In pores larger than this, selectivity ratios are rather low for the methane mixtures, but nearly an order of magnitude higher for the less strongly adsorbed nitrogen. Suzuki et al.[861] reported GCMC simulations of N2 adsorption in slit micropores and compared them with experimental data for pitch-based ACFs. The walls of the model pore were smooth graphitic surfaces. Agreement between simulations and experiments was rather poor in the sense that simulations
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showed a steep jump, in contrast with the experimental isotherm, which exhibited gradual uptake. Vishnyakov et al.[862] studied ethane adsorption in slit-like pores with uniform walls. They compared two models for ethane, one of them assuming a longer molecule. They found orientational transitions of ethane molecules near the walls when temperature is decreased from 180 to 169 K. On the contrary, with the longer molecules these transitions were not observed. At lower temperatures, ca. 140 K, orientation of ethane molecules perpendicular to the walls is preferential. In a subsequent paper, Klochko et al.[863] continued the study of ethane properties in slit-shaped graphitic pores. They reported results of GCMC simulations at different temperatures using several pore widths (from 0.95 to 3.8 nm), and showed that the properties investigated do not change monotonically with the increase of pore width up to 2.1 nm. In the micropore interval, molecular orientation in the adsorbed layers nearest to the walls strongly depends on the pore width. Suzuki et al.[864] analyzed the mechanism of pore Þlling for carbon tetrachloride in a graphitic micropore using GCMC simulations and pores with widths from 0.7 to 1.8 nm. They could classify the simulated isotherms in three groups according to the pore width: (i) 0.7 Ð 0.9 nm; (ii) 1.0 Ð1.5 nm; and (iii) 1.6 Ð1.8 nm. The difference in the isotherms was attributed to different packing structure of CCl4 molecules. The radial distribution for pores between 0.98 and 1.04 nm showed an unusual ordered feature, which is close to that of the plastic crystalline form of bulk CCl4 at 253 K reported in the literature.[865] Later, Suzuki et al.[866] reported GCMC simulations of CCl4 adsorption in graphitic slit-shaped pores at room temperature. They found that an assembly of spherical molecules had a symmetrical packing structure that depends on pore width. They calculated the coordination number and the intermolecular distance of each structure using geometric arguments. Since they assumed perfect symmetry in geometrical calculations, they called this approach a Òquasi-symmetry analysisÓ. Jin and Wang[867] have studied the adsorption of chlorodißuoromethane (HCFC-22) in activated carbon slit pores using GCMC, Gibbs ensemble MC, and Widom test particle method simulations. They tested the interaction parameters employed by calculating the phase diagram of HCFC-22. They also employed GCMC simulations to estimate the optimum pore width for adsorption of HCFC-22, and found that a width of 1.75 nm gives a very sharp maximum adsorption. Figure 3.58 depicts the structure of the ßuid in the pores of this width in the form of local density proÞles as a function of the density of active sites and the relative pressure. At the lowest pressure considered, the contact layers in the pores with 0.8 and 1.6 sites/nm2 are more pronounced than those for 0.0 sites/nm2. With increasing pressure the differences diminish, particularly for the cases of 0.8 and 1.6 sites/nm2. Due to the dipole Ðdipole interactions of the Stockmayer potential, the chlorodißuoromethane molecules aggregate internally and no distinct inner layers emerge in the pores; instead, a rather wide and ßat peak appears [Fig. 3.58(d)Ð(l)] compared
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Figure 3.58 Local density proÞle in slit-shaped pores of 1.75 nm width with different active site densities and partial pressures, at 300.2 K. (Reproduced from Jin and Wang.[867] Copyright 2001 American Institute of Physics.)
with, for example, the Lennard-Jones ßuid CCl 4 reported by Suzuki et al.[864] From analysis of the inßuence of the active sites on adsorption, Jin and Wang[867] estimated that the optimum density of active sites was 0.8 sites/nm2 when the adsorption is conducted at ambient temperature and pressure and the exhaustion pressure is 0.011 MPa. In this case, the maximum amount of HCFC-22 would be recovered. Votyakov et al.[868] reported a theoretical study of phase diagrams of simple ßuids conÞned in narrow, slit, and cylindrical pores. They concluded that the shape of the observed phase diagram depends not only on pore geometry but also on relative strengths of ßuid Ðwall and ßuid Ð ßuid interaction potentials. They also found that the lattice model correctly accounts for all of the general features of the phase diagram arising from ßuid Ðwall interaction, pore size, and pore shape. Miyahara et al.[869] performed MD simulations to generate adsorption isotherms in cylindrical nanopores. The isotherms were employed to test a model proposed to replace the Kelvin model, which underestimates pore sizes. Their model takes into account the contribution of the pore-wall potential and the curvature-dependent surface tension. Chakrabarti and Kerkhof[870] used MC simulations to systematically investigate the role of wall structure on a ßuid of ßat hexagonal molecules conÞned
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between two graphite walls. They found that the molecular centers of mass in different layers undergo an order Ðdisorder transition as the wall separation increases, irrespective of the details of the wall structure. Wall structure thus becomes insigniÞcant for the intervening ßuid even down to a surprisingly low wall separation. Kamakshi and Ayappa[871] studied structural transitions of nitrogen adsorbed in slit-shaped graphitic pores using GCMC and CEMC simulations. They studied several pore widths ranging from 0.7 to 1.4 nm at different temperatures. For the smallest pore studied a single layer at the center of the pore could be formed, and the orientations of the adsorbate are predominantly with the molecular axis parallel to the wall forming an incommensurate herringbone structure. At slightly larger pore widths and in the single-layer regime, most molecules are adsorbed with their axis tilted toward the graphite sheet. When two distinct wall layers are formed, the orientation distributions reveal that adsorbed molecules can exist in two ordered phases (herringbone and triangular incommensurate) at low temperatures. The herringbone structure is similar to the one found in adsorption on the graphite basal plane. Suzuki et al.[872,873] brießy reported a GCMC simulation-assisted porewidth determination of molecular sieve carbons using N2 adsorption at ambient temperature. The method employed had been previously discussed.[844] Computer simulations combined with experimental data were employed to determine the pore size distribution by Stoeckli et al.[874,875] These authors employed CO2 adsorption at 273 K to analyze seven previously characterized microporous carbons. MC simulation generated isotherms in slit-shaped graphitic pores. The resulting pore size distributions were in good agreement with experimental results obtained with a modiÞed Dubinin equation, liquid probes of different molecular dimensions, STM observations, and modeling based on methane adsorption at 308 K. Boro«wko et al.[876] employed MC simulations to study adsorption of associating ßuids in slit-like and spherical pores. They focused their attention on hard-sphere associating ßuids with two bonding sites in cavities of planar and spherical symmetries. Their main goal was to investigate how geometrical restrictions, imposed by the ßuid conÞnement, change the distribution of the particles and how the bonds formed are oriented with respect to the surface. Gusev and coworkers[877 Ð 879] proposed a self-consistent method to characterize activated carbons using supercritical adsorption and GCMC simulations. Several simulations of methane adsorption in model slit-like graphitic pores with different widths were performed. In fact, they calculated 40 isotherms in pores of sizes from 1.65 to 15 molecular diameters. Then, the experimental adsorption isotherm was Þtted with this set of isotherms. This kind of problem is usually considered as a least-squares problem, but, as in the case of the integral adsorption equation, it is an ill-posed problem. In mathematical terms it is Rmn V n ¼ Am (V j 0)
(3:170)
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where Rmn is an m n matrix of adsorbed quantities at the ith pressure in the jth pore, Vn is a vector of length n of the volumes Vj, and Am is a vector of length m containing the experimental adsorbed quantities. To solve the mathematical problem, the authors employed a nonnegative least squares routine combined with the singular value decomposition method. The last method takes care of singularities in the matrix R. The results enabled the authors to successfully predict the adsorption isotherm of methane on the same solid at temperatures more than 60 K higher. Sweatman and Quirke[880,881] characterized nonporous (Vulcan carbon black) and porous (two unidentiÞed samples and AX21-MAST ultrahigh surface area activated carbon from Amoco) materials using gas adsorption at ambient temperature and high pressure (up to 20 bar). They employed Gibbs ensemble simulations to determine molecular models for nitrogen, methane, and carbon dioxide, and GCMC together with experimental data to generate the isotherms for model carbon pores. Figure 3.59 shows the databases, generated from GCMC simulations, used for CO2, CH4, and N2. CO2 adsorption at high pressure is substantial for both narrow slit pores (overlapping strongly attractive gas Ðsolid potentials) and wider pores (near-critical capillary condensation of CO2). CH4 and N2 are adsorbed in a manner consistent with supercritical
Figure 3.59 GCMC-generated databases for (a) carbon dioxide, (b) methane, and (c) nitrogen adsorption on model carbon pores of different widths. (Reproduced from Sweatman and Quirke.[880] Copyright 2001 American Chemical Society.)
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adsorption. From these data and the resulting pore size distributions, the authors concluded that CO2 reveals more micropore structure than nitrogen and methane, in agreement with thorough experimental studies.[882] Sweatman and Quirke also investigated the ability of pore size distributions obtained from one gas to predict the adsorption of the other gases at the same temperature, and concluded that CO2 distributions are the most robust in the sense that they can predict adsorption of methane and nitrogen with reasonable accuracy. The same authors[883] modeled the adsorption in slit-shaped pores using MC simulations. They generated databases of adsorption isotherms for N2, CO, CH4, and CO2 in a wide range of pressure, pore widths, and temperatures. They discussed the implications of the obtained results for materials characterization procedures based on gas adsorption data. Ohba and Kaneko[884] studied the relationship between DR plots and the micropore width distribution of slit-shaped graphitic pores using GCMC simulations of nitrogen at different temperatures. They found that the simulated DR plots were almost the same below [ln( p0/p)]2 ¼ 60 for different half-widths of pore size distributions having Gaussian and Gaussian-like distributions. They concluded that the micropore volume calculated from the plots for pore widths greater than 1.6 nm is considerably underestimated, while for pore widths smaller than 1.4 nm the estimated value is quite reasonable. They also found that the higher the temperature, the narrower is the linear region of the plot. Zhou and Wang[885] reported GCMC and MD simulations of adsorption and diffusion of supercritical CO2 in slit graphitic pores. They found that the isotherms exhibit a maximum at a particular pressure. This maximum adsorption declines and occurs at higher pressures with increasing pore width, except for the narrow pores. The diffusion coefÞcients are strongly dependent on the density in the pore at supercritical conditions. Using GCMC simulations, Suzuki et al.[886] estimated the average kinetic energy (deÞned as the difference between the potential minimum and the differential heat of adsorption) of Ar, O2, and N2 adsorbed in slit-shaped graphitic pores. They found that the minimum kinetic energy is obtained for pore widths ca. 1.6 times larger than the adsorbate molecular diameter. Setoyama et al.[887] studied the relationship between a high-resolution as plot and the pore size distribution of activated carbons using GCMC simulations. They employed slit-like graphitic pores of different widths. As no pore effects were observed below relative pressures ca. 0.6 for a pore width w ¼ 3.5 nm, as plots for the simulated adsorption isotherms were constructed using the standard isotherm simulated for a pore width w ¼ 3.5 nm. The simulated as plots exhibited Þlling and cooperative swings as in previous experimental works,[283] and varied with the micropore structure. The authors concluded that the subtracting pore effect method is applicable for pore systems of width 0.7 nm, but it underestimates the speciÞc surface area for pores of width 0.6 nm. Gubbins and coworkers studied the adsorption of water[888] and methaneÐ water mixtures[889,890] on porous activated carbons. They employed slit-like
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pores with graphitic walls, which are doped by placing oxygenated sites on the pore surface to modulate the hydrophobic behavior of activated carbon surfaces. They employed standard GCMC simulations to generate the adsorption isotherms for pure components and for mixtures on pores with different doping degrees but equal width. Figure 3.60 shows the variation of water uptake with site density (n) for a pore of 2 nm at 300 K. The results are shown in terms of both the total number of molecules and the number of water molecules per site. At relatively low coverage (0 , n , 3), the number of adsorbed molecules is proportional to the number of sites (the sites are sparsely located and there is little chance of cooperative effects). At higher site densities (n . 7), the addition of sites has little effect (both pore surfaces are covered by water molecules forming a rough layer, screening any attractions from the walls of the remaining unoccupied sites). The authors also showed that water adsorption does not occur via formation of a monolayer followed by further layers, as is common for simple nonassociating ßuids such as methane, but rather through formation of 3D clusters centered on the active sites on pore walls. Cooperative ÒbridgingÓ effects greatly enhanced the amount of water adsorbed. They also showed a transition from hydrophobic to hydrophilic behavior due to addition of active sites, for example, a nonactivated pore is hydrophobic with selectivity to water of only 0.065, while a pore with 0.44 active sites/nm2 is almost Þlled with water molecules and clearly hydrophilic, with the water selectivity increasing to 217. Yin et al.[891] studied the effects of pore structural parameters and LennardJones interaction parameters on GCMC simulations of N2 adsorption on activated carbons. They employed a slit-like graphitic pore with different structural
Figure 3.60 Water adsorption as a function of site density, n, for a pore of 2 nm, a temperature of 300 K, and an activity Þxed at 0.001 nm23 corresponding to a partial pressure of 0.0419. Open circles (right ordinate), number of molecules adsorbed; solid circles (left ordinate), number of molecules per associating site. (Reproduced from Mu¬ller et al.[888] Copyright 1996 American Chemical Society.)
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parameters (e.g., carbon atom density of the pore wall, wall thickness, and interlayer spacing), and showed that increasing the carbon atom density in the pore wall shifts the adsorption isotherm to lower pressures. This effect is more marked for monolayer formation than for pore condensation at higher pressures. Similar effects were found on increasing pore wall thickness, especially when it is increased from one to two layers; introducing more than Þve layers is equivalent to a system with an inÞnite number of layers. As could be expected, the authors also found a strong dependence of the results on the interaction parameters. A rather complete description of their model solid has been published elsewhere.[847,892] Bojan and Steele[893] reported GCMC simulations of Ar adsorption at 90 K in pores of different shapes. In all cases, the pore walls were perfectly ßat graphitic planes that have been assembled to form pores with rectangular cross-sections characterized by having one dimension Þxed at a value that allows four layers of argon in the full pore. The second dimension of the rectangle was varied from 4 to 8 and to 12 molecular diameters. They found that the presence of corners can be quantitatively treated in terms of 1D theory, and that the remaining adsorption on the walls gives monolayer arrangements with liquid-like 2D densities. They also analyzed the local isotherms for each kind of site and found that local isotherms corresponding to the corners closely approximate 1D systems, and that the wall local isotherms are those for multilayer adsorption on strips of wall that are bordered by Ar atoms. The character of the multilayer part of the local isotherms corresponding to the walls is that of pore Þlling rather than adsorption on an open surface, with hysteresis loops in some cases. Nicholson[894] analyzed energetic and structural heterogeneity in model slitshaped pores by means of GCMC simulations of methane and CO2 adsorption. The energetic heterogeneity was modeled by generating thermally disordered surfaces that were roughened on an atomic scale. Structural heterogeneity was modeled using smooth-wall slit-shaped pores having a range of pore widths. The author focused on the calculation of isotherms and isosteric heats. He found that a rapid decrease of the adsorption heat with increasing adsorbate density (something often found experimentally) could not be satisfactorily accounted for by energetic heterogeneity. On the other hand, plots of adsorption heat against adsorbate density were shown to be particularly sensitive to structural heterogeneity. Figure 3.61 shows composite isotherms and heat-density curves for three hypothetical pore size distributions. The symmetrical distribution and the distribution skewed to high pore widths both gave isosteric heat curves that are qualitatively similar to expected experimental results of rapid heat decrease with increasing adsorbate density. He concluded that isosteric heats are very sensitive to the micropore width and proposed that deconvolution of isosteric heat curves may form the basis of a valuable method for assessing micropore size distributions. McCallum et al.[895] compared GCMC simulations with experimental data for adsorption of water on activated carbon. The pore size distribution was determined with N2 adsorption using DFT. They also determined the
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Figure 3.61 Composite isotherms and heat curves for methane adsorption at 298 K in smooth-walled slit pores having the discrete distribution functions illustrated. (Reproduced from Nicholson.[894] Copyright 1999 American Chemical Society.)
density of acidic and basic surface active sites using the Boehm method. They modeled the active sites using what they called the Òeffective single groupÓ model. This considers that each surface group can only bind one water molecule and that all oxygenated groups have the same binding energy with water molecules. They found good agreement between simulations and experiments. However, they recognized that the single group model still has signiÞcant defects; in particular, it fails to predict the very low-pressure data accurately. Lo«pez Ramo«n et al.[896] studied the adsorption of CH4, CF4, and SF6 in model pores of various sizes using MC simulations. By comparing the simulated isotherms, integrated over a pore size distribution, with experimental isotherms for a microporous carbon, estimates of the pore size distribution were obtained, one for each adsorptive. Figure 3.62 shows the pore size dependence of the
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adsorption energy (q) obtained by Þting the Hill Ð de Boer isotherm to simulation data for CH4, CF4, and SF6. The very light scatter among different temperatures indicates that q is to a very good approximation temperature-independent. As the lines drawn show, the variation of q with pore size matches well SteeleÕs 10 Ð 4Ð 3 potential. Since each adsorptive has a different size and interaction strength with the solid, each one probed different ranges of pore size; thus each adsorptive provided a partial pore size distribution. The authors argued that the complete distribution can be determined by combining the distributions obtained. They could also determine the transport properties of the solid. Thompson and Glandt[897] studied the irreversible random sequential adsorption of spherical particles on a porous solid using computer simulations. For several particle sizes and porosities, they found that the kinetics follows FederÕs limiting power law[898] for random sequential adsorption on a plane surface. Cracknell and Gubbins[899] compared methane adsorption on aluminophosphates with a model porous carbon using GCMC simulations. Their model for the porous carbon consisted in a slit of a certain width between two inÞnite graphite layers, with an inÞnite number of other graphite layers stacked behind these. Their main conclusion was that aluminophosphates would not be convenient media for methane storage. Patrykiejew[900] studied adsorption on randomly heterogeneous surfaces using MC simulations. He demonstrated that the commonly used approaches to adsorption on heterogeneous surfaces, based on mean Þeld theories, are valid only at high temperatures. Vuong and Monson[901] studied adsorption in heterogeneous porous solids using GCMC simulations. Their molecular model treats the adsorbent as a matrix of particles arranged in a predetermined structure. Even though they have chosen the parameters to represent adsorption of methane in silica gel, their results are general enough to be tested with other systems. They also calculated the isosteric adsorption heats and presented a new derivation of the necessary expressions, free from some unnecessary assumptions currently used. They concluded that the isosteric heat of adsorption is very sensitive to the adsorbent microstructure. This effect is mainly due to the gasÐsolid contribution to the total energy. On the other hand, the contribution made by lateral interactions is quite insensitive to solid microstructure. The calculated isotherms showed reasonably good agreement with experimental data but there was not so good agreement for the isosteric heats. This suggests that their model may not exhibit enough heterogeneity. In a subsequent paper, Sarkisov and Monson[902] investigated the applicability of the GibbsÐDuhem integration method to calculate the phase equilibrium in these systems. They conÞrmed the presence of coexisting vapor and disordered liquid and inhomogeneous phases. They also found a second phase transition associated with wetting of the porous material by the ßuid, and that this transition is more sensitive to microstructure variations. Moreover, this transition appears for particular realizations of the solid matrix and it does not seem to survive averaging over several realizations. To describe the porous solid structure, Gavalda et al.[903] employed a similar approach in order to study the properties of a carbon aerogel. The mesopore space was represented by carbon spheres in a
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Figure 3.62 Variation with pore size of the Monte Carlo simulated adsorption energy for CH4 (squares), CF4 (circles), and SF6 (triangles). The lines represent the minimum of the SteeleÕs 10Ð 4 Ð3 potential for CH4 (dotted line), CF4 (solid line), and SF6 (dashed line). (Reproduced from Lo«pez-Ramo«n et al.[896] Copyright 1997 American Chemical Society.)
connected network. The matrix is generated as a random close-packed structure of slightly overlapping spheres, and then the spheres are removed until the desired porosity is matched. The spheres are Þnally replaced by a model microporous carbon, generated using the reverse MC method, Þtting the experimental carbon radial distribution function obtained by X-ray diffraction. The Þnal solid matches the surface area, porosity, and pore size distribution of the aerogel very closely. To calculate N2 isotherms on this material, a parallelized GCMC algorithm was employed, and fair agreement with experimental data was achieved. The disagreement between experiments and simulations was attributed to errors in the density of the spheres, in the pore size distribution, and the possibility that the simpliÞed model system may not be truly reßecting the details of the real system. Gelb and Gubbins[904,905] studied the kinetics and liquid Ð liquid phase separation of binary mixtures in cylindrical pores using MD and quench MD and MC simulations. Their main conclusion is that the picture of phase-separation kinetics obtained from a single pore model appears to break down for sufÞciently narrow pores. In very small pores, for temperatures close enough to the apparent critical point there is no crossover to a slow-growth mode. The main domain growth mechanism at all but the earliest times is the condensation of neighboring domains. This process is not very visible in the smallest pore they studied, suggesting that in the smaller pores there is a second growth mechanism.
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Recently, Grabowski et al.[906] employed MC simulations for a simple lattice gas model of multilayer adsorption on preadsorbed layers. They discussed the effects of mixing of the preadsorbed gas with the adsorbate as well as the wetting behavior of preadsorbate on the mechanism of Þlm development. They demonstrated that the mixing properties of the adsorbed and preadsorbed species are responsible for the order of layering transitions. If the system exhibits a phase separation, the layering transitions retain their Þrst-order character. On the contrary, when the adsorbate dissolves in the preadsorbed layer, formation of the Þrst layer is a continuous process. Bottani[907] studied N2 adsorption on a columnar carbonaceous solid using GCMC simulations. This kind of solid has been recently reviewed by Dai.[908] The model adsorbent consisted of a regular hexagonal array of 40 amorphous carbon columns placed on an amorphous surface. He concluded that adsorption on this system presents several common characteristics with porous materials. Nevertheless, hysteresis was not found in the simulated isotherms, probably because spaces between columns were all interconnected. In opposition with the case of ßat surfaces, quadrupolar interactions seem not to play an important role due to the columnar structure of the solid. Nitrogen remains in a liquid-like state in the intercolumnar spaces at high pressures; if lateral interactions are assumed as the hard-disk model, the density obtained for the adsorbed phase is higher than that of the real solid. The isotherms were also analyzed in terms of the supersite theory, previously mentioned (see end of Section 3.3.3.1), and good agreement was obtained. Sahimi and coworkers[909,910] reported the results of extensive equilibrium MD simulation of adsorption of single-component, binary, and ternary gas mixtures in two types of model microporous materials: pillared clays and carbon molecular sieve membranes. They employed their simulations to test a new statistical mechanical theory of adsorption.[911] The theory employs one adjustable parameter for a one-component system. To represent the adsorption data for the mixture, they employed an expression based on statistical mechanical perturbation using a hypothetical system in which cross-interaction between unlike species is neglected. This approach was satisfactory from low to moderate loadings. They found excellent agreement between their model and the simulations. Grabowski et al.[912] performed MC simulations of mixed multilayer adsorption to study layering transitions and wetting phenomena in nonideal mixtures. They determined the phase diagram of several systems and demonstrated that the systems studied exhibit strong effects of enhanced adsorption of one component due to adsorption of the second one. They also showed that the existence of preadsorbed particles of one component might considerably change the surface wetting by the second component. The addition of strongly adsorbed particles into the system might lead to a crossover from intermediate to strong substrate regime. They found that, at least for the systems they studied, the wetting temperature appears to be practically unaffected by the second component. Cao and Wang[913,914] reported GCMC simulations of CH4 adsorption on layered pillared pores. Their results suggested that a pore width of 1.02 nm is
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optimal for methane storage. More recently, the same authors[915] simulated CCl4 adsorption in slit-shaped pores of activated carbon and compared them with experimental measurements on an activated carbon prepared by chemical activation with KOH. Adsorption isotherms corresponding to pore widths between 1.14 and 4.57 nm were simulated. The pore width of 2.28 nm corresponded to the highest uptake for pressures .20 kPa. This pore width agreed with the maximum in the pore size distribution of the activated carbon studied; however, the isotherm simulated for this pore width signiÞcantly overestimated the CCl4 uptake. Adsorption on fullerenes and carbon nanotubes. In the following paragraphs we shall review results obtained from simulations of adsorption on fullerenes and carbon nanotubes. Martõ«nez-Alonso et al.[916,917] studied adsorption of simple gases (N2 and Ar at 77.4 K, and CO2 at 273.2 K) on C60 fullerene combining GCMC simulations and experimental isotherms. The experimental data were obtained with a high-purity well-crystallized C60 commercial sample. Other materials were employed as references (e.g., a graphitized carbon black (Vulcan 3-G), a nongraphitized carbon black (Vulcan 9), and polycrystalline diamond). In the simulations they employed a perfect crystalline structure (fcc) of C60 molecules with lattice parameters and density matching the experimental values. A map of the simulation cell was obtained with N2 as probe molecule and it is shown in Fig. 3.63. The agreement between simulated and experimental isotherms for all gases studied was excellent. Since the sample employed was
Figure 3.63 Topographic map of the C60 model solid employed in the simulations obtained with a nitrogen molecule as probe. X and Y units are arbitrary, and Z units are angstroms. (Adapted from Martõ«nez-Alonso et al.[916] Copyright 2000 American Chemical Society.)
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of high quality, the authors did not Þnd hysteresis as in previously published data by other authors.[918,919] This was explained based on sample purity and crystallization degree that was unreliable in older studies. The adsorption energy distribution functions were calculated from the experimental isotherms, and the fullerene sample gave a distribution very similar to that of polycrystalline diamond. The energy map corresponding to the model solid was converted into a distribution function and compared with the experimental one. Both distributions agreed quite well and the experimental distribution smoothly included all the features exhibited by the distribution of the model solid. The authors deconvoluted the distribution corresponding to the model solid and found three main peaks that perfectly matched the peaks found by Papirer et al.[422] It must be pointed out that Papirer et al. obtained their results using IGC of n-alkanes (see Section 3.3.2.2.). The C60 solid exhibits three preferential sites for adsorption (Fig. 3.63): one is located between four fullerene molecules, the second is located in the channels formed between two fullerene molecules, and the third is the top of the C60 molecules. Ar and CO2 are adsorbed in a solid-like phase in the voids of the fullerene solid. The contribution of this ÒinternalÓ space to the total area was estimated to be 30%. Values of cross-sectional areas of the employed gases were also given. In a subsequent paper, Tasco«n and Bottani[920] performed GCMC simulations for nitrogen adsorption on a defective fullerene, which was created by generating a vacancy in the fcc structure of the perfect solid. The main differences, inferred from simulated N2 adsorption, could be explained based on the difference in surface areas and heterogeneity degree between the two solids. Very recently, the same authors[921] have studied ethylene adsorption on C60 using GCMC simulations. The results validated the simulation model employed and conÞrmed the assignment of adsorption sites previously reported for other gases. The analysis of the adsorption energy distributions with the aid of the gas Ð gas interaction potential suggested that ethylene is adsorbed in a liquidlike state in the voids of the solid, and that the adsorbed molecules prefer a T-shaped stacking, in agreement with calculations and experiments reported by other authors.[922] The study of adsorption on carbon nanotubes is in its beginnings since new methods for mass production are still in development. Nevertheless, experimental data are available since several years ago,[923] with which simulations could be compared. Maddox and Gubbins[924,925] Þrst reported GCMC simulation studies of simple ßuid adsorption in carbon nanotubes. They calculated the isotherms and isosteric heats for argon and N2 on three types of nanotubes, one single-wall with a diameter of 1.02 nm, the second double-wall with 4.78 nm, and the third an open-ended double-wall with 4.78 nm. They found type I isotherms (IUPAC classiÞcation) for both gases on the single-wall nanotube. On the double-wall tube, N2 exhibits a type VI isotherm indicating continuous layer formation, and at relative pressure close to 0.5 they detected capillary condensation. On desorption, they found a hysteresis loop representative
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of type IV isotherms. Figure 3.64 shows the uptake dependence of Ar isosteric adsorption heat in a 4.78 nm double-wall nanotube at two temperatures (77 and 55 K). Unlike the single-wall tube, for which changes in adsorption heat were slight, the isosteric adsorption heat on the double-wall tube shows a steady rise from zero adsorption to a peak when the Þrst layer is complete (ca. 5 mmol/g), followed by a rapid drop. The authors provided an explanation based on ßuid Ð wall and ßuid Ð ßuid interactions. Capillary condensation (shown as a dashed line) is seen at 77 K, and layering transitions (also shown as dashed lines) are seen at 55 K. An interesting result was the dependence of the shape of the hysteresis loop on the length of an open-ended nanotube. The authors argued that the critical temperature for capillary condensation might be quite strongly dependent on the average pore length. Simonyan et al.[926] studied Xe adsorption on (10, 10) single-wall carbon nanotubes at 95 K using computer simulations compared with experimental data.[927] Adsorption occurred primarily inside the nanotubes, and interstitial and external adsorption were comparatively negligible in the pressure range covered. Figure 3.65 compares the isosteric adsorption heats of Xe on the inside of a nanotube in an array and on an isolated nanotube. The difference is mainly that the former is shifted to a lower-pressure range because of the attractive interaction between a Xe atom and neighboring tubes. As it can be seen, the isosteric adsorption heat determined from the simulations ranged from ca. 3000 to 4500 K as function of coverage, in agreement with the experimental desorption activation energy of 3220 K. The authors concluded that the curvature of the nanotube does not substantially perturb the adsorption potential from that of a graphene sheet.
Figure 3.64 Isosteric adsorption heats for Ar in a 4.78 nm double-wall carbon nanotube at 55 and 77 K. Dashed lines, capillary condensation (77 K) and layering transitions (55 K). (Adapted from Maddox and Gubbins.[925] Copyright 1995 American Chemical Society.)
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Figure 3.65 Isosteric adsorption heats of Xe at 95 K on the inside of a nanotube in an array (hollow circles) and on an isolated nanotube (full squares) as a function of pressure. (Reproduced from Simonyan et al.[926] Copyright 2001 American Institute of Physics.)
Maddox et al.[928] compared computer simulations of binary mixture adsorption in carbon nanotubes and MCM-41 silica. Ayappa[929] reported GCMC simulation of binary mixture adsorption on single-wall carbon nanotubes (SWNT). For mixtures whose species have different sizes, he found that the most energetically favored species is adsorbed at higher temperatures; at lower temperatures and intermediate nanotube diameters, a complete exclusion of the larger species in favor of the smaller one is observed. This transition in nanotube ßuid composition is accompanied by a decrease in the total potential energy of the system. At all temperatures and when the mixture components are of the same size, the one with higher afÞnity for the solid is preferentially adsorbed. Yin and coworkers[930,931] reported GCMC simulations of N2 adsorption on a square array of open and closed SWNT with diameters of 0.6Ð 3 nm. They analyzed the effect of tube separation and found that for large separations a two-stage adsorption occurs, corresponding to monolayer formation followed by condensation. The agreement with experimental results was poor probably because a square array of nanotubes is not very realistic. In a subsequent paper, Alain et al.[932] extended their study to multiwall carbon nanotubes and compared N2 adsorption data on different nanotubes. They found qualitative agreement between experimental measurements and simulations. The simulations suggested that interstitial adsorption could be important in nanotube arrays; however, the experimental adsorbed amount does not reach the levels expected from simulations. They explained this fact by considering that the square array needs to be modiÞed and that experimental data suffer from the presence of impurities in the samples. Yin et al.[933] compared the adsorption of methane measured gravimetrically on samples of SWNT with results of GCMC simulations. They also
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compared the nanotubes with an activated carbon. Their main conclusion was that the optimal nanotube size to be employed in methane storage applications is 2.0 nm with a separation between tubes of approximately 1 nm. Wang and Johnson[934 Ð 936] compared hydrogen adsorption on a SWNT with a slit-shaped graphitic pore. They considered quantum effects through implementation of the path integral formalism and found that these effects are important even at room temperature for adsorption in tube interstices. They compared their simulations with experimental data for carbon Þbers and activated carbon and found a fair agreement with the latter. Their results could not explain the large uptakes reported for SWNT and carbon Þbers. They also concluded that an array of nanotubes is not a suitable material for achieving the US Department of Energy (DOE) targets for vehicular hydrogen storage. Similar conclusions have been reached by Yin et al.[937] from the GCMC simulations of hydrogen adsorption, at 298 and 77 K, on triangular arrays of carbon nanotubes. In connection with this subject, Cheng et al.[938] have reviewed the issue of hydrogen storage in carbon nanotubes and proposed a number of topics in which urgent research is needed to accelerate practical applications. Challa et al.[939] studied adsorption and separation of hydrogen isotopes in (10, 10) carbon nanotubes using GCMC simulations. They found good agreement between simulations and predictions made using IAST. At high loadings, the selectivity determined from multicomponent simulations remained roughly constant, whereas IAST predicted a continuous selectivity increase. Kostov et al.[940] studied hindered rotation of hydrogen adsorbed in the interstices of carbon nanotube bundles. They predicted a large rotational barrier, ca. 40 meV. Sorescu et al.[941] reported results of oxygen adsorption on graphite and the (8, 0) SWNT using spin-polarized density functional calculations. They considered both physisorbed and chemisorbed oxygen species. Kaneko and coworkers[942 Ð 944] used N2 adsorption to study the microporosity of heat-treated single-wall carbon nanohorns. They compared their experimental results with model calculations using a gas Ð solid potential developed to describe interaction with the interior and exterior of nanotubes. The potential is based on the Lennard-Jones 12Ð 6 function and is derived from the one used for a smooth-wall graphite cylinder.[945] The interaction potential function analysis showed the presence of three sites, namely an interstitial site, an intraparticle monolayer site, and an intraparticle core site. The Þrst two are responsible for primary micropore Þlling (i.e., an upward swing of the as plots below as ¼ 0.5). From the experiments performed, the authors concluded that partial oxidation produces windows on the walls of the tubes; therefore, oxidation could be employed to control the porosity of the sample. Paredes et al.[355] carried out GCMC simulations of N2 adsorption and compared them with experimental results on SWNT (Nanoledge). The nanotubes were modeled in bundles forming a hexagonal array, which was selected on the basis of STM imaging of SWNT bundles. Simulated N2 isotherms at 77.5 K agreed remarkably well with experimental results,[355,932,942,946] particularly at low pressures where gas Ðsolid
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interactions are dominant. The distribution of molecules over the gas Ð solid energy, calculated from the simulations (Fig. 3.66), exhibited two peaks for endohedral adsorption, one of them associated with molecules near the wall and another due to molecules located close to the tube axis [when the tube diameter is large enough to allow this situation, which is not the case for (5, 5) tubes]. The distributions for molecules adsorbed outside the tubes resembled the ones obtained for adsorption on irregular surfaces. Calbi and coworkers[947,948] and Gatica et al.[949] studied the phases of noble gases and methane adsorbed inside nanotube bundles and on their external surface. They employed several classical methods: ground state calculation, grand potential energy minimization, and GCMC simulations. Their results for Ne, Xe, and CH[947] are similar to those found in GCMC simulations of Kr 4 and Ar.[949] At low chemical potential, the particles form a quasi-1D phase within a groove formed by two contiguous nanotubes. At higher pressures, there occurs a three-stripe phase aligned parallel to the groove, except in the case of Xe. This regime is followed by monolayer and bilayer phases. Calbi et al.[950] also analyzed the mutual effects of interactions between an adsorbed gas and an adsorbing porous environment when possible expansion of the pore is considered. They studied H2 and He on carbon nanotube bundles allowing the possibility of gas intercalation between two graphene planes when the distance between them is allowed to change. They concluded that dilation of the bundle signiÞcantly increases the binding energy of adsorption while intercalation between two graphene sheets is energetically unfavorable for both gases. Stan and Cole[951] used both classical and quantum cases to investigate the low coverage adsorption in carbon nanotubes. They concluded that it is possible to adsorb enough quantities of many species to be measurable in a thermodynamic or scattering experiment. Ohba and Kaneko[952] studied the evaluation of internal area of carbon nanotubes using nitrogen GCMC simulations. They concluded that the BET analysis is not applicable in the normal relative pressure range (0.05 Ð 0.35). They found a good linear plot for relative pressures lower than 0.05, in agreement with simulations that showed monolayer completion for this pressure. Zhao et al.[953] studied adsorption of several gases (NO2, O2, NH3, N2, CO2, CH4, H2O, H2, and Ar) on SWNT and bundles using Þrst principles. They calculated the equilibrium position, adsorption energy, charge transfer, and electronic band structures of different kinds of nanotubes. They found, as expected, that the interstitial and groove sites are stronger than the interior of the nanotube. They also found that the electronic properties of SWNT are sensitive to adsorption of certain gases such as NO2 and O2. Quantum effects of gases adsorbed on nanotubes have been studied by Calbi and Cole,[954] and the heats of adsorption for Ar (9.97 kJ/mol), CH4 (12.4 kJ/mol), and Xe (15.8 kJ/mol) are in excellent agreement with the experimental values. Methane adsorption has been recently studied by Tanaka et al.[955] using nonlocal DFT. They found that the total adsorption capacity of nanotubes is larger than for slit-shaped pores of the same size.
Figure 3.66 Distribution of N2 molecules at 77.5 K according to the gas Ð solid energy in (a) (5, 5),(b) (18, 0), (c) (14, 0), and (d) (10, 10) carbon nanotubes. Thicker line, endohedral adsorption; thinner line, exohedral adsorption. (Reproduced from Paredes et al.[355] Copyright 2003 American Chemical Society.)
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Nevertheless, adsorption in nanotube interior is less than that for the slit-shaped pore. They showed that methane adsorption inside and outside the isolated SWNT is enhanced by methane molecules adsorbed on the opposite side of the surface. In discussing recent progress in the preparation and utilization of carbon nanotubes as adsorbents, Ding et al.,[359] included a review on theoretical investigations of carbon nanotubes for hydrogen storage. According to these authors, the ultimate goal in nanotube synthesis should be to gain control over geometrical aspects of nanotubes, such as location and orientation and the atomic structure of nanotubes, including helicity and diameter. Tasco«n and Bottani[956] have also included sections on gas physisorption in conÞned spaces in a brief review of gas adsorption on carbon nanotubes. Darkrim et al.[957] analyzed the experimental data and simulation results obtained for adsorption of hydrogen in carbon nanotubes. They oriented their review to the potential use of carbon nanotubes for hydrogen storage. As could be expected, they concluded that synthesis and puriÞcation of this material must be optimized and mass production methods must be developed before any application for gas storage could be designed. Yang and Yang[346] used ab initio molecular orbital theory to study hydrogen adsorption on graphite; the objective was to get some insight into hydrogen adsorption in carbon nanotubes. They compared adsorption energies on different points of the surface and different densities of adsorbed molecules. Their results are included in Table 3.14. Although the adsorption energies involved are typical for chemisorption (thus falling out from the scope of this review), they are included here due to their relevance to the important topic of hydrogen storage in carbon nanotubes. The authors found good agreement between their calculated adsorption energy for hydrogen on adjacent sites on a basal plane (ca. 113 kJ/mol) and the experimental value measured by the same team on carbon nanotubes (ca. 96 kJ/mol).[958] They also proposed a mechanism to explain the hydrogen
Table 3.14
Calculated Adsorption Energies for Hydrogen on Several Model Sites at the Graphite Surface Model
H on armchair edge H on zigzag edge H adjacent basal sites H on alternating basal sites 2H on armchair edge 2H on zigzag edge
Eads (kJ/mol) 2365.3 2377.6 2113.1 2194.4 2238.2 2269.9
Source: Adapted from Yang and Yang,[346] with permission from Elsevier.
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storage capacity of nanotubes, which involves H2 dissociation on the residual metal catalyst particles, followed by H spillover and adsorption on the nanotubes. Gu et al.[959] studied the separation of a binary gas mixture (CO and H2) using SWNT and GCMC simulations and concluded that at 293 K the selectivity of CO decreases with an increase in bulk pressure. They found that, at a given pressure and temperature, selectivity ßuctuates for different van der Waals distances and nanotube diameters. For example, at 0.157 MPa and 293 K for a tube diameter of 0.892 nm and van der Waals distance between tubes of 1 nm, if the feed is formed by a 50% mixture of both gases, CO could be enriched up to 98% in the adsorbate, so the selectivity rises to a value of 60. Other ensembles: In this section, we brießy summarize several ensembles that are also employed in computer simulations and some results obtained with them. The Þrst one is known as the Gibbs ensemble and has been developed by Panagiotopoulos.[960] The basic idea is to attempt to simulate phase coexistence properties by following the evolution in phase space of a system composed of two distinct regions. The two regions have different densities and compositions and are at thermodynamic equilibrium both internally and with each other. Figure 3.67 shows a scheme of the proposed system. Regions I and II contain a certain number of particles, whose possible movements are also indicated in Fig. 3.67. The movements are translations of particles within the cell, particles moving to the other cell, and changes in the volume of a cell by moving the dividing wall. Both regions could be envisaged as large macroscopic volumes of coexisting vapor and liquid, with an interface that has a negligible effect on the total system properties. Movements of particles within a given region or across the boundary are accepted with probabilities deÞned as usual in the MC method. The new type of movement is a relative volume change of the cells
Figure 3.67 Scheme of the system employed to deÞne the Gibbs ensemble. (Adapted from Panagiotopoulos,[960] with permission from Taylor and Francis.)
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(i.e., the total volume of the system is kept constant). Once the volume of a cell is changed, the new conÞgurations in each cell would be obtained by scaling the positions of the particles to the new volume, a procedure familiar from NPT ensemble simulations. If DEI and DEII are the resulting changes in conÞgurational energy of the two regions, the total reversible work required to bring about this change is given by: I II V þ DV V DV II DEmin ¼ DEI þ DEII N I kT ln kT ln N VI V II (3:171) The last two terms result from ideal gas contribution to the change in system entropy. Since both regions are to be kept at constant temperature, the surrounding medium must provide a heat input equal to 2TDSideal. The total system is under NVT conditions and thus the probability of acceptance, P, of the conÞguration with the changed volume is again given by the classical expression:
DE P ¼ min 1, exp (3:172) kT The Þnal expression for this probability is obtained by replacing Eq. (3.171) into (3.172). Clearly, if this type of movement is considered in addition to the normal displacement steps, the equilibrium conÞguration of the total system would be one in which the pressure in both regions would be the same. The main difference with respect to a normal NPT ensemble simulation is that in this case the pressure is not externally Þxed but is found by the system itself. When a particle is moved to the other region, the appropriate energy change is given by: I II N þ1 N 1 II DEmin ¼ DEI þ DEII N I kT ln kT ln þ N NI N II V II VI þ kT ln II kT ln I (3:173) N 1 N þ1 Again, the acceptance probability is obtained by replacing this expression into Eq. (3.172). In this case, the formalism reduces to the grand canonical ensemble in region I if region II is inÞnite. In essence the proposed simulation method combines elements of the NVT, NPT, and mVT ensembles in a way that, at least in principle, results in two regions in internal equilibrium that obey the following conditions: PI ¼ PII
and
mIi ¼ mIIi , for all species present.
(3:174)
The requirements given in expression (3.174) are necessary and sufÞcient conditions for phase equilibrium between regions I and II, as was originally proved by Gibbs. This type of simulation should theoretically result in correct
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values for the coexistence properties of a system at a given temperature, avoiding unstable states. If in a one-component system the initial conditions are chosen so that the system is in an unstable state (@P=@V . 0), the system itself will rearrange into two stable phases (each with @P=@V , 0). The equilibrium density of each region is uniquely determined by the condition of phase equilibrium and the temperature. The size of each region has not been speciÞed yet, but it was assumed that the system was macroscopic. In a simulation of Þnite length, it is necessary to implement a microscopic system. This issue is resolved by considering each region as composed of a large number of identical subcells, or image cells, with a microscopic number of molecules and applying conventional periodic boundary conditions. The author applied this method to study the liquid Ð gas coexistence for a pure Lennard-Jones 6 Ð12 ßuid at several temperatures between the triple point and the critical point. Panagiotopoulos[961] applied his simulation method to study the adsorption and capillary condensation of ßuids in cylindrical pores. He discussed the conditions to attain mechanical equilibrium between two segments of a pore. Finally, Panagiotopoulos et al.[962] presented an alternative derivation of the Gibbs ensemble MC simulation and a generalization to gas mixtures and membrane equilibria. They compared the results obtained with other methods and found good agreement. An additional advantage of this method is that it requires a short computational time to obtain the equilibrium properties. The other simulation method, recently proposed by Neimark and Vishnyakov,[963 Ð 965] and known as gauge cell MC, is employed to determine the equilibrium transition and the true limits of stability (spinodals) of vaporlike and liquid-like metastable states. It is based on the construction of a continuous adsorption isotherm in the form of a van der Waals loop that includes stable, metastable, and unstable equilibrium states, and a thermodynamic integration along the metastable and unstable regions of the isotherm. This integration is performed employing MaxwellÕs rule of equal areas. The energy barrier separating the metastable and stable states and, correspondingly, the probability of spontaneous capillary condensation and evaporation can also be determined. The authors compared their simulations with experimental results and found good agreement. To construct a continuous trajectory of states with a given average density between the densities of the vapor-like and liquid-like spinodals, the authors render the GCMC simulation in two cells in thermal equilibrium with an inÞnite heat bath. One of the cells represents the pore and the other is a gauge cell of limited capacity. Since the phase diagram for the gauge cell is necessary in the other calculations, it is determined independently using Gibbs ensemble simulations. Thus, the ßuid in the gauge cell is employed as a reference, and for the total system the canonical ensemble is considered. Mass exchange between cells is allowed but cell volumes are kept constant, so mechanical equilibrium conditions are not required. Therefore, the conditions of isothermal
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equilibrium arise from the equality of chemical potentials in the conÞned and reference ßuids. The limited capacity of the reference cell constrains density ßuctuations in the conÞned ßuid and allows the conÞned ßuid to be kept in a state that could be unstable in contact with the bulk. The method was tested with experimental data[966 Ð 968] for N2 adsorptionÐ desorption on MCM-41 silica. As Fig. 3.68 shows, the simulated isotherms differ signiÞcantly from the experimental ones in the region prior to capillary condensation; this difference was assigned to energetic heterogeneities present in the real system.[969] However, the inßection point on the capillary condensation step agrees with the position of the theoretical phase transition in the pore of mean size predicted by the gauge cell method. The proposed method to calculate the
Figure 3.68 Comparison of calculated and experimental isotherms on MCM-41 silica at 77.4 K, for pores with internal diameter of either (a) 4.42 or (b) 3.55 nm. (Reproduced from Neimark and Vishnyakov.[963] Copyright 2000 from the American Physical Society.)
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energy barriers between the metastable and stable states uses the grand potential in the saddle point that corresponds to an unstable state on the backward trajectory of the phase diagram. The calculated barriers and the corresponding Arrhenius factors for the transition determine the conditions of spontaneous condensation and evaporation. The authors also showed that the spontaneous condensation observed in all GCMC simulations occurred close to the spinodals when the Arrhenius factor became nonvanishing. 3.4.
SUMMARY AND CONCLUSIONS
Thermodynamic models for adsorption can now be validated using both experimental and computer simulation results. Determination of thermodynamic quantities is almost a standard routine connected to the majority of both experimental and simulation techniques. New developments are regularly reported concerning new adsorption equations or models to explain experimental data of very different nature. Gas mixture adsorption is a Þeld still waiting for a better theory that could explain the experimental data. The ideal adsorbed solution theory cannot explain all the facts and needs to be replaced by a new model, which should include nonideal effects, and adsorbent surface heterogeneity in particular. This Þeld is acquiring increasing relevance because of its technological implications. The determination of adsorption heats can now be performed through direct or indirect methods with a great degree of accuracy. The foundations of gas Ð solid interface calorimetry have been well established by combining adsorption microcalorimetry with adsorption in quasi-equilibrium. Their work has brought this type of calorimetry to its present development status. The experimental results reported so far, obtained from different calorimetries, concur with the values calculated from adsorption isotherms. There is a more or less explicit agreement concerning the importance of adsorption heat in studying adsorption phenomena. Practically all the information that could be extracted to describe any system is included in its heat of adsorption. Adsorption calorimetry, using different adsorbates, is now employed to probe the effects of various types of surface modiÞcation treatments on the surface chemistry of solids. The technique is particularly employed to investigate and characterize activated carbons. Recent studies show good agreement between the results from this technique and immersion calorimetry. Thus, the combination of these techniques can characterize the whole range of porosity of carbonaceous adsorbents even using a single adsorbate. Use of the Clausius Ð Clapeyron equation to determine the isosteric adsorption heat has several limitations, theoretical and experimental, which are very well known. Nevertheless, there are still published works in which the experimental limitations do not seem to be fully taken into account. Thus, in such papers the reported values for the heat of adsorption are not fully reliable and should be carefully analyzed.
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IGC is now a standard technique allowing the determination of adsorption isotherms, thermodynamic parameters, as well as kinetic information concerning the adsorption process. This technique enables the determination of trueadsorption Ð equilibrium thermodynamic properties while operating under inÞnite dilution conditions or zero-coverage. Among others, the low time consumption and the possibility of using very different probe molecules (including adsorptives with low vapor pressure), are characteristics that make this technique applicable to almost all types of carbon materials. Use of different probes to determine the pore size distribution of a solid can be considered a standard technique. Nevertheless, it must be pointed out that, when using several adsorbates, each one is providing a partial distribution. To obtain the complete distribution it is necessary to combine the results obtained with several adsorbates, which probe different pore sizes. The most important condition that the selected probes must fulÞll is that the size range covered by each one must have an overlapping region with the tested range of other probes. New methods combining the use of different probes with computer simulations are rendering good results. It has been found in experiments and computer simulations that the adsorption heats of very different molecules, generally organic ones, tend to a value that is twice or higher the enthalpy of condensation. The common feature of these systems is the porous nature of the solid adsorbent. This effect has been observed also in the case of supercritical adsorption. On ßat surfaces, the heat of adsorption always tends to the enthalpy of condensation as the saturation limit is approached. It has been suggested that the origin of this phenomenon is in the gas Ðsolid interaction and its ratio is related to the gas Ðgas interaction. Nevertheless, the problem remains unresolved and deserves a systematic study before the correct answer is found. In the past, serious controversy arose concerning the validity of the analysis of high-temperature adsorption isotherms to obtain information about the heterogeneity degree of the adsorbent surface. This matter, in our opinion, has been resolved in favor of accepting this kind of analysis, which nowadays could be considered as a standard technique. Several arguments have been presented claiming that the residual 2D pressure analysis is better than the one based on HenryÕs law. Nevertheless, the authors of this proposal did not compare their theoretical predictions with experimental data. Thus, their arguments cannot be accepted, at least until a formal testing is done. Several authors have demonstrated the validity of HenryÕs law analysis for heterogeneous surfaces using very carefully designed computer simulations. Other authors also support this conclusion but using different arguments. Determination of the adsorption energy distribution function is a problem that remains not fully resolved. In fact, there is no agreement regarding the best method to calculate the distribution function from the experimental adsorption isotherm. The main problem arises from the ill-posed nature of the integral adsorption equation, which imposes a numeric solution to solve it. Regularization
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methods need the use of a regularization parameter that strongly affects the solution obtained. Thus, when the surface is not known it is not possible to discard solutions obtained for different regularization parameters that produce a good Þt to the experimental isotherm. It is true that certain methods have been proposed to select the right parameter but they still need to be validated. There is agreement in one aspect of the use of the adsorption energy distribution function, which is that the method employed to solve the problem is almost irrelevant provided the results are used to compare a series of samples differing in their heterogeneity degree. There are many examples in the literature showing the consistency of the conclusions derived from the adsorption energy distribution function when the method is employed as a comparison procedure. Using computer simulations of adsorption on model heterogeneous solids, it has been demonstrated that the energy distribution functions could be extracted from the isotherms. The monolayer capacity has been proposed as a criterion to choose the best among the possible solutions. New studies have been started relating the use of the integral adsorption equation with gas mixtures and to simultaneously determine the pore size distribution. Gas mixture adsorption is a subject that is increasingly being studied with computer simulations due to its potential technological applications. There is also increasing interest from the basic research point of view, since there are several behaviors that need a theoretical interpretation. It must be pointed out that in the literature there is less information than expected concerning the investigation of cooperative effects, which seem to play an important role in these systems. Computer simulations have proved to be useful to determine the phase diagram of adsorbed species on any kind of surface. Moreover, it is possible to identify and characterize the thermodynamic properties of each phase. By far the most extensively studied surface is the basal plane of graphite. This surface is currently employed as reference in most cases. Noble gases, nitrogen, oxygen, carbon dioxide, methane, and small hydrocarbons are the most widely studied adsorbates. For them the phase diagrams, the structure of each phase, and the phase transitions that take place are known. In all cases, computer simulations reproducing the experimental data have been reported. The limitations of classical simulation methods have been well established and the speciÞc advantages of each method to simulate certain kinds of systems are well known. New methods, besides the classical ones, have been proposed to study dynamic and conÞgurational properties of the adsorbed phase. In general, these new methods have been validated using experimental data, with different degrees of success. Quantum computer simulations are employed in physical adsorption problems to study certain effects, mostly of theoretical interest at the present time. It has been established as a valid methodology to model a solid and then simulate the adsorption of different probes as a validation of the model. There remains a certain degree of controversy concerning the importance of modeling the internal walls of pores in a more realistic way. In fact, several
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authors have reported differences in behavior of adsorbed ßuid due to changes in the structure of the wall, while others have indicated that no inßuence was found. The problem with this subject is the lack of a systematic study to settle the controversy and to assign the observed differences in adsorbate behavior either to the adsorbate or to the structure of the pore or both. Thus, it is better to model the solid structure as close as possible to the real solid. The same applies to the adsorbate molecules. In this sense, the main limitation is the computer time required. Nevertheless, computer processing speed is still growing continuously. The importance of different types of molecular interactions in adsorption is known. This fact allows the use of approximations depending on the conditions in which a system is simulated. There is a more or less generalized agreement that the isosteric adsorption heat is strongly affected by the microstructure of the adsorbent, particularly in the case of porous solids. This magnitude is better suited for structural analysis than other thermodynamic quantities. While using computer simulations, it is necessary to study pore systems rather than single-pore solids if the aim of the study is to analyze the adsorptionÐ desorption isotherms and other thermodynamic magnitudes. Single-pore analysis is suitable for certain restricted studies but the conclusions cannot be generalized to explain the adsorption Ð desorption isotherms. Computer simulations are being employed to elucidate the nature and mechanism of the hysteresis loop found in adsorption Ð desorption isotherms. There are some evidences showing that hysteresis could be due to surface heterogeneity and not exclusively to porosity. Adsorption in carbon nanotubes is being increasingly studied with several purposes. The main goal is to determine the actual capacity of this material as a gas storage device. There is still controversy about the actual adsorption capacities mainly due to the lack of well-puriÞed samples in sufÞcient amounts. The tubes with the smallest diameters are true realizations of 1D systems, thus providing an excellent substrate to test theoretical models. These systems have as much importance, in this sense, as mesoporous silica with regular arrangement of pores of uniform size.
ACKNOWLEDGEMENTS We thank the Editor of this series, Prof. L.R. Radovic, for his encouragement to prepare this review and for his careful reading of the manuscript and valuable suggestions. E.J.B. acknowledges Þnancial support from Consejo Nacional de Investigaciones Cientõ«Þcas y Te«cnicas (CONICET), Comisio«n de Investigaciones Cientõ«Þcas de la Pcia. de Buenos Aires (CIC), Universidad Nacional del Litoral, and Universidad Nacional de La Plata. J.M.D.T. thanks the Spanish CSIC for Þnancial support.
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Index
enthalpy, 217 – 219, 221, 222, 226, 229, 236, 240, 245, 248, 249, 255, 262, 274, 283, 286, 290, 312, 313, 315 entropy, 222 – 224, 226, 236, 241, 249, 250, 262, 280, 284, 312, 315 gas, 7, 115, 130, 212, 337 heat, 213, 214, 226, 232 – 234, 236, 237, 239 – 241, 243, 244, 247, 248, 250 – 252, 254, 257, 271, 280, 281, 286 – 288, 291, 293, 304, 327, 330, 333, 347, 367, 374, 386, 393 isosteric, 215, 222 – 227, 229, 231, 234 – 236, 245, 246, 262, 264 – 280, 284, 286, 287, 289, 296, 303, 307, 309, 312, 315, 328, 330, 332 – 334, 345, 348, 349, 352, 353, 356, 357, 369, 376, 378, 382 – 384, 393, 396 hysteresis, 223, 248, 266, 363, 365, 368, 380 – 383, 396 integral equation, 213, 233, 314 – 337, 395 isotherm (equation, model), 249, 261 – 279, 290 Brunauer, Emmett and Teller (BET), 223, 224, 237, 274, 304, 306, 309, 317, 318, 320, 325, 326, 334, 361, 386
Activation, chemical, 289 physical, 289 Activated carbon, 60, 210, 211, 212, 222, 223, 225– 227, 232, 233, 236, 237, 240, 241, 243– 245, 247 – 250, 252, 253, 255– 266, 268 – 270, 273– 275, 277, 278, 285 – 289, 293, 303, 312, 322, 323, 325, 326, 328, 331, 332, 334 – 337, 362, 366, 370, 372 – 376, 381, 385, 393 commercial (CECA), 223, 226, 234, 235, 243–247, 250– 252, 254, 257, 260, 269– 273, 275, 278, 286 – 289, 310, 312, 326, 330 – 335 Activated carbon fibers (ACF), 226, 248, 250, 253, 256, 261, 266, 267, 268, 270, 336, 368, 369 Adsorption calorimetry, 226, 243– 251, 251– 261, 293, 393 chemical (chemisorption), 247, 262, 275, 276, 313, 388 energy distribution (function), 213, 268, 269, 281, 284, 285, 312, 315, 317, 319, 320, 323, 324, 326–335, 367, 382, 394 425
426 Adsorption (contd.) Dubinin-Astakhov (DA), 226, 231, 249, 258, 259, 263– 265, 268, 269, 328 Dubinin-Radushkevich (DR), 223, 225, 231, 249, 256, 262, 263, 266, 268, 270, 272, 362, 374 Dubinin-Radushkevich-Kaganer, 327 Dubinin-Serpinsky (DS), 258, 259 Dubinin-Stoeckli (DS), 223, 255, 263, 264, 366, 367 Freundlich, 224, 245, 249, 324, 328, 335, 363 Gibbs, 218 Henry’s law, 236, 241, 280, 292, 313, 334, 345, 355, 394 Jaroniec-Choma, 263, 264 Jovanovic, 326, 328, 335 Langmuir, 223, 233– 235, 242, 248, 249, 266, 312, 318, 323, 324, 326, 328, 330, 333, 336 To´th, 227 Kelvin equation (model), 371 potential, Lennard-Jones, 297– 299, 306, 312, 331, 353, 357, 359, 375, 385, 391 Polanyi, 272, 273 Steele, 357, 363, 378, 379 theory (behavior, mechanism) of volume filling of micropores 250, 263, 266, 268, 367, 370 Amorphous carbon, 73, 77, 78, 132, 299, 308, 314, 329, 360, 361 Basal plane, see Graphene and Graphite Boehm (titration) method, 246, 286, 292, 377 Boltzmann equation (distribution, expression, factor), 227, 338, 365 Buckminsterfullerene, see C60 and Fullerene C60 (see also Fullerene), 313, 381 C70, 112, 313 Calorimetric titration, see Immersion calorimetry
Index Canonical ensemble, 227 – 229, 338, 341, 391 Capillary condensation, see Porosity Carbon aerogel, 266, 378, 379 Carbon black(s), 210, 232, 236, 248, 250, 251, 256, 258, 260, 263, 284, 287, 288, 304, 307, 310, 312, 319, 320, 323, 329, 330, 335, 357, 360, 361, 373, 381 ‘graphitized’, 223, 231, 242, 250, 284, 285, 289, 299, 301, 303, 304, 307, 310, 311, 320, 334, 335, 381 Carbon (or charcoal) fabrics (cloth), 35, 36, 269, 286 Carbon fibers, 5, 17, 23 – 37, 42, 64, 112, 210, 224, 281 – 283, 330, 360, 385 PAN-based, 23, 26 – 37, 42, 43, 282, 283 pitch-based, 23, 24, 26 – 37, 42, 43, 253, 267, 282, 369 vapor-grown (VGCF), 13, 23, 24 – 26, 27, 31, 276, 282 Carbon membrane, 365, 380 Carbon molecular sieve(s), 227, 232, 252, 260, 261, 274, 278, 279, 289, 372, 380 Carbon nanohorns, 277 Carbon nanotubes, 211, 214, 237, 250, 262, 275 –277, 344, 381 – 389, 396 single-wall (SWNT), 250, 251, 276–278 Carbosil, 335, 336 Carbyne, 74 Char(s), 245, 257, 292, 310 Charcoal, see Activated carbon Chemical vapor deposition (CVD), 61, 73, 75, 77, 79, 80 – 82, 83 –87, 90, 91, 94 – 96, 106 – 108, 110, 116, 118, 119, 123, 127, 128, 130, 137, 142, 146, 150 – 152, 156, 157, 159, 160 – 188, 201, 203, 261 DC arc jet (plasma), 73, 83, 84, 86, 106, 111, 114 –116, 119, 121, 122, 125, 126, 160, 168 – 174, 177 – 179, 188, 199, 201
Index hot filament (HF), 73, 83, 84, 86, 89, 94, 106, 107, 111, 114– 119, 122, 125, 126, 129, 130, 137, 143, 152, 159, 160, 161– 164, 168, 169, 178, 179, 188, 195, 199 microwave (MW) plasma, 83, 84, 106, 111, 114, 116, 119, 125, 126, 128 – 130, 132– 135, 137, 143 – 145, 147, 152, 155, 158, 160, 164–167, 169, 175, 178, 179, 188, 199, 201 oxygen-acetylene flame (combustion), 73, 83, 84, 90, 92, 113, 118– 122, 125, 126, 149, 160, 178– 188, 201 radio frequency (RF) plasma, 84, 123, 125, 126, 160, 174 – 178, 199, 201 Chromatography, inverse gas (IGC), 211, 261, 279– 293, 330, 335, 382, 394 reverse-flow gas (RF-GC), 292, 293 size exclusion, 269 tracer pulse (perturbation), 268 Clausius-Clapeyron equation, 217, 226, 227, 235, 236, 248, 264– 266, 273 – 277, 393 Coal(s), 223, 245, 257, 262, 268, 290 – 293, 309, 363 Coke(s), 16, 17, 64, 360 pitch, 17 Compressive strength, 48, 51, 72 Crystallite size, 17, 131, 132, 150 Density, 45, 99, 100, 140, 194 bulk, 8, 10, 15– 20, 23, 38, 39, 47 – 49, 51– 53, 55– 59, 61 Density functional theory (DFT), 233, 234, 235, 249, 263, 323, 332, 337, 345, 363, 366, 368, 369, 376, 385, 388 Diamond, cutting tools, 188– 190 dislocations, 139 doping (doped), 71, 83, 94, 151– 160, 191, 197 fibers, 197, 198
427 field emission displays, 194 growth, 80, 82, 91 – 94, 116 – 135, 144 – 151 epitaxial, 83, 110, 135 – 144, 153, 154, 156, 157 heteroepitaxial, 139 – 144, 152, 191, 202 homoepitaxial, 96, 110, 119, 136 – 139, 152, 155, 156, 158, 174, 186 parameter (a), 147 – 150 micromechanical devices (sensors), 190 natural, 72, 78 – 80, 96, 139, 152, 153, 186, 190, 200 nucleation, 80, 82, 94 – 116 polycrystalline, 84, 96, 116, 132, 138, 139, 146, 151, 156, 157, 163, 176, 177, 183, 189, 190, 191, 193, 194, 196, 198, 199, 202, 203, 381, 382 Schottky diodes, 192 single crystal(s), 83, 136, 139, 151, 152, 156, 189, 191, 199, 202 stacking faults (errors), 139, 150 surface acoustic wave (SAW) devices, 193 – 194 synthetic, 78 – 80, 139, 152, 153, 188 transistor, 192 twinning, 139, 150 wear-resistant coatings, 190 Diamond-like carbon (DLC), 77, 98, 102, 103 – 107, 110, 187, 194 Differential scanning calorimetry (DSC), 250, 252 – 254 Diffusivity (diffusion coefficient), 99, 100, 106, 140, 236, 251, 343, 365, 367, 369, 374 Dispersion (dispersive) interactions (forces), 262, 270, 281, 288, 289, 332 Dubinin theory, see Adsorption, theory of volume filling of micropores Electrical conductivity (conductance), 10, 44, 47, 59, 60, 64, 155 Electrical resistivity (resistance), 48, 71, 72, 79, 151, 153 –155, 157 Electromagnetic shielding, 62
428 Electron affinity, 72, 151, 159, 189, 194 Electron cyclotron resonance (ECR), 128, 166 Electrostatic interaction(s), 301, 353 Exfoliation, 2 – 4, 37– 43 Fire-protective materials, 63 Fowler-Guggenheim equation, 324, 331, 332 Fractal (dimension), 39, 42 Fracture strength, 112 Free energy, see Gibbs free energy Fullerene(s), 74, 82, 94, 102, 108, 118, 158, 211, 214, 285, 344, 381 –389 GCMC, see Monte Carlo simulation Gaussian (distribution), 262, 275, 305, 306, 317, 320, 326, 327, 336, 366, 374 Gibbs ensemble, 389, 391 Gibbs free energy, 107, 117, 200, 216, 226, 236, 240, 241, 262, 281, 282, 286, 312 Glassy (glass-like, vitreous) carbon(s), 196, 289, 290 Grand canonical ensemble, 227, 293, 294, 304, 341, 390 Graphene (layer, plane, sheet), 76, 154, 277, 278, 285, 337, 372, 383, 386 Graphite(s), 72– 79, 81, 88, 94, 96, 101, 102, 105, 116, 117, 136, 137, 140– 143, 145, 153, 158, 168, 186, 189, 200, 202, 210, 223, 232, 251, 254, 266, 276 –278, 281, 285, 299, 300, 301, 303, 306, 307, 311– 313, 337, 344– 361, 372, 378, 388 basal plane (see also Graphene), 1, 4, 5, 24, 39, 45, 107, 143, 213, 224, 231, 233, 251, 282, 300, 329, 337, 347, 348– 350, 352 –354, 356– 358, 363, 366, 367, 388, 395 exfoliated, 1, 3 – 8, 10– 17, 17– 23, 30, 38, 39, 42, 44, 45, 48, 50– 62, 64, 253, 301, 306
Index medical dressings, 57 –59 sorption capacity, 50 – 58, 64 thermal conductors, 59 thermal insulators, 59 exfoliation, 1 – 65, 5 – 23 exfoliative, 4 – 6, 44, 52, 53, 63, 64 expandable, 4, 44 expanded, 4 film(s), 1, 4, 112 flake(s), 1, 4, 5, 8, 10, 12, 13, 15, 17, 24, 26, 37, 44, 45, 49, 50, 60, 63 flexible sheet(s), 1, 5 – 7, 13, 14, 17, 43 – 64 gallery (ies), 3, 10, 12, 13, 15, 37 intercalation compounds (GIC), acceptor-type, 10, 11 donor-type, 10, 11 interlayer, 106 – 108 natural, 1, 5 – 7, 10, 15, 17, 24, 26, 43 – 45, 48, 50, 64, 271, 281 particles, 1, 15, 39 worm-like, 1, 2, 4, 5, 7, 11 – 13, 17, 18, 20 – 23, 30, 39, 40, 45, 56 pyrolytic, 2 (see also HOPG) single crystal, 2, 5, 60 Graphitic carbon(s), 43, 123 Graphitization, 17, 23, 24, 42, 43, 64, 76, 160, 224, 320, 329 Graphitized carbon, 43, 64, 291 Hall effect, 155, 158 Helmholtz free energy, 228, 242, 307 Henry’s law (constants; see also Adsorption isotherm), 225, 232, 246, 269, 274, 279, 284, 293 – 314, 320, 365 Highly oriented pyrolytic graphite (HOPG), 5, 143 Ideal adsorption solution theory (IAST), 242, 278, 312, 345, 346, 366, 385, 393 Immersion calorimetry, 211, 212, 250, 254 – 261, 289, 293, 393 Interlayer (d002) spacing, 4, 17, 27, 28, 31, 32, 43, 143, 154
Index Interstitial (atom, carbon, impurity, position, site), 139, 152–154, 156, 158 Lennard-Jones (fluid, potential), 231, 233, 242, 298 Lorentz-Berthelot (combining, mixing) rule(s), 300– 302, 353, 357 Maxwell-Boltzmann distribution, 305 Mercury porosimetry, 21, 56, 320, 362 Mesocarbon microbeads (MCMB), 360 Molecular dynamics (MD) simulation (methods), 156, 213, 337, 338, 342 – 357, 359, 361, 363, 365, 367 – 369, 371, 374, 379, 380 Molecular orbital theory ab initio, 388 Hu¨ckel (extended), 357 Molecular sieving carbon, see Carbon molecular sieve Monte Carlo (MC, GCMC) simulation (techniques), 213, 267, 337, 338 – 347, 349– 357, 360–363, 365 – 382, 384– 386, 389–391, 393 reverse (RMC), 379 n-type, see Semiconductor Neutron diffraction (scattering), 253, 277, 354, 356 Nuclear magnetic resonance (NMR), 268, 293 p-type, see Semiconductor Partition function, 228– 230, 304, 305 Phase transition, 3, 346, 355 Polanyi (-Dubinin) potential (theory), 262, 273 Polarizability, see QSAR Pore size distribution, 23, 213, 227, 253, 255, 256, 261, 269, 272, 286, 288, 322, 331, 335, 336, 362, 365–367, 372, 374, 376 – 379, 381, 394, 395 Porosity (pores), 39, 59, 60, 212, 262, 275, 277, 280, 315, 336, 366, 379, 393
429 capillary condensation, 363, 365, 376, 382, 383, 391, 392 crevice-like (wedge-shaped), 2, 4, 21, 56 ellipsoidal (elliptic), 4, 39 slit-like (slit-shaped), 224, 231, 233, 262, 264, 268, 286, 329, 336, 344, 345, 346, 361 – 381, 385, 388 structure, 18, 20, 21, 38, 59, 256, 286, 293, 332, 337, 378 Preferred orientation, 5, 45, 145 – 147, 149, 361 Quantitative structure-activity relationship (QSAR), 254, 255, 266 ionization potential, 254 molar volume, 252, 266 molecular connectivity, 255 parachor, 252, 266 polarization (polarizability), 252, 254, 266, 281, 282, 291, 349 electronic, 291 Raman spectroscopy (spectra), 43, 132 – 134, 159, 185 Refractive (refraction) index, 71, 72, 195 Residue compounds, 1, 2, 3, 5 – 10, 13, 14, 21, 27, 37, 44, 45, 52 Scanning electron microscopy, micrographs (SEM), 1, 2, 7, 11, 13, 16 – 19, 21, 24 – 28, 33, 35 – 37, 61 Scanning tunneling microscopy (STM), 261, 357, 372, 386 Semiconductor(s), 191, 195 n-type, 151, 152, 157, 158, 160, 192 p-type, 79, 151, 153, 156, 158, 159, 192 wide-gap, 135, 151 Soret effect, 85 Substitutional (atom, position, site, solubility), 79, 152 – 158, 160
430 Surface area, 7, 12, 17, 60, 98, 210, 237, 238, 248, 255– 258, 262, 264, 268, 269, 280, 284, 289, 299, 303, 304, 306, 309, 310, 313, 331, 334, 335, 374, 379 Surface chemistry (complexes, groups), 212, 244, 245, 247, 248, 257, 270, 271, 281, 284, 286, 287, 292, 330, 332 acidity (acidic functional groups), 282, 286, 292, 377 basicity (basic functional groups), 260, 282, 377 functional groups, 61, 280, 283, 288, 331 oxygen (oxidation), 241, 257 –260, 288 Temperature-programmed desorption (thermodesorption, TPD), 244, 246, 252, 259, 333, 360, 361 Tensile strength, 47– 51 Thermal conductivity, 44, 47, 48, 59, 62, 64, 71, 79, 127, 134, 151, 166, 167, 189– 191, 194, 343 Thermal expansion (coefficient), 4, 48, 71, 72, 97– 100, 102, 127, 140, 185, 202
Index Thermal insulation (insulator), 5, 61 – 63 Thermal shock resistance, 102, 194 Transmission electron microscopy, micrographs (TEM), 31, 32 high-resolution (HRTEM), 103 van der Waals constant, 357 distance, 389 equation (model, theory), 318, 352, 357 forces (energy, interactions), 353, 359 loop, 391 volume, 266, 267 Virial coefficient, 293 – 314, 357 Weibull distribution, 317 Wigner-Polanyi equation, 333 X-ray diffraction (pattern, peak, scattering), 5, 7, 12, 13, 17, 26, 27, 29, 31 – 34, 36, 42, 43, 132, 144, 145, 149 X-ray photoelectron spectroscopy (XPS), 246, 251, 258, 259, 284, 285 Young’s modulus, 47, 48, 98, 112, 194
