Adsorption by carbons

DEDICATION

The genesis of this book can be traced back to July 2003, the date of the Carbon 2003 Conference. This presented Eduardo J. Bottani and myself with an excellent opportunity to introduce our project to lain Craig, the Commissioning Editor with whom we discussed the scope and contents of the book. Soon afterwards, the publication of the book was approved by Elsevier Science and we established initial contacts with some prospective authors. However, the unexpected death of Eduardo J. Bottani on October 24,2003, meant that I now had a dual responsibility, not only to the publisher and the authors who had already agreed to contribute chapters, but also to the memory of Eduardo, to whom I wish to dedicate this book. Needless to say, I accept full responsibility for any faults in the editing as Eduardo passed away before we began the work in earnest. Prof. Eduardo Jorge Bottani was born in Bahia Blanca, Argentina, on July 2, 1955. After completing his studies in Chemistry (speciality: Physical Chemistry) at the Universidad Nacional de La Plata (UNLP), he went on to gain a PhD in the same university and speciality in 1982. His thesis, carried out under the supervision of Prof. Lydia E. Cascarini de Torre, was entitled "Study of interactions in physically adsorbed molecules." Except for several periods ofstudy abroad, first at Louvain-Ia-Neuve, Belgium, and later at State College, PA, USA (with Prof. W.A. Steele), Eduardo J. Bottani spent most of his life in La Plata and his entire professional career at INIFTA, a renowned research institute devoted to Basic and Applied Physical Chemistry. It was here while a member of the Physical Adsorption Laboratory that he held several positions as a research scientist for CIC. Towards the end of his life he also collaborated with Profs A.J. Arvia and E.A. Castro, successive directors of the Institute, in organizational tasks. While carrying out his scientific research, he taught General, Inorganic and Physical Chemistry at UNLP (his Alma Mater which, I regret to say, returned him much less than he had given her). Later on, he was given the post of Visiting Professor at the Universidad Nacional del Litoral (UNL) in the city of Santa Fe, where, together with Prof. H.S. Odetti, he formed a flourishing research team. I first met Eduardo on October 12, 1992, when Lydia Cascarini and he welcomed me at Ezeiza Airport in Buenos Aires (the date is easy to remember as it was exactly 500 years to the day after a famous discovery known to all mankind). This was the beginning of a period of collaboration that has culminated in the production of this book. Since 1999, Eduardo J. Bottani spent one month a year in Oviedo, where we combined our efforts in investigating gas physisorption on different materials such as carbon blacks, fullerenes, and carbon v

vi

Dedication

nanotubes. Moreover, he and I shared an interest in art (especially architecture) and made many weekend visits to different monuments of our Spanish cultural heritage. At the time he passed away, Prof Bottani was Deputy Director of INIFTA and General Secretary of the Argentine Chemical Society (Asociaci6n Qu£mica Argentina, AQA). Shortly before, he had been appointed Editor-in-Chief of the Journal of the Atgentine Chemical Society, where he took up the challenge of converting the traditional Anales de la AQA into a truly international journal. He was also responsible for the organization of a number of Argentine Conferences on Chemistry. All of these facts about his life show that Eduardo J. Bottani was at the summit of his career at the time of his death, sadly yet another unfortunate case of a gifted person with a promising future brought to a premature end. Eduardo is survived by his wife Jovita Montoni de Bottani, daughter Estefania, and sons Eduardo and Ezequiel, to whom, together with his mother, Dona Elvira Gar6foli de Bottani and rest of the family, friends, and colleagues I offer this book as a token of my esteem. Juan M.D. Tasc6n

FOREWORD

It has been a great pleasure for me to write a foreword for this very interesting book on Adsorption by Carbons in response to an invitation I first received from the editors in August 2003 when the book was still only a project. This invitation has afforded me the opportunity and the privilege of uniting the efforts of an outstanding group of renowned scientists as authors of the different chapters, some of whom have been either my colleagues or disciples. Part 1 of the book is of an introductory nature. Thus, Chapter 1 provides an updated overview of adsorption by carbons, differentiates the features of adsorption on nonporous and porous carbons, and identifies the main obstacles still hindering the study of gas adsorption by porous carbons. Recent major developments and research needs in this field are also mentioned. Chapter 2 presents a survey of carbons in the context of adsorption and classifies them on the basis of structural criteria. This chapter might help nonspecialists in carbon to find materials that they can use for adsorption purposes. Part 2 of the book addresses the fundamental aspects of adsorption by carbons. The first few chapters deal with the energy aspects of gas adsorption. Thus, Chapter 3 focuses on thermodynamic quantities, with particular attention being paid to their significance and relation to experimental results. Cursory descriptions of the classical and statistical thermodynamic approaches are presented in the form of essential equations. Chapter 4 presents two types of simulation techniques (Monte Carlo and Molecular Dynamics) that help us to understand the behavior of molecules on surfaces of carbons and other materials. It is pointed out that the former method is more useful for studying transport properties, whereas the latter provides information about the thermodynamic properties at the adsorbent/adsorbate interface. New areas under development in this field are outlined. Chapter 5 focuses on models of porous carbons that are useful for predicting and explaining the behavior of adsorbed phases. The discussion encompasses both classical single-pore models (e.g., the well-known slit-shaped pore) as well as more realistic models that include factors such as connectivity or tortuosity. The connection between models and experimental techniques and the need for improving methods of obtaining experimental data are emphasized. Chapter 6 deals with adsorption hysteresis or, to be more precise, the origin of adsorption hysteresis. It addresses the peculiar characteristics of hysteresis in the case of carbon adsorbents, namely, structural lability and the presence of surface chemical structures (principally, oxygenated groups) that modify the energetics and wettability behavior of carbon surfaces. The surface heterogeneity of carbons is analyzed in Chapter 7 on the basis that practically all real adsorbents XVll

xviii

Foreword

are heterogeneous. The big differences within the ensemble of carbon materials (ranging from higWy homogeneous graphites to extremely heterogeneous activated carbons) are discussed and the factors that cause heterogeneity are analyzed. The wetting of solid surfaces by liquids is addressed next in Chapter 8. To analyze the wetting of carbon, the study was extended from graphite (by far the most widely studied carbon surface) to include other materials such as carbon nanotubes, the geometry of which greatly affects the wetting properties. The theory and simulation of gas adsorption on carbon nanotube bundles is addressed in Chapter 9, which focuses on the structural, dynamic, and thermal properties of gases adsorbed at sites such as grooves between pairs of nanotubes, interstitial channels, or inner spaces inside the individual tubes. This chapter serves as a background for Chapter 15, which belongs to Part 3 of the book. The section on fundamentals ends with Chapter 10, which follows two general approaches (the generalized Gaussian model and the bivariate model) to characterize the energy topography of carbon surfaces. The former model is attractive due to its simplicity and works well with substrates with a rough-surface adsorptive energy. The bivariate model is applicable to heterogeneous surfaces with two kinds of sites. The series of 10 chapters that constitute Part 3 of the book deals mainly with the use of adsorption as a means of characterizing carbons. Thus, the first three chapters in this section complement each other in the use of gas-solid or liquid-solid adsorption to characterize the porous texture and/or the surface chemistry of carbons. Porous texture characterization based on gas adsorption is addressed in Chapter 11 in a very comprehensive manner and includes a description of a number of classical and advanced tools (e.g., density functional theory and Monte Carlo simulations) for the characterization of porosity in carbons. Chapter 12 illustrates the use of adsorption at the liquid-solid interface as a means to characterize both pore texture and surface chemistry. The authors propose these methods (calorimetry, adsorption from solution) to characterize carbons for use in such processes as liquid purification or liquid-solid heterogeneous catalysis, for example. Next, the surface chemical characterization of carbons is comprehensively treated in Chapter 13, which discusses topics such as hydrophilicity and functional groups in carbon as well as the amphoteric characteristics and electrokinetic phenomena on carbon surfaces. The next block (Chapters 14-18) is principally devoted to the characterization of several types of carbon that deserve attention for their novelty. Thus, fullerenes, which are dealt with in Chapter 14, are studied as adsorbents with various objectives in mind: for the fundamental investigation of their surface energetics; as tools for the preconcentration and analysis of species in solution; or even as possible substrates for hydrogen storage. This last topic is still a "hot" one in the case of carbon nanotubes, which explains why two whole chapters (besides Chapter 9) have been dedicated to this type of material. One of them (Chapter 15) addresses hydrogen adsorption from a more theoretical point of view, while the other (Chapter 16) takes a look at the actual knowledge obtained from the experimental results published in the literature and therefore

Foreword

xix

offers the reader a complementary, more practical view. Chapter 15 identifies two problems that continue to obstruct progress in research, namely, the variability of the materials being studied by different teams and the lack of reliable computational methods for determining adsorption potentials or chemisorption interactions. Chapter 16 discusses the nature of different types of adsorption sites on nanotube surfaces and concludes that further research is needed to make such sites more easily identifiable, particularly high energy binding sites. The next two chapters deal mainly with the use of adsorption to characterize porous solids. In the case of activated carbon fibers (Chapter 17), methods to characterize microporosity, and particularly ultramicroporosity, by physical adsorption are of particular relevance for understanding the behavior of these adsorbents and extending the range of their applications. Moreover, in Chapter 18 the pore structure of ordered mesoporous carbons is shown to differ greatly from that of conventional activated carbons for which most of the available data treatment methods have been developed. Therefore, suitable procedures for correctly analyzing the pore structure of these novel carbons are proposed in this chapter. Two chapters related with the solid-liquid interface conclude Part 3. The electrochemical behavior of carbons is the subject of Chapter 19, which discusses the characteristics of carbon electrode materials with reference to concepts such as roughness or fractality, and also the electrochemical kinetics on carbon electrodes. Chapter 20 deals with the application of scanning probe microscopy to the study of inorganic and organic adsorbates deposited on highly oriented pyrolytic graphite (HOPG) at the submonolayer and monolayer level. The basal plane surface of HOPG is taken as a model system, thanks to its atomic-scale smoothness and low chemical reactivity. Part 4 of the book deals with the applications of adsorption in different fields of technology with explanations as to why carbons exhibit a particular behavior. First of all, gas-phase applications are addressed, either for the removal of pollutants (both volatile organic compounds and inorganic gases, Chapter 21) or for gas separation and storage (Chapter 22). These two chapters present comprehensive summaries of the surface science involved in these important processes and provide clues for selecting the right carbons to be used as adsorbents. Another application of carbons in the field of energy is that of electrochemical energy storage. Chapter 23 discusses the two most important current lines of investigation, namely, lithium batteries and supercapacitors, and relates their performance to carbon characteristics and identifies present research needs. Finally, Chapters 24-27 deal with the environmental applications of carbons as adsorbents for the removal of pollutants from aqueous solutions. These four chapters are highly complementary. Thus, Chapter 24, which addresses the problems associated with the removal of inorganic species, finds its "alter ego" in Chapter 25, which deals with the adsorption of organic solutes from dilute aqueous solutions. Both chapters provide insights into the fundamental reasons for the performance exhibited by a carbonaceous adsorbent. The global topic of water purification using carbons as adsorbents is addressed in Chapter 26, which

xx

Foreword

deals with the science and technology involved in the removal of a surprising variety of pollutants from water employing activated carbon, either in powdered or in granular form. Finally, Chapter 27 is somewhat complementary to Chapter 25 as it discusses the sorption of viscous organics (as opposed to dilute organic solutes). However, there is a significant difference in the type of adsorbent. Indeed, the removal of viscous organics (e.g., heavy oils and biomedical molecules) requires a macroporous adsorbent (e.g., exfoliated graphite) rather than a microporous one. From the preceding overview it is easy to imagine the enormous effort required of the editors and the authors of the different chapters to bring this important piece of work to a satisfactory conclusion. I believe that this will become a reference book for any person interested in the subject of adsorption and carbons. It will be useful not only to those beginning their study of activated carbons and related materials, but also to specialists wishing to further explore this interesting field of research. New discoveries are constantly being made in this area, leading to the solution of numerous problems, both of a theoretical nature and in the applied field ofmodern science and technology. Let me convey again my congratulations to the editors and my esteem for Prof Bottani of whom I have a fond memory. Finally, may I wish Prof Tascon further success in this interesting field of research. Prof Dr. Juan de Dios Lopez-Gonzalez Granada and Madrid, Spain

PREFACE

The essential aim of this work is to fill the gap that exists between the fields of adsorption and carbon materials, an area that, to our knowledge, has not been encompassed so far in one single book. Several books address the phenomenon of adsorption from both a fundamental and an applied perspective, while publications on the structure, properties, and applications of carbons, either general or restricted to specific types of materials, are increasingly common. There are, also, a number of works devoted to porosity in carbons or other solids. However, adsorption is involved in many areas other than porosity characterization. In short, the interplay between adsorption and carbon materials has not been addressed yet in one volume. There is a vacuum of knowledge between both fields that, if filled, could give birth to new concepts and ideas. Adsorption cannot occur without the active and mutual participation of the adsorbent and adsorbate. Indeed, the book is purposely entitled "Adsorption by Carbons" (rather than, for instance, "Adsorption on Carbons") to emphasize the dynamic character of adsorption and the active participation of the carbonaceous adsorbent, which not only provides adsorption sites but also attracts adsorbates to its surface. The book consists of four parts. Part 1 which is the shortest (two chapters), introduces the reader to the field of adsorption by carbons and to the realm of carbon materials. The following eight chapters address the fundamental aspects of adsorption by carbons through such topics as adsorption energetics, computer simulations, modeling, surface heterogeneity, and so on. Indeed, this second part ofthe book develops a series ofconcepts that contribute to a better understanding of what follows in the third section, in which adsorption is mainly envisaged as a tool to characterize carbon surfaces. The third part, consisting of 10 chapters, begins with a look at the adsorption methods used to study the porous texture and surface chemistry of carbons, and then follows with chapters devoted to several novel types of materials to conclude with a discussion on certain aspects of the electrochemistry of adsorption by carbons. Finally, the fourth part (seven chapters) deals with the most significant technological applications of adsorption by carbons, either at the gas-solid or at the liquid-solid interface, which have direct implications especially for the fields of environment and energy. Overall, the ensemble of 27 chapters tries to cover the subject of adsorption by carbons as comprehensively as possible. In my view, the main strength of the book derives from the stature of the contributing authors. I have always thought that Eduardo Bottani and I were being a little overambitious (perhaps even daring?) in inviting the best specialists in the various areas to contribute chapters. Some were our friends, others were XXI

xxii

Preface

just acquaintances we had met at conferences, and there are still a few whom I still do not know personally. But all of them share one thing in common, and that is that they are leaders in their respective fields. The important thing is that we succeeded in our invitation, and I am very happy with the result of this collective effort. The book has an undeniably international flavor, as it includes authors from 13 different countries. Apart from a possibly slight imbalance in favor of the New World (USA and Argentina), the geographical distribution of the authors is fairly representative of the places where adsorption by carbons is being investigated. I will purposely avoid citing authors' names here, as this would make the preface outstandingly long. Let me simply thank all the authors collectively for having accepted the invitation to produce their chapters, for the care they have taken in preparing them, and for their continued willingness to help me. My thanks are extended to the staff of Elsevier, particularly lain Craig, Commissioning Editor, Kristi Green, Administrative Editor, and Sunita Sundararajan, Project Manager, for their very professional assistance at many stages of book's preparation. Last but not least, my warmest thanks go to Prof Dr Juan de Dios LopezGonzalez for having accepted to write a foreword to this book. Neither Eduardo Bottani nor I are direct descendants of the scientific school that originally spread from Granada University under his guidance. The international reputation that the Spanish-speaking scientific community enjoys in the field of adsorption by carbons owes much to the efforts of that school. Interestingly, the first papers that came to the attention of Eduardo and myself at the beginning of our research careers in the late 1970s were those of Professor Lopez-Gonzalez and coworkers. Thus we shared the same introductory academic experience in two such distant places as far apart as La Plata and Madrid! I refer, of course, to physical distance, since few countries are so close to each other emotionally as are Argentina and Spain. Juan M.D. Tascon

LIST OF CONTRIBUTORS

Alejandro J. Arvia Instituto de Investigaciones Fisicoquimicas Te6ricas y Aplicadas (INIFTA) Universidad Nacional de La Plata-Consejo Nacional de Investigaciones Cientificas y Tecnicas La Plata, Argentina [email protected] Teresa J. Bandosz Department of Chemistry City College of New York New York, NY, USA [email protected] Fran~ois

Beguin Centre de Recherche sur la Matiere Divisee CNRS-U niversite Orleans Cedex, France [email protected] Henry Bock Department of Chemical and Biomolecular Engineering North Carolina State University Raleigh, NC, USA [email protected] Hans-Peter Boehm Department of Chemistry and Biochemistry University of Munich, Germany [email protected] Mary J. Bojan Department of Chemistry The Pennsylvania State University University Park, PA, USA [email protected] Agustin E. Bolzan Instituto de Investigaciones Fisicoquimicas Te6ricas y Aplicadas (INIFTA) UNLP-CIC-CONICET La Plata, Argentina [email protected] (or) [email protected] XX111

xxiv

List of Contributors

Eduardo J. Bottani Instituto de Investigaciones Fisicoquimicas Te6ricas y Aplicadas (INIFTA) UNLP-CIC-CONICET La Plata, Argentina M. Mercedes Calbi Department of Physics Southern Illinois University Carbondale, IL, USA [email protected] Diego Cazorla-Amoros Departamento de Quimica Inorganica Universidad de Alicante Alicante, Spain [email protected] Milton W. Cole Department of Physics The Pennsylvania State University University Park, PA, USA [email protected] Hans Darmstadt Departement de genie chimique Universite Laval Quebec, Canada [email protected] Renaud Denoyel MADIREL, CNRS-Universite de Provence Marseille, France [email protected] DuongD. Do School of Engineering University of Queensland St Lucia, Qld, Australia [email protected] HaD. Do School of Engineering University of Queensland St Lucia, Qld, Australia [email protected]

List of Contributors

Catherine Faur-Brasquet Ecole des Mines de Nantes Nantes cedex, France [email protected] Elzbieta Frackowiak Institute of Chemistry and Technical Electrochemistry Poznan University of Technology Poznan, Poland fracko@fct. put.poznan.pI Silvina M. Gatica Department of Physics The Pennsylvania State University University Park, PA, USA [email protected] Keith E. Gubbins Department of Chemical and Biomolecular Engineering North Carolina State University Raleigh, NC, USA [email protected] Michio Inagaki Faculty of Engineering Aichi Institute of Technology Yakusa, Toyota, Japan [email protected] Norio Iwashita National Institute of Advanced Industrial Science and Technology Onogawa, Tsukuba, Japan [email protected] Timur S. Jakubov Department of Applied Chemistry Royal Melbourne Institute of Technology Melbourne, Australia [email protected] J. Karl Johnson Department of Chemical and Petroleum Engineering University of Pittsburgh Pittsburgh, PA, USA National Energy Technology Laboratory Pittsburgh, PA, USA [email protected]

xxv

xxvi

List of Contributors

Feiyu Kang Department of Materials Science and Engineering Tsinghua University Beijing, China [email protected] Pierre Le Cloirec Ecole des Mines de Nantes Nantes cedex, France [email protected] Angel Linares-Solano Departamento de Quimica Inorganica Universidad de Alicante Alicante, Spain [email protected] Amelia Martinez-Alonso Instituto Nacional del Carbon, CSIC Oviedo, Spain amelia@incar. csic. es Aldo D. Migone Department of Physics Southern Illinois University Carbondale, IL, USA [email protected] Carlos Moreno-Castilla Departamento de Quirnica Inorganica Facultad de Ciencias Universidad de Granada Granada, Spain [email protected] Gayle Newcombe Cooperative Research Centre for Water Quality and Treatment Salisbury, South Australia Australia [email protected] James P. Olivier Micromeritics Instrument Corp., Inc. Norcross, GA, USA [email protected]

List of Contributors

xxvii

Jorge Pikunic Department of Chemical and Biomolecular Engineering North Carolina State University Raleigh, NC, USA [email protected] Antonio J. Ramirez-Pastor Laboratorio de Ciencias de Superficies y Medios Porosos Universidad Nacional de San Luis, CONICET San Luis, Argentina [email protected] Jose L. Riccardo Laboratorio de Ciencias de Superficies y Medios Porosos Uniyersidad Nacional de San Luis, CONICET San Luis, Argentina [email protected] Franfoise Rouquerol MADIREL, CNRS-Universite de Provence Marseille, France [email protected] Jean Rouquerol MADIREL, CNRS-Universite de Provence Marseille, France [email protected] Ryong Ryoo National Creative Research Initiative Center for Functional Nanomaterials and Department of Chemistry (School ofMolecular Science BK21, Korea Advanced Institute of Science and Technology Daejeon, Korea [email protected] (or) [email protected] Roberto C. Salvarezza Instituto de Investigaciones Fisicoquimicas Te6ricas y Aplicadas (INIFTA) La Plata, Argentina [email protected] Kenneth S.W. Sing BruneI University Uxbridge, UK [email protected]

xxviii

List of Contributors

Shivaji Sircar Department of Chemical Engineering Lehigh University Bethlehem, PA, USA [email protected], [email protected] William A. Steele Department of Chemistry The Pennsylvania State University University Park, PA, USA [email protected] Fabian Suarez-Garcia Instituto Nacional del Carbon, CSIC Oviedo, Spain [email protected] Juan M.D. Tascon Instituto Nacional del Carbon, CSIC Oviedo, Spain [email protected] Fernando Teran Arce Instituto de Investigaciones Fisicoquimicas Teoricas y Aplicadas (INIFTA) Universidad Nacional de La Plata-Consejo Nacional de Investigaciones Cientificas y Tecnicas La Plata, Argentina [email protected] Masahiro Toyoda Faculty of Engineering Oita University Oita, Japan [email protected] Eugene A. Ustinov School of Engineering University of Queensland St Lucia, Qld, Australia [email protected] Maria E. Vela Instituto de Investigaciones Fisicoquimicas Teoricas y Aplicadas (INIFTA) Universidad Nacional de La Plata-Consejo Nacional de Investigaciones Cientificas y T ecnicas La Plata, Argentina [email protected]

List of Contributors

Giorgio Zgrablich Laboratorio de Ciencias de Superficies y Medios Porosos Universidad Nacional de San Luis CONICET, San Luis, Argentina Departamento de Quimica Universidad Aut6noma Metropolitana-Iztapalapa Mexico D.F., Mexico [email protected]

Jose L. Zubimendi Instituto de Investigaciones Fisicoquimicas Te6ricas y Aplicadas (INIFTA) Universidad Nacional de La Plata-Consejo Nacional de Investigaciones Cientificas y Tecnicas La Plata, Argentina

xxix

ADSORPTION ON ACTIVATED CARBON FIBERS Angel Linares-Solano and Diego Cazorla-Amoros Deptamento de Qufmica Inorganica, Universidad de Alicante, Alicante, Spain

Contents 17.1 Introduction 17.2 Preparation of ACFs 17.3 Characterization of ACFs 17.4 Some Examples of ACF Applications 17.5 Conclusions Acknowledgments References

43 1 433 43 6 447 449 449 449

17.1 INTRODUCTION

Activated carbon fibers (ACFs) are porous carbons with a fiber shape and a well-defined porous structure that can be prepared with a high adsorption capacity. Although the ACFs are very promising materials, they have not still a market as important as the activated carbons (ACs) due to their difference in production costs. The main characteristics and advantages of the ACFs are as follows [1-3]. (i) They have both high apparent surface area and adsorption capacity. (ii) They have fiber shape with a small diameter (ranging between 10 and 40 f-Lm), which is a very important characteristic for new applications requiring higher packing density (i.e., gas storage) [3]. (iii) ACFs are light materials and can be easily woven into different fabrics (i.e., cloths, felts). Adsorption by Carbons ISBN: 978-0-08-044464-2

© 2008 Elsevier Ltd.

All rights reserved.

431

43 2

Chapter 17 Adsorption on Activated Carbon Fibers

(iv) The pore size distribution of the ACFs, being essentially microporous materials, is narrow and uniform although mesoporous ACFs can also be prepared. (v) The narrow diameter essentially eliminates mass transfer limitations, the adsorption-desorption rates being very rapid. Since the ACFs are fibrous materials that can be easily molded and woven, filters can be designed that do not have the settling and channeling problems of the conventional granular and powder ACs [1]. Due to their low hydrodynamic resistance, they can be used as thin cloths for the treatment of high flow of gases, very useful for control of gas-phase pollution [2]. The development of ACF and AC cloths is closely related to that of carbon fibers (CFs). This makes that the raw materials used for the preparation of ACFs be, chronologically, the same as for CFs. Thus, in 1966, viscose and acetate cloths were, like for CFs, the first materials used to obtain ACFs [4,5]. The low yield of the ACFs, and CFs, obtained from the above precursors, oriented the research towards the seek of other raw materials for the preparation of cheaper CFs and ACFs with a higher yield. In this way, ACFs were prepared from 1970 using lignin (with the brand of Kayacarbon ALF), polyvinylchloride [6] (i.e., Saran polymer, already used to obtain ACs) and phenolic precursors [7]. The high yield and the good mechanical properties of the ACFs obtained make these precursors very useful for this application. In fact, Economy and Lin [8] developed ACFs from a phenol formaldehyde precursor, which are commercialized since 1976 under the name of Novolak. In 1980, Kuray Chemical Co. Ltd commercialized ACFs from phenolic resin under the name ofKynol 1 . The preparation of PAN-based ACFs was initiated in 1976 by Toho Rayon. Ltd2 and the use of pitch to obtain ACFs started in 1985, and these ACFs were commercialized by Osaka Gas Co. Ltd (AD'ALL) 3 . Due to the low price of the pitch and high yield of the ACFs obtained, the manufacture of pitch-based ACFs has increased considerably, the pitch being one of the main precursors of ACFs nowadays [1]. The research on ACFs is not different from what is usual for other materials. It focuses on understanding the preparation process, the characterization of the materials, and the analysis of their performance in given applications. A literature search on this topic gives us more than 600 contributions, taking into account only the papers published in journals. The research on ACFs starts more than 30 years ago regarding their preparation (as it has been detailed above). However, most of the work done concentrates mainly in the last 20 years, and it is essentially focused on their characterization and applications. Since a detailed review of all these contributions is out of the scope of this chapter, we will only make reference to the most representative works done on the aspects that will be described anon. 1 Nippon Kynol Inc., Japanese Patent 7583, 1980. 2Toho Rayon Co. Ltd., Japanese Patent 30810, 1978. 3Renoves A series, Application of AD 'ALL (Activated Carbon Fibre), Product Catalogue.

17.2

Preparation of ACFs

433

Thus, this chapter on adsorption in ACFs will cover the following sections: (i) the fundamentals on the preparation routes, (ii) the characterization by gas adsorption and other complementary new techniques, and (iii) some examples of applications of ACFs.

17.2 PREPARATION OF

ACFs

Once the precursor (i.e., pitch, polymer) is transformed into a fiber shape by a suitable spinning process and is carbonized after a proper stabilization stage, the activation of the resulting CF is needed to increase its adsorption capacity. The starting points for the activation of the CF precursor are not different from those for conventional granular or powder ACs. To prepare ACFs, the precursor and the method of preparation need to be appropriately selected. These two factors have great importance as they determine the final porous structure of the ACF. For a given precursor, the main stage determining the porous structure is the method of activation. The objective of activation is both to increase the number of pores and to increase the size of the existing ones, so that the resulting porous carbon has a high adsorption capacity. The preparation of porous CFs can be achieved by any of the following three methods: (i) the pyrolysis of appropriate precursors, (ii) the controlled carbon gasification with a reactant gas (i.e., physical activation), and (iii) the so-called chemical activation. Apt examples on the first method can be found in the work done by Oya and co-workers [9, 10]. The polymer blending technique can be very useful to create porosity during a heat treatment in an inert atmosphere of a mixture of two polymers. In this method a pyrolyzing and a carbonizing polymer are blended and, after the heat treatment, pores are formed due to the volatilization of the pyrolyzing polymer. The preparation of ACFs by physical activation includes a controlled gasification of the CFs at temperatures between 800 and 1000°C with an oxidant gas, so that carbon atoms are removed selectively. The removal of the outer and less ordered carbon atoms leads to the creation of new micropores and/or the widening of their size, which results in an increase in their pore volume. Thus, for a given precursor, the pore size distribution in the ACF depends on the preparation conditions (mainly temperature, time, and gas flow), the activating agent used, and the presence ofcatalysts. Some representative examples of the influence of the experimental conditions mentioned earlier can be found elsewhere [2, 11-21]. In order to have an efficient activation process, the reaction must take place inside the CFs, at least, predominantly compared with the reaction occurring outside. If there exists only external reaction, the obtained material does not develop porosity. However, if the reaction occurs inside the fiber, there is porosity development: the higher the amount of carbon removed, the higher the porosity development.

Chapter 17 Adsorption on Activated Carbon Fibers

434

Carbon dioxide and steam are the activating agents most commonly used, whose reactions with carbon are endothermic. These gases react with the carbon atoms in the precursor according to the following reactions: C + CO 2

*+

2CO

LliH

= 159.0kJjmol

Although the activation with carbon dioxide or steam produces essentially microporous ACFs, strong differences have been found between these two activating agents regarding the porous texture and the mechanical properties of the ACFs [12, 13]. The addition of metals such as cobalt, silver, rare earth metals, or platinum either to the starting pitch (followed by spinning, stabilization, and carbonization) or to the CF, followed by gasification with steam, allows the preparation of ACFs with significant mesoporosity [14-19, 21]. The chemical activation process consists of mixing a carbonaceous precursor with a chemical activating agent, followed by a pyrolysis stage [22-25]. The material after this stage is richer in carbon content and presents a much ordered structure and, after the thermal treatment and the removal of the activating agent, has a well-developed porous structure. Different compounds can be used for the activation; among them, KOH, NaOH, H 3 P0 4 , and ZnCl2 have been reported in the literature [22-25]. The chemical activation presents advantages over the physical one that can be summarized as follows: (i) the chemical activation uses lower temperatures and pyrolysis time, (ii) it usually consists of one stage, (iii) the yields obtained are higher, (iv) it produces highly microporous ACs and (v) it is a suitable method for applying to materials with a high ash content [23-25]. On the other hand, the chemical activation presents disadvantages such as the need of a washing stage after the pyrolysis and the corrosiveness of the chemical agents used. Although the work done on physical activation of CFs is wide, the research on chemical activation of CFs is scarce and mainly corresponds to the use of lalkaline hydroxides as activating agents [26, 27]. The chemical activation must be done under well-controlled experimental conditions in order not to destroy the fiber shape. The resulting ACFs are essentially microporous materials (i.e., pore size below 2 nm) although differences exist depending on the activating agent used and the starting CF. In the activation by hydroxide, the main variables affecting the final porous texture are hydroxide/carbon ratio, heating rate, temperature, and time ofpyrolysis. Moreover, there are two additional parameters that have recently been r~ported [24,25]: nitrogen flow rate and the washing stage (washing with water or washing with hydrochloric acid), which have an important role in porosity development. Figures 17.1 and 17.2 contain N 2 adsorption isotherms of ACFs prepared by physical and chemical activations, as examples of the results that can be

17.2

Preparation of ACFs

435

60 - - - - - - - - - - - - - - - - - - - ,

50 40 ~ (5

E E

30 20 10 o.a..--------r----r--~-....-__._-__r_-,.______r-__l

o

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

P/PO

Figure 17.1 N 2 adsorption isotherms for chemically activated samples.

60 - . - - - - - - - - - - - - - - - - - - - - - ,

50

94% burn-off

40 ~ (5

E E

30

20

o.....--,....--~----r---_r__,r__~-___r__-_r___,r---"___l

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

P/PO

Figure 17.2 N 2 adsorption isotherms for samples activated by CO 2 •

obtained [27]. The isotherms are of type I in all the cases and very high adsorption capacities (BET [stands for Brunauer, Teller, and Teller] surface areas close to 3000 m 2 I g) and very high micropore volumes (close to 1 mll g) can be reached. Only at high porosity development, the knee of the isotherms becomes wide, indicating the presence of supermicroporosity (i.e., pore size between 0.7 and 2nm) and narrow mesoporosity (i.e., between 2 and 7nm). We can see that chemical activation allows to noticeably overpass the maximum adsorption capacity reached by physical activation.

Chapter 17 Adsorption on Activated Carbon Fibers

In summary, as it happens with granular and powder carbons, a proper selection of the CF and the activation method and experimental conditions permits the preparation of ACFs with a tailored pore size distribution, with the additional advantage of their fiber shape and small diameters that allow faster mass transfer rates when compared with conventional ACs.

17.3

CHARACTERIZATION OF ACFs

Because the ACFs are porous carbons that have no significant differences compared with other porous carbons, the techniques used for their characterization are almost the same. Since the porosity in carbons is the responsible for their adsorption properties, the analysis of the different types of pores (size and shape), as well as the pore size distribution, is very important to foresee the behavior of these porous solids in final applications. We can state that the complete characterization of the porous carbons is complex and needs a combination of techniques, due to the heterogeneity in the chemistry and structure of these materials. There exist several techniques for the analysis of the porous structure, from which we can underline physical adsorption of gases, mercury porosimetry, small-angle neutron and X-ray scattering (SANS and SAXS), transmission and scanning electron microscopy (TEM and SEM), scanning tunnel microscopy (STM), immersion calorimetry, etc. Regarding the evaluation of porosity of ACs, physical adsorption of gases is, undoubtedly, the most widely used technique [28]. Different adsorptives, such as N 2 , CO 2 , Ar, He, CH 4 , benzene, and nonane, can be used for this purpose [28-39]. Due to the considerable sensitivity of nitrogen adsorption isotherms to the pore structure in both microporous and mesoporous regimes and to its relative experimental simplicity of the pore structure, measurements of subcritical nitrogen adsorption at 77 K are the most used. However, the main disadvantage of N 2 adsorption at 77 K is that when it is used for the characterization of microporous solids, diffusional problems of the molecules inside the narrow microporosity (i.e., pore size below 0.7 nm) may occur [29, 33, 34, 37]. Moreover, there is an additional experimental difficulty in the adsorption of subcritical nitrogen because very low relative pressures (10- 8 -10- 4) are required to extend the range of porosity studied to the narrow microporosity, which requires more sophisticated and expensive adsorption equipments. To overcome these problems, the use of other adsorptives has been proposed [29-31, 33-35, 37-39]. It is important to note that gas adsorption is only sensitive to the open porosity, that is, the porosity that is accessible to the adsorptive used. Thus, there are pores that do not communicate with the surroundings; such pores are called "closed pores." The closed state depends on the probe size, particularly, in the case of gas adsorption. This closed porosity is not associated with the adsorption properties and permeability of the molecules but does affect the mechanical

17.3 Characterization of ACFs

437

properties and the density of the solid material, which is of special relevance to the case of ACFs. From the point of view of gas adsorption, which is the main objective of this chapter, there are no differences in the results obtained between the ACFs and the granular and powder ACs, except for the kinetics of gas adsorption due to the special pore structure of the ACF [2, 40, 41] and for the higher packing density that can be obtained with them due to their fiber shape [3]. In this way, although there are important differences in the pore structure and distribution of porosity among the ACFs and the conventional ACs (this aspect will be described in a next section), the adsorption isotherms are not sensitive to them and do not allow to distinguish the shape of the porous carbons (i.e., fiber, granular, powder, monolith). As an example of the above statement, Fig. 17.3 contains the N 2 adsorption isotherms for powder AC with different adsorption capacities [3]. These isotherms, compared with those in Figs. 17.1 and 17.2, clearly demonstrate that the adsorption isotherms do not permit neither to distinguish the ACF from the AC nor to deduce differences in the pore size distribution. However, the unique fiber shape and porous structure of the ACF are advantages that permit to deepen into the fundamentals of adsorption in microporous solids [31]. ACFs are essentially microporous materials [13, 31], with slit-shaped pores and a quite uniform pore size distribution [42, 43]. Thus, they have simpler structures than ordinary granulated ACs [31] and can be considered as model microporous carbon materials. For this reason, important contributions to the understanding of adsorption in microporous solids for the assessment ofpore size distribution have been made using ACF [31,33,34,39, 42-46], which merit to be reviewed.

50 , - - - - - - - - - - - - - - - - - - - - - - - - ,

40

~

30

C\I

Z

(5

~

20

10

O __--r----.----~-___r__-~-___r__-_r_-___r_-~-___l o 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

P/Po

Figure 17.3 N 2 adsorption isotherms for granular and powder activated carbon samples.

Chapter 17 Adsorption on Activated Carbon Fibers

In this sense, we will discuss first the usefulness of ACFs to understand micropore characterization from gas adsorption and, after that, we will focus on the latest contributions to the research on the activation-pore structure relationship for ACFs. The knowledge on the latter aspect is essential for its implication on future development of applications for the ACFs.

17.3.1 Adsorption on the ACF and Its Usefulness to Understand Micropore Characterization Due to the small size of the micropores (i.e., size below 2 nm), adsorbate filling at low relative pressures may occur. The presence of micropores in ACFs, and in most of the ACs, causes that most of the adsorption takes place within them and, at least, 90 % of the total surface area corresponds to micropores. The adsorption in microporosity is not so well understood and simple to interpret as for adsorption in mesopores or nonporous solids, which has led to an important research effort since more than 50 years ago, trying to establish experimental methods and refined models useful to explain adsorption in micropores (i.e., assessment of micropore volume and micropore size distribution [28, 35, 36, 47-49]. When the pore size is similar to the size of the adsorbate molecule and the adsorption temperature is below the critical temperature, a number of peculiarities occur that should be emphasized [50]: (i) The equilibrium time for the adsorption may be extremely long, what may be a source of error for the evaluation of microporosity. For example, this occurs for N 2 at 77 K in samples with narrow microporosity (size below 0.7 nm). When the size of the molecule is similar to the size of the pore, the activation energies for passing the molecules through the pore entrance and for the diffusion of the molecules inside the micropores can make the kinetics of adsorption very slow and a temperature-dependent process. (ii) The interaction energy between a free surface of a solid and an adsorbate molecule is rather lower than in a micropore, as a consequence of the overlap of the adsorption potential from neighboring walls. This overlap leads to a strong adsorption of the gas by the micropore and, then, to an enhancement of the heat of adsorption. (iii) The adsorption process in the micropores occurs by a volume filling mechanism rather than a surface coverage mechanism. Then, the amount adsorbed for different adsorptives (expressed as volume of liquid) at a relative pressure near unity is very similar. (iv) Surface areas ofsome well-developed ACs are unrealistically high, compared with the calculated for 1 g of carbon in the form of an extended graphite layer plane, counting both sides (2630 m 2 / g).

The first point presented above, i.e., the diffusional limitations of N 2 adsorption at 77 K, is extremely important considering that it is the most widely used adsorptive for the characterization of the porous materials, which can lead to

17.3 Characterization of ACFs

439

misinterpretations. One material that without doubt shows the unsuitability of N 2 adsorption is the CMS used for the separation of N 2 /0 2 or CH 4 /C0 2 and hence with a microporosity in the size of 0.3-0.4 nm. As an example, CF without any activation treatment does not give N 2 adsorption at 77 K but exhibits a quite fast CO 2 adsorption at temperatures above 298 K and an increasing methane uptake with increasing adsorption temperature [51]. This reflects that it is an activated process extremely sensitive to the temperature and the molecule size (0.33 and 0.38 nm for CO 2 and CH 4 , respectively [52]). Some additional examples of CMSs are collected in the following data that include the micropore volume deduced from CO 2 adsorption, measured in our laboratory, for non-activated carbon fibers obtained from different precursors (i.e., carbon fibers from coal tar pitch and from petroleum pitch). It must be noted that the N 2 adsorption is negligible for all of them, but V(C0 2 ) (ml/g) =0.18, 0.25, 0.19, and 0.05. These examples show that their microporosity cannot be evaluated through N 2 adsorption at 77 K. Consequently, this strong limitation (that occurs not only on CMSs but also on ACFs with low activation degrees - see below) needs to be solved. Two approaches can be considered taking into account the two experimental variables mentioned above, i.e., molecule size and temperature: (i) the use of an smaller size adsorbate making the adsorption at the boiling temperature and (ii) the use ofan adsorbate at temperatures higher than the boiling point; at these conditions, the kinetic energy of the molecules is increased and they can overcome the activation energy for diffusion within the porosity. He adsorption at 4.2 K has been proposed [30, 31, 38] as a promising method for the accurate determination ofmicroporosity. A He atom is the smallest atom; it has a spherical shape and interacts weakly with any solid surface [30]. He adsorption requires lower equilibrium times and the amount adsorbed is higher than in the case of N 2 at 77 K. From this research the authors concluded that the micropore analysis by N 2 adsorption at 77 K is insufficient and may give misleading conclusions [30]. In spite of the interesting results obtained with He, the experimental conditions used (adsorption at 4.2 K) make this technique not available for routine characterization of microporous solids. CO 2 adsorption, either at 273 or at 298 K [29, 33-37, 39, 49, 50], is another useful alternative for the assessment of the narrow microporosity. In such case, though the critical dimension of the CO 2 molecule is similar to that of N 2 , the higher temperature of adsorption used for CO 2 results in a larger kinetic energy of the molecules, which are able to enter into the narrow porosity. In this way, CO 2 adsorption has demonstrated that CO 2 is an appropriate complementary adsorptive for the analysis of the microporosity [37]. In the following, the usefulness of CO 2 adsorption at 273 K to achieve a rather complete characterization of the porous texture of microporous carbons will be discussed. We will base our study on the results already published [33-35, 37] in which samples with different characteristics were used and CO 2 adsorption experiments at high pressures (up to 4 MPa) were performed. In this study, the ACFs with different contents of microporosity have been very useful. The use

440

Chapter 17 Adsorption on Activated Carbon Fibers

of high pressures also was of utmost importance as it permitted the comparison of both N 2 and CO 2 adsorptions at comparable relative pressures. Since N 2 adsorption is done at 77 K and CO 2 at 273 or 298 K, the experiments cannot be directly compared, which introduces strong concerns about the similarities and differences among both adsorptives. Thus, a better way to compare the two experiments is to plot the characteristic curves [33-35, 37]. These characteristic curves, obtained applying the Dubinin-Radushkevich (DR) equation [47] to the adsorption isotherms, are the plot of the logarithm of the volume ofliquid adsorbed versus the square of the adsorption potential corrected for the affinity coefficient ((3) of the adsorptive ((AI (3)2 = (R TIn ifo If) I (3)2, T being the temperature, f the fugacity, and 10 the saturation fugacity). Figure 17.4 contains the characteristic curve for N 2 adsorption at 77 K, calculated from an adsorption isotherm within the usual relative pressure range of 10-3 - 1, and the characteristic curve for CO 2 adsorption at 273 K, deduced from the isotherm done at subatmospheric pressures. The figure shows that both characteristic curves have a similar shape and could overlap, but there is a gap of adsorption potential that is not covered with these adsorption experiments. To cover this gap and, consequently, to demonstrate that the adsorption mechanism for both adsorptives is similar, there are two possibilities. The first one is to use high pressures for CO 2 trying to cover a higher range of relative fugacities, which will allow us to analyze the whole range of porosity and the peculiarities

(AI(3)2 (kJ/mol)2 200 400 600 800 1000 1200 1400 1600 1800 2000 0+---+-----+-----+-----1--+----+----+-----+------+------1

o

o

(Alf3)2

100

200

300

400

500

-0.5 -0.5 -1

-1.5

~

:5

~

E-1.5~~

-2 -2.5 -3 -3.5 -4

Figure 17.4 Characteristic curves for an activated carbon fiber (ACF) that includes the N 2 adsorption data at 77 K (relative pressure from 10-3 to 1) (0) and the CO 2 adsorption data at 273 K at subatmospheric pressures (.).

17.3 Characterization of ACFs

44 1

(AI(3)2 (kJ/mol)2

o

o

200

800

600

400

1000

o

1200

1400

1600

(A/j3)2 200 300

100

400

1800

2000

500

-0.5 -0.5 -1

-1.5

5:' of:

s:

c- -1.5 O"'''2!-~ ............. '"n, '- ...........

-2

-..........,.......

....... '

-2.5

-3

-2.5

............ .....................

..

"--"'"-,,

, -,

........-

................

-3.5

......... , ........

.

.........

.................

......IiI...

-4-&...-------------------------1 Figure 17.5 Characteristic curves for an activated carbon fiber (ACF) that includes the N 2 adsorption data at 77 K (relative pressure from 10-3 to 1) (0), the CO 2 adsorption data at 273 K at subatmospheric pressures (.) and the CO 2 adsorption isotherm at high pressures (Li).

of CO 2 adsorption at temperatures higher than the boiling temperature (but below the critical temperature). Figure 17.5 contains the same characteristic curve presented in Fig. 17.4, but now it includes the data obtained at high CO 2 adsorption pressures. The figure clearly shows that the N 2 characteristic curve superimposes over the CO 2 one. This indicates that there is a large similarity in the mechanism by which these two gases are adsorbed in the different ranges of porosity. This characteristic curve (shown as an example by many others [33-35,37, 50]) allows us to state that CO 2 adsorption at 273 K provides similar information as adsorption of N 2 at 77 K. The second possibility to cover the gap in the characteristic curves shown in Fig. 17.4 is to use lower relative pressures for N 2 adsorption (i.e., below 10-3 and up to 10-7 ). Thus, a series of ACFs with different degrees of activation, and consequently with different degrees of microporosity, will be discussed next. In the case of an ACF (see Fig. 17.6) with very narrow microporosity, the characteristic curve for N 2 at 77 K remains always below that for CO 2 , in agreement with the kinetically restricted adsorption for N 2 in these types ofsamples. We can see that the amount of N 2 adsorbed is lower than that of CO 2 in all the relative pressure range studied. In the case of an ACF with a higher degree of burn-off (see Fig. 17.7), the characteristic curve for N 2 superimposes over that for CO 2 up to a value of (AI (3)2 higher than about 400 (k]/mol) 2. From this value on, a large deviation downward occurs. This behavior has been observed with other microporous carbon materials and, in fact, it is a common problematic feature

44 2

Chapter 17 Adsorption on Activated Carbon Fibers

(AI(3)2 (kJ/mol)2 0

0

500

1000

1500

2000

2500

3000

-2

-4

5:' ~

-6

-8

-10

-12

Figure 17.6 Characteristic curves for sample CFC14: (.) CO 2 adsorption at subatmospheric pressures; (A) CO 2 at high pressures; (~) N 2 at 77 K. (Reproduced with permission from Ref. [33]. Copyright 1996 American Chemical Society.) (AI(3)2 (kJ/mol)2 500

1000

1500

2000

2500

3000

3500

-2

-4

> ~ -6 -8

-10

-12 .......- - - - - - - - - - - - - - - - - - - - - - -

Figure 17.7 Characteristic curves for sample CFSSO: (.) CO 2 adsorption at subatmospheric pressures; (A) CO 2 at high pressures; (~) N 2 at 77 K. (Reproduced with permission from Ref. [33]. Copyright 1996 American Chemical Society.)

of the characteristic curves for N 2 adsorption in microporous carbons and hence a limitation of its use in such low relative pressures (i.e., from 10- 3 to 10- 7 ). The limitations of N 2 to characterize materials with narrow microporosity are reinforced in the next example. Figure 17.8 [33] contains a magnification

443

17.3 Characterization of ACFs

(A/~)2 (kJ/mol)2

200

o

300

400

500

600

-2 .........--..

-6

-8..1..-------------------.. . . Figure 17.8 Characteristic curves for samples CFC14, CFC40, and CFSSO in the (A/~)2 range of 200-600 (k]/mol)2 for the N 2 adsorption isotherm at 77 K. (Reproduced with permission from Re£ [33]. Copyright 1996 American Chemical Society.)

of the characteristic curve for N 2 for ACFs with different degrees of burnoff The adsorption potential, (AI (3)2, at which the large deviation downward starts depends on the burn-off of the sample as it is clearly shown in Fig. 17.8. These deviations that happen at adsorption potentials (A/~)2 between 250 and 400 (k]/mol)2 (i.e., at relative pressures of N 2 lower than 10- 5 for the sample with a 50 % burn-off [BO] for CFS50- and lower than 10- 4 for the sample with a 14 % BO for CFC14) show that N 2 adsorption in the narrow microporosity is influenced by diffusional limitations. With increasing burn-of£ the porosity widens, the accessibility ofN2 increases, and hence the relative pressure at which N 2 can enter into the porosity decreases. It must be noted that the large deviation downward has also been related by other authors to a change in the adsorption mechanism at very low relative pressures [53]. Usually, many researchers calculate the pore size distribution from the adsorption isotherms applying a model, which accounts for the heterogeneity of the pore size distribution. Thus, the general adsorption isotherm [54] is used in which different pore size distribution functions and local adsorption isotherms can be used. If the DR or Dubinin-Astakhov (DA) equations are used and a Gaussian distribution of micropores is assumed, simple equations are obtained which may show, at least semiquantitatively, the pore size distribution. This can be a direct and simple way to compare the two adsorptives analyzed (i.e., N 2 and CO 2). If the pore size distributions obtained from the two adsorptives are similar, the commented similarities between CO 2 and N 2 should be reinforced. Figure 17.9 presents the pore size distributions obtained for the sample with the widest micropore distribution (sample CFS50, Fig. 17.7), applying the DubininStoeckli (DS) equation [28] to the CO 2 and N 2 data. It must be remembered that because the high-pressure CO 2 adsorption data provide information for the whole range of relative fugacities, this type of calculations and comparisons are

444

Chapter 17 Adsorption on Activated Carbon Fibers

o

2

3

4

L (nm)

Figure 17.9 Pore size distributions obtained for the sample CFSSO applying the DubininStoeckli (DS) equation to the CO 2 and N 2 adsorption data.

straightforward. Figure 17.9 shows that there is a good concordance between both distributions, confirming the validity of CO 2 to characterize the microporosity and its reliability at subatmospheric pressures to characterize the narrow microporosity. The mean pore size for the CO 2 distribution is somewhat smaller than for N 2 , which can be a consequence of the downward deviation observed for the characteristic curves for N 2. These results obtained with ACFs are important for their relevance in the use of N 2 adsorption in the characterization of porosity. To "measure" the narrow microporosity with N 2 at 77 K, low relative pressures (i.e., from 10-4 to 10-7 , i.e., high adsorption potentials) must be used. These low relative pressures need more sophisticated and expensive adsorption equipments and cannot be reached with conventional ones. Additionally, as a consequence ofthe diffusional limitations, N 2 adsorption at 77 K cannot be used to determine the micropore volume of the narrowest porosity. All this makes necessary the use of other adsorptives to analyze this range of porosity. The research done shows that He adsorption at 4.2 K [30, 31, 38] or CO 2 adsorption at 273 K at subatmospheric pressures [33-35, 37, 50] can be used for this purpose, although the second one is more convenient from an experimental point of view. In fact, because the adsorption temperature used for CO 2 adsorption is 273 K, the saturation pressure for this gas is high and, hence, the relative pressures are low (about 10-4). These low relative pressures can be easily reached with conventional equipments working up to 0.1 MPa, avoiding also the additional diffusional limitations that happen with N 2 •

17.3.2 Understanding the Activation-Pore Structure Relationship of ACFs: Effect of Activating Agent and Burn-Off Degree An additional issue of special relevance for the characterization of the ACFs is their fiber shape, since it introduces differences on the porous texture

17.3 Characterization of ACFs

445

compared with the conventional ACs. In fact, it is not only important to determine the pore volume and pore size distribution of the ACF, but also the distribution of the pores across the fiber diameter, which will be a result of the activation process (i.e., activation temperature, activating agent, and CF used). Although a remarkable effort has been done on the porosity analysis and structural characterization of the ACF [55-57], the research on pore distribution within the fibers is scarce and very recent [58-60]. We have dedicated an important effort to analyze the development ofporosity in isotropic pitch-based CFs [13, 58-63]. The previous studies showed that the ACFs had a different evolution of porous structure with burn-off depending on the activating gas used (steam and CO 2 ) [13, 61-63]. From the N 2 and CO 2 adsorption data at 77 and 273 K, respectively, and the measurements of tensile strength and fiber diameter [13], it was shown that CO 2 essentially develops narrow microporosity (size lower than 0.7 nm) and causes a steady decrease in the tensile strength with burn-o~ while the fiber diameter does not change significantly. In comparison, steam activation results in a wider pore size distribution and, after the initial stages of the activation, the tensile strength remains nearly constant and the fiber diameter decreases. From these results, we speculated that CO 2 activation deepens into the bulk of the fiber, whereas steam mainly focuses the activation in the external parts. The confirmation of this interpretation can only be carried out analyzing the porosity development across the fiber diameter, on a single CF, using a technique with a lateral resolution of some micrometers. SAXS can be a useful technique for this purpose, provided that a micrometersize beam with a sufficient intensity is available. It must be noted that SAXS technique gives information about the structure of matter on a micro- and mesoscopic scale; then, SAXS can be used to characterize the porosity of ACs in a size range from few angstrom to about 2000 A. The use of this technique for that purpose is becoming more important, as reflected in the considerable number of papers published on this subject [62, 64-73]. This growing use is due to the fact that, unlike gas adsorption techniques, the SAXS intensity profile is also sensitive to the shape and orientation of the scattering objects so that additional information can be obtained. The availability at ESRF of X-ray microbeams with sizes down to less than 2 f.,Lm (Microfocus Beamline, ID13), together with a position-resolved X-ray scattering method makes the technique named as f.,L-SAXS suitable for analyzing single fibers [74, 75]. Experiments demonstrating the successful use of this technique in fibrous materials were carried out, e.g. on cellulose [74, 75] and CFs [76]. In the work carried out with CFs [76] the internal structure of single CFs from different precursors (PAN-based fiber and mesophase-pitch based fibers) was investigated. In this way, we have applied for the first time the f.,L-SAXS technique to the characterization of a single ACF and we have shown the usefulness of the technique to measure a single ACF and to get positionresolved information on the pore distribution across the fiber diameter [58-60]. In the following, main conclusions obtained will be briefly reviewed.

446

Chapter 17 Adsorption on Activated Carbon Fibers

(a)

(b)

1.E-2

0.1

(c)

10 Intensity

100

1000

Figure 17.10 Two-dimensional scattering patterns corresponding to (from left to right): (a) CF, (b) CFC29, and (c) CFC50. (Reproduced with permission from Re£ [58]. Copyright 2002 Elsevier Science Ltd.)

Figure 17.10 presents the two-dimensional scattering patterns corresponding to the original CF and ACF with two degrees of activation (samples CFC29 and CFC50), once the background has been subtracted. Samples CFC29 and CFC50 are ACFs prepared by CO 2 activation up to 29 and 50 % burn-off: respectively. These two-dimensional scattering patterns have been plotted for a maximum value of scattering vector (q = 41T sin(8)jA.) of 10 nm- 1 and correspond to measurements performed in the center of the fibers. This figure shows that the original CF, which cannot be characterized by N 2 adsorption, has some scattering, which is low, as it corresponds to its low micropore volume determined by CO 2 adsorption at 273 K (V = 0.18 ml/g). The comparison of the scattering pattern of the original CF (Fig. 17.10(a)) and the ACFs (Fig. 17.10(b) and (c)) shows that the scattering intensity increases with the bum-off degree, which agrees with gas adsorption results. These measurements clearly show the usefulness of the technique for the characterization of single fibers, even though they can have low porosity (which is the case of the original CF). Once the suitability of f..L-SAXS technique for the characterization of the porous texture of a single CF is demonstrated, the next step is to use the microscopic position resolution of this technique for characterizing the porosity development across the fiber diameter for CO 2 -and steam-activated CFs. Thus, the second series of experiments carried out in this work consisted in obtaining the scattering measurements in different regions of the same fiber, across the fiber diameter. From the scattering results, the Porod invariant (PI), which is a parameter related with the porosity development, was estimated for each scattering measurement [77]. From these calculations, the pore distribution across the fiber diameter could be deduced. The results showed that the scattering profiles, as a

17.4 Some Examples of ACF Applications

447

function of the position of the fibers, are different for CO 2-and steam-activated materials. In the case of steam, the scattering from all the internal zones is very similar and much lower than from the external part of the fiber. On the other hand, in the case of CO 2, the porosity is much more developed in the center compared with the steam-activated CFs. All the J.1-SAXS results indicate that CO 2 activation produces a more extensive porosity development across the fiber diameter than steam that focuses in the external zone of the fibers, which agrees with the decrease in fiber diameter for steam activation compared with CO 2 [13]. This means that CO 2 molecules penetrate more easily than H 20 into the carbon matrix. These results, obtained due to the fiber shape, provide the first direct proof of the different behavior of CO 2 and steam as activating agents and of the different pore distribution that produces the activation with these gases.

17.4

SOME ExAMPLES OF ACF ApPLICATIONS

Since the applications of porous carbons are treated in detail in Part IV of this book, in this section we will provide a list of applications trying to emphasize the advantages of the ACF over the conventional AC. There are a large number of applications in which the performance of the ACF has been extensively analyzed. They range from conventional gas-and liquid-phase adsorption to antibacterial and energy storage uses. Anon, we will mention some of them:

(i) Gas-phase adsorption: The use of ACFs for gas-phase adsorption has been extensively studied since it is one of the main uses of ACs. The advantage of the ACF over the conventional AC is a consequence of their porous structure. As we have already mentioned, the microporous ACFs essentially contain microporosity that is readily available to the adsorbate, and the mass transfer limitations due to the diffusion within meso-and macroporosity are absent [1, 2], making the adsorption process faster. Moreover, the ACFs avoid the settling and channeling effects of the ACs [1,2]. Consequently, a large number of works on the use of ACFs for gas-phase adsorption can be found. As an example we can mention the adsorption of gases such as S02 [78,79], NO x [80, 81], and VOC [2,41]. (ii) Liquid-phase adsorption: Liquid-phase adsorption on ACFs has similar advantages as gas-phase adsorption and their use for drinking water treatment and removal of organic compounds is well documented [2, 40, 41]. Essentially, the main advantage is the faster adsorption rate when compared with the AC. (iii) Carbon molecular sieves (CMSs): CFs and ACFs have been studied for the preparation and use as CMSs for the separation of gases such as C0 2 /CH 4

448

(iv)

(v)

(vi)

(vii)

Chapter 17 Adsorption on Activated Carbon Fibers

and Nz/O z [51, 82-84]. It was shown that the narrow microporosity of the nonactivated CF can be useful for this application and that the porosity of the ACF can be tailored by cracking of hydrocarbons to develop good quality CMSs. Antibacterial use of ACFs: Related to water treatment, Oya and coworkers developed for the first time antibacterial ACF consisting on Ag-containing samples [15-18]. ACFs as catalyst and catalyst support: There are interesting examples on the use of ACFs as catalyst and catalyst support [85-88]. The use of ACFs for this purpose is a consequence of the application of carbon materials in catalysis for decades [89]. The versatility of the carbon materials (i.e., porosity and surface chemistry), together with the special properties of the ACF, makes these materials rather interesting, and the number of papers on this subject has increased considerably since 1997. An interesting example is the oxidation of SOz to H zS0 4 by Oz and in the presence of water [85, 88]. ACF as catalyst support of different metal catalysts was studied analyzing the influence of the catalyst dispersion and activity (i.e., Refs [87] and [88]). Gas storage (CH 4 and Hz): The storage of gases such as methane and hydrogen is of special interest for their use as fuel in conventional applications. They both have considerable advantages from an environmental point of view. The main limitation for the use of these gases is their storage in the onboard fuel tank with a sufficiently high energy density. One possibility is the storage of these gases in carbon materials, which is a subject of strong research effort. The research is much more advanced in the case of methane [3, 90]. The use of porous carbons for vehicular fuel and for large-scale transportation of methane is a consequence of the enhanced adsorption of this gas within the microporosity. The advantage of the ACFs over ACs is their essentially microporous character and higher packing density, although the larger price of the ACF is detrimental [3, 90]. In the case of Hz, the limitation is much stronger than with methane due to its very low boiling point. The work done on adsorption of Hz in ACFs and ACs, shows that the highest values of hydrogen adsorption are close to 1 wt % at 10 MPa [91], a rather low value compared with the targeted 6.5 wt % value. Supercapacitors: The use of ACFs (mesoporous and microporous ACFs) as supercapacitors has been reported elsewhere [92]. The interest of mesoporosity instead ofmicroporosity for this application in propylene carbonate electrolytes (i.e., non-aqueous electrolytes) is a consequence of the size of the ions that cannot enter into the narrowest microporosity. Then, all the available surface is not used for the double-layer formation resulting in a lower capacitance (EDLC) than expected from the apparent surface area of the porous carbon. Additionally, the role of the surface chemistry on the EDLC is very important for this application.

References

17.5

449

CONCLUSIONS

ACFs are fibrous microporous carbons that can easily be activated, rendering adsorbents with high adsorption capacities and high surface areas, as happens with classical ACs. Although their adsorption behavior does not differ from other forms of microporous carbons, their fiber shape allows to get better performance in some applications. For this reason, ACFs can be considered, in relation to the classical ACs, as a new and more powerful generation of microporous carbons. The microporosity of ACFs, as also happens with other forms of ACs, is responsible for most of their applications (i.e., volatile organic compound [VOC] removal, gas separation, methane and hydrogen storage). For some of the abovementioned applications, narrow microporosity (micropore < 0.7 nm) is a key factor to understand their behavior, to enhance their performance and applications and to improve their preparation process. Consequently, the microporosity and particularly the narrow microporosity need a correct characterization microporosity that has to be done by using physical adsorption. N 2 at 77 K is the adsorptive most widely used. However, for CFs and ACFs (with low degree of activations) that have CMS properties, N 2 at low relative pressures and low adsorption temperature (77 K) is worthless because it presents diffusional adsorption problems, and hence a lack of adsorption equilibrium, in narrow mlcropores. CO 2 at 273 K is a useful adsorptive that has an adsorption mechanism quite similar to N 2 (confirmed by the high-pressure adsorption data). Its use is strongly recommended as a complement to N 2 at 77 K to perform a correct characterization of the microporosity.

ACKNOWLEDGMENTS The authors thank MCYT (Proj. PPQ2003-03884) for financial support.

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45 2

Chapter 17 Adsorption on Activated Carbon Fibers

41. Brasquet, C. and Le Cloirec, P. (1997). Adsorption onto activated carbon fibers: application to water and air treatments. Carbon, 35, 1307-13. 42. Kaneko, K., Shimizu, K., and Suzuki, T. (1992). Intrapore field-dependent micropore filling of supercritical N 2 in slit-shaped micropores.]. Chem. Phys., 97, 8705-11. 43. Matsumoto, A., Kaneko, K., and Ramsey,J.D.F. (1993). Neutron scattering investigations of the structure and adsorption properties of activated carbon fibers. Stud. Surf. Sci. Catal., 80, 405-12. 44. Kobayashi, N., Enoki, T., Ishii, C., et al. (1998). Gas adsorption effects on structural and electrical properties of activated carbon fibers.]. Chem. Phys., 109, 1983-90. 45. Li, Z., Kruk, M.,Jaroniec, M., and Ryu, S.-K. (1998). Characterization ofstructural and surface properties of activated carbon fibers.]. Colloid Interface Sci., 204, 151-6. 46. Alcaniz-Monge, J., Linares-Solano, A., and Rand, B. (2001). Water adsorption on activated carbons: study of water adsorption in micro- and mesopores.]. Phys. Chem. B, 105, 7998-8006. 47. Dubinin, M.M. (1960). The potential theory of adsorption of gases and vapors for adsorbents with energetically non uniform surfaces. Chem. Rev., 60, 235-41. 48. Dubinin, M.M. (1966). Porous structure and adsorption properties of active carbons. In Chemistry and Physics of Carbon (P.L. Walker, ed.). Marcel Dekker, 51-120. 49. Ravikovitch, P.I., Vishnyakov, A., Russo, R., and Neimark, A.V. (2000). Unified approach to pore size characterization of microporous carbonaceous materials from N 2 , Ar, and CO 2 adsorption isotherms. Langmuir, 16, 2311-20. 50. Linares-Solano, A., Salinas-Martinez de Lecea, C., Alcaniz-Monge,J., and CazorlaAmoros, D. (1998). Further advances in the characterization of microporous carbons by physical adsorption of gases. Tanso, 185, 316-25. 51. de la Casa-Lillo, M.A., Alcaniz-Monge, J., Raymundo-Pinero, E., et al. (1998). Molecular sieve properties of general-purpose carbon fibres. Carbon, 36, 1353-60. 52. Breck, D.W. (1974). Zeolite Molecular Sieves. John Wiley, p. 636. 53. Ehrburger-Dolle, E. (1997). Analysis of the derived curves of adsorption isotherms. Langmuir, 13, 1189-98. 54. McEnaney, B., Mays, T.J., and Causton, P.D. (1987). Heterogeneous adsorption on microporous carbons. Langmuir, 3, 695-9. 55. Donnet, J.B., Qin, R.Y., Park, S.J., et al. (1993). Scanning tunneling microscopy study of activated carbon fibers. J. Mater. Sci., 28, 2950-4. 56. Huang, Z.H., Kang, F.Y., Huang, W.L., et al. (2002). Pore structure and fractal characteristics of activated carbon fibers characterized by using HRTEM.]. Colloid Interface Sci., 249, 453-7. 57. Nakayama, A., Suzuki, K., Enoki, T., et al. (1996). Electronic and magnetic properties of activated carbon fibers. Bull. Chem. Soc. ]pn., 69, 333-9. 58. Lozano-Castello, D., Raymundo-Pinero, E., Cazorla-Amoros, D., et al. (2002). Characterization of pore distribution in activated carbon fibers by microbeam small angle X-ray scattering. Carbon, 40, 2727-35. 59. Lozano-Castello, D., Raymundo-Pinero, E., Cazorla-Amoros, D., et al. (2002). Microbeam small angle X-ray scattering (f,.LSAXS): a novel technique for the characterization of activated carbon fibers. Stud. Surf. Sci. Catal., 144, 51-8. 60. Lozano-Castello, D., Cazorla-Amoros, D., and Linares-Solano, A. (2003). Microporous solid characterization: use of classical and "new" techniques. Chem. Eng. Technol., 26, 852-7.

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°

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Chapter 17 Adsorption on Activated Carbon Fibers

78. Raymundo-Pinero, E., Cazorla-Amoros, D., Salinas-Martinez de Lecea, C., and Linares-Solano, A. (2000). Factors controlling the S02 removal by porous carbons: relevance of the S02 oxidation step. Carbon, 38, 335-44. 79. Kisamori, S., Mochida, I., and Fujitsu, H. (1994). Roles of surface oxygen groups on poly(acrylonitrile)-based active-carbon fibers in S02 adsorption. Langmuir, 10, 1241-5. 80. Yang, C.M. and Kaneko, K. (2002). Nitrogen-doped activated carbon fiber as an applicant for NO adsorbent.]. Colloid Interface Sci., 255, 236-40. 81. Shirahama, N., Moon, S.H., Choi, K.H., et ai. (2002). Mechanistic study on adsorption and reduction ofN0 2 over activated carbon fibers. Carbon, 40, 2605-11. 82. Kawabuchi, Y., Kawano, S., and Mochida, I. (1996). Molecular sieving selectivity of active carbons and active carbon fibers improved by chemical vapour deposition of benzene. Carbon, 34, 711-17. 83. de la Casa-Lillo, M., Moore, B.C., Cazorla-Amoros, D., and Linares-Solano, A. (2002). Molecular sieve properties obtained by cracking of methane on activated carbon fibers. Carbon, 40, 2489-94. 84. Villar-Rodil, S., Martinez-Alonso, A., and Tascon, J.M.D. (2002). Carbon molecular sieves for air separation from Nomex aramid fibers.]. Colloid Interface Sci., 254, 414-6. 85. Mochida, I., Kuroda, K., Miyamoto, S., et ai. (1997). Remarkable catalytic activity of calcined pitch based activated carbon fiber for oxidative removal of S02 as aqueous H 2S0 4 , Energy Fuels, 11, 272-6. 86. Raymundo-Pinero, E., Cazorla-Amoros, D., and Linares-Solano, A. (2003). The role of different nitrogen functional groups on the removal of S02 from flue gases by N-doped activated carbon powders and fibres. Carbon, 41, 1925-32. 87. Macias-Perez, M.C., Salinas Martinez de Lecea, C., and Linares-Solano, A. (1997). Platinum supported on activated carbon cloths as catalyst for nitrobenzene hydrogenation. Appl. Catal. A Gen., 151,461-75. 88. de Miguel, S.R., Villella, J.I., Jablonski, E.L., et ai. (2002). Preparation of Pt catalysts supported on activated carbon felts (ACF). Appl. Catal. A Gen., 232, 237-46. 89. Radovic, L.R. and Rodriguez-Reinoso, F. (1997). Carbon materials in catalysis. Chern. Phys. Carbon, 25, 243-358. 90. Lozano-Castello, D., Alcaniz-Monge, J., de la Casa-Lillo, M., et al. (2002). Advances in the study of methane storage in porous carbonaceous materials. Fuel, 81, 1777-803. 91. de la Casa-Lillo, M., Lamari-Darkrim, F., Cazorla-Amoros, D., and Linares-Solano, A. (2002). Hydrogen storage in activated carbons and activated carbon fibers. ] Phys. Chern. B, 106, 10930-4. 92. Shiraishi, S. (2003). Polymer blend technique for designing carbon materials. In Carbon Alloys (E. Yasuda et aI., eds). Elsevier Science Publishers B.V., pp. 447-57.

OVERVIEW OF PHYSICAL ADSORPTION BY CARBONS Kenneth S.W. Sing Brunei University, Uxbridge, UK

Contents Introduction Physisorption on Nonporous Carbons 1.3 Physisorption by Porous Carbons 1.4 Concluding Remarks References

1.1

1.2

3 5 7 11 12

1.1 INTRODUCTION Physical adsorption (physisorption) phenomena were already well-known in the early years of the twentieth century, when various attempts were made to explain the underlying principles [1]. Some investigators followed Polanyi [2] in picturing the adsorbed state (the adsorbate) as a thick multimolecular film under the influence oflong-range forces emanating from the surface. Others were more strongly influenced by the monumental work of Langmuir [3] and considered that the adsorbate was normally in the form of a monolayer. A third approach, which was based on the application of the Kelvin equation, drew attention to the role of capillary condensation [4, 5]. The interest in physisorption was further strengthened in 1938 by the publication of the Brunauer-Emmett-Teller (BET) theory ofmultilayer adsorption [5, 6]. Over the past 50 years the BET theoretical model has been subjected to a considerable amount of criticism [7], but the BET method has remained the most popular procedure for determining the surface area ofadsorbents, catalysts, and various other porous and finely divided materials. Adsorption by Carbons

ISBN: 978-0-08-044464-2

© 2008 Elsevier Ltd.

All rights reserved.

3

4

Chapter 1 Overview of Physical Adsorption by Carbons

Langmuir had mentioned in his 1916 paper [3] that it was inconceivable that a well-defined monolayer could be formed in very narrow, molecular-sized pores of an activated carbon, but it was left to Dubinin [8, 9] to introduce the concept of "micropore filling." In his original theory of volume filling, Dubinin [8] adapted Polanyi's concept of the adsorption potential expressed as a temperatureinvariant characteristic curve. It was subsequently realized [7, 10, 11] that a physisorption isotherm of the typical "Langmuir" shape (now referred to as a Type I isotherm [10]), is generally associated with micropore filling and not monolayer coverage. It is also generally accepted that micropore filling is dependent on the overlap of adsorption forces [7] and should not be regarded as a form of capillary condensation since it does not involve the formation of a meniscus. Three groups of pores of different width, w, were defined by Dubinin [9]. The classification, which was adopted in a revised form by the IUPAC [10], is as follows: in micropores w<1"'V2 nm; in mesopores W 1"'V2-50 nm; in macropores W >1"'V50 nm. It also expedient [11] to subdivide the micropores into ultramicropores (w <1"'V1 nm) and supermicropores (w 1"'V1-2 nm). However, all these dimensions are somewhat arbitrary and imprecise because the stages of pore filling are dependent on the gas-solid system as well as the pore geometry [11]. Similarly, there is no precise definition of the currently popular term "nanopore," which is often applied to a pore in the supermicropore or narrow mesopore range. Highly porous carbons can be produced from a variety of natural and synthetic precursors [11, 12]. Relatively inexpensive activated carbons are useful adsorbents, but generally their surface and pore structures are exceedingly complex [11, 13]. However, it is now possible to prepare a number of more uniform carbonaceous adsorbents. For example, molecular sieve carbons (MSCs) are available with narrow distributions of ultramicropores, which exhibit welldefined molecular selectivity [11], and carbon nanotubes, aerogels, and membranes are also amongst the most interesting advanced materials for research and development [12, 14]. Carbon blacks with specific surface areas of up to 100 m 2 / g can be regarded as essentially nonporous [15] since they give reversible Type II isotherms in the IUPAC classification [10]. Early physisorption measurements on carbon blacks [1] were designed to test the validity of surface areas determined the BET method [6]. Carbon blacks were considered [5] to be especially suitable for this purpose because the discrete nature of their spheroidal particles allowed electron microscopy to be used for the evaluation of the particle size distribution. Certain well-characterized carbon blacks are still extremely useful as reference adsorbents [11, 16]. In its original state, the surface of a carbon black is energetically heterogeneous [15], but as discovered by Beebe et al. [17] the heterogeneity is considerably reduced by heat treatment in an inert atmosphere. As a result of this form of "graphitization," adsorption isotherms of the noble gases and lower hydrocarbons are transformed from Type II to Type VI in the IUPAC classification [10] - the latter having stepwise multilayer character [7, 11, 18]. By studying the energetics of adsorption of many polar and nonpolar molecules on highly I"'V

1.2

Physisorption on Nonporous Carbons

5

graphitized carbon blacks, Kiselev and his coworkers were able to confirm [19] that the gas-carbon interactions were essentially nonspecific (i.e., insensitive to the polar nature of the adsorptive molecule). In contrast, polar molecules (dipolar or quadrupolar) were found to undergo pronounced specific interactions with exposed hydroxyls or cationic sites on the surface of oxides and zeolites. In recent years various new experimental techniques and computerized procedures have become available for the determination and analysis of physisorption data. It is perhaps all the more surprising that some widely used methods are still based on old and over-simplified principles. This short overview is not intended to provide a critical survey of current research on gas adsorption by carbons and indeed the recent advances in research and development are amply described in the following chapters of this book. However, it is pertinent in this introductory overview to draw attention to some of the major obstacles, which have restricted progress and which now offer the opportunity for further research. The distinctive features of gas/carbon physisorption systems are also briefly compared with the adsorptive behavior of oxides and zeolites.

1.2 PHYSISORPTION ON NONPOROUS CARBONS As already indicated, a well-defined stepwise (Type VI) isotherm is obtained when a noble gas or lower hydrocarbon is adsorbed on a basal graphitic surface at an appropriate temperature [7, 11]. The regular steps can extend up to four or five molecular layers, but become less sharp with increased distance from the adsorbent surface. An increase in temperature also produces a progressive blurring of the layer-by-layer adsorption [7]. The appearance of such regular multilayer steps in isotherms on uniform surfaces supports the view that (a) the influence of the surface structure can extend well beyond the first adsorbed layer and (b) the multilayer steps are associated with a form oflocalized physisorption. Exfoliated graphite and graphitized carbon black are especially useful for studying monolayer structures and phase changes in the subrnonolayer region of physisorption isotherms [11, 18]. Small discontinuities may be due to a bimodal distribution of surface sites [18] or other abnormal effects [11], but on a uniform surface such substeps are associated with two-dimensional (2-D) phase changes [11]. These 2-D transitions on graphite can be clearly revealed and characterized by means ofadsorption energy [20] or heat capacity [21] measurements. There is no sign of any stepwise character in the reversible Type II isotherms of argon, krypton, and the lower hydrocarbons on ungraphitized carbons [11]. Similar Type II isotherms are also given by the adsorption of these nonpolar gases on most inorganic oxides - an exception being methane on the (100) face of MgO [11]. These results are of course consistent with the heterogeneous nature of ungraphitized carbon and oxide surfaces. Turning now to nitrogen adsorption at 77 K, we find that ungraphitized carbons, oxides and other nonporous adsorbents all give typical Type II isotherms 11

6

Chapter

1

Overview of Physical Adsorption by Carbons

and when they are normalized (or reduced to unit area) these isotherms are almost identical over a wide range of pipO. On the surface ofgraphitized carbons, however, nitrogen isotherms at 77 K are of "hybrid" shape. In the multilayer range above plpo rv 0.5 they have the characteristic Type II shape, but at lower plpo they are stepwise (a fairly sharp first layer step and a wavy second layer step). The fact that at 77 K the path of the nitrogen multilayer isotherm is rather insensitive to change in the adsorbent structure is of some practical importance. It is one reason why nitrogen adsorption is used for the assessment of the surface area and pore size distribution [7, 11]. When physisorption occurs on the heterogeneous surface of an ungraphitized carbon or an oxide, an increase in surface coverage is normally accompanied by a progressive decrease in the differential energy of adsorption [11, 21]. On the graphitized surface any initial decrease in adsorption energy is restricted to a region of very low surface coverage and thereafter the differential energy either remains almost constant or increases to a maximum at high surface coverage. In this respect, there is an interesting difference between the behavior of n-hexane and benzene [11]. In the case of hexane, the marked increase in adsorption energy is the result of fairly strong lateral interactions between the adsorbed molecules, whereas the almost constant adsorption energy given by benzene appears to indicate very little adsorbate-adsorbate interaction over a wide range of surface coverage [11, 21, 22]. Interpretation of the variation of differential adsorption energy with surface coverage may not always be straightforward. For example, a strong adsorbentadsorbate interaction may allow some compression of the monolayer resulting in repulsion rather than attraction between neighboring molecules [23]. Also, the almost constant differential adsorption energy may be due to compensation between the effect of surface heterogeneity and the attractive adsorbateadsorbate interactions [24]. In the case of adsorption on a uniform surface, Henry's law is to be expected at low surface coverage [11,22]. Unless the operational temperature is relatively high, the Henry's law region is normally restricted to a very small part of the isotherm (e.g., below plpo rvl x 10-4 ) and the deviations may be in either direction. From a fundamental standpoint, the virial analysis of low-coverage adsorption data is important since it is analogous to the treatment of imperfect gases and nonideal solutions [22]. Many different equations have been used to interpret monolayer-multilayer isotherms [7, 11, 18, 21, 22] (e.g., the equations associated with the names: Langmuir, Volmer, Hill-de Boer, Fowler-Guggenheim, Brunauer-EmmettTeller, and Frenkel-Halsey-Hill). Although these relations were originally based on adsorption models, they are generally applied to the experimental data in an empirical manner and they all have limitations of one sort or another [7, 10, 11]. The multilayer Frenkel-Halsey-Hill (FHH) equation is usually expressed in the following form: log

pO) k ( -p =n-r

(1.1)

1.3 Physisorption by Porous Carbons

7

where n is the amount adsorbed at the relative pressure pj pO and k and rare empirical constants [7, 22]. The FHH plots of log [log (p jpO)] vs log n are generally linear over a wide multilayer range (e.g., pjp°1'"'...l0.4-0.9). A characteristic value of r is obtained from the slope of the FHH plot. In the case of nitrogen adsorption at 77 K on nonporous carbons and silicas, the derived values of r are generally remarkably constant (r = 2.70), which confirms the almost "universal" character of the nitrogen multilayer [11]. Linear FHH multilayer plots are also given by other adsorptives such as butane, neopentane, methanol, dichloromethane, and benzene, but the corresponding values of r appear to be somewhat more variable [11, 25-28]. Recent fundamental studies of physisorption by nonporous carbons have involved the application of molecular simulation [23, 29], density functional theory, and lattice gas models [30]. Important aspects studied have included the way in which the molecular packing in each layer is likely to be affected by a systematic alteration of the lattice parameters and interaction energies and the resulting changes in the isotherm shape [21, 30].

1.3

PHYSISORPTION BY POROUS CARBONS

Activated carbons having BET areas well in excess of 1000 m 2 / g can easily be prepared by the carbonization and activation of a variety of precursors [11, 12]. By the carefully controlled carbonization and activation of uniform precursors (e.g., viscose rayon) under conditions of low burnoffit is possible to obtain ultramicroporous carbons having molecular sieve properties and giving high-affinity, reversible Type I isotherms [11] (designated Type la) with no detectable supermicroporosity or mesoporosity. Many activated carbons have complex nanoporous structures as revealed by the composite nature of their physisorption isotherms [11]. For example, hysteresis loops of Type H4 in the IUPAC classification [10] are usually obtained after extensive burnoff More uniform nanoporous and mesoporous carbons can be produced, however, by the application of special pretreatment and activation procedures [11, 12]. Certain carbon aerogels also give well-defined Type IV isotherms [14]. As already indicated, much of the pioneering work on micropore filling was carried out by Dubinin [8, 9]. The first version of the temperature-invariant "characteristic curve" for micropore filling was expressed in the exponential form (1.2)

where np is the micropore capacity, A is the "adsorption affinity," and E is a characteristic energy for the given system. From Eqn (1.2), we can easily

8

Chapter

1

Overview of Physical Adsorption by Carbons

arrive [7] at the well-known Dubinin-Radushkevich (DR) equation in its usual linear form

log(n)

= log (n

p) -

Dlog

2

(~)

(1.3)

where the constant D is related to E. Thus, the plot of log (n) against lo~ (po Ip) should be linear with slope D and intercept log (n p ). To obtain vp (the micropore volume) from np ' it is necessary to assume that the density of the adsorbate is the same as that of the liquid adsorptive at the operational temperature [11]. Ultramicroporous carbons generally give linear DR plots [7, 11] over wide ranges of pipO, but the extent of the linear region is much more restricted with most nanoporous carbons [11]. Also, DR plots on many nonporous and mesoporous carbons exhibit similar ranges of linearity [7]. Since D, E, and np are all empirical parameters, their significance is questionable. In consequence, it must be emphasized that the simple DR plot cannot always give a true assessment of the effective micropore volume [11]. The Dubinin-Astakhov (DA) equation, which was proposed as a more general characteristic curve equation [9], can be conveniently expressed in the form

.!!..- = exp np

[_(~) N] 13 Eo

(1.4)

where N is another empirical constant and E is replaced by f3E o (13 being a scaling factor). A limited amount of experimental evidence appears to confirm an inverse relation between Eo and the pore width, w, and also between Nand the extent of the pore size distribution (the extreme value of N = 3 being given by an ultramicroporous carbon molecular sieve). A complementary approach introduced by Stoeckli and his coworkers [31, 32] was based on the notion that the simple DR equation is invalid if the microporosity is heterogeneous. It was argued that the overall isotherm can be regarded as the sum of the DR isotherms corresponding to individual groups of micropores and that for a continuous distribution ofpore size the summation can be replaced by integration. A Gaussian pore size distribution was assumed and the integral transform was solved by the use of a mathematical device equivalent to an "error function." The mathematical elegance of Stoeckli's contribution is impressive, but it must be kept in mind that it does not allow for the effects of surface heterogeneity or changes in the various molecular interactions in controlling the different stages of pore filling [11]. In addition to the well-known monolayer equations already referred to (e.g., the Langmuir, Hill-de Boer and virial equations), there are others such as those associated with the names of Freundlich, Sips, and Toth, which have been applied to physisorption isotherms on microporous solids [11]. These relatively simple, empirical equations are useful for the interpolation and extrapolation of chemical engineering data, but they are not capable of throwing any new light

1.3 Physisorption by Porous Carbons

9

on the mechanisms of surface coverage or pore filling. As pointed out by various authors [7, 11, 18], the range of fit of a particular equation is not enough by itself to confirm the validity of the underlying theory. It follows that all derived quantities such as surface area and pore size require critical appraisal before their physical validity can be accepted [7, 10, 11]. Considerable interest has been shown in recent years in the presentation of physisorption isotherms in a generalized integral form. This kind of generalized treatment was first applied to the submonolayer region [21], but much of the current interest is centered on the analysis ofmicropore filling isotherms [33, 34]. In principle, the approach provides a means of constructing model isotherms by systematically combining hypothetical "local" isotherms and energy distribution functions. Thus, the generalized expression for the overall adsorption, n(p) can be written in the integral form

n(p) = no

f n*(p, E)f(E)dE

(1.5)

where no represents either the monolayer capacity or the micropore capacity, n*(p, E) is the local isotherm corresponding to the adsorption energy E, and f(E) is the distribution function for the adsorption energy. Although Eqn (1.4) can be derived from Eqn (1.5), it is not possible to arrive at an unambiguous interpretation of the energy distribution function without additional information since f (E) may be associated with surface heterogeneity and/or a micropore size distribution. Thus, for the filling of micropores an equivalent generalized expressIon IS

n(p)

= np

f n*(p, w)f(w)dw

(1.6)

where f (w) is now the micropore size distribution. Various empirical procedures, which can be used for the analysis ofphysisorption isotherms, are based on the comparison with standard adsorption data obtained on nonporous reference materials [7, 11]. These procedures have the advantage that they do not depend on any a priori assumptions concerning the mechanisms of adsorption or pore filling. The standard isotherm on the chemically similar reference adsorbent is plotted either as a multilayer thickness curve of t vs pipO or preferably in the reduced form of as vs pipO. The dimensionless quantity as is defined as nlns ' ns being the amount adsorbed at a preselected plpo (usually 0.4). The as plot is constructed by plotting n for the given nanoporous adsorbent against the corresponding as for the nonporous reference. Deviations from linearity can be attributed to the various stages of micropore or mesopore filling and, if certain conditions are satisfied, it is possible to derive approximate values of internal and external areas and ultramicropore and supermicropore volumes [11]. By analyzing the as plots of many adsorptives on various nanoporous carbons, Sing and his coworkers have obtained a considerable amount of experimental evidence [11, 35] to support the view [35] that the mechanisms of micropore filling are to a large extent dependent on the ratio of pore size:molecular

10

Chapter

1

Overview of Physical Adsorption by Carbons

diameter. If the pore width is no more than about two molecular diameters (i.e., if w<"'-'2o-) there is a significant overlap of adsorbent-adsorbate interactions [35,36] and the ultramicropores are filled at very low plpo. This has been termed [7, 35] "primary micropore filling" and is manifested in a pronounced distortion of the initial part of the isotherm [37] - and the corresponding as plot. The wider micropores (supermicropores) are filled over a range of higher plpo by a cooperative process [11, 35], after monolayer adsorption has taken place on the pore walls, but before the onset of capillary condensation [7]. Two major problems are encountered in the classical interpretation ofthe capillary condensation range ofa physisorption isotherm. The first is concerned with the validity of the Kelvin equation and the second with the existence of adsorption hysteresis. It is generally accepted that the Kelvin equation breaks down completely below a certain pipO when the condensate loses its stability [7, 11]. In addition to this complete failure of the Kelvin equation, it now seems likely [11, 14, 38] that the effective values of surface tension and molar volume require progressive adjustment as the pore width is reduced below, say, 10 nm. The presence of adsorption hysteresis cannot be reconciled with the laws of classical thermodynamics. It is evident that there are various forms of adsorption hysteresis [7], which require different explanations [7, 39, 40]. In the capillary condensation range, well-defined hysteresis loops are generally associated with delayed condensation or percolation [11] through pore networks or "ink bottles" [38, 39]. In the case of activated carbons, delayed condensation is likely to be the most important mechanism [11], but we cannot rule out the other effects. The computational procedures now used in the application of density functional theory and molecular simulation for the prediction and analysis of physisorption isotherms are based on the statistical mechanics of confined fluids [14]. These important advances are described in several chapters of this book and therefore the present introductory remarks are confined to a few general comments. Whichever computational procedure is adopted [39, 40], it is first necessary to define a 3-D model of the pore structure within a solid of known and uniform composition [14]. It has been customary to assume that the pores of different width are all of the same shape (e.g., slits in activated carbons). Further assumptions made by many investigators are that the filling or emptying of each group of pores can occur independently and reversibly, that the internal surface is uniform and that the solid-fluid and fluid-fluid interactions can be expressed in terms of standard potential functions [14]. The Monte Carlo method is generally considered [14, 39] to be the most convenient means of using computer simulation to generate adsorption equilibrium data by application of the Boltzmann distribution law in order to accept or reject the random movements of large numbers of molecules. Although the thermodynamic parameters may be readily changed, grand canonical Monte Carlo (GCMC) molecular simulation is usually preferred with the chemical potential being taken as the independent variable. Because of the present availability of commercial software, the nonlocal version of density functional theory (i.e., NLDFT) is now widely used for pore

1.4 Concluding Remarks

11

size analysis. With the aid ofNLDFT, it has been possible to generate a series of "individual pore isotherms" for nitrogen adsorption at 77 K on a wide range of graphitic slit-shaped pores [14, 34]. The NLDFT-derived isotherms have been found to be in excellent agreement with results obtained by GCMC simulation and also in broad agreement with the corresponding experimental data [14, 40]. The NLDFT calculations have shown inter alia the effects produced by changing the operational temperatures and the dimensions of the probe molecules. For example, although the molecular dimensions of nitrogen and carbon dioxide are similar, their adsorptive behavior was shown [40] to depend on the difference in operational temperatures (e.g., 77 K for nitrogen and 273 K for carbon dioxide). Indeed, this difference had already been successfully exploited by RodriguezReinoso and his coworkers [41] by using carbon dioxide at 273 K for probing the very narrow pores (of w "'-'0.35 nm) in activated carbons. The highly distinctive character of the adsorption of water vapor by porous carbons has long been of great interest [5, 7]. Some microporous carbons give well-defined Type V water isotherms, the steep riser often being associated with a fairly narrow hysteresis loop. The low affinity of the carbon surface for water is evidently due to the small number of hydrophilic sites and the relatively weak nonspecific interactions [11] (dispersion forces). However, the initial uptake of water at low p/ pO can be increased by surface oxidation, which leads to the formation of additional hydrophilic sites and the appearance of a small knee [7] (i.e., a change in isotherm shape from Type V to Type IV). The clustering of hydrogen-bonded water molecules finally leads to complete pore filling of narrow slit-shaped pores [33,42]. This is in contrast to the hydrophobic behavior of Silicalite [11, 42], which has an interconnected tubular pore structure. Thus, thin layers of hydrogen-bonded water molecules can be accommodated in slitshaped pores of "'-'0.5 nm, but this is not possible in tubular pores of similar width because it would involve too much distortion of the hydrogen-bonded water structure [42, 43].

1.4

CONCLUDING REMARKS

As already indicated, there are two related obstacles have impeded progress in the vast amount of research on the physisorption of gases by porous carbons. First, we have to contend with the complexity of the surface and pore structure ofmost carbon adsorbents; and secondly, we have to face the difficulties involved in the interpretation of physisorption isotherms. The simplest structural model for a microporous carbon is the slit-pore model, in which each pore is in the form of a parallel-sided and rigid graphitic slit. It is also assumed that the filling and emptying processes are not dependent on the spatial arrangement of the pores. It therefore follows that for a given gas/carbon system and temperature, the notional thermodynamic state of the adsorbate (e.g., its chemical potential and enthalpy) is solely dependent on the distribution of

Chapter

12

1

Overview of Physical Adsorption by Carbons

slit width. Obviously, this simple model cannot account for nonequilibrium effects such as delayed condensation or network percolation or for any significant variation of pore shape. Although the slit-pore model is still popular, it is evident [43, 44] that considerable refinement of the model is now possible. For example, allowance can be made for nonuniformity of the internal surface in the form of pit defects and corrugated layers [44]. Also included in the more sophisticated models [44] are randomly etched graphite surfaces and different assemblages of microcrystals of graphite or graphene platelets. By the statistical modeling of the topological features of pore networks [45] and the application of fractal analysis [46], it is also possible to identify various short-range patterns and different degrees of structural disorder. The rapid developments now taking place in the computer modeling of pore networks are of considerable interest to both theoreticians and experimentalists. We can expect further progress in this direction, but as pointed out by Levitz [45] it must be kept in mind that a particular statistical model may not be a unique representation of the real material. It is therefore equally important to extend the present limited range of well-characterized ordered and partially disordered carbons. The development of user-friendly equipment has facilitated the use of gas adsorption alongside other techniques for the characterization of highly active carbons of all types. In the near future, the limitations of the most popular procedures for the analysis of physisorption isotherms and the derivation of surface areas and pore size distributions (e.g., by the BET, DR, and Barrett-JoinerHalenda (BJH) methods) will inevitably remain a serious handicap. However, it should be kept in mind that it is always useful to closely examine the isotherm shape and apply an empirical method of analysis [11]. There is no immediate prospect of finding any suitable alternative to nitrogen for routine physisorption measurements, but in future nitrogen adsorption at 77 K should be regarded as only the first stage in the characterization of porous carbons. The next stage will depend on the nature of the carbon and its application (e.g., for gas storage or separation, water treatment, respiratory protection or catalysis). This is likely to involve equilibrium and dynamic adsorption measurements with selected probe molecules of different size, shape, and molecular structure. We can also anticipate an increased need for chemical engineering data, which will necessitate multicomponent adsorption measurements at high and low pressures.

REFERENCES 1. Deitz, V.R. (1944). Bibliography of Solid Adsorbents. National Bureau of Standards. 2. Polanyi, M. (1916). Adsorption of gases by a solid non-volatile adsorbent. Verb. Deut. Physik. Ges., 18, 55-80. 3. Langmuir, I. (1916). Constitution and fundamental properties of solids and liquids. I. Solids. J. Am. Chern. Soc., 38, 2221-95.

References

13

4. Foster, A.G. (1932). Sorption of condensable vapors by porous solids. I. Applicability of the capillary theory. Trans. Faraday Soc., 28, 645-57. 5. Brunauer, S. (1944). The Adsorption of Gases and Vapors. Oxford University Press. 6. Brunauer, S., Emmett, P.H., and Teller, E. (1938). Adsorption of gases in multimolecular layers.]. Am. Chern. Soc., 60, 309-19. 7. Gregg, S.J. and Sing, K.S.W. (1982). Adsorption, Suiface Area and Porosity. Academic. 8. Dubinin, M.M. (1955). A study of the porous structure of active carbons using a variety of methods. Q. Rev. Chern. Soc., 9, 101-14. 9. Dubinin, M.M. (1966). Porous structure and adsorption properties of active carbons. In Chemistry and Physics of Carbon (P.L. Walker, ed.). Marcel Dekker, pp. 51-119. 10. Sing, K.S.W., Everett, D.H., Haul, R.A.W., et al. (1985). Reporting physisorption data for gas/solid systems. Pure Appl. Chern., 57, 603-19. 11. Rouquerol, F., Rouquerol, ]., and Sing, K. (1999). Adsorption by Powders and Porous Solids. Academic. 12. Rodriguez-Reinoso, F. (2002). Production and applications of activated carbons. In Handbook of Porous Solids (F. Schuth, K.S.W. Sing and ]. Weitkamp, eds). Wiley/VCH, pp. 1766-827. 13. McEnaney, B. (2002). Properties of activated carbons. In Handbook of Porous Solids (F. Schuth, K.S.W. Sing, and]. Weitkamp, eds). Wiley/VCH, pp. 1828-63. 14. Pikunic, ]., Lastoskie, C.M., and Gubbins, K.E. Molecular modeling of adsorption from the gas phase. In Handbook of Porous Solids (F. Schuth, K.S.W. Sing, and ]. Weitkamp, eds). Wiley/VCH, pp. 182-236. 15. Sing, K.S.W. (1994). Physisorption of gases by carbon blacks. Carbon, 32,1311-7. 16. Badalyan, A. and Pendleton, P. (2003). Analysis of uncertainties in manometric gas adsorption measurements. Langmuir, 19, 7919-28. 17. Beebe, R.A., Biscoe,]., Smith, W.R., and Wendell, C.B. (1947). Heats ofadsorption on carbon black.]. Am. Chern. Soc., 69, 95-101. 18. Young, D.M. and Crowell, A.D. (1962). Physical Adsorption of Gases. Butterworths. 19. Kiselev, A.V. (1965). Non-specific and specific interactions ofmolecules ofdifferent electronic structures with solid surfaces. Disc. Faraday Soc., 40, 205-18. 20. Rouquerol,]., Rouquerol, F., and Grillet, Y. (1989). Energetical aspects ofnitrogen and argon adsorption. Pure Appl. Chern., 61, 1933-36. 21. Rudzinski, W. and Everett, D.H. (1992). Adsorption of Gases on Heterogeneous Suifaces. Academic. 22. Steele, W.A. (1974). The Interaction of Gases with Solid Surfaces. Pergamon. 23. Aronovich, G.L. and Donohue, M.D. (2001). Surface compression in adsorption systems. Colloids Surf. A, 187, 95-108. 24. Vernov, A. and Steele, W.A. (1993). Computer simulations ofbenzene adsorbed on graphite. In Fundamentals ofAdsorption IV (M. Suzuki, ed.). Kodansha, pp. 695-701. 25. Carrott, P.J.M., Ribeiro Carrott, M.M.L., Cansado, I.P.P., and Nabais, ].M.V. (2000). Reference data for the adsorption of benzene on carbon materials. Carbon, 38,465-74. 26. Carrott, P.J.M., Ribeiro Carrott, M.M.L., and Cansado, I.P.P. (2001). Reference data for the adsorption of methanol on carbon materials. Carbon, 39, 193-200. 27. Carrott, P.J.M., Ribeiro Carrott, M.M.L., and Cansado, I.P.P. (2001). Reference data for the adsorption ofdichloromethane on carbon materials. Carbon, 39, 465-72. 28. Carrott, P.J.M. and Sing, K.S.W. (1989). Multilayer adsorption of nitrogen and alkanes by non-porous carbons and silicas. Pure Appl. Chern., 61, 1836-40.

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Chapter 1 Overview of Physical Adsorption by Carbons

29. Sweatman, M.B. and Quirke, N. (2001). Characterization of porous materials by gas adsorption: comparison of nitrogen at 77 K and carbon dioxide at 298 K on activated carbon. Langmuir, 17, 5011-20. 30. Do, D.D. and Do, H.D. (2002). Analysis of adsorption data of graphitized thermal black with DFT-lattice gas theory. Adsorption, 8, 309-24. 31. Stoeckli, H.F., Houriet,J.P., Perret, A., and Huber, U. (1979). The adsorption of simple gases by strongly activated carbons in relation to heterogeneity. In Characterization of Porous Solids (S.J. Gregg, K.S.W. Sing, and H.F. Stoeckli, eds). Society of Chemical Industry, pp. 31-9. 32. Stoeckli, H.F. Characterization of microporous ca~bons by adsorption and immersion techniques. In Porosity in Carbons O.W. Patrick, ed.). Edward Arnold, pp.67-92. 33. Jorge, M. and Seaton, N.A. (2002). Characterization of the surface chemistry of activated carbon by molecular simulation of water adsorption. In Characterization of Porous Solids VI (F. Rodriguez-Reinoso, B. McEnaney, J. Rouquerol, and K. Unger, eds). Elsevier, pp. 131-8. 34. Sweatman, M.B. and Quirke, N. (2001). Modeling gas adsorption in slit-pores using Monte-Carlo simulation. Mol. Simul., 27, 295-321. 35. Carrott, P.J.M. and Sing, K.S.W. (1988). Assessment of microporosity. In Characterization of Porous Solids I (K.K. Unger, J. Rouquerol, K.S.W. Sing, and H. Kral, eds). Elsevier, pp. 77-100. 36. Everett, D.H. and Powl, J.C. (1976). Adsorption in slit-like and cylindrical micropores in the Henry's law region. J. Chem. Soc. Faraday Trans. I, 72, 619-36. 37. Kenny, M., Sing, K.S.W., and Theocharis, C. (1993). The use of high-resolution adsorption measurements for the study ofporous solids. In Fundamentals ofAdsorption IV (M. Suzuki, ed.). Kodansha, pp. 323-32. 38. Ravikovitch, P.1. and Neimark, A.V. (2002). Density functional theory of adsorption in spherical cavities. Langmuir, 18, 1550-60. 39. Vishnyakov, A. and Neimark, A.V. (2003). Monte Carlo simulation test of pore blocking effects. Langmuir, 19, 3240-7. 40. Neimark, A.V. and Ravikovitch, P.I. (2000). Density functional theory of adsorption hysteresis and nanopore characterization. In Characterization of Porous Solids V (K.K. Unger, G. Kreysa, and J.P. Baselt, eds). Elsevier, pp. 51-60. 41. Rodriguez-Reinoso, F., Garrido, J., Martin-Martinez, J.M., et al. (1989). The combined use of different approaches in the characterization of microporous carbons. Carbon, 27, 23-32. 42. Carrott, P.J.M., Kenny, M.B., Roberts, R.A., et al. (1991). The adsorption ofwater vapor by microporous solids. In Characterization of Porous Solids II (F. RodriguezReinoso, J. Rouquerol, K.S.W. Sing, and K.K. Unger, eds). Elsevier, pp. 685-92. 43. Kaneko, K. (2000). Specific intermolecular structures of gases confined in carbon nanospace. Carbon, 38, 287-303. 44. Bandosz, T.J., Biggs, M.J., Gubbins, K.E., et al. (2003). Molecular models of porous carbons. In Chemistry and Physics of Carbons, Vol. 28 (L.R. Radovic, ed.). Marcel Dekker, pp. 41-228. 45. Levitz, P.E. (2002). Statistical modeling of pore networks. In Handbook of Porous Solids (F. Schuth, K.S.W. Sing, andJ. Weitkamp, eds). Wiley/VCH, pp. 37-80. 46. Neimark, A.V. (2002) Fractal analysis. In Handbook of Porous Solids (F. Schuth, K.S.W. Sing, andJ. Weitkamp, eds). Wiley/VCH, pp. 81-105.

OVERVIEW OF CARBON MATERIALS IN RELATION TO ADSORPTION Juan M.D. Tasc6n Instituto Nacional del Carbon, CSIC, Oviedo, Spain

Contents Introduction Structures of Elemental Carbon: Carbon Allotropes and Polytypes 2.3 The Sp2 Carbon Forms: Graphitic, Graphitizable, and Nongraphitizable Carbons 2.4 Structural Characterization of Carbon Materials: The Basic Structural Units and Their Stacking and Orientation Degrees 2.5 Conclusions Acknowledgments References 2.1

15

2.2

17 21

24 42 43 43

2.1 INTRODUCTION The importance of adsorption for different carbon materials and, conversely, the contribution of each type of carbon to the field of adsorption is very different. This reflects the wide variability in properties of solid carbons [1, 2], which makes their surface properties important in very different fields and for different reasons. Thus, graphite, due to its relatively simple structure, has often been used 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 ("graphitized"), have often been used as reference nonporous adsorbents, as they only exhibit an external surface. The absence of open porosity and high chemical inertia are attributes that make glass-like carbon a material frequently used in Adsorption by Carbons ISBN: 978-0-08-044464-2

© 2008 Elsevier Ltd. All rights reserved.

15

16

Chapter

2

Overview of Carbon Materials in Relation to Adsorption

electrodes for electrochemical applications; for this reason, glass-like carbon has special relevance for liquid-solid adsorption in the context of electrochemistry. Furthermore, the adsorption behavior (for both gases and liquids) of highly porous carbons such as activated carbons is of great interest because of their relevance for technologies such as pollution control, heterogeneous catalysis, or gas and electric energy storage to mention just a few applications [3]. It is not surprising therefore that a great number of adsorption studies on carbons have been carried out using these materials as adsorbents. A corollary to this is the vast abundance of adsorption studies addressing the characterization of (micro)porosity in activated carbons. On the opposite side of the spectrum of surface area development, carbon fibers (CFs) [4, 5], used principally as reinforcement in composites, are virtually nonporous and exhibit a surface area that is only slightly greater than their geometrical area. Since the surface characteristics of carbon fibers are important in fields such as interfacial fiber-matrix behavior in composites, researchers in this area have adapted their methodologies, or developed new ones, to study adsorption on these low-surface area solids. This explains, for instance, the widespread application of inverse gas chromatography to this class of carbons [6]. Newer fibrous forms of carbon such as carbon nanofibers (CNFs) and carbon nanotubes (CNTs) are also being studied for their adsorption properties, although in this case the aim is to investigate not only their interaction with matrices in composites, but also their possible use as media for gas storage. The examples given above show that, although only a few types of carbons (particularly activated carbons) appear to dominate the scene where carbonaceous solids and adsorption are concerned, the carbon materials involved belong to very different classes, from highly crystalline to highly disordered. Carbon fibers (more specifically, those produced from pitches) reproduce within themselves the wide variety of carbon properties, depending chiefly on the nature of the precursor and preparation conditions. Thus, in order to provide an overview of carbons in relation to adsorption, it is necessary to be comprehensive and consider all possible classes of carbon materials, though paying particular attention to those that are most relevant to adsorption. This approach is the one adopted this chapter, which mainly attempts to classify the carbons, compare their 'properties, and introduce them to those interested in their adsorption behavior. The classification criteria used here are chiefly associated with crystalline structure (particularly, nanotexture), which we believe to be the property that offers the most thorough classification of carbon materials. Whenever available, structural models (rather than e.g. micrographs) will be used here to schematically illustrate the structural features of the various classes of carbonaceous solids. For more extensive or detailed information on carbon materials, the reader is referred to a number of comprehensive publications [1, 2, 7-15], some of which are particularly focused on structural aspects [11-14]. In this chapter, we will try to follow the terminology norms for carbon as a solid developed by the International Committee for Carbon Characterization and Terminology, and later adopted by the IUPAC [16]. Some

in

2.2

Structures of Elemental Carbon: Carbon Allotropes and Polytypes

17

previous reviews [7, 8] also include detailed information on the terminology employed for these materials. For the adsorption terminology (especially in connection with the characterization of porous solids, pore size classification, etc.), we will follow the corresponding IUPAC norms [17,18].

2.2 STRUCTURES OF ELEMENTAL (ARBON: (ARBON ALLOTROPES AND POLYTYPES

Carbon has an atomic number of 6 and its ground-state electron configuration is [He]2s22p 2. Like some other p-block elements (e.g., P, S, Sn), solid elemental carbon exhibits the phenomenon of allotropy (i.e., occurrence of the element in different forms that vary in structure and equation of state). Although other approaches (e.g., LCAO) have been used [7, 13] to justify the occurrence of different structures for this element in solid form, the hybridization concept provides a very intuitive explanation and is very useful for classifying carbon-based solids. In this approach, one of the s electrons can be promoted and hybridized with different numbers of p orbitals to give rise to three types of hybrid orbitals: Sp3, Sp2, and sp. These are at the origin of the three basic carbon structures, respectively, diamond, graphite, and carbynes. Table 2.1 summarizes the relationship existing between the type ofchemical bond, the stereochemistry, and the corresponding structures for carbon in solid form. In the diamond structure, carbon atoms are present in Sp3 hybridization, with a tetrahedral stereochemistry and a face-centered cubic structure that is shown in Fig. 2.1. Besides natural diamond, synthetic diamond has been produced since General Electric first announced its successful high-pressure synthesis in 1955. Sintered polycrystalline diamond, different types ofdiamond films, and diamondlike carbon are other types ofdiamond-related synthetic materials, some ofwhich are noncrystalline [13, 19]; these solids have their own terminology [10,20]. Unlike other carbonaceous solids, diamond has a rather limited and specific relevance to adsorption. Indeed, ever since the publication of a pioneering work Table

2.1 Relationship between hybridization, stereochemistry, and structures of solid carbon

Sp3

Tetrahedral

Sp2

Planar trigonal

sp

Linear

Diamond Lonsdaleitea Hexagonal graphite Rhombohedral graphitea Carbynes

aThese can be regarded as polytypes rather than different structures.

18

Chapter

2

Overview of Carbon Materials in Relation to Adsorption

(a)

(c)

Figure 2.1 Relationship between the graphite (a), lonsdaleite (b), and diamond (c) structures: c is the interlayer distance. (Reprinted from Re£ [23] with permission from Elsevier.)

in 1961 when an industrial diamond powder was first used as an adsorbate for nitrogen and argon [21], adsorption work on diamonds has mainly tended to confine itself to well-defined surfaces [22]. A second type of solid made up of carbon atoms in Sp3 hybridization is lonsdaleite. This structure consists of tetrahedra of carbon atoms assembled into a wurtzite-type hexagonal network. Lonsdaleite, a rare mineral, has been found in meteorites (e.g., the famous metallic meteorite Canyon Diablo, Coconino Co., Arizona, USA). Lonsdaleite can also be prepared by subjecting graphite to static pressure [19]. Figure 2.1 shows an analogy existing between lonsdaleite, diamond, and graphite structures, where the cross-hatched hexagons of carbon atoms adopt boat, armchair, and planar configurations, respectively [23]. As is well known, fullerenes are the only molecular solids in the realm of carbon materials. Their structure consists of polyhedra formed by the assembling of a series of pentagonal and hexagonal rings of carbon atoms. The hybridization state of fullerenes is intermediate between Sp3 and Sp2 (the Sp3 character deriving from the curvature in the polyhedron), this state being [24] Sp2.28 for the molecule of C 60 or buckminsterfullerene, the archetype of this carbon structure. Something similar occurs with carbon nanotubes, where curvature is present in the cylinder itself and in the two fullerene hemispheres that are thought to close up its ends. More information on this point is given below in this section, when the ternary diagram (CSp3, C Sp2, Csp) of carbonaceous solids is discussed. The review by Bandosz et al. [15] contains much information on a number of fullerene-related materials such as exo- and endohedral fullerenes, heterofullerenes (e.g., C s9 N, C 69 N), and fullerites (i.e., molecular solids formed by the aggregation of fullerenes at moderate temperatures and pressures; they can in turn condense into polymerized fullerites or accommodate intercalate species to form fullerite intercalation compounds). Graphite is the next allotrope of carbon. This consists of sheets of Sp2 carbon atoms with a planar trigonal stereochemistry that form a flat, condensed

2.2

Structures of Elemental Carbon: Carbon Allotropes and Polytypes

19

a

a A

A

c

A

B

B

A

A

A

Simple hexagonal graphite

Bernal graphite

Rhombohedral graphite

Figure 2.2

Graphite structures: simple hexagonal, Bernal hexagonal, and rhombohedral: a is the distance between nearest-neighbours, and c is the interlayer distance. A, B, C denote the stacking sequence ofgraphenes. (Reprinted from Ref. [25] with permission from Elsevier.)

system of hexagonal rings. In turn, these sheets, called graphenes, are bound to each other in the z-axis direction by a very weak metallic-type bond (similar in strength to van der Waals forces). Two possible types of graphene stacking exist (Fig. 2.2): hexagonal, Bernal type (ABAB ... sequence), and rhornbohedral (ABCABC ... sequence). The so-called simple hexagonal structure (AA ... sequence) [25], also depicted in Fig. 2.2, is only hypothetical. The rhombohedral structure is irreversibly transformed into the hexagonal one at temperatures above 1600 K. For this reason, it is not found in synthetic graphites obtained by thermal treatment. In addition, attempts to prepare pure rhombohedral graphite have so far failed. Due to the minor importance of rhombohedral graphite, from this point on, the terms "hexagonal graphite" and "Bernal graphite" will be referred to simply as graphite. In fact, this simplification has already been explicitly accepted by the IUPAC terminology norms [16]. Carbynes are white solids made up of carbon atoms with sp hybridization. Two main possibilities [23] exist for this linear structure: polyine (-C:=C-C:=C-) and polycumulene (==C==C==C==C==); theoretical predictions and experimental evidence also point to the existence of cyclic carbynes [10]. According to a classification based on the type of bond present (Table 2.1), and also according to chronology, carbynes (rather than fullerenes) should be considered as the third allotropic form of carbon. Our scarce knowledge of carbynes and doubts about whether they really exist in pure form [10, 15, 26] are factors that have contributed to this erroneous interpretation. Moreover, lonsdaleite and rhombohedral graphite should be considered as polytypes rather than new structures with a different equation of state [27]. Strictly speaking, therefore, they should not be regarded as true allotropes of carbon (Table 2.1). A series of impure varieties termed (X- and ~-carbynes, chaoite, carbon VI, and carbons VIII-XIII have been reported. Some of these solids have a natural origin (e.g., chaoite was discovered in the crater of the meteorite Ries, Bavaria, Germany), whereas others have been synthesized through reactions such as the oxidative dehydropolycondensation of acetylene [28]. This type of structure has been detected in macroscopic amounts in the presence of heteroatoms, e.g., in polyvinyl cyanides, H-(C=C)n-CN (where n = 2 - 4). Attempts to prepare

Chapter

20

2

Overview of Carbon Materials in Relation to Adsorption

large quantities of carbynes led a decade ago to the discovery [29] of carbolites, a class of solids with a low mass density that exhibits different structures depending on the gas present when they were synthesized. The fact that the structure of carbolite is complementary to that of graphite and a series of intriguing physical properties make this esoteric (according to Dresselhaus [30]) carbon phase appealing. Phase diagrams for carbon typically depict the zones where diamond, lonsdaleite, and graphite exist (plus those for the liquid and vapor states) without considering the rest of the solid phases. Some diagrams that are very rich in detail, such as the one shown in Fig. 2.3, depict several zones of formation of metastable phases or spontaneous transformations (depicted as A up to ]), this knowledge having been obtained principally from efforts to convert graphite into diamond [31]. However, no information is provided on other carbon phases. Thus, authors such as Dresselhaus [30] and Donnet [32] have suggested the need to define precisely the areas of stability of novel carbon forms and include them in such diagrams. For instance, Delhaes [13] has suggested a tentative area for carbyne existence that encompasses ~4000-5000 K, and zero to a few gigapascal. In this regard, the ternary diagram shown in Fig. 2.4 represents a significant step forward as it shows the different carbon materials as a function of the type of hybridization [27]. The three corners in the triangle correspond to the Sp3, Sp2, and sp "pure" states, and along the three sides are carbon forms with intermediate hybridization states spn. Thus, along the Sp2_Sp3 side are the carbon nanotubes (near the Sp2 corner) and fullerenes (2 < n < 3, where n increases with the decreasing number of carbon atoms in the fullerene molecule, i.e., with an increasing degree of curvature). The two other sides of the triangle include

50 I I

30

r

DIAMOND

20

II

E

40

C? Q. ~

:; (/)

Q)

a:

I

,

~

Q)

(/)

G

~H

,F

, \

, .....

D

LIQ.

t

10

! 0 0

1000

3000 4000 2000 Temperature (K)

5000

6000

Figure 2.3 Phase diagram for carbon. The letters indicated correspond to various transformations between graphite, diamond, and lonsdaleite. (Reprinted from Ref. [31] with permission from Elsevier.)

2.3 The Sp2 Carbon Forms: Graphitic, Graphitizable, and Nongraphitizable Carbons

21

Diamond lonsdaleite

~Ollapse Carbyno(polyyne)diamonds mLCp (m=3,0
C20 , P/H=oo C21 , P/H=3 . C22 , P/H =2 Fullerenes

\

~

'Amorphous

'~carb.o. n.\~. .

/.

Hypothetical D-G hybrids

C82 , P/H =0.6

C73 , P/H =0.5

Condensation

Polycyclic , / networks

Carbyne

Monocyclic ...-... Graphynes ~ Layer-chain rings, carbons mLCp cyclo[N]carbons (m = 2, 0 < P < 1)

Graphite

Figure 2.4 Ternary diagram (Csp 3, C Sp 2, Csp) of carbonaceous solids. (Reprinted from Ref. [27] with permission from Elsevier.)

materials such as the less-known "graphynes" and monocyclic cyclo [N] carbons (1 < n < 2), and the hypothetic "superdiamonds" (1 < n < 3, n =f. 2). There are similar diagrams for more specific types of carbon materials - for instance, the ternary diagram (CSp 3, C Sp 2, H), which can be used to classify noncrystalline carbons such as amorphous carbon (a-C) films, hydrogenated carbon (a-C:H) films, or diamond-like carbons (DLC), to mention just a few [10, 13].

2.3

THE Sp2 CARBON FORMS: GRAPHITIC,

GRAPHITIZABLE, AND NONGRAPHITIZABLE CARBONS

Carbonaceous solids that are inside the triangle in Fig. 2.4 obviously contain mixtures of the three hybridization states. Japanese researchers [33, 34] recently coined the term "carbon alloys" to designate materials typically made up of carbon atoms in multicomponent systems, where the components undergo physical or chemical interactions with each other. This very broad concept extends to mixtures of different phases (as occurs, for instance, in carbon-carbon composites), and also to materials containing heteroatoms. The interesting point in the present context is that, according to the above definition, carbon atoms with different hybrid orbitals are considered as different components.

22

Chapter

2

Overview of Carbon Materials in Relation to Adsorption

The ensemble of carbon materials containing the three types of hybridization includes many materials of practical interest, which are often referred to as "engineering carbons." In what follows, we will group all of these (Sp3+Sp2+Sp) solids under the common term "carbon forms." If one excludes some specific cases such as that of "diamond-like" amorphous carbon, these materials mainly contain carbon atoms in Sp2 hybridization. According to Marsh [35], "Although diamond has a greater emotional appeal than graphite as an allotrope of carbon structure, it is the graphite lattice which dominates discussions of structure within carbons." Indeed, it has become commonplace to consider the majority of carbon forms within the framework of the (hexagonal, Bernal type) graphite lattice, which is taken as reference for the highest degree of structural perfection. Hiittinger [36] has highlighted the potential of this anisotropic lattice as a common framework for many high-performance carbon materials, while Chung [37] has reviewed the special physical and chemical properties on which many applications of graphite and related solids are based. Both authors have identified oxidation sensitivity as one of the main shortcomings for practical applications, especially at high temperatures. The IUPAC [16] has adopted as a criterion for considering a material as graphite (or, more precisely, as a graphitic carbon), the requisite that the graphenes therein must be arranged parallel to each other in a tridimensional crystalline network. Conversely, one should not use the term graphitic carbon/material for solids (nongraphitic carbons), which do not exhibit a longrange tridimensional graphitic structure, even if they have been heat-treated at temperatures > 2500 K, in the so-called graphitization process. Nongraphitic carbons can in their turn be subdivided into graphitizable and nongraphitizable. As early as 1951, Franklin [38] established a classification into graphitizable and nongraphitizable carbons based on whether they were transformed or not into graphite by thermal treatment at 2273 K, and proposed the structural models that are reproduced in Fig. 2.5. According to Franklin's concept, graphitizable solids contain a series of units oriented in an approximately parallel fashion to each other (pregraphitic arrangement). In nongraphitizable

~~!IJb

~,~~~\\\~

~~C~~ ~~~~-'~~ Figure 2.5 Franklin's original schemes for graphitizable (lift) and nongraphitizable (right) carbons. (Reproduced from Re£ [38] with permission from the Royal Society.)

2.3 The Sp2 Carbon Forms: Graphitic, Graphitizable, and Nongraphitizable Carbons

23

solids, however, these units are arranged randomly and are cross-linked by disordered carbon species. The precise nature of these cross-links was not specified. It was assumed that on heating at high temperatures, these cross-links may be broken, but the activation energy needed for the motion of whole crystallites is high, and graphite is not formed. This model has been (and is still) widely accepted by the carbon community, despite its being considered as oversimplified, since in actual fact it is known that there is a continuum with no gap between extreme graphitizable and nongraphitizable situations [39]. Later on, the IUPAC [16] established a definition of nongraphitizable (also termed nongraphitizing) materials as "those non-graphitic solids that are not transformed into graphitic carbon by a simple thermal treatment at temperatures up to 3300 K and atmospheric pressure or lower" (i.e., through the graphitization process). This definition is empiric and somewhat arbitrary. The most representative type of nongraphitizable carbons is char, defined as a product of carbonization ofnatural or synthetic organic matter that has not passed through a fluid stage during carbonization. Other typically nongraphitizable carbon forms are carbon black, soot (plus aciniform carbon, an unsuccessful term that was coined to encompass the two previous types), glass-like (or "glassy") carbon, activated (also termed "active") carbon, wood charcoal, and many types of coal (bituminous coking coal and some anthracites being exceptions). The so-called graphitizable (also termed graphitizing) materials constitute a group that is complementary to the previous one. The IUPAC has simply defined them as those nongraphitic carbons that upon heat treatment are converted to graphitic carbon. The most representative type ofgraphitizable material is coke, which has been defined as a solid rich in nongraphitic carbon produced by the pyrolysis of an organic material that has passed, at least in part, through a liquid or liquid-crystalline stage during the carbonization process. There are a number of coke types, according to the precursor (e.g., petroleum coke, pitch coke, coal coke), the heat treatment temperature (e.g., green coke, calcined coke), or a combination of these and the production process (e.g., fluid coke, delayed coke, sponge coke, needle coke). Pyrolytic carbon, carbonaceous mesophase, and many types of pitch and carbon fibers (excluding, for instance, isotropic pitches and carbon fibers derived from them) are typical examples of graphitizable carbon forms. The difference between the definitions for char and coke derives from the formation of a mesophase or liquid crystal during the pyrolysis of certain types of precursors of carbons with a high degree of structural perfection [40]. Carbonaceous mesophase is formed from polyaromatic molecules with a laminar structure that are grouped together in parallel stacking by means of van der Waals forces (mesogens). Mesogens therefore adopt a pregraphitic arrangement that will transform into graphitic carbon when they are heated at higher temperatures. As an illustration of the thermal behavior of a typically graphitizable material, Fig. 2.6 shows a succession of optical micrographs for a pitch that generates mesophase during pyrolysis [40]. The initially formed mesogens group into anisotropic mesocarbon microspheres, which become separated from the

24

Chapter

Mesogens

2

Overview of Carbon Materials in Relation to Adsorption

Mesophase

Coalesced mesophase

Coke

Figure 2.6 Scheme of the carbonization process of a pitch (temperature increases from left to right). (Reproduced from Re£ [40] with permission from Taylor and Francis Group.)

fluid isotropic phase. As the temperature increases, polymerization and condensation reactions take place, the microspheres grow and coalesce, and viscosity increases until solidification takes place in the form of anisotropic coke. There are some exceptions to the rule that graphitizable materials must pass through a fluid stage to transform into graphite. On the one hand, it is well known that sucrose and other simple organic compounds give rise to nongraphitizable carbons, whereas they melt at low temperatures before the beginning of carbonization. However, this is not a significant exception since this involves just melting (""'459 K for sucrose) rather than carbonaceous mesophase formation and the like. Another, more important, exception is that of highly ordered graphitic carbon that can be produced by the carbonization-graphitization of polyimides, which takes place through the formation of a system of flat pores without any mesophase formation [41]. Moreover, the final product of this transformation has been shown to be one of the most perfect types of synthetic graphite ever produced, comparable in structural order to highly oriented pyrolytic graphite [1, 2]. Therefore, the above classification into graphitizable and nongraphitizable solids, which is phenomenological and somewhat arbitrary, is not strictly speaking true, and can only be considered as an approximate rule for classifying materials with a predominant Sp2 character into two main classes depending on their ability to transform into graphite.

2.4

STRUCTURAL CHARACTERIZATION OF CARBON

MATERIALS: THE BASIC STRUCTURAL UNITS AND THEIR STACKING AND ORIENTATION DEGREES

As Fig. 2.6 reveals, optical microscopy with polarized light makes it possible to distinguish various intermediate products formed from a precursor of graphitic carbon at different stages of pyrolysis. The observed morphology is the so-called optical texture, which enables carbon solids to be classified according to their degree of anisotropy. Besides optical microscopy, other techniques

2.4 Structural Characterization of Carbon Materials

25

with a higher degree of resolution, principally transmission electron microscopy (TEM), have significantly contributed to the characterization of the structure of carbon materials. To return to the case above, this technique provided direct evidence for the formation of flat pores and their sudden transformation into graphitic flat sheets at 2823 K upon the graphitization of Kapton polyimide. In this process, plane stacking changed from turbostratic (i.e., disordered in the c direction, see Section 2.4.3) to graphitic [41]. Oberlin and her group [42,43] have been widely recognized for their extensive studies of carbonaceous materials by TEM, mainly by combining selected area diffraction with dark-field and light-field imaging. One of the important concepts they established is that of basic structural unit (BSU) , defined as a planar aromatic structure of less than 10-20 rings and between two and four layers. A related concept is that of local molecular orientation (LMO), defined as an array ofBSUs with a near-common orientation. The arrangement ofBSUs, with a higher or lower degree ofLMO (in general, the regions of LMO are similar in size to the individual BSUs for carbons prepared at temperatures between 873 and 1273 K [39]), has increased our understanding of the mechanism ofgraphitization considerably. Thus, a high degree of cross-linking between the BSUs in nongraphitizable carbons leads to only a slight growth in the extent and order of LMO. On the other hand, lack of cross-linking in graphitizable carbons will allow the BSU elements to rearrange and coalesce with thermal treatment. The BSU concept also helps to explain the presence of intrinsic pores in certain carbon materials [44]. Figure 2.7 sketches the possible arrangements ofBSUs in carbons [42]. These can be reduced to two symmetries: spherical or cylindrical. All possible textures derive from these two basic arrangements if one considers the variable radii of curvature of lamellae; thus, an infinite radius of curvature gives rise to flat lamellae. We will come back to this figure when discussing the types of orientation found in carbonaceous materials (Sections 2.4.1 to 2.4.3). X-ray diffraction (XRD), generally considered the "ideal" technique for the structural characterization of materials, not only allows the structures of different carbon allotropes and polytypes to be distinguished from each other, but also enables the degree to which the structure of a given carbon form departs from the ideal graphite structure to be determined. By applying the Debye-Scherrer equation (adapted to carbon materials by Warren) to the (002) and (10) peaks, it is possible to calculate, respectively, the height (Lc) and width (La) of the graphitelike crystallites in these solids. Emmerich [45] has provided a useful comparison of the trends of variation of L c and Lc with heat treatment temperature for graphitizable and nongraphitizable carbons. The recent efforts of a group of Japanese researchers to normalize the application of XRD to carbon materials also deserves special mention [46]. Raman spectroscopy is another useful technique for classifying carbon materials according to structural criteria. Thus, the Raman spectra ofmost carbon forms contain, at least, two main bands termed G band (after graphite, r-v1575 cm- i ) and D band (after defects, r-v1355 cm- i ) [47]. Figure 2.8 illustrates the evolution of these two bands and the second-order spectrum (2600-3200 cm- i , G' band

26

Chapter

2

Overview of Carbon Materials in Relation to Adsorption

-

1nm (a)

(d)

I.

Fiber. axiS

(f)

Figure 2.7 Sketches ofthe possible arrangementofbasic structural units (BSU)s. (a and b), true spherical symmetry (a, concentric texture; b, radial texture); (c-e), statistical spherical symmetry (c, crumpled sheets ofpaper; d, lamellar structure with infinite radius ofcurvature or infinite local molecular orientation (LMO); e, lamellar structure with a long-range statistical orientation); (f and g), cylindrical symmetry (f, true cylindrical symmetry; g, statistical cylindrical symmetry). (Reproduced from Re£ [42] with permission from Taylor and Francis Group.)

at '"'-'2700 cm- 1) for carbon solids with a different degree of structural order (decreasing from top to bottom in this figure) [48]. One can clearly see the decrease in intensity and widening of the D band, the parallel increase in the G band, and the disappearance of the G' band when moving progressively from

27

2.4 Structural Characterization of Carbon Materials

GC2

.' .....

GA2

OCA

_~ .. W.' _

~'

j ".,.•.... ._~

OVA

FC1

CM3 f

1000 1200 1400 1600 1800

$

•

2600 2800 3000 3200

Figure 2.8 Raman spectra of various carbon materials with an approximately decreasing degree ofstructural order in the following sequence: natural graphite (GC2), high surface area graphite (GA2), calcined needle coke (QCA), green needle coke (QVA), isotropic carbon fiber (FC1), and subbituminous coal (CM3). (Reprinted from Ref. [48] with permission from Elsevier.)

graphites to higWy disordered materials such as coals. The intensity ratio of the G and D bands as well as their wavenumbers and widths are useful quantitative criteria for comparing the degree of structural order of different carbon forms. The information provided by XRD is not equivalent to that obtained from Raman spectroscopy. Rather it is complementary. More specifically, XRD reflects the degree of graphitization in terms of the stacking of the basic constituents, whereas Raman spectroscopy reflects their degree of orientation. This is illustrated in Fig. 2.9, which shows the variation of two parameters derived from each of these techniques (respectively, the graphite-like interlayer spacing dOO2 ' and the [ID/(ID+ Ie)] intensity ratio) for a wide and varied set of carbons (including 45 different samples of graphitic, graphitizable, and nongraphitizable solids) [49]. For low values of both parameters, a horizontal line is obtained where data corresponding to various types of graphite accumulate. For these materials, d002 approaches the ideal value of 0.3354 nm. However, the graphite

28

Chapter

2

Overview of Carbon Materials in Relation to Adsorption

0.41

• •

0.39

•

E

c

......... C\I

0

0.37

0

u

0.35

0.33 0

20

40

60

80

100

'01(10+ 'G) (%)

Figure 2.9

Comparison of structural parameters deduced from X-ray diffraction and Raman spectroscopy for a wide set of carbon materials. (Ref. [49] - reproduced by permission of the Royal Society of Chemistry.)

samples studied correspond to solids with different degrees of BSU orientation; therefore, the Raman intensity ratio varies from 0 to f"V40 %. A transition zone (line of intermediate slope) is followed by a zone with a wide dispersion of points that corresponds to the most disordered materials studied. For these materials, the [ID/(ID+ Ie)] ratio oscillates between 60 and 80 %, whereas d002 increases (vertical straight line). Here, the solids have their BSUs oriented at random and do not significantly differ from each other as examined by Raman spectroscopy. However, by means ofXRD they can be differentiated from the degree of stacking of graphenes inside their basic units (d002 varies from f"V0.35 to >0.40 nm). The importance ofthe degree oforientation ofthe basic constituents ofcarbon materials is highlighted in Fig. 2.10, proposed as early as 1985 by Inagaki [50], which depicts the main types of orientation found in carbons. This scheme has many points in common with the one shown in Fig. 2.7. In the following subsections we will use these two schemes as a basis for describing the main classes of nanotexture (defined here as arrangement of BSUs) found in carbonaceous solids, which afford a useful classification for understanding the behavior of carbons both in general and as adsorbents. Although, strictly speaking, lamellar and random orientations are special cases of spherical symmetry [42], we will treat them as separate types of texture to facilitate the classification of carbon solids into a larger variety of types. 2.4.1 Planar Orientation

This type of orientation is characteristic of graphite, of which some very perfect forms, such as kish graphite (precipitated from molten iron at high temperatures), highly oriented· pyrolytic graphite (HOPG), polyimide-derived

29

2.4 Structural Characterization of Carbon Materials

ORIENTED TEXTURE

RANDOM TEXTURE

PLANAR ORIENTATION

:I:~;e~

WS?

~ RANDOM ORIENTATION

f~~t1

~~COaXial

~~fer~nce AXIAL ORIENTATION ~~IS ~ ("'- ~ Radial Concentric

Reference point

POINT ORIENTATION

~

~ Radial -~---....

-----... - - - - -.... ~

Degree of orientation Degree of graphitization Heat treatment temperature

Figure 2.10 Types of orientation of the basic constituents of carbon materials. (Reprinted from Re£ [1] with permission from Elsevier.)

graphite films, or natural graphite flakes (e.g., from Ticonderoga [New York, USA], Madagascar, or Sri Lanka) represent paradigmatic cases of a high degree of structural order in the realm of carbon materials. As indicated in Section 2.1, some of the major connections of graphite with adsorption work have to do with carrying out measurements on a well-controlled surface, or, in the case of theoretical studies, to use its structure as a model for simulating the adsorption of different molecules on its surface. Moreover, HOPG is a material of choice for techniques such as scanning tunneling and atomic force microscopies and, as such, has often been used to directly visualize large molecules adsorbed on its surface. It is well known that various atoms, ions, and even molecules can be received into the graphite interlayer space between hexagonal layers of carbon atoms. In this way, intercalation compounds with rather unique properties are formed [1, 51]. When graphite intercalation compounds such as graphite hydrogen sulfate are subjected to very rapid heating (or flash heating), a type ofgraphite made up of flakes called exfoliated graphite is produced. Exfoliated graphite has a worm- or accordion-like shape with numerous macropores [44] (the macropores being the spaces left between successive flakes) and has a close relevance to adsorption, either for fundamental work (as it has a highly homogeneous surface) or connected with applications, either per se (e.g., in the removal of oil spills from sea water) [52], or as monolithic supports to deposit other adsorbent or catalyst phases [53]. A less widely known type of graphite is "high surface

30

Chapter

2

Overview of Carbon Materials in Relation to Adsorption

area graphite," produced by extensive milling [54] and used as catalyst support or adsorbent [55]; it exhibits surface areas ranging between 100 and 300 m 2 / g. Various intermediate situations between perfect planar orientation and random orientation are found in solids such as pyrolytic carbons and cokes (i.e., typically graphitizable materials). Heat treatment temperature and the type ofprecursor (in the case ofcokes) are the main factors that determine the actual arrangement, i.e., tending toward either planar or random orientation. Unlike these solids, natural microcrystalline graphite (also termed "amorphous" graphite in certain contexts) should be classified as a randomly oriented material. This type ofgraphite is made up of very small domains that are oriented at random toward each other. Inside each domain, graphenes are stacked as in the most perfect types of graphite. The empty circle at the intersection of the two dashed lines in Fig. 2.9 corresponds to a natural microcrystalline graphite (from Mexico), which, according to the Raman band intensity ratio [ID/(ID+ Ie) = 67.5 %], is among the most randomly oriented materials studied by Cuesta et al. [49], whereas on the basis of XRD (d002 = 0.335 nm) it presents a high degree of graphitization. Likewise, synthetic isotropic high-density graphite, produced by cold isostatic pressing for use in a number of applications such as the structural parts of nuclear fission reactors [1], must be considered as randomly oriented from the point of view of nanotexture. On the other hand, graphite foams [56, 57], which are produced from mesophase pitches, are materials made up of an interconnected network of long graphite filaments and thus they exhibit isotropic material properties, though only on the macroscopic scale. On the nanoscale, however, they exhibit high Lc and La values, indicative of the presence of large graphitic domains. 2.4.2 Axial Orientation

Axial orientation is typical of materials with a tubular geometry (indeed, a fibrous morphology of carbon materials is possible, thanks to this axial orientation scheme). Axial orientation encompasses two extreme characteristic types: coaxial and radial. One of the best examples of coaxial orientation of BSUs is that of multiwall carbon nanotubes (MWCNTs), which consist of a series of concentric cylinders. Figure 2.11 shows one of the many examples of TEM micrographs of MWCNTs from the literature [58]. The parallelism of graphenes (in the so-called Russian doll arrangement) can be clearly seen and follows approximately the model that is depicted in an inset in the same figure. However, MWCNTs generally contain defects such as pentagonal and heptagonal rings, the presence of which produces bending and/or capping of individual nanotubes to yield structures such as carbon nanobamboos [59] and nanocones [60] (also termed nanohorns). The latter type of material has been quite frequently studied as adsorbent by Iijima, Kaneko and coworkers [61]. As in the case of fullerenes, readers interested in further information on these and other even more exotic nanotube-related solids (e.g., nanotubes with helical and toroidal structures) are referred to the review by 13artdosz et al. [15]. Adsorption by carbon nanotubes (especially the single-wall ones, SWCNTs) constitutes the

2.4 Structural Characterization of Carbon Materials

31

Figure 2.11 TEM image ofa concentric multiwall nanotube. The scale bar is 4 nm. The inset in the upper left comer illustrates the concentric arrangement of graphenes. (Reproduced from Re£ [58] with kind permission of Springer Science and Business Media.)

subject of Chapters 9, 15, and 16, and thus, we feel that the relevance to adsorption of these materials does not need to be dwelt upon any more at this point. Closely related to MWCNTs are CNFs, which can also be produced by the decomposition of hydrocarbon gas in the presence of transition-metal catalyst particles (catalytic chemical vapor deposition, CCVD) [62]. CNFs are highly graphitizable [63] as their main constituent is a layer ofpyrolytic carbon grown on an initially hollow graphitic filament generated on a catalyst particle. Some CNFs exhibit coaxial orientation, there being some doubt as to the distinction between them and MWCNTs [64]. CNFs can exhibit other characteristic nanotextures. One is the so-called platelet type, formed by platelets that are stacked on top of each other perpendicularly to the fiber axis. Other types are the herringbone and stacked-cup ones, which are depicted in Fig. 2.12; these two types of CNFs can be grown by the same method (chemical vapor deposition, CVD) , and they exhibit similar TEM images but differ in nanotexture and, hence, in their properties and potential applications [65]. As in the case of CNTs, CNFs are being actively investigated as adsorbents (if necessary, after activation), mainly in connection with gas storage.

32

Chapter

(a)

(b)

2

Overview of Carbon Materials in Relation to Adsorption

(c)

(d)

Figure 2.12 (a) and (c) Atomic models of stacked-cup and herringbone carbon nanofibers and (b) and (d) their respective simulated TEM images. (Reprinted from Ref. [65] with permission from Elsevier.)

The other extreme type of axial orientation consists of a radial alignment of carbon layers. This is typically found in ultrahigh-modulus, mesophase-pitchbased carbon fibers, which exhibit a radial arrangement in the cross-section of the fibers. Figure 2.13 shows two SEM micrographs of this type of fibers, where wedge-arranged straight layers are clearly visible, especially in the lower micrograph [66]. According to Mochida and coworkers [67,68], melt spinning (which is the basis of the preferred process for producing these fibers) is the most important step for determining the structures of mesophase-pitch-based CFs. During this process, microdomains (already present in the liquid crystal mesophase pitch) are aligned parallel to the fiber axis, forming fibrils. The fibrils are made up of a number of pleat units aligned parallel to the fiber axis. In turn, the pleats are composed ofgraphitic units. The radial open wedge probably forms by anisotropic shrinkage along the circumference of the fibers in the outer area at high temperature. Edie [69] has summarized the types of traverse textures that occur in mesophase-pitch-based CFs. The corresponding schemes are reproduced in Fig. 2.14, which highlights the striking variety of nanotextures that can be obtained from this type of precursor. It is worth mentioning at this point that the term" graphite fibers," still overused in certain contexts, is only justified when the material has a three-dimensional graphitic order. This term should therefore be limited to a few highly ordered mesophase-pitch-based CFs, which are truly graphitic, the general term "carbon fibers" being applied to the rest of the CFs. Less ordered, polyacrylonitrile (PAN)-based high-modulus and high-strength CFs have an intermediate, statistically cylindrical symmetry, which can be

2.4 Structural Characterization of Carbon Materials

33

Figure 2.13 SEM micrographs of mesophase-pitch-based carbon fibers. (Reprinted from Re£ [66] with permission from Elsevier.)

Radial

Onion-skin

Flat-layer

Radial-folded

Random

Line-origin

Figure 2.14 Traverse textures of mesophase-pitch-based carbon fibers. (Reprinted from Ref. [69] with permission from Elsevier.)

34

Chapter

2

Overview of Carbon Materials in Relation to Adsorption

generated by introducing an elongation parallel to the fiber axis into the socalled crumpled sheets of paper model (Fig. 2.7, c and g) (see below) [42]. More detailed accounts on the nanotexture of these important carbon forms can be found elsewhere [70]. As is well known, the main field of application of CFs is as a reinforcement of polymeric matrices in composite materIals for aeronautic, aerospace, and other advanced uses. Improvement of the degree of adhesion between CFs and binders in these composites depends to a large extent on the surface properties of the fibers. This has been the motive of much research work on the surface properties of CFs, including many adsorption studies, which have been reviewed by various authors [4, 5,71]. Much less ordered than PAN-based high-strength CFs are the isotropic CFs. They are produced by the carbonization of isotropic pitch fibers (or other fibrous precursors such as phenolic resins or cellulose, including rayon), without any attempt to obtain a preferred orientation of the polyaromatic molecules in the fiber direction. Consequently, they have a random nanotexture and belong to the "low modulus" class of CFs [16]. Rather than being used for high-performance reinforcement purposes, they find their application as thermal insulators for furnaces or as reinforcements for cement [1]. Another important use of isotropic CFs is as a feedstock for the production of activated carbon fibers, a material dealt with in Section 2.4.4.

2.4.3 Point Orientation Like axial orientation, point orientation, which is characteristic of materials with a spherical geometry, falls into two extreme characteristic types. One is concentric, found, for instance, in carbon blacks [72] and carbon nanoonions [73], both of which consist of successive concentric spherical layers of BSUs. Figure 2.15 is a TEM image [74] of several carbon nano-onions (also termed multilayered fullerenes), which clearly illustrates the phenomenon of point concentric orientation. Many similar (but generally not so clear-cut) micrographs have been published for submicrometric, spherical carbon black particles as examined by TEM. A "venerable, and much reproduced" [75] model for the nanotexture of this material [76] can be seen in Fig. 2.7a. Carbon blacks have many connections with adsorption work since the inert nature of their surface and virtual absence of porosity (while exhibiting [15] external surface areas of up to 150 m 2 / g, thanks to their small particle size) have made them suitable as reference nonporous carbon materials, especially those that have been thermally treated at high temperatures. However, it is necessary to be cautious on this point since it is common in the literature to refer to such solids as "graphitized carbon blacks." It is true that, upon heat treatment, the outermost layers of certain carbon blacks may become polyhedral through the wiping-out of defects at boundaries between BSUs [77]. Correspondingly, graphitization begins to occur there, but the size of the flat regions is known never to surpass about one-third of the particle diameter [42]. Therefore, carbon blacks are generally considered nongraphitizable as a whole [15].

2.4 Structural Characterization of Carbon Materials

35

Figure 2.15 High-resolution TEM micrograph of carbon nano-onions. (Reprinted from Re£ [74] with permission from Elsevier.)

Carbon black is produced industrially in the form of different products (e.g., furnace black, thermal black, channel black, lampblack, acetylene black) with specific properties. In addition to the relevance of carbon black for basic research on adsorption, or as a reference solid, applications of this material in fields such as elastomer reinforcement, as modifier of certain properties of plastics (UV protection, electrical conductance, color), or as xerographic toners make its surface and interfacial properties extremely important. Soot is a randomly formed particulate material similar in nature to carbon black. The main (pragmatic, rather than conceptual) difference between these two carbon forms is that soot is generally formed as an unwanted by-product of incomplete combustion of pyrolysis, whereas carbon black is produced under strictly controlled conditions. Bansal and Donnet [78] have reviewed various possible mechanisms for the formation of soot and carbon black. Soot can retain a number of tars and resins on its surface. There is therefore some interest in studying the adsorption of polyaromatic hydrocarbons in soots, especially those of environmental significance such as diesel soot. Fullerene soot (also known as fullerene black, as in fact it is produced under controlled conditions) is a material generated in various fullerene synthesis processes by condensation of carbon species from the gas phase [79]. The subject of soot versus fullerene formation led the discoverers of buckminsterfullerene to propose a new mechanism for soot formation, known as the icospiral growth mechanism [80], which was refined later [81]. In this model, growth takes place in the form of a spiraling structure which, depending on the availability of a number of pentagonal rings, will either close up (fullerene) or curl around itself like a nautilus shell (soot). This is a field to which adsorption work

Chapter

E C

1J ,

2

Overview of Carbon Materials in Relation to Adsorption

0

-->..

A _-+ ----.... G-- ~__~ _.....~....

IISS-lllJI

A

o

B

11 11 1111'1 II.

c

m:n.-:::::z:ma E

F

Figure 2.16 Schematic model of the alignment of aromatic layers in carbon spherules with radial point orientation of basic structural units (BSUs). Several types of sections and the corresponding cross-sections of the spherules are also indicated. (Reprinted from Ref. [82] with permission from Elsevier.)

could contribute interesting results in order to clarify (i) the still eXIstIng controversy about the possible connection between fullerenes and soot/carbon black formation and (ii) the structure of soot/carbon black particles, which remains unresolved [75] despite the fact that these materials are among the oldest known carbonaceous solids. The radial arrangement is the other extreme type of point orientation. One of the carbon materials exhibiting a nanotexture very close to this model is the carbon spherule formed from mixtures of polyethylene and polyvinyl chloride by carbonization under pressure (30 MPa) [82]. A similar, although less "perfect" situation corresponds to mesophase spheres (Fig. 2.6), which are close to the radial point orientation near their surface. However, in their centers the orientation of the layers is not radial [83]. Figure 2.16 shows a model for the nanotexture of carbon spherules, where small aromatic layers are assumed to align approximately on circular conical surfaces with a common vertex at or near the center of the spherule. This proposed model was supported by an electron microdiffraction study of various micro-areas of sections of the spherules and by scanning electron microscopy, which evidenced the formation of a definite system of cracks on heat treatment to 3073 K [82].

2.4.4 Random Orientation Positioned directly opposite to planar orientation in Fig. 2.10 is random orientation, which is typical of highly disordered carbon materials such as chars, activated carbons, wood charcoals, or low-rank coals. The basic constituents of these materials are randomly intermingled, many of the spaces between them forming either opened or closed pores. "Pure" random orientation is found in

2.4 Structural Characterization of Carbon Materials

37

carbon materials just after the carbonization of some precursor polymers, and also in glass-like carbon [2]. The latter carbon form is nongraphitizable and exhibits uncommon properties such as impermeability to gases and extremely low chemical reactivity. One of the structural models proposed to account for the behavior of glass-like carbon is the "ribbon" model of Jenkins and Kawamura [84, 85], illustrated in Fig. 2.17. This assumes that the molecular orientation in the polymer precursor material is retained to some extent after carbonization. According to this model the "fibrils" in the polymer become curved and twisted ribbons of graphite-like carbon. Since the basic constituents of glass-like carbon cannot be directly imaged by TEM due to their very small size, the modeling of their nanotexture has often been based on a TEM examination of high-temperature-treated samples. Thus, the "shell" model, proposed by Shiraishi [86] for heat-treated glass-like carbon, involves cage-like components enclosing closed pores [87]. The hexagonal layers are locally oriented in a concentric scheme. This model is considered [2] to be realistic as it agrees with the presence of closed porosity in this material and, hence, gas impermeability. More recently, Harris [75, 88] proposed a new structural model that is applicable to nongraphitizable carbons in general, based on fullerene-like elements. This model is based on the examination ofTEM images, where fullerene-related particles have been observed by the authors in nongraphitizable carbons, in most of the cases treated at high temperatures. According to this DI0del, these carbons consist of discrete fragments of curved carbon sheets, in which pentagonal and heptagonal rings are dispersed at random throughout networks of hexagons. Harris has argued that this model, schematized in Fig. 2.18, is applicable to glass-like carbons prepared at temperatures of around 1273 K, since this structure probably has a low reactivity and permeability to gases compared with the "ribbon" model, particularly if there is a high proportion of completely closed particles. Glass-like carbons treated at higher temperatures are probably formed by larger basic building blocks that resemble incomplete giant fullerenes.

j • • • Lc

t

Figure 2.17 Jenkins-Kawamura "ribbon" model for glass-like carbon. (Reproduced from Ref. [85] with permission from the Royal Society.)

Chapter

2

Overview of Carbon Materials in Relation to Adsorption

Figure 2.18 Harris model for the structure of nongraphitizable carbons based on fullerenelike elements. (Reproduced from Ref. [88]. Copyright Maney Publishing.)

The next carbon forms that we will consider within the random orientation framework are activated carbons (ACs) (as well as the chars from which they are prepared). ACs (and highly porous carbons in general) have a disordered structure, which is not, however, amorphous, as has been sometimes claimed. In ACs, there is a certain two-dimensional order, but no three-dimensional graphitic ordering. The disorder in the c direction is termed "turbostratic." This concept was coined to describe a graphite-like structure with a random orientation of layer planes along the a axis and a rotation of layer planes along the c axis, so that the interlayer spacing is 0.344 nm (cf 0.335 nm in a graphite single crystal). Early models used to describe the structure of ACs included the Franklin model itself (Fig. 2.5), and a ribbon-like structure [89] somewhat similar to the Jenkins and Kawamura model for glass-like carbon (Fig. 2.17). Interestingly, these models were based on results obtained with polyvinylidene chloride (PVDC) (or Saran) char, a typical nongraphitizable material (unlike the wellknown graphitizability of polyvinyl chloride [PVC] char). Various arguments have been used to criticize these and other models based on the occurrence of Sp3 carbon besides Sp2 carbon in nongraphitizable materials [10, 75]. Oberlin and coworkers [42,90] (Fig. 2.7c) used a "crumpled sheets of paper" model to describe the nanotexture of porous carbons. Figure 2.19 depicts this model and includes an enlarged sketch of pores in sucrose-based carbons [91]. In Fig. 2.19a, each zone of molecular orientation is represented by a shaded area inside of which each individual stack is shown either as a rectangular unit or as two parallel segments depending on whether they are observed in perspective

39

2.4 Structural Characterization of Carbon Materials

(a)

(b)

Figure 2.19 Sketches of crumpled sheet nanotexture of a sucrose-based high-temperature char. (a) Enlarged representation of pores and (b) model of crumpled sheets of paper. (Reprinted from Re£ [91] with permission from Elsevier.)

or edge-on. In sucrose-based carbons, which are typically nongraphitizable, the BSUs are locally oriented in very small regions, so that the LMO is smaller than 10 nm, and the LMOs are distributed at random in a given fragment. According to Rouzaud and Oberlin [91], during the release of heteroatoms that takes place when the sucrose is carbonized, the diameter ofLMOs remains practically constant, whereas their thickness decreases. Due to this, numerous small pores develop with an irregular entangled shape following the crumpled sheets of paper model [39]. Harris and coworkers [92, 93] have proposed that their model that is based on fullerene-like elements developed for nongraphitizable carbons in general (Fig. 2.18) may be applicable to PVDC chars and sucrose chars heat-treated to 2373-2873 K, where they detected closed nanoparticles that were usually faceted and often hexagonal or pentagonal in shape. The authors argue that such particles derive from fullerene-related structures present in the original, freshly prepared carbons (when examined by TEM, the low-temperature carbons were usually featureless and did not reveal a detailed structure, although occasionally some very small closed particles were found there) [88]. The model based on these findings (Fig. 2.18) predicts a micropore size of the order of 0.5-1.0 nm, which is similar to the pore sizes observed in many (ultra)microporous chars or carbons activated to low burn-off The empty spaces left between the fullerene-like fragments in Fig. 2.18 are not slit-shaped, but Harris [75] argues that micropores in carbons may have random shapes, as has been found either experimentally or by theoretical calculations. Harris [75] has also pointed out that his model based on fullerene-like elements has some connections with the so-called random schwarzite structure [94], which is based in turn on the ordered schwarzite structure [95] (the term schwarzite was coined after the German mathematician H.A. Schwarz, who first investigated the periodic minimal surfaces). The key feature of schwarzite is the occurrence

Chapter

4°

(a)

2

Overview of Carbon Materials in Relation to Adsorption

(b)

Figure

2.20 Possible structures for ordered schwarzite (a) and random schwarzite (b). (Reprinted with permission from Ref. [94]. © 1992 The American Physical Society.)

of negative curvature (in the Gaussian sense of the word) due to the presence of heptagonal rings. In an ordered schwarzite there is only negative curvature (Fig. 2.20a), whereas random (amorphous) schwarzites (Fig. 2.20b) contain pentagons (besides heptagons) and therefore combine concave and convex surfaces to yield solids that contain pores of molecular dimensions. Whatever the significance of the similarity between Harris' and schwarzite models (the random schwarzite shown in Fig. 2.20b should contain pores in the order of 0.5-1.0 nm, as in the model in Fig. 2.18), it is certain that schwarzites, if they occurred, would bring a new flavor to adsorption studies on carbons in both fundamental and applied fields. Their structure is continuous, with no edges or dangling bonds and would act as a kind of carbon sponge [96] with homogeneous pores of (perhaps tunable) molecular dimensions. Studies on the simulation of gas adsorption on schwarzites are reviewed in Chapter 14. However, despite many attempts to synthesize schwarzites [15], these efforts seem to have been fruitless to date, at least in the case of the ordered ones. Something similar occurs with certain hypothetical combinations (Fig. 2.4) of Sp3, Sp2, and sp hybridized atoms (graphdiynes, fullerenediynes), which could form potentially porous, molecular carbon solids [96, 97]. To obtain these, active research programs based on synthetic chemistry routes have been launched [15, 98]. To return to activated carbons, these can occur in very different physical forms: granular (or particulate), powdered, fibrous, or even membrane (the latter can be either unsupported, or, more commonly, supported). These basic physical forms can be combined with binders and extruded to form pellets, monoliths, or even paper. All of these materials, which are very frequently used as adsorbents, differ significantly in shape, but not in their intrinsic nanotextural features. All of them are isotropic and have their BSUs randomly oriented. Although they are specifically treated in Chapter 17, activated carbon fibers (ACFs) and derived cloths and felts deserve special mention here due to their uniform pore size distribution (PSD) and small and uniform fiber diameter, which confer on them, respectively, both size selectivity and rapid

2.4 Structural Characterization of Carbon Materials

41

adsorption/desorption kinetics. As announced at the end of Section 2.4.2, ACFs are produced from nongraphitizable (and hence isotropic) fibrous precursors [99, 100], and therefore, their nanotexture is also random. Indeed, anisotropic carbon fibers cannot be activated physically, and perhaps only chemical activation with a strong alkali may render them porous. The uniformity in pore size of ACFs is generally attributed to their small diameter (rv 10 f.Lm), so that many pores are directly open to the outer surface, porosity development proceeding by pore deepening rather than the creation of new pores. In some outstanding cases of pore size homogeneity such as polyaramid-derived ACFs, a certain "memory effect" seems to exist, whereby a highly ordered structure in the precursor yields a denser, less defective char than those prepared from other precursors [101, 102]. Carbon molecular sieves (CMSs) are porous carbons with an even narrower distribution of pore size (or, more precisely, of pore entrance size), which have the ability to differentiate between molecules of similar dimensions on the basis of adsorption kinetics. A key step in producing CMSs is the deposition of carbon on pore entrances [103], which is carried out usually by the CVD of hydrocarbons. Needless to say, CMSs have a nanotexture that is as randomly oriented as that of the parent ACs or ACFs on which the CVD was carried out. A type of carbon with a characteristic bimodal PSD is carbon gel [104]. The porosity of carbon gels consists of mesopores located between the constituent particles (or "nodules" [105]) and micropores located within these particles [15]. The various existing types of carbon gels (carbon xerogels, aerogels of cryogels) differ from each other in the type of drying (evaporative, supercritical, or freezedrying, respectively) to which their organic precursor gels (e.g., resorcinolformaldehyde gels) were subjected. Carbon gels retain to a large extent the mesoscopic structure of their parent organic gels [15]. They are therefore nongraphitizable and isotropic. Their nanotexture is random, as one might expect for carbons derived from the polymers used to produce the parent organic gels. We will not discuss here models for pores in carbons, as this topic is treated in Chapter 5, and elsewhere in specialist [15] or general reviews [106, 107]. For similar reasons, we will not discuss porosity control [44, 108] in detail. However, porous carbons prepared by the template technique, especially the ordered ones, deserve special attention. Ordered mesoporous carbons have been known to scientists since 1989 when two Korean groups independently reported their synthesis using mesoporous silicas as templates [109, 110]. Further achievements have been described in more recent reports [111, 112]. One might have expected that the nanotexture of these materials would merely reflect the nature of the precursor used, namely phenol-formaldehyde [109] or sucrose [110] in the two first ordered mesoporous carbon syntheses (as is well known, these two precursors would have yielded randomly oriented, isotropic carbon had they been pyrolyzed/activated under more conventional conditions). However, the mesopore walls in some ordered mesoporous carbons exhibited a graphite-like, polyaromatic character [113, 114], as described in Chapter 18. This information was obtained by nitrogen adsorption at low relative pressures, as in classical

Chapter

42

2

Overview of Carbon Materials in Relation to Adsorption

studies of highly homogeneous exfoliated graphite surfaces [115-117], and were in agreement with XPS results. Ryoos group has gone a step further and prepared a family of mesoporous carbons composed of graphitic framework structures consisting of discoid graphene sheets. This was the first case of porous carbons having a structural regularity on both the meso- and atomic scale [118]. The range of mesopores achievable by the template method is limited by the structure of the available templates. To overcome this limitation, Li and Jaroniec [119] developed a method, whereby, in contrast with the so-called colloidal templating technique (which involves a fluid-type carbon precursor), the so-called colloid-imprinted carbons are prepared by imprinting solid particles ofa mesophase pitch (used as carbon precursor) with colloidal silica particles. The primary pore structure ofthe resulting mesoporous carbons (which have spherical mesopores in the ""'-'6-60 nm range) can be preserved upon graphitization. In addition, the latter treatment made the resulting materials more energetically homogeneous and attractive for chromatographic separations [120]. The case of zeolite-templated, ordered microporous carbons (ZTCs) appears even more intriguing. Kyotani and coworkers [121, 122] were the first to succeed in synthesizing this type of material by carbonizing a precursor (acrylonitrile, furfuryl alcohol) polymerized in zeolite nanochannels, followed by the deposition of carbon from propylene by CVD. Some of the ZTCs obtained had [123] a BET surface area as high as 4100 m 2 / gl, (the surface area value decreased to 3730m2 /g 1 when calculated by the "subtracting pore method" [124]) a finely tailored micropore size and a long-range periodicity originating from the parent zeolite. The material was observed by scanning tunneling microscopy [125] to consist of carbon clusters about 1 nm in size. The porosity therefore is probably made up of the voids that separate the clusters. These clusters must have formed inside, and adapted themselves to the supercages of the zeolite Y template, and would appear to consist of nanographenes with a curved topology. In connection with the latter point, we believe that the recent discovery [126] of a method to isolate individual graphenes may pave the way for unexpected findings in the field of carbons in general and in that of adsorption by carbons in particular. This first example of a truly bidimensional material that is also the thinnest conceivable object will shed light on whether or not graphenes of different sizes are flat or curved, continuous or discontinuous, and whether they may be made to curl into, e.g., random, or even ordered, schwarzites. We are undoubtedly at the dawn of an exciting new era of carbon science.

2.5

CONCLUSIONS

The well-known basic structures of diamond and graphite are offset by others (carbynes) which, although they are scarce and even their existence is doubted, contribute to our understanding of structural trends in carbonaceous solids as a function of the type of chemical bond present.

References

43

Carbon forms with major Sp2 hybridization may be phenomenologically classified into graphitizable and nongraphitizable. The criterion established to differentiate these two classes is too empirical, and there are important exceptions (e.g., polyimide-derived carbons) to this rule. Nevertheless, these two concepts are useful for purposes of classification. Structural criteria provided by techniques such as X-ray diffraction, Raman spectroscopy, and, especially, transmission electron microscopy help to establish a rational classification of the wide range of carbon materials. The degrees of graphitization and orientation of the basic constituents justify the properties of very different types of carbon solids. The planar, axial, point, and random types of orientation of the BSUs, plus the situations in between, give rise to a wide variety of solids that have different relations with adsorption. Although random nanotexture is particularly relevant as it gives rise to a well-developed porosity, other nanotextures are also important in relation to other aspects of adsorption by carbons. Models developed to describe the molecular structure of carbons are subject to continuous improvements due to the need to obtain accurate descriptions of features evidenced by experimental results.

ACKNOWLEDGMENTS Financial support from the Spanish CSIC is gratefully acknowledged.

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a.L.

Chapter

2

Overview of Carbon Materials in Relation to Adsorption

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ENERGETICS OF GAS ADSORPTION BY CARBONS: THERMODYNAMIC QUANTITIES Eduardo J. BottanP and Juan M.D. Tasc6n 2 Ilnstituto de Investigaciones Fisicoqufmicas Te6ricas y Aplicadas (lNIFTA), UNLP-CIC-CONICET, La Plata, Argentina; 21nstituto Nacional del Carb6n, CSIC, Oviedo, Spain

Contents 3.1 Introduction 3.2 Classical Thermodynamics 3.3 Statistical Mechanics 3.4 Thermodynamic Quantities and Experimental Results 3.5 Conclusions Acknowledgment References

3.1

53 54 59 66 71

71 72

INTRODUCTION

This chapter is concerned with the energetics of gas adsorption on carbons, or more specifically the thermodynamic quantities involved when carbon materials are employed as the adsorbents. Out of these solids, activated carbons, due to their exceptional surface area development and consequent technological implications, are the carbonaceous adsorbents that have attracted the attention of most publications. A more comprehensive account of the energetic aspects of adsorption on carbons has been published elsewhere [1]. The behavior of molecules adsorbed on the surface of a solid depends on the properties of both the adsorbent surface and the adsorbate itself Among the most relevant characteristics of the adsorbent are its chemical nature, its Adsorption by Carbons ISBN: 978-0-08-044464-2

© 2008 Elsevier Ltd. All rights reserved.

53

Chapter 3 Energetics of Gas Adsorption by Carbons: Thermodynamic Quantities

54

topography, and the presence of impurities. For the adsorbate, it is important to consider molecular size, shape, and its electronic configuration. It has also been demonstrated that temperature or, more precisely, the thermal energy of the adsorbate and lateral interactions are factors from which a balance is established that defines the thermodynamic properties of the adsorbed phase. Since it is the interactions that determine the behavior of the adsorbed phase, the problem reduces itself to one single concept: energy. This justifies the relevance of the thermodynamic aspects of adsorption that constitute the subject analyzed here. Relevant previous publications on adsorption energetics include, besides the classical text by Gregg and Sing [2], a more recent book by Rouquerol et al. [3] on adsorption by powders and porous solids. This book covers thermodynamic aspects of adsorption at the gas-solid and liquid-solid interfaces, and an entire chapter is devoted to adsorption on activated carbons. In addition, two books by Bansal et al. [4, 5] review in commendable detail the literature on adsorption by activated carbons. The task of reviewing the thermodynamics of gas adsorption by carbons is complicated by several factors. One of them is the variability of carbon materials discussed in Chapter 2. 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 recent work, assuming that older studies may be outdated by new ones thanks to advances in instrumentation and to the logical progress of SCIence. This chapter includes cursory descriptions of the classical and statistical thermodynamic approaches to gas adsorption in the form of a summary of the main equations. These aspects provide the basic knowledge necessary to design, understand, and interpret the experiments and the data derived from them. We complete this with a brief description of the basic principles and applications that constitute the bridge between theory and experiments. In every section, a certain logical order of presentation is maintained. We group the results obtained on homogeneous surfaces followed by those obtained from heterogeneous solids. Each group begins with adsorption of simple gases and is followed by other adsorbates of increasing complexity. Finally, papers dealing with adsorption of gas mixtures are discussed.

3.2

CLASSICAL THERMODYNAMICS

Several formalisms have been developed leading to what may be called practical thermodynamics. These treatments include the analog of solution thermodynamics, where the adsorbent and the adsorbate are considered as components in a two-phase equilibrium [6]. Another way to study the system is to use the surface excess approach, whereby the properties of the adsorbed phase are determined in terms of the properties of the real two-phase multicomponent

3.2 Classical Thermodynamics

55

system and the properties of the same system without an interface [7]. This method could be considered as an extension of solution thermodynamics [8]. Its main shortcoming is that specification of the reference system is sometimes problematic. The most preferred approach for studying the thermodynamics of adsorption on solids 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 inertness of the adsorbent presupposes that no chemical reactions between it and the adsorbate are possible, 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. According to the law of conservation of energy, the total energy U is a constant provided that the system is isolated and its volume remains constant. Thus, oUS,V,n

=0

(3.1)

where V is the volume, n is the amount of substance, and S is 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 in his classical papers on the thermodynamics of small systems [9], it is possible to divide the adsorption space into small elements. These elements are sufficiently large to enable the characterization of the gas contained in them, and small enough to allow the thermodynamic properties inside them to be considered as local ones. Since the first law of thermodynamics must be valid for each of the space elements, Eqn (3.1) takes the form (3.2) where the superscript identifies the space element and J.L is the chemical potential. 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. A more useful form of Eqn (3.2) can be derived through the concept of spreading pressure, by assuming that the force per unit area perpendicular to the surface of the solid is different from the force per unit area on the plane parallel to the surface. The resulting equation is dU(a)

= TdS(a) -

c/J(a)dA(a) -

pd V(a)

+ j.Ldn(a)

(3.3)

Equation (3.3), written for the adsorbed phase, can be used to derive expressions relating to experimental quantities like the amount adsorbed at a given temperature and pressure, such as

{s(a) - S(g)} d T = {V(a) -

V(g)}

dp + ~d

(3.4)

56

Chapter 3 Energetics of Gas Adsorption by Carbons: Thermodynamic Quantities

where p is the vapor pressure of the adsorbed layer, and where the tildes indicate a mean molar quantity. From Eqn (3.4), it is possible to obtain ClausiusClapeyron-type expressions. Moreover, ifthe spreading pressure is kept constant,

sea) v(a) -

S(g)

(3.5)

V(g)

or, if a constant temperature is maintained,

(d¢) = dp

[v(a) _

V(g)]

n(a)

A

T

(3.6)

Several enthalpies can be obtained to describe the adsorption equilibrium. The first is the so-called equilibrium enthalpy, qeq:

_q = eq

[;(a)

+pv(a) + cPA n(a)

-

[;(g)

-pV(g)

(3.7)

Assuming that the gas phase is ideal and that the density of the adsorbed phase is close to the density of the bulk liquid it is possible to arrive at (3.8a) or dlnp ) ( dT cf>

(3.8b)

Equation (3.8) shows that the equilibrium enthalpy can be calculated from experimental data, i.e., if the dependence of the isotherm on temperature at constant spreading pressure is known. However the use ofEqns (3.8a) and (3.8b) is cumbersome because it requires the previous calculation of the spreading pressure instead of the use of raw experimental data, i.e., n(a) vs p. Furthermore, the molar quantities appearing in Eqn (3.7) are not the natural variables for adsorption systems. In preference to molar quantities, partial molar entropy and internal energy are generally used; these quantities measure the changes in these properties when an infinitesimal change occurs in the number of adsorbed moles at constant temperature, pressure, and area. To be able to relate these quantities to experimental measurements, differentiation of the chemical potential of the adsorbed phase (in Eqn (3.7)) and rearrangement finally leads to (3.9) This expression gives the definition ofthe enthalpy known as isosteric enthalpy of adsorption. Equation (3.9) can be simplified to

T (V(g) -

(3.10) v(a))

3.2 Classical Thermodynamics

57

Again, as in the case of Eqn (3.8), if the adsorbed phase is assumed to be liquid-like, Eqn (3.10) reduces to

(

dlnp ) dT n,A

(3.11)

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 adding gas, in a reversible manner, to the calorimeter containing the adsorbent. An alternative process could be considered as a way to simplify the problem. Instead of adding gas to the system, imagine that the adsorbed molecules are transferred from the gas phase to the adsorbed phase by the action of a piston that changes the gas phase volume by an amount d V(g) . Assuming that the area of the adsorbate is unchanged during the process, that the adsorbed phase is liquid-like, and that the gas phase is ideal, it is possible to derive the expression _ qad -

qst

+ V (g)

(

dp ) d (a) n

(3.12) 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 enthalpies of adsorption are obtained either calorimetrically or from the dependence of the isotherms on temperature. Although the definitions given above for the different enthalpies of adsorption are rigorous, it is necessary to show that they exhibit the same properties as the enthalpy of vaporization, i.e., the heat necessary to vaporize one mole ofliquid at constant pressure and using a reversible and isothermal process. Moreover, only the isosteric enthalpy is related in a simple way to the heat required in a process that is reversible and isothermic. Suppose that moles of adsorbate are transferred to the gas phase at constant temperature and pressure. According to the first law of thermodynamics:

an

(3.13) If the area of the solid is kept constant, this expression leads to

(oQ) A

ou(a)) = (On(a)

On(a) + T,p,A

OV(g)) +p ( - on(g) On(g)

(OU(g))

-On(g)

on(g)

+ p (ov(a)) -On(a)

on(a) T,p,A

(3.14)

Using the definitions of mean molar and partial molar quantities, Eqn (3.14) becomes (3.15)

Chapter 3 Energetics of Gas Adsorption by Carbons: Thermodynamic Quantities

58

Since Bn(g)

= -on(a) = On, Eqn (3.15)

can be written as (3.16)

According to Eqn (3.9) 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 infinitesimal amount of adsorbate from the adsorbed phase to the gas phase at constant temperature, pressure, and area. Up to this point the essential equations have been presented. Now, it is possible to analyze the work carried out in connection with the classical thermodynamic approach. The first systematic study of a thermodynamic adsorption quantity was perhaps the work done by de Boer and coworkers [10] on the determination, interpretation and significance of the enthalpy and entropy of adsorption. Their papers analyzed almost all aspects of the experimental determination of the entropy and how to interpret the values obtained in terms of two extreme models, i.e., those of mobile and localized adsorption, which today have lost much of their usefulness. To catalog the behavior of the adsorbed film as localized or mobile is a very simplistic solution and it has been demonstrated [9] that in most cases the adsorbed film is neither completely localized nor completely mobile. This approach also is somehow outdated because numerical simulations provide a better microscopic interpretation of the system's behavior. Fomkin et al. [11] have reported a slightly different treatment in which they use Eqn (3.11) to calculate the isosteric heat of adsorption of perfluoropropane adsorbed on PAC (powdered activated carbon) microporous carbon. Agarwal et al. [12] determined the entropy of the adsorbed phase for methane, ethane, ethylene, propane, carbon dioxide, and nitrogen adsorbed at high pressures on activated carbon. Bottani et al. [13] also employed the classical approach to obtain the entropy of the adsorbed phase for N 2 and CO 2 adsorbed on "graphitized" carbon blacks. The authors discussed several problems regarding the precision of the obtained values using Eqn (3.11) or equivalent equations, and how they could be employed to characterize the surface of carbonaceous materials. More recently, Sircar et al. [14] employed the Gibbsian Surface Excess model to describe the multicomponent adsorption of gas mixtures. They also showed that this model for multicomponent adsorption could define unambiguously the isosteric heats of adsorption for the components of a gas mixture. These variables can be experimentally determined using multicomponent differential calorimetry and then be used to describe the nonisothermal behavior of practical adsorbents. Mezzasalma [15] 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. Milewska-Duda et al. [16] employed the thermodynamic approach described above to derive an adsorption isotherm, similar to the BET equation, which

3.3 Statistical Mechanics

59

can describe adsorption in microporous structures provided that restrictions for pore capacity are taken into account. Asnin et al. [17] demonstrated that the classical thermodynamic approach does not contradict the molecular statistical theory and that it yields equations that are more general. Based on Eqn (3.4) and similar expressions for the internal energy, they analyzed the particular case of the Freundlich adsorption isotherm. With data obtained from Kr adsorption on high-modulus carbon fibers, Drzal et al. [18] determined the isosteric heat of adsorption and the entropy of the adsorbed phase and demonstrated that such fibers, which undergo a high-temperature graphitization treatment, possess a very homogeneous surface very similar to that of the basal plane of graphite. Sircar [19] has presented a thermodynamic treatment ofgas mixture adsorption on heterogeneous adsorbents with particular emphasis on the estimation of the isosteric heat of adsorption. He stated that the isosteric heat of adsorption on an energetically heterogeneous adsorbent could vary substantially depending on the fractional loadings of the adsorbates, which, in turn, depend on the equilibrium gas-phase pressure, temperature, and composition. Myers [20] has developed thermodynamic equations for adsorption of multicomponent gas mixtures on microporous adsorbents based on the principles of solution thermodynamics. He argued that the conventional spreading pressure and surface variables, which describe bidimensional films, must be abandoned for adsorption in micropores, in which spreading pressure cannot be measured experimentally or calculated from intermolecular forces. Li et al. [21] recently reviewed the progress made 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. [22] reported values of the free energy, enthalpy, and entropy of adsorption of volatile organic compounds (exemplified by benzene and methylethylketone) on seven samples of activated carbon. The starting point for their development was Eqn (3.11) for the isosteric heat of adsorption. Linders et al. [23] determined adsorption heats from the adsorption equilibrium constant and found that these values agree quite well with those obtained from uptake experiments using the integrated form ofEqn (3.11). They analyzed the experimental data obtained for n-butane adsorbed on two commercial activated carbons (Kureha and Sorbonorit B3) and for hexafluoropropylene adsorbed on activated carbon.

3.3

STATISTICAL MECHANICS

The statistical mechanics formalism is probably the most efficient way to connect molecular models with experimental data. We present here a brief summary of the most important equations used for numerical simulations. Of all the statistical ensembles that can be employed, the canonical and grand canonical

60

Chapter 3 Energetics of Gas Adsorption by Carbons: Thermodynamic Quantities

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 the volume elements dr l' dr 2' • • • , dr N located at r l' r 2' •• • , r N is given by the Boltzmann expression (3.17)

where

zt)

is the normalization factor given by (3.18)

Here V is the volume available to the gas molecules and U(r 1 , r 2 , ••• , r N ) is the potential energy of the N molecules. Thus U can be taken as the sum of two terms, gas-solid (Ugs ) and gas-gas (Ugg ) interaction energies: N

L

U(r1,r2, ... ,rN)=LUgs(r;)+

Ugg(rij)

(3.19)

l~i<j~N

i=l

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 (3.19) 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 [8]. 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, 7) [24]. For the adsorbed phase the partition function can be written as z(a) N Q( N " V T) -- N!A3N

(3.20)

where A is a factor that includes the kinetic properties of the molecule. Equation (3.20) shows that the partition function can be written as the product of a configurational factor and a kinetic or nonconfigurational factor, A. This greatly simplifies the application of this approach to the theory of physical adsorption [8]. The main assumption implicitly contained in Eqn (3.20) is that the structural properties of the molecules are independent of the intermolecular interactions in all the important configurations of the system. Even though there is evidence to suggest that this is not strictly true, it is possible to derive the appropriate expressions to calculate the extent of the changes in those properties

61

3.3 Statistical Mechanics

when the molecule is adsorbed. The thermodynamic properties of the system can be calculated from the following expressions:

(3.21)

A=-kTlnQ alnQ )

U=-k a(l/T) (

Q) aln-kT ( av(a)

(3.22) N,v(a),A

(3.23)

P-

N,T,A

Q

A,. (aln o/-kT - -)

aA

(3.24) NT vCa)

where A is the Helmholtz free energy, U is the total energy, p is the pressure, and
(3.25)

where V* is the volume of the gas in its standard state and thus equal to NkT. Using Eqns (3.20) and (3.22) give -U(a)

== k [ alnZt) ]

a(l/T)

_ vCa) A NCa)

3

kN(a) aInA a(l/T)

(3.26)

Equations (3.20) and (3.25), for the gas phase, gives

- U(g)

3

==

kN(g) -alnA -a( 1/ T)

(3.27)

From Eqns (3.26) and (3.27)

au(a) [ a 2 lnZt) ] U = aN(a) = -k aNa(l/T)

alnA 3

-(a)

vCa) ,A,NCa)

+k a(l/T)

(3.28)

and u(g)

fJ(g)

=-

N(g)

alnA 3

= k--a(l/T)

(3.29)

62

Chapter 3 Energetics of Gas Adsorption by Carbons: Thermodynamic Quantities

Since the isosteric heat is given by

qst =

_U(a)

+ [;(g) + kT

(3.30)

substituting Eqns (3.28) and (3.29) into (3.30) yield

qst

=k[

a2lnZt) ]

+ kT

(/)

aNa 1 T

(3.31)

VCa),A,NCa)

In the canonical ensemble approach, the adsorbed phase is treated as a separate phase with a known volume and containing a fixed number of molecules at constant temperature. This approach is somewhat unrealistic even though the results obtained can be successfully correlated with experimental data [8]. If we consider that the gas-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 fixed variables are the volume, temperature and chemical potential. The unknown quantities would be, e.g., the number of molecules, energy, and pressure. The chemical potential of the adsorbed phase, once the equilibrium condition has been 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 defined 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-solid interactions. The grand partition function for the system with gas-solid interactions is given by

a= L

N~O

Q N (V, T) exp

(J-LN)

(3.32)

kT

where QN is the canonical partition function and J-L is the chemical potential. Assuming ideal behavior for the gas, and using Eqn (3.20), the following set of equations can be derived for the thermodynamic properties of the system: alnS) N- ( N ) ( alna T, V,A alnS )

U=-k ( a(l/T)

(3.33)

(3.34) JL,V,A

4>A+pV = kT In

a

(3.35)

As indicated at the beginninmg of this section, the statistical mechanics approach is employed to connect molecular models with experimental data. It is used as well to give a theoretical basis to empirical models or to test

3.3 Statistical Mechanics

other theoretical models. For example, an isotherm equation was derived by Chen and Yang [25] for the adsorption of gases and vapors on microporous and mesoporous solids based on statistical mechanics principles. The empirical Dubinin-Astakhov (DA) and Dubinin-Radushkevich (DR) equations were then shown to be approximated forms of such an isotherm equation. Another example is the isosteric heat of adsorption of simple fluids on flat surfaces derived from a two-dimensional equation of state. Good agreement was found between the calculated values and the experimental results taken from the literature [26] for many adsorbate-adsorbent systems. The comparison was satisfactory for a wide variety of adsorbate-adsorbent systems, which was taken as an indication that molecules confined within micropores may be treated as two-dimensional fluids. Garbacz et al. [27] 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 in order to describe several sets of experimental data, especially the ones containing "graphitized" carbon black as an adsorbent. Floess and VanLishout [28] calculated the adsorption energy for different surfaces and pore configurations summing the Lennard-Jones potential for the gas-solid interaction of a molecule with a graphite finite-size basal plane surface. They showed that restricted diffusion occurs only for a small range of pore sizes between c. 0.64 and 0.58 nm. In larger pores, the adsorbate is mobile, whereas pores smaller than 0.58 nm are assumed to be largely inaccessible. Murata and Kaneko [29] proposed a new equation of the absolute adsorption isotherm [30] for a supercritical gas in order to describe the adsorption of methane on activated carbons. The environmental aspects of supercritical gases confined in nanospaces have been reviewed by Kaneko [31]. The model assumes that the adsorption in micropores is slightly enhanced compared with that on a flat surface. The authors supported this assumption on the basis of comparison plots of experimental data obtained on activated carbons and flat surfaces like nonporous carbon black. Several aspects of the adsorption of self-associating molecules in microporous structures have been developed by Talu and Meunier [32]. Their approach is similar to that of 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 by three parameters: Henry's law constant, saturation capacity, and reaction constant for "cluster" formation in the micropores. To describe a set ofisotherms obtained over a certain temperature interval, the theory can be used with five temperature-independent parameters to determine the entire phase behavior including the heat of adsorption. Besides obtaining a good agreement with experimental data, they found that the dimerization enthalpy of water in the micropores is lower than that in the vapor phase. Rudzinski and Panczyk [33] 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 the rate of adsorptiondesorption with the chemical potentials of bulk and adsorbed molecules. Of the

Chapter 3 Energetics of Gas Adsorption by Carbons: Thermodynamic Quantities

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. In particular, it uses as starting point both the Langmuir isotherm and the integral adsorption equation. The authors concluded that the parameters obtained with the statistical rate theory reproduced very well the behavior of both the kinetic and equilibrium aspects of isothermal adsorption measurements, and the parameters had a fully physical meaning. The absolute rate theory can fit the kinetic adsorption measurements at constant temperature (kinetic adsorption isotherms) using many sets of parameters, but some of the parameters determined always lacked physical meaning. Pan et al. [34] used the nonlocal density functional theory (DFT) [35] and the three-process Langmuir model (TPLM) [36] to predict the adsorption heats of propane and butane on carbon and compared these results with experimental data determined from isotherms measured on BAX-activated carbon (Westvaco) in the 297-333 K temperature interval. Both models agreed in showing that the adsorption heat for butane was c. 10 kJ/mol higher than that of propane at the same loading. The satisfactory 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 classic technique. Following the same approach, Pan et al. [37] also predicted the adsorption heats of three binary gas mixtures (C0 2-C 2 H 4 , CH 4-C 2 H 6 , and CH 4-C 3 H g ) on homogeneous (BPL-6 carbon) and heterogeneous carbons (Westvaco BAX) at 350 K (here, homo/heterogeneity refers to the pore sizes). The isosteric heats showed complex behavior for the nonideal systems (the CH 4 -C 2 H 6 and CH 4-C 3 H g 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 [38] proposed an equation of state for the 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 the desorption quantities (enthalpy, entropy, and free energy), which have the advantage of being linearly correlated with the desorption properties of the pure components of the mixture. Bhatia [39] 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 CO 2 adsorption on Carbolac measured by Carman and Raal [40]. He concluded that the experimental data are best predicted when adsorbate mobility, based on the chemical potential gradient, is taken to have an activation energy equal to the isosteric heat of adsorption at low coverage, obtained from the Henry's law region. He also concluded that the choice of the local isotherm

3.3 Statistical Mechanics

65

affects the predictions for the dependence of the diffusivity on coverage, even among isotherms that fit the equilibrium data equally well. Shekhovtsova and Fomkin [41] 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 [42] to describe the behavior of several adsorbates on activated carbons. The adsorbates employed included several alkanes, hydrogen sulfide, and carbon monoxide. The isosteric heats of adsorption for all gases were determined using the Clausius-Clapeyron equation. Cerofolini and Rudzinski [43] have reviewed the theoretical principles of single gas and mixture adsorption on heterogeneous surfaces. Their review is chronologically arranged from the earliest to the latest approaches. In the same book, Tovbin [44] reported the application of lattice-gas models to explain mixed-gas adsorption equilibria on heterogeneous surfaces; he also discussed [45] the kinetic aspects of adsorption-desorption on flat heterogeneous surfaces. The book [46] also contains other papers on different aspects of adsorption for the reader interested in surface diffusion processes. It is generally accepted that the adsorption of binary and ternary vapor mixtures by activated carbon beds can be successfully described by combining the Dubinin equation with the theory of Myers and Prausnitz [47]. A major advantage of this approach lies in the simplicity of the parameters required to describe the adsorption of vapor mixtures over a wide range of pressures and temperatures. Moreover, the combination of this method with computer simulation models developed by Ladugie et al. [48] extends the theory to the case of dynamic adsorption by activated carbons. Wintgens et al. [49] employed this approach to investigate the adsorption of vapor mixtures on activated carbons. The components were immiscible in the liquid state. They concluded that it

is possible to predict the adsorption of vapor mixtures corresponding to miscible and immiscible liquids if the variation of the characteristic energy of one component is taken into account. Riccardo and coworkers [50, 51] reported the results of a statistical thermodynamic approach to study linear adsorbates on heterogeneous surfaces based on Eqns (3.33)-(3.35). In the first paper, they dealt with low dimensional systems (e.g., carbon nanotubes, pores ofmolecular dimensions, corners in steps found on flat 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 correctly assessing the configurational entropy of the adsorbed phase. Rzysko et al. [52] presented a theoretical description of adsorption in a templated porous material. Their method of solution uses expansions of size-dependent correlation functions into Fourier series. They tested

66

Chapter 3 Energetics of Gas Adsorption by Carbons: Thermodynamic Quantities

their method for model systems composed of hard spheres, or more specifically a hard sphere fluid in a polydisperse hard sphere disordered quench matrix.

3-4

THERMODYNAMIC QUANTITIES

AND EXPERIMENTAL RESULTS

The connection between experimental results and thermodynamic quantities gives rise to different problems depending on the experimental design employed to obtain the data. In what follows we will 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 carry out these experiments at constant pressure (or spreading pressure), but in general experiments are not carried out under these conditions. This is the reason why Letoquart et al. [53] recommend expressing the experimental data in terms of internal energy. In this way, writing the necessary expressions to calculate all the thermodynamic quantities is straightforward. Another problem arises from the fact that most thermodynamic equations have been deduced for a closed system, which is often not the experimental situation [53]. As usual, we consider the solid adsorbent to be inert, in the sense that its internal energy is 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 the exchange of matter and a certain amount of work. In this case, one is tempted to introduce thermodynamic potentials, i.e., to introduce entropy. Nevertheless, we feel it more prudent to find a way to relate the experimental data with the internal energy without introducing any additional hypothesis. The evaluation of internal energy change allows the energy conservation law to be used in two ways. We assume that our system contains c components distributed among 'P phases. During the adsorption process the system receives some work (W), heat (Q), and a certain amount of moles of the ith component (LlNi ) from the exterior, each one having a known molar internal energy, B ie . Under these conditions the change in internal energy is given by i=c

~E

= W+Q+" L...J B·

Ie

~N.I

(3.36)

i=l

Alternatively, if the ith component has a molar internal energy Bij 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 j=cp i=c

LlE

= LLLl (NijBij) i=l i=l

(3.37)

3.4 Thermodynamic Quantities and Experimental Results

Using Eqns (3.36) and (3.37) it is easy to obtain the expression that gives the experimentally determined thermal effect, Q, in terms of the internal energies. The result is j=({) i=c

i=c

"" d (N..lJ e lJ..) - "" Q = "" ~~ ~ e·Ie dN. - W I

j=l i=l

(3.38)

i=l

Consider an infinitesimal 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 Eqn (3.38). Thus (3.39) where we have used the fact that dN = dNa + dNg . If we also use the fact that the gas admitted into the adsorption cell is at the same temperature (thus its internal energy does not change), it is possible to write Eqn (3.39) as follows: (3.40) N ow it is necessary to calculate the work involved, d W. Given that the gas is ideal, it follows that:

dW=PoV

(3.41)

This equation is easily transformed into (3.42) 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 Eqn (3.42) leads to

dW = RTdNa + VgdP

(3.43)

Substituting into Eqn (3.40): (3.44) This equation can be written in an equivalent form to show that it corresponds to a differential heat of adsorption. (3.45) 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

68

Chapter 3 Energetics of Gas Adsorption by Carbons: Thermodynamic Quantities

and the slope of the isotherm. We must now consider the fact that Eqn (3.45) is valid if the gas is reversibly admitted into the adsorption cell, a condition that is seldom obtained. We must now develop the expressions corresponding to a finite addition of gas. The heat experimentally measured corresponds to a change in the number of adsorbed moles, flNa = N z - N l . Equation (3.45) must be integrated, giving

The result is

Q = (B az -

Bg ) N aZ - (B al - Bg ) N al -

RT (Naz - N al )

-

Vg (Pz - Pl )

(3.47)

The first and second terms of this equation are the integral heats of adsorption, Qint. Thus,

Q

= Qint_ Qint-RTdN z 1 a

Vg (PZ -P) 1

(3.48a)

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, these pressures and the volume of the adsorption cell (the so-called dead space). In a completely analogous way, it is possible to obtain an expression corresponding to the adiabatic heat of adsorption. The final result is

(3.48b) Now we will discuss a series of papers using the classical thermodynamic, the statistical thermodynamic, direct determination of the heat of adsorption, or a combination of these methods. The theory behind each paper has been outlined in the previous sections as well as in the present one. Della Gatta [54] has considered the energy changes occurring during adsorption in gas-solid and solution-solid systems in connection with the measurement of the adsorption enthalpies. He focused on the description of heat-flow microcalorimeters and calibration techniques. Piper et al. [55] 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 surrounding temperature by simple conduction), compensation calorimeters (the sample temperature is made equal to the surroundings by means of power compensation), and the "isoperibol" calorimeter (this is a conventional temperature rise calorimeter, also known as Thomsen or Berthelot calorimeter) [3].

3.4 Thermodynamic Quantities and Experimental Results

Groszek [56, 57] studied the adsorption of simple gases (C0 2, CH 4 , S02' 02' He, and N 2) on microporous carbons using flow adsorption microcalorimetry. Shen and Bulow [58] demonstrated that the isosteric adsorption technique (Eqns (3.11) or (3.31)) is a useful and effective tool to obtain highly accurate thermodynamic data for microporous adsorption systems like the heat of adsorption given by Eqn (3.47). They studied the adsorption of CO 2 and N 2-0 2 mixtures on a super-activated, almost entirely microporous, carbon (M-30, from Osaka Gas) and three faujasite-type zeolites. They also estimated the energetic heterogeneity of the solids due to specific interactions between the adsorbate and the solid. Salem et al. [59] determined several thermodynamic functions from the excess and absolute adsorption isotherms for N 2, Ar, and methane on an activated carbon (AS, used for respiratory protection) and on a 13X zeolite. They concluded that for a consistent thermodynamic interpretation ofhigh-pressure excess adsorption data it is necessary to consider the specific adsorption quantities (the ones that can be measured directly). However, such quantities depend very much on the initial values of adsorption, i.e., the region of Henry's law. If this region is not included in the experimental data, the integral molar and specific adsorption quantities are estimated with a systematic error of unknown magnitude. Another conclusion they reached is that a molecular interpretation of high-pressure adsorption 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 difficult task in the case of macroporous and nonporous solids. Rychlicki and Terzyk [60] determined the heat of adsorption and the integral molar entropy of methane adsorbed on microporous carbons with different degrees of oxidation. They found that the oxidation of the micropore surface affected the adsorption of methane because of the existence of an endothermic effect during adsorption probably due to specific adsorbate-adsorbent interactions. A similar effect was found in the case of CCl4 adsorption [61, 62]. These authors also studied the adsorption of methanol, ethanol and CCl4 on a series of microporous carbons [63] and compared the data obtained with the adsorption of the same adsorbates on a "graphitized" carbon black. They concluded that at low coverage, association of the studied gases in the micropores does not occur. The adsorption of gas mixtures has been extensively studied. For example, Wendland et al. [64] applied the Born-Green-Yvon approach using a coarse grained density to study the adsorption of subcritical Lennard-Jones fluids. In a subsequent paper, they tested their equations with simulated adsorption isotherms of several model mixtures [65]. They compared the adsorption of model gases with an 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 [66], Nguyen and Do [67] developed a new technique for predicting the multicomponent adsorption equilibria of supercritical fluids in microporous carbons. They concluded that the degree of adsorption enhancement, due to the proximity of the pore

70

Chapter 3 Energetics of Gas Adsorption by Carbons: Thermodynamic Quantities

walls, is different for different adsorbates and that it increases with a decrease in pore size. They found good agreement between their model and experimental data. Do and Do [68] have recently reviewed the adsorption of supercritical fluids in porous and nonporous carbons. Ustinov and Do [69] proposed a model for binary mixture adsorption accounting for energetic heterogeneity and intermolecular interactions based on statistical thermodynamics. This model is able to describe the molecular rearrangement of a mixture in a nonuniform adsorption field inside a cavity. The Helmholtz free energy obtained has upper and lower limits, which define a permissible range in which all possible solutions may occur. 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 Raoult's law exhibited by N 2-0 2 mixtures. Bakaev and Steele [70] 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, unlike the regular bulk solutions, which for the same approximation have a quadratic dependence on mole fractions. Experimental separation factors (selectivities) for methane-ethane mixtures on activated carbon [71] were compared with those calculated according to the lattice gas model of mixed adsorption [70] or by means of the ideal adsorption solution theory (lAST). The lattice gas model under discussion provided only rough evaluations of the selectivities in mixed adsorption but, unlike the lAST predictions, showed no dependence on the composition of the gas phase or its total pressure. 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. More recently, Ustinov and coworkers [72, 73] developed a thermodynamic approach based on an equation of state to model the gas adsorption equilibrium over a wide range of pressure. Their model is based on the Bender equation of state, which is a virial-like equation with temperature dependent parameters based on the Benedict-Webb-Rubin equation of state [74]. They employed the model [75, 76] to describe supercritical gas adsorption on activated carbon (Norit R 1) at high temperature, and extended this treatment to subcritical fluid 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. More recently, Li et al. [77] have reviewed the thermodynamic basis ofa novel model ofthe combined cycle ofa solar-powered adsorption-ejection refrigeration

Acknowledgment

71

system. They described the adsorption isotherms using a virial-like equation and the heats of adsorption were calculated with expressions derived from Eqn (3.48a).

3.5

CONCLUSIONS

The determination ofadsorption thermodynamic quantities such as adsorption heats can now be performed through direct or indirect methods with a great degree ofaccuracy. The foundations of gas-solid interface calorimetry have been well established by combining adsorption microcalorimetry with adsorption in quasi-equilibrium. The experimental results reported so far, obtained from different calorimetries, concur with the values calculated from adsorption isotherms. 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. The use of the Clausius-Clapeyron equation to determine the isosteric adsorption heat has several limitations both theoretical and experimental, that are well known. Gas mixture adsorption is a field that is still waiting for a better theory to explain the experimental data. The Ideal Adsorbed Solution Theory cannot explain all the facts and needs to be replaced by a new model that includes nonideal effects, and adsorbent surface heterogeneity in particular. This field is acquiring increasing relevance because of its technological implications. Adsorption calorimetry, based on the use of different adsorbates, is now employed to probe the effects of various types of surface modification treatments on the surface chemistry of solids. The technique is employed in particular to investigate and characterize activated carbons. Recent studies show good agreement between the results from this technique and immersion calorimetry. In summary, the determination of thermodynamic quantities is almost a standard routine connected to the majority of experimental and simulation techniques. Thermodynamic models for adsorption can now be validated using both experimental and computer simulation results. New developments are regularly reported concerning new adsorption equations or models to explain experimental data of a very different nature.

ACKNOWLEDGMENT

Financial support from the Spanish CSIC is gratefully acknowledged.

72

Chapter 3 Energetics of Gas Adsorption by Carbons: Thermodynamic Quantities

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41. Shekhovtsova, L.G. and Fomkin, A.A. (1990). Discrete site model for methane adsorption on microporous adsorbents. Bull. Acad. Sci. USSR Div. Chem. Sci., 39, 867-70. 42. Wang, C.H. and Hwang, B.J. (2000). Characterizing the adsorption behaviors of various adsorbates on activated carbons via the multi-layer theory. J. Chin. Inst. Chem. Eng., 31, 333-8. 43. Cerofolini, G.F. and Rudzinski, W. (1997). Theoretical principles of single- and mixed-gas adsorption equilibria on heterogeneous solid surfaces. In Equilibria and Dynamics of Gas Adsorption on Heterogeneous Solid Suifaces, Studies in Suiface Science and Catalysis, Elsevier, Vol. 104 (W. Rudzinski, W.A. Steele and G. Zgrablich, eds). pp. 1-103. 44. Tovbin, Y.K. (1997). Application of lattice-gas models to describe mixed-gas adsorption equilibria on heterogeneous solid surfaces. In Equilibria and Dynamics of Gas Adsorption on Heterogeneous Solid Suifaces, Studies in Suiface Science and Catalysis, Elsevier, Vol. 104 (W. Rudzinski, W.A. Steele and G. Zgrablich, eds). pp. 105-52. 45. Tovbin, Y.K. (1997). Theory of adsorption-desorption kinetics non flat heterogeneous surfaces. In Equilibria and Dynamics of Gas Adsorption on Heterogeneous Solid Suifaces, Studies in Suiface Science and Catalysis, Elseveir, Vol. 104 (W. Rudzinski, W.A. Steele and G. Zgrablich, eds). pp. 201-84. 46. Rudzinski, W., Steele, W.A., and Zgrablich, G., eds. (1997). Equilibria and Dynamics of Gas Adsorption on Heterogeneous Solid Suifaces, Studies in Suiface Science and Catalysis, Elsevier, Vol. 104. 47. Myers, A.L. and Prausnitz, J .M. (1965). Thermodynamics of mixed-gas adsorption. AIChEJ., 11, 121-7. 48. Ladugie, P., Lavanchy, A., and Touzani, R. (1992). Study of a simple model for chemical adsorption by active carbon beds. Math. Eng. Ind., 3, 247-64. 49. Wintgens, D., Lavanchy, A., and Stoeckli, F. (1999). Static adsorption, by activated carbons, of vapour mixtures corresponding to immiscible liquids. Adsorpt. Sci. Technol., 17,761-9. 50. Ramirez-Pastor, A.J., Pereyra, V.D., and Riccardo, J.L. (1999). Statistical thermodynamics of linear adsorbates in low dimensions: application to adsorption on heterogeneous surfaces. Langmuir, 15, 5707-12. 51. Riccardo, J.L., Ramirez-Pastor, A.J., and Roma, F. (2002). Multilayer adsorption with multisite occupancy: an improved isotherm for surface characterization. Langmuir, 18, 2130-4. 52. Rzysko, W., Sokolowski, S., and Pizio, 0. (2002). Theory of adsorption in a polydisperse templated porous material: hard sphere systems. J. Chem. Phys., 116, 4286-92. 53. Letoquart, C., Rouquerol, F., and Rouquerol, J. (1973). Heats of adsorption.l. Heats of physisorption derived in terms of internal energy from experimental data. J. Chim. Phys., 70, 559-73. 54. Della Gatta, G. (1985). Direct determination of adsorption heats. Thermochim. Acta, 96,349-63. 55. Piper, J., Morrison, J.A., Peters, C., and Ozaki, Y. (1983). Heats and entropies of adsorption ofN 2 on grafoil at 79.3K.J. Chem. Soc. Faraday Trans. I, 79, 2863-74. 56. Groszek, A.J. (1997). Heats of adsorption and desorption of CO 2, CH 4 , S02' O 2 and N 2 on microporous carbons. Carbon, 35, 1399-405.

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57. Groszek, AJ., Avraham, I., Danon, A., and Koresh,].E. (2002). Interaction of0 2 , N 2 and He at room temperature with carbon molecular sieves sensed by adsorption measurements. Colloid Surf. A, 208, 65-70. 58. Shen, D. and Bulow, M. (1998). Isosteric study of sorption thermodynamics of single gases and multi-component mixtures on microporous materials. Microporous Mesoporous Mater., 22, 237-49. 59. Salem, M.M.K., Braeuer, P., Szombathely, M.V., et al. (1998). Thermodynamics of high pressure adsorption of argon, nitrogen, and methane on microporous adsorbents. Langmuir, 14, 3376-89. 60. Rychlicki, G. and Terzyk. A.P. (1995). Energetics of methane adsorption on microporous activated carbons.]. Therm. Anal., 45,1183-7. 61. Rychlicki, G., Terzyk, A.P., and Szymanski, G.S. (1993). Thermodynamic properties of CCl4 adsorbed on microporous activated carbon. Polish]. Chern., 67, 1121-30. 62. Rychlicki, G., Terzyk, A.P., and Zawadzki, ]. (1994). The influence of carbon surface oxidation on thermodynamic properties of carbon-tetrachloride adsorbed at different temperatures. Polish]. Chern., 68, 557-63. 63. Rychlicki, G., Terzyk, A.P., and Zawadzki,]. (1993). Low-coverage adsorption of methanol, ethanol and carbon-tetrachloride on homo and heterogeneous surface differential heat and integral molar entropy. Polish]. Chern., 67, 2019-28. 64. Wendland, M., Salzmann, S., Heinbuch, D., and Fischer,]. (1989). Born-GreenYvon results for adsorption ofa simple fluid on plane walls. Mol. Phys., 67,161-72. 65. Wendland, M., Heinbuch, D., and Fischer,]. (1989). Adsorption of simple gas mixtures on a plane wall: Born-Green-Yvon for structure, adsorption isotherms and selectivity. Fluid Phase Equil., 48, 259-77. 66. Ding, L.P. and Bhatia, S.K. (2001). Application of heterogeneous vacancy solution theory to characterization of microporous solids. Carbon, 39, 2215-29. 67. Nguyen, C. and Do, D.D. (2001). Multicomponent supercritical adsorption in microporous activated carbon materials. Langmuir, 17, 1552-7. 68. Do, D.D. and Do, H.D. (2003). Adsorption of supercritical fluids in non-porous and porous carbons: analysis of adsorbed phase volume and density. Carbon, 41, 1777-91. 69. Dstinov, E.A. and Do, D.D. (2002). Mixed gas equilibrium adsorption on zeolites and energetic heterogenity of adsorption volume. Langmuir, 18, 3567-77. 70. Bakaev, V.A. and Steele, W.A. (1996). Adsorbed mixtures on a heterogeneous surface. The lattice gas model. Langmuir, 12, 6119-26. 71. Richter, E., Schutz, W., and Myers, A.L. (1989). Effect of adsorption equation on prediction of multicomponent adsorption equilibria by the ideal adsorbed solution theory. Chern. Eng. Sci., 44, 1609-16. 72. Dstinov, E.A., Vashchenko, L.A., and Polyakov, N.S. (2001). Statistical model of equilibrium adsorption of non-ideal mixtures on zeolites. Russ. Chern. Bull., 50, 220-7. 73. Dstinov, E.A., Do, D.D., Herbst, A., et al. (2002). Modeling of gas adsorption equilibrium over a wide range of pressure: a thermodynamic approach based on equation of state.]. Colloid Interface Sci., 250, 49-62. 74. Benedict, M., Webb, G.B., and Rubin, L.C. (1940). An empirical equation for thermodynamic properties of light hydrocarbons and their mixtures I. Methane, ethane, propane and n-butane.]. Chern. Phys., 8, 334-45.

Chapter 3 Energetics of Gas Adsorption by Carbons: Thermodynamic Quantities

75. PoIt, A., Platzer, B., and Maurer, G. (1992). The Bender equation of state for 14 polyatomic pure substances. Chern. Tech. (Leipzig), 44, 216-24. 76. Platzer, B. and Maurer, G. (1993). Application of a generalized Bender equation of state to the description of vapour-liquid equilibria in binary systems. Fluid Phase Equilibria, 84, 79-110. 77. Li, C.H., Wang, R.Z., and Lu, Y.Z. (2002). Investigation of a novel combined cycle of solar powered adsorption-ej ection refrigeration system. Renewable Energy, 26~ 611-22.

MONTE CARLO AND MOLECULAR DYNAMICS Mary

J.

Bojan and William A. Steele

Department of Chemistry, The Pennsylvania State University, University Park, PA, USA

Contents 4.1 Introduction 4.2 Overview of Computer Simulations 4.3 Conclusions References

4.1

77 78

97 98

INTRODUCTION

Computer simulations have become an indispensable tool in the efforts to forge links between the behavior of molecules on the atomic level and experimentally measurable properties. This has been especially true in the area of surface science in general and specifically in studies of carbon surfaces. Due to the abundance of experimental data for gases interacting with carbon surfaces, and because carbon surfaces are relatively simple, many of the pioneering simulations of surface phenomena involved studies of gases interacting with homogeneous (graphite) and heterogeneous carbon surfaces. Pioneering studies include the Monte Carlo (MC) simulations of Ar interacting with graphite by Rowley et al. [1-3] and the molecular dynamics (MD) simulations of N 2 on graphite by Talbot et al. [4-6]. As computers became more powerful, the expense of computing dropped, making it possible to simulate systems of ever-increasing size and complexity. At the same time, the complexity and cost of experimental work has made simulations even more indispensable since simulation results often suggest interesting directions for experimentation while they continue to aid in the interpretation of the results. The goal of MC and MD simulations is to calculate properties of a particular macroscopic thermodynamic system from the configurations (positions and Adsorption by Carbons ISBN: 978-0-08-044464-2

© 2008 Elsevier Ltd. All rights reserved.

77

Chapter 4 Monte Carlo and Molecular Dynamics

velocities) of many microscopic states. The techniques differ in their approach to generating the configurations. With MC a completely stochastic (probabilistic) algorithm is used, while in MD, the method is deterministic. In this context an ensemble is a collection of a large number of systems (made up of particles) constructed to be a replica on a macroscopic level of the thermodynamic system of interest. In MD, the configurations in a particular thermodynamic ensemble are generated by solving the equations of motion for the collection of classical particles (atoms or molecules) moving in a potential field created by other particles or by a surface. In MC, new configurations are generated by making random changes to molecular positions that are accepted when they drive the system toward the desired thermodynamic ensemble. The experimentally accessible properties of a system are state functions such as p (density), j.L (chemical potential), TJ (shear viscosity), C v (heat capacity), D (diffusion coefficient), and S(k) (structure factor). They depend on the thermodynamic state of the system characterized by variables such as temperature (T), pressure (P), volume (V), and number of particles (N). The configurations determined in MC and MD simulations are the positions (and momenta, for MD) of particles at an instant in time (or space). The collection of these configurations describes the mechanical (or microscopic) state of the system. Statistical Mechanics provides the connection between the thermodynamic state and the mechanical state. Simply put, the theory tells us that if I know the positions of a collection of molecules as a function of time, I know everything about the thermodynamic properties of the system. This means properties such as P, j.L, S (entropy), E (internal energy), and phase equilibria, can be calculated from the configuration information. Furthermore, if the positions and velocities of a collection of molecules as a function of time are known, everything about the dynamic properties of the system can be determined as well (e.g., transport coefficients, diffusion, spectroscopic properties, and response times). There is an important assumption underlying these statements: that I know how the particles interact with each other and their surroundings, i.e., it is assumed that we know the potential energy surface = U pot • Thus the goal of MD and MC simulations is to produce a large number of configurations constructed in such a way as to be replicas on a microscopic level of the thermodynamic system of interest. In this way, the configurations can be used to determine the thermodynamic and dynamic properties of interest and can be studied to understand the microscopic behavior that gives rise to thermodynamic properties.

4.2

OVERVIEW OF COMPUTER SIMULATIONS

It is impossible in a short space to explain all that one needs to know to understand and perform computer simulations. Here we will attempt to lay the framework and refer the reader to texts [7-10] where the details can be

79

4.2 Overview of Computer Simulations

explored. Both MD and Me simulations can be broken into the following steps. (1) (2) (3) (4)

Select a model Initialize a system Generate configurations (positions and momenta) using either MC or MD Calculate properties of interest from the configurations

4.2.1

Selecting the Model This can be broken into three main steps:

(1) Describe how the molecules interact with each other and the surroundings (or define the potential energy surface Upot ) (2) Set dimensions and boundaries (3) Choose the ensemble

4.2.1.1

Potential energy surface

The most important step in the simulation is the development of the potentials. The more closely the model potential fits reality, the more reliable the results will be. The ideal potential then would be a potential that is obtained from a quantum electronic calculation. However, such potential energy surfaces are complex and time consuming to calculate, and difficult to use directly. In practice, most model potentials take simple mathematical forms with parameters that can be determined either from experimental data or by fitting to results of ab initio calculations. Fortunately, there are many good publications devoted to the development of models for gas-surface interactions in general [11] and specifically for interactions of gases with carbon surfaces (Steele) [12-16] so only

a brief description need be given here. The models for gases interacting with carbonaceous surfaces can be broken into terms that depend on the coordinates of the interacting particles and the surface. First, one must describe the interaction of the adsorbate molecules with one another. For monatomic adsorbates, this can be done via an approximate (double) sum over distinct pairs of interacting molecules: (4.1) U2

(rij) is a function that describes the pair interaction and rij is the distance

between the interacting particles and equals Iri 12-6 potential function is commonly used:

-

~

I.

The Lennard-Jones (L-J)

(4.2)

80

Chapter 4 Monte Carlo and Molecular Dynamics

where B gg and lTgg are the potential well depth and hard sphere collision diameter, respectively, and the gg subscripts indicate parameters determined for the adsorbate-adsorbate interaction. The values of the parameters are obtained from previous studies of the bulk phases [13]. If a more complex adsorbate is being studied, (N2 , CO 2 , water, etc.) the orientation dependence should be added to the model. For the linear N 2 molecule, e.g., a three-site L-J pair potential is typically used [17]. The three sites correspond to the N atoms and the center of mass. The interaction between the atomic sites is taken to be a L-J 12-6 potential function, and partial charges are placed on the three sites in the molecule to reproduce the known quadrupole moment. The other essential term in the description of the model describes the interaction ofthe molecule with the carbon surface. In the earliest computer simulations of carbonaceous surfaces, graphite was chosen as a model system since there was already a great deal of experimental data available and because the development of a model potential to describe the interaction of molecules and atoms with the surface was relatively easy. Typically, the description of the interaction of a monatomic molecule with the graphite surface is approximated as a sum of the interaction of an adsorbate particle with each atom in the surface.

U1

(r;)

= 4e~ [ (~~

y2- (~~ r]

(4.3)

Ul (rJ = 4egs [ ( ~s 12 _ ( ~~' )6] )

where U 1 (ri ) is a function that describes the interaction often denoted by ugs (ri ) and ri is the distance between the interacting particle and a C atom in the surface. In the basic model of the potential, U 1 (rJ is taken to be a L-J (12-6) function, but here B gs and lTgs are often determined through use of combining rules:

B gs

= ( BggB ee )

1/2

,

(4.4)

where the CC subscript denotes parameters for the interaction of pairs of C surface atoms. In most studies, the value for the carbon surface parameters is taken to be Bee = 34 K and cree = O.34nm. These were determined by fitting the L-J 12-6 potential to experimental data. (See Chapter 2 in Steele's book for review of early development of potential parameters [16].) In the work of Rowley et al. [1-3], the grand canonical Monte Carlo (gcmc) method was used to simulate Ar interacting with graphite. The surface was approximated as a continuum. In such a case, the sum in Eqn (4.3) is replaced by an integral in the x, y, and z dimensions (the graphite solid) and the potential reduces to a L-J 9-3 form that is a function only of the distance of the atom

4.2 Overview of Computer Simulations

81

from the surface. A slightly more realistic potential frequently used is known as the summed 10-4 potential. It is the result of assuming that the variation in the potential in the basal plane of graphite is negligible so that one can integrate the 12-6 function in the x and y dimensions and leaving a potential form where one must sum over the planes (layers) of graphite.

(4.5) Here Zi is the distance of the adsorbate above the surface, as is the area per carbon in the graphite basal plane, and the sum over j denotes the jth layer in the graphite with zij( = Zi + jd) being the distance of the adsorbate from the jth layer and d is the distance between basal planes (= 0.340 nm). An early use of this potential was in the high-temperature study of the adsorption of methane in porous carbon ofBojan et al. [18]. For studies where the periodicity of the graphite surface plays a role in the determination of properties, (e.g., low-temperature determinations of the structure oflayers adsorbed on graphite), the Fourier expanded molecule-surface potential of Steele is commonly used [4-6, 19]. For complex geometries such as heterogeneous surfaces (see Bojan et aI., coal pores [20]) and fullerenes [21] (Martinez-Alonso et aI., Ar on C 60 ), a full sum ofthe direct atom-atom potentials is needed. In the recent simulation studies of carbon nanotubes, some studies have used asummed atom-atom potential description (e.g., see the work of Stan et al. [22]) while others use a continuum cylindrical pore model [23, 24]. These two terms (the adsorbate-adsorbate interaction and the adsorbatesolid interaction) are the essentials that must be included in the interaction potential. However, depending on the degree ofaccuracy needed in the potential description, terms can be included to take three body effects into account. Although this contribution to the gas-surface potential can account for as much as 10% of the interaction [25], to simplify computations, three-body interactions are often included implicitly via parameters in the potentials. Potentials of this nature are referred to as effective pair potentials. 4.2.1.2 Boundary conditions

Once the model potential has been selected, appropriate system size and boundary conditions must be set. When working with a flat surface (e.g., graphite), the solid surface is typically located at Z = 0 and a reflecting wall is placed at a distance Zmax above the surface. Any particles that reach this top of the simulation cell undergo an elastic collision. This is done to insure conservation of mass. The height above the plane is chosen to minimize volume size without influencing the properties of the adsorbed system. The x and y dimensions of the system are made as large as possible (or as needed), given the constraints of the model and computer resources. At the x and y borders, periodic boundary conditions are typically imposed. This is the mathematical equivalent of having

82

Chapter 4 Monte Carlo and Molecular Dynamics

an infinite surface in the x and y dimensions. This is done simply by having particles that cross a simulation boundary on one side of the simulation cell enter the simulation cell on the other side, with the same direction (and speed). For a model where a periodic surface potential is being used, the x and y dimensions must be an integral number of unit cells so that there will be no discontinuities in the potential at the boundaries. For studies in cylindrical pores (nanotubes, coal pores), the carbon potential defines the x, y dimensions (or r, () dimension) and periodic boundary conditions are imposed along the z-dimension (axis of the cylinder) rendering the pore effectively infinite in length. Details of how these boundary conditions are implemented in a simulation can be found in books such as those by Allen and Tildesley [7], Frenkel and Smit [8], and Haile [9]. In choosing system size, one must also consider the properties being calculated. The size must be chosen to reproduce the proper thermodynamic state (e.g., give the appropriate density) and the dimensions must be large enough so that the imposition of periodic boundary conditions does not affect the value of the properties being calculated. In practice, this means that the dimensions of the box must be large compared to the extent of the long-range interactions or the correlation length of the property of interest. Most attractive interactive forces die away quickly so that boundaries on order of 5 or more molecular diameters are usually sufficient when calculating many thermodynamic properties such as density and energy distributions, chemical potential, and structure. However, for properties that depend on interactions that do not die away quickly (such as electrostatic energies) or properties where the correlation length is long, larger system sizes are necessary. Problems with size effects (incorrect results due to use of small system sizes) have been seen, e. g., in simulation studies of surface solid formation and surface melting. For example, see the recent work by Roth [26], where the structure and melting of Kr adsorbed on graphite was studied using MD simulation. Roth found that the use of a small system size resulted in an increase in the melting temperature of 10K or more depending on the system size when reflecting boundary conditions were used. In other words, when too small a system size is used, the surface structure appears to be more ordered than in a very large system.

4.2.1.3 Ensemble selection Since the goal of a simulation is to calculate properties of a particular macroscopic thermodynamic system from the configurations of many microscopic states, the final consideration in model selection is the choice of the thermodynamic state of the system. This can be done by fixing three thermodynamic variables (such as pressure, P, temperature T, internal energy, E) and designing the simulation so that these functions remain constant throughout the calculation. The choice of the thermodynamic state defines the ensemble and since the ensemble is chosen based upon the properties of interest, more details about the different ensembles will be given in Section 4.2.4.3.

4.2 Overview of Computer Simulations

4.2.2 Initialization Once the model has been chosen and set up, the simulation needs only to be initialized. The key in initializing the simulation is to be sure to start at some reasonable configuration. This means that all particles in the initial configuration must have positions (and velocities in an MD simulation) that are inside the simulation boundaries and that particles do not overlap. One way to do this is to assign specific (lattice) positions to the number of particles in the simulation cell using the particles' diameter (at least) to provide for adequate spacing between particles. Another simple way to initialize is to use a configuration (positions and velocities) from a previous simulation that used the same geometry. A third way is to use the gcmc algorithm for creating and deleting particles to initialize the system, i.e., allow particles to be created in this algorithm until the required density (or number of particles) is achieved then switch to the algorithm for the ensemble being used in the simulation. Once initial positions and velocities of the particles in the simulation have been assigned, a number of simulation steps are done to equilibrate the system. The total number of steps that is needed in this part depends on the model and the density of the system. In practice, the investigator must ascertain the number of steps needed for equilibration for their situation. This is done by monitoring one or more of the average properties as a function of time (or number of steps). When the block averages (averages taken over small blocks of time say 500-1000 steps) remain constant, one can assume that the system has equilibrated and data gathering (or production) runs can begin. During the data-gathering phase of the simulation, configurations and thermodynamic averages can be saved. These are the results that are used to calculate the properties of interest.

4.2.3 Generating Configurations Although there are variations: the two main ways of generating configurations (positions or positions and velocities) are MD and MC techniques. These two methods will be described by considering a collection of atoms or molecules (particles) in the canonical or microcanonical ensemble, i.e., we will assume that the number of particles, the volume and either the temperature (T) or total potential energy (E) are held constant in the simulation. (NVT, NVE). MC and MD techniques for generating configurations in the other ensembles (with other thermodynamic variables held constant) have been developed and are described in Allen and Tildesley [7] and Frenkel and Smit [8].

4.2.3.1 Molecular dynamics In MD, solving the classical equations of motion generates configurations (positions and momenta). These can be written as

rnd 2 r

Newton's equation F = rna = - second-order differential equation dt 2

Chapter 4 Monte Carlo and Molecular Dynamics

dr p v=-=Hamilton's equation dt m d coupled first-order differential equations d F=mv=J!..

dt

dt

where m is the mass, F is the force, a is the acceleration, t is the time, v is the velocity, p is the momentum = mv, and r is the position. Given the initial positions and velocities of the particles, the initial accelerations can be calculated from the forces.

F

=-

dUtot(r) dr

= ma

(4.6)

where Utot(r) is the potential that describes the interaction of the particles in the simulation with each other and with the solid or any other external field. Integrating the equations of motion produces positions and velocities of the particles as a function of time. The algorithms for solving these equations are well known with the Verlet and Predictor-Corrector methods being the most commonly used. (For further details of the derivation and implementation of these algorithms see Allen and Tildesley [7], and Frenkel and Smit [8].) In a typical simulation, it is necessary to perform on the order of 40 000 or more steps in the integration and use 500-1000 configurations to calculate the dynamic and thermodynamic averages needed to determine the properties of interest. Because the integration of the equations of motion is done with respect to time, it is the size of the time step (dt in the equations of motion) that determines the stability (correctness) of the solutions. Physically, this means that the time step must be small compared to the characteristic timescale of the properties of interest to obtain meaningful results. For dynamic properties such as diffusion, the time steps needs to be two or three orders of magnitude smaller than the characteristic timescale of the property. For example, in the simulation studies of diffusion in cylindrical carbon pores [27], the mean square displacements of adsorbed molecules needed to be calculated for over 5 s in order to obtain surface diffusion constants. The requirement is that the mean square displacement become linear in time within this time (see Fig. 4.1). To get stable results a time step of 1.6 x 10-3 ps was assumed and approximately 3000 time steps (300 configurations) were used to determine the diffusion constants. For simulations where properties such as density, chemical potential, and energy are being calculated, time steps on the order of 10- 3 ps are typical and give stable thermodynamic results. However, if the systems being studied are undergoing processes with longer timescales (e.g., solid rearrangements or chemical reactions), longer timescales are needed and often multiple time scales need to be considered. Because the time dependence of atomic properties is known, both thermodynamic and dynamic properties can be calculated. This is the main advantage of MD as a method for generating configurations.

85

4.2 Overview of Computer Simulations

6....-----------r"'----------.. NP=10

NP=30

NP=50 NP=60

NP=75 NP=90

o........ :;;;;;;....---------'---------~ 5.0 2.5 0.0 Time (ps)

Figure 4.1 The time dependence of the mean square displacements for adsorbed methane at T = 300 K in the direction parallel to the pore axis is shown for a range of time sufficient for the squares of the molecular displacement to become linear functions of time. NP denotes the total number of molecules in the pore. The slopes of the linear portions of the plots give the self-diffusion constant D = 2 x slope.

4.2.3.2 Monte Carlo The basic approach to generating configurations using Me can be outlined using the following steps: (1) Generate configurations by assigning coordinates randomly, i.e., choose three random numbers (RN) between 0 and 1 for each molecule. These RN determine the x, y, and z coordinates of each particle. (2) Test the configuration: Is it acceptable? The criteria for acceptance are based on the potential energy of the configuration. One calculates Utot = total potential energy of the particles in the configuration. Then the probability of acceptance is given by P = N exp [ - Utot/kT] , where N exp is a normalizing factor so that P will range from o to 1. If the configuration has total potential energy that is negative, the probability P will be unity and the configuration will be accepted. However, if the total potential energy is positive, P will be small and the probability is high that the configuration will be rejected.

The problem with this basic approach is that when configurations are generated randomly, many impossible configurations are generated: For example, it

86

Chapter 4 Monte Carlo and Molecular Dynamics

is highly probable that two particles in a randomly generated configuration will overlap (occupy the same space). This results in an enormous positive energy, and the probability of that configuration existing is negligibly small. In other words, if we start a simulation by randomly assigning positions to all of the particles, we will usually find ourselves in a region of space far from equilibrium. In fact most configurations generated randomly will be be rejected, thus rendering the technique useless. The solution to this is to use a technique known as importance sampling or often referred to as SMART MC (see Frenkel and Smit [8, Chapter 3] for a beautiful explanation). In this technique a simulation is started with particles whose positions are already at or near equilibrium (this is the SMART part of it) and as we generate new configurations, these configurations are tested. If a newly generated configuration is highly improbable, the configuration is rejected and we return to the previous (probable) configuration and try again. In other words, if we ever start to move away from equilibrium, we take a step back (reject the move) and try moving in another direction. One of the simplest and earliest methods used to generate configurations can be used to illustrate the process. In this method (the Metropolis Method), new configurations are generated by randomly selecting a particle then displacing that particle by a small amount. The direction and size of the displacement is determined by the selection of more random numbers chosen to determine dx, dy, and dz, which represent the distance moved in the x, y, and z directions, respectively. The maximum size of the displacement (which depends on the system size, density of particles, temperature, etc.) is set during initialization. Once a new configuration has been generated the energy change that occurs due to the displacement is calculated: (4.7)

If ~ U is negative, the new configuration is accepted. If ~ U is pOSItIve, the configuration is accepted with a probability that will eventually produce a Boltzmann distribution. This is done by choosing another random number between 0 and land if exp[-~U/kT] is greater than the random number, the new configuration is accepted. However, if exp[-~U/kT] is less than the random number then the configuration is rejected. It is important to note that in order for the MC simulation technique to work, the sequence of configurations must form a Markov Chain. A Markov Chain is a sequence of trials that satisfy the following conditions:

(a) The outcome of each trial belongs to a finite set of outcomes called the state space. (b) The outcome of each trial depends only on the outcome of the trial that immediately preceeds it. In computer simulations, one scheme that is guaranteed to produce a Markov Chain imposes the condition of microscopic reversibility [7, 8]. This is simply

4.2 Overview of Computer Simulations

the condition that the probability of a transition (change to a new state) must be equal to the probability of the new state reverting back to the original state. In the Metropolis Method, a Boltzmann distribution is used to decide the probability of each transition. We can select other distributions (other ways of sampling) as long as we make sure that the condition of microscopic reversibility is satisfied. This becomes desirable when the efficiency of the simulation is low (when the percent of accepted moves is small). Techniques that use modified distributions for sampling are known as biased sampling techniques and are discussed in Chapter 13 of Frenkel and Smit [8]. For many MC simulations the maximum size of the displacement (dx, dy, dz) can be adjusted so that the percentage of moves that will be accepted is about 50 %. This percentage is easily adjusted by increasing the displacement to reduce the acceptance ratio or decreasing the displacement to increase the ratio. The actual value can be varied with density, i.e., the higher the density, the smaller the displacement needed to achieve high acceptance rates. Although some studies have been done to try to determine the best acceptance criteria [28], in practice, the value is usually determined via trial and error. There are many variations on the Metropolis Method. The most common is probably the gcmc method as developed by Norman and Filinov [29]. In this method, the chemical potential, volume, and temperature of the system are held constant and the number of particles is allowed to vary in each step of the simulation. This is done by adding creation and deletion steps to the Metropolis algorithm, and the acceptance criteria (probability distribution function for acceptance) is defined as a function of the chemical potential and density of the state. Unlike the displacement move, the acceptance rates for the creation/deletion move is typically small: rv2-10 % with the smaller acceptance ratios corresponding to simulations at high density. It is easy to understand why this occurs when one realizes that newly created particles are placed in randomly chosen locations within the simulation cell. As the density ofthe system increases, the chances that a particle will be created in a space already occupied by another particle is rather high and overlapping configurations are always rejected. The acceptance rates can be improved by incorporating a biased sampling scheme into the algorithm. See, e.g., Bojan et al. [30], where a nonuniform distribution function derived from the average potential field of the adsorbed molecules was used to increase the efficiency of the sampling distribution. A similar scheme is employed by Jiang and Gubbins [31] in their Gibbs ensemble MC simulation of CH 4 on graphite. So far, the discussion of MC algorithms has applied to monatomic adsorbates. When an adsorbate with orientation dependence is being studied, the MC displacement step should be followed by a random reorientation of the chosen molecule as well. The addition of this type of move, like the creation/deletion step, is likely to decrease acceptance probabilities and thus the efficiency of the simulations. Cracknell et al. [32] describe a biased sampling technique that is appropriate for increasing the efficiency of this step. A very clear description of

88

Chapter 4 Monte Carlo and Molecular Dynamics

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200

300

400

500

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Figure 4.2 Simulated isotherms are compared with the experimental data for CO 2 at the temperatures indicated. The curves for T> 195 K show the experimental data from Re£ [34] and the points are simulated. At 195 K, the curve shows the data of Beebe et ale [35], the triangles show the experimental data from Ref. [34] and the circles show simulated data from Ref. [34].

the gcmc algorithm as it applies to the adsorption of water in graphite slit pores is given in a recent paper by Uhlberg and Gubbins [33]. As in MD simulations, a MC simulation is performed for a number of moves to reach equilibrium. In most MC methods, the number of attempted moves to equilibrate is on order of 1 to 100 million. This is followed by another 100 million moves that provide the configurations needed to determine the desired thermodynamic averages. Using the gcmc simulation technique, Bottani et al. [34] studied the adsorption of CO 2 on graphite at four different temperatures. Figure 4.2 is a comparison of the simulation with experimental results showing excellent agreement. Each point on the simulated isotherms was obtained using the gcmc algorithm to generate 2 x 106 configurations. After each set of 100 moves the total number of particles (N) in the simulation cell is recorded and an average of the number of particles is obtained by averaging the 2 x 104 values of N obtained in this way. Since the chemical potential is fixed, the pressure can be calculated and by repeating this process at many values of the chemical potential the adsorption isotherm is obtained. Once the connection between experiment and simulation has been established, the investigators can explore the molecular configurations in the adsorbed film in more detail. Figures 4.3 and 4.4 show results obtained from the CO 2 simulation study that are not experimentally available. The first layer adsorption (Fig. 4.3) can be used to determine the monolayer capacity and thus the area per molecule in the monolayer (Am) as a function of temperature. However

4.2 Overview of Computer Simulations

100 90 80

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50

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.s ;£

T=273.2K

T = 195.5 K

40 30 20 10 0

0

20

40

60

80

100

120

140

160

N tot [molecules]

Figure 4.3 Plots of the simulated values of the number of molecules in layer 1 (Nt) versus the total number adsorbed (Ntot ) are shown for three temperatures. Note that Nt = 78 for a total number of 90 molecules at 195 K.

the area per molecule depends on the orientation of the CO 2 molecule on the surface. The molecule occupies much less space (and Am would be much smaller) if the molecule stood on end as opposed to lying flat on the surface. The snapshot of the CO 2 configuration at 195 K (Fig. 4.4) shows the orientation of the molecules on the surface and thus tells much about the structure of the adsorbate. The inclusion of the known quadrupole moment as part of the CO 2-C0 2 interaction energy has a significant effect on the simulated isotherms, which do not agree with experiment if the quadrupolar interactions are omitted. Furthermore, this interaction favors pair orientations that are T -shaped. The fluid molecules shown in the lower panel of Fig. 4.4 are mostly parallel to the surface and often in T -configurations. (Note that the low-temperature two-dimensional (2D) solid for CO 2 forms a herringbone lattice with all pairs in nearly T -orientations.) Taken together, these data help provide a more detailed picture and understanding of both the experimental and simulation results.

4.2.4 Determining Properties from Configurations The determination of dynamic and thermodynamic properties from computer simulations relies upon the assumption that observed (macroscopic) properties can be calculated by finding the time-averaged value of the property from MD « A > time) or the ensemble-averaged value of a property from MC) « A > ens') The goal of a computer simulation is to generate enough states or configurations of the system of interest to be able to evaluate such time or ensemble averages.

Chapter 4 Monte Carlo and Molecular Dynamics

9°

Figure 4.4 Shapshots of 90 molecules of adsorbed CO 2 at 195 K. The black bands indicate the central carbon atoms in each molecule. The upper panel is a side view of all 90 molecules and the lower panel is a top view of the 78 molecules in the first layer only.

4.2.4.1 Ensemble averaging In a MC simulation, the ensemble average of a property is determined by summing the value of the property in each configuration and dividing by the total number of configurations [7]. In general,

A obs = (A) ens A obs = (A)ens

= (A (f (r))) = -

1

Tobs

Tobs

= (A(f(r))) =

LA (f (r))

(4.8)

T=l

1

Tobs

-

LA(f(T))

'T obs T=l

where A obs is the observed value of a property, ens is the ensemble-averaged value of the property, fer) is the generalized coordinates (positions only) T is the index over state points, and 'Tobs is the total number of states or points generated by the MC prescription.

91

4.2 Overview of Computer Simulations

For example, in the simulation of Ar and CO 2 on C 60 fullerene by MartinezAlonso et al. [21] , the simulated isotherm was compared to experimental isotherms. Using a grand canonical ensemble, the isotherm was obtained by calculating the average number of particles in the simulation cell (Nens ) for each fixed value of the chemical potential using the MC method to generate configurations (positions of the particles in the simulation cell). 1

N ens = (N(r)) = -

Tobs

LN(r)

(4.9)

robs T=l

1

N ens = (N(r)) = -

Tobs

LN(r)

robs

1

where N(r) is the total number of particles in the simulation volume in the rth configuration. In addition to the isotherm, the configurational information can be used to obtain local density distributions of the particles on an adsorbing surface. For instance, if the adsorbent is made up of C 60 particles, the density as a function of distance from the surface shows the layers of adsorbate forming and lends insight into the structure of the surface layers as shown in Fig. 4.5. 2.5 , . . - - - - - - - - - - - - - - - - - - - - - - - - - - . ,

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2.6

2.8

3.0

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Figure 4.5 Simulated densities of Ar at 77.5 K (thick line) and CO 2 at 195.5 K (thin line) adsorbed on an fcc array of C60 molecules approximated as spherical bodies are plotted as a function ofdistance from the solid adsorbent. Adsorption on the outermost layer ofC60 spheres produces three density peaks: one at 1.4 nm in the deep (and strongly interacting) crevices located in the centers ofthe squares formed by four C60 molecules; one at 1.8 nm in the crevices between pairs of neighboring C60's; and one at rv2.1 nm for adsorbed molecules directly over a C60. Peaks at larger distances reflect structure in the adsorbed fluid, with the CO 2 density decreasing to zero after second layer formation at 195.5 K because of its relatively small amount in the simulation box compared to the Ar multilayer densities at 77.5 K.

92

Chapter 4 Monte Carlo and Molecular Dynamics

4.2.4.2 Time averaging In MD simulations, both the positions and velocities of the particles are calculated and because their time dependence is known, both thermodynamic and dynamic properties can be calculated. This is the main advantage of MD as a method for generating configurations. In this case, the time-averaged properties can be evaluated [7]:

A obs = (A)time

lim

1 {tobs

= (A (r(t))) = - - 1n

A (f(t))dt tobs 0 tobs lim 1 A obs = (A)time = (A(r(t)) = - - - A(r(t))dt tobs~oo tobs 0

(4.10)

tobs~oo

f

where A obs is the observed value of a property, < A >time is the time-averaged value of the property, and is the generalized coordinates (positions and momenta) as a function of time. In the recent simulation by Matties and Hentschke [36, 37], the adsorption and melting ofbenzene on graphite was studied via MD simulations. In addition to determining static properties such as the center of mass density distributions and tilt angles as a function of temperature by obtaining time averages, they were also able to obtain dynamic properties such as the surface diffusion constants in the monolayer and the orientational velocity autocorrelation function (OVAF).

ret)

OVAF = Z (r)

= (vxy (t) • vxy (t + r))

(4.11)

This function is a measure of the reorientation of the component of the velocity vector parallel to the surface vxy . It is calculated by choosing a molecule and following its motion as a function of time for a specified time period, averaging the velocity autocorrelation function (the dot product of the 2D vector velocity at the time t, vxy(t) with the velocity at a later time in the trajectory (vxy(t + r)). This average is calculated for all molecules and for many different initial starting times. The determination of this function can be used to understand the motion of the adsorbed benzene molecules on the surface. Negative values of this time-correlation function are the result of a constraining environment representative of a solid structure so it serves as an indicator of the transition from a solid to a liquid monolayer as temperature is increased [36]. Matties and Hentschke [37] are also able to show that even at high coverage (multilayer adsorption) and high temperature there is some semblance of solid order in the adsorbed benzene layers (see Fig. 4.6).

4.2.4.3 Results using different thermodynamic ensembles Historically, simulations using the microcanonical ensemble were among the earliest ones reported. The algorithm is easy to 5mplement both conceptually

93

4.2 Overview of Computer Simulations

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and technically since the volume (V) (simulation boundaries) and the number of particles (N) remain constant. In addition, the total potential energy (E) is held constant: (N, V, E). Although the total density (N/ V) is constant in a bulk phase, in simulations of surface phenomena the presence of the external potential (adsorbing surface) produces large variations in the density, making this ensemble useful for studying structures of adsorbed phases and energy distributions.

94

Chapter 4 Monte Carlo and Molecular Dynamics

Furthermore, while the total energy is held constant, the energy is distributed between the molecules adsorbed and in the gas phase. Therefore, the distribution of energy between these two phases can be explored and compared to experimental isosteric heats of adsorption. For example, the paper by Steele et al. [38] summarizes the results obtained for N 2 adsorbed on graphite using MD simulations in the microcanonical ensemble. Besides calculating heats of adsorption, they were able to study how the energy of the adsorbate molecules varied along the surface and use this to understand the 2D phase diagram of N 2 on graphite and the role of the quadrupole moment in the formation of the surface structures. However, despite the ease of simulations in this ensemble, it is not easy to devise an experiment where the internal energy is held constant and it is more natural to look for a technique that corresponds to the more common experimental situation of constant temperature. Canonical ensemble (N, V, T) is a variation on the microcanonical ensemble where the temperature is held constant rather than the energy. In the constraint method described by Evans and Morris [39], this is done in a MD simulation by rescaling the velocities to maintain a constant kinetic energy. A more rigorous algorithm developed by Nose [40] and reformulated by Hoover [41] introduces an additional degree of freedom into the simulation that acts as a heat bath. Energy is exchanged with the artificial coordinate and its velocity introduced to maintain a constant temperature, but nevertheless allowing for fluctuations in the kinetic energy. Studies of these techniques show that the Nose algorithm does indeed produce the correct canonical distribution in both position and momentum space. However, the isokinetic scheme has been shown to give correct canonical ensemble averages for properties that depend on coordinates [42]. Kim and Steele [43] used isokinetic MD simulations to study the phase diagram of the methane monolayer on a corrugated graphite surface. They were able to compare their simulation results for the structure of the methane monolayer to the results of neutron scattering experiments and found good agreement. Trajectory plots (plots of positions of the molecules as a function of time) obtained from this simulation at four temperatures are shown in Fig. 4.7. These traj ectories show the transition from a commensurate to an incommensurate solid, even hinting at the possibility of a two-phase coexistence. The study of phase transitions and structure is one of the goals of computer simulations; however, determining the pressure in the canonical and microcanonical ensemble can be difficult. It is done using either thermodynamic integration [44, 45], or the test particle method of Widom [46]. Both of these techniques are computationally intensive, so the development of an ensemble where the pressure can be held constant is desirable. In the isobaric, isothermal ensemble (fixed P, N, T) the pressure is held constant by varying the volume of the simulation cell. Finn and Monson [47] have developed a method for studying adsorption in an isobaric algorithm. Unfortunately, if this method is used in a simulation involving a solid surface one would have to be sure that variations of the volume are accompanied by increases or decreases in the surface area of the adsorbent. This can create significant problems in the potential

4.2 Overview of Computer Simulations

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Figure 4.7 Plot of the in-plane trajectories of adsorbed molecules at four temperatures are shown here for an incommensurate solid methane monolayer adsorbed on graphite. At the lowest temperatures, the figures show large solid patches with a few drifting particles near the patch edges. As T increases, molecules begin to enter different sublattices and to jump from one to another. (Each plot has a duration of 88 ps.) The dots are for molecules that are vibrating over a single site on the graphite and those molecules that shift from one site to another give rise to larger excursions. The trajectory plots at 55 and 56 K seem to indicate the two-phase coexistence. This possibility is supported by simulated methane-methane interaction histograms for these temperatures that show two peaks in the energy distribution, one near the maximum value for solid and one near the maximum value for the liquid. The fact that this behavior extends over a range of T is probably a finite size effect.

description (discontinuities at the boundaries must be avoided) as well as in the determination and interpretation of most structural properties. Another popular method for studying phase transitions involves the use of the grand canonical ensemble (fixed /-L, V, T), which is most commonly implemented using the MC method (gcmc) described in Section 4.2.3.2. Since the development of this technique it has become the method of choice for the determination of structural and thermodynamic properties of most adsorbateadsorbent systems. For example, Bottani et al. have recently presented gcmc simulation results for gases such as N 2 , Ar, and CO 2 adsorbed on carbon nanotubes [48] and on C 60 [49]. In their studies, the authors simulate the adsorption isotherms (number ofa particles as a function of P or /-L), and energy distributions that allow comparison of their simulations with experiments. Furthermore, after

Chapter 4 Monte Carlo and Molecular Dynamics

establishing a firm connection between simulation and experiment, the authors use the density profiles obtained from the simulation to understand where gas molecules adsorb. In studies of bundles of carbon nanotubes, by looking at density distributions they see significant adsorption in the interstitial channels and external surface at low pressures before all interior sites are full even though it is clear that adsorption inside nanotubes is preferred to adsorption outside the tubes (see Fig. 4.8). The Gibbs ensemble is a technique that allows one to study phase equilibria without an interface, by combining two simulations at the same time. In this method originally proposed and developed by Panagiotopoulos [50] two simulation cells are set up: each cell represents one of the two phases in equilibrium with each other. In this algorithm, the total N, V, and T are held constant; however, N and V vary in the separate simulation cells. The acceptance conditions for the various MC moves maintain the same chemical potential (i.e., equilibrium) in the two simulation cells. The method involves the execution of three types of MC trial moves. The first is the displacement of a randomly

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6 11 1621 2631 3641 46

X

Figure 4.8 Maps of the average density of nitrogen adsorbed in three nanotube bundles. The contours are for constant density in the x, y planes; Le., for an observer looking in the z direction parallel to the pore axes. The pore diameters are (a) 1.37 nm, (b) 1.43 nm, and (c) 0.69nm. The in-plane coordinates x, yare defined so that unit x, y== 0.07, 0.14nm, respectively. The larger blobs show density contours inside the tubes and the smaller ones are for molecules adsorbed in the interstices between the hexagonally packed tubes. The interaction potential for the N 2 is diatomic; thus, the approximate molecular length is 0.1 nm greater than the width which is 0.35 nm. The consequence is that the tube of (c) is too small to admit the N 2 molecules so that the adsorption shown there is essential all interstitial. Also, in (a) and (b), the N 2 appears to lie parallel to the tube axis and is adsorbed on the tube walls. The differences between the (a) and (b) contours are at least partly due to the differences in the numbers of molecules in these systems. These amount to 334 and 199 in (a) and (b).

4.3 Conclusions

97

chosen molecule in each cell to maintain internal equilibrium. The second is a change in the volume of one of the simulation cells that is accompanied by a corresponding volume change in the other such that the total volume remains constant. The third type of move involves the transfer of a randomly chosen particle from one simulation cell to the other (to maintain chemical equilibrium). Panagiotopoulos [51] extended the technique to simulate the coexistence offluids adsorbed in micropores. In this study, he simulated both the coexistence between the pore fluid and the bulk fluid (to obtain the adsorption isotherm) and capillary condensation in cylindrical pores. Since its development this method has been used in studies of both vapor-liquid [31] and liquid-liquid [52] phase transitions in carbon nanopores.

4-3

CONCLUSIONS

MC and MD are versatile techniques that have been shown to be powerful methods of enhancing our understanding of molecular behavior both of carbon surfaces and of the many other solid adsorbents presently in use. Although this chapter has dealt with the basics of computer simulation, there are many areas where simulators have been active that have not been dealt with in the chapter (e.g., see Chapters 5,6,8-10, and 15). In general, MD is used when transport properties are desired and MC, when thermodynamic properties are the subject of interest. An important feature is that a wide variety of experimental systems are encountered in this field, starting with flat, homogeneous, chemically uniform surfaces such as graphite, metals, and single crystals of ionic material. The algorithms initially developed to deal with such cases were soon modified and altered to handle porous materials or materials with impurities and/or imperfections in their exposed surfaces. This has enabled the researcher to dispense with the older theories that by necessity included approximations that inevitably had the possibility of invalidating the results of analyses based on such oversimplified models. It is probably fair to say that many of the advanced algorithms now in use might never have been developed if they were not required for the simulation of relevant adsorption systems. Fortunately, the advances in the analysis of complex adsorption systems have coincided with the impressive improvements in computing power needed to carry out these analyses. There are still new and exciting areas under development. These include the path integral Monte Carlo (PIMC) method where quantum systems interacting with graphite can be studied. Manousakis et al. have used the PIMC technique to study 4He and H 2 films [53-57] on graphite. They are able to simulate the low temperature structural properties, including 2D phase transitions. Johnson et al. have developed a path integral gcmc technique that allows them to calculate adsorption isotherms. Using this method, Wang and Johnson have simulated H 2 and He in carbon slit pores [58] and carbon nanotubes [59]. They have studied

Chapter 4 Monte Carlo and Molecular Dynamics

H 2 storage in graphite nanofibers [60], the feasibility of using carbon nanotubes to separate hydrogen isotopes [61] and phase behavior of H 2 and He isotopes in nanotubes [62]. Another exciting new direction that is developing is a technique known as reverse MC [63] (also see Chapter 5 of this book). In this method, rather than performing a simulation to gather configurations on an assumed solid, MC moves are made on the atomic configuration of a simple model adsorbent in an attempt to move from the original configuration to a configuration, which agrees with a previously chosen experimental property of the adsorbent such as the structure factor. The generation of carbon adsorbents whose structures match the available experimental data has been investigated by Gubbins and coworkers [64-67] using this method. Reference [66] gives a brief review of previous efforts to deal with the structural problem for porous carbons. Once model adsorbents are generated using the constrained Me technique, Gubbins et al. perform standard gcmc simulations ofN2 adsorbed on their model systems to determine pore size distributions, porosity and heats of adsorption of the model surfaces. Although this technique is quite computer-intensive, the resulting structures appear to be good representations of porous carbon as indicated by the agreement with experiment of simulations of the adsorption of simple gases in the model samples.

REFERENCES

1. Rowley, L.A., Nicholson, D., and Parsonage, N.G. (1976). Grand ensemble Monte Carlo studies of physical adsorption I. Results for multilayer adsorption of 12-6 argon in the field of a plane homogeneous solid. Mol. Phys., 31, 365-87. 2. Rowley, L.A., Nicholson, D., and Parsonage, N.G. (1976). Grand ensemble Monte Carlo studies of physical adsorption II. The structure of the adsorbate. Critique of theories of multilayer adsorption for 12-6 argon on a plane homogeneous solid. Mol. Phys., 31, 389-407. 3. Rowley, L.A., Nicholson, D., and Parsonage, N.G. (1978). Long-range corrections to grand canonical ensemble Monte Carlo calculations for adsorption systems. J. Comput. Phys., 26, 66-79. 4. Talbot, J., Tildesley, D.J., and Steele, W.A. (1984). A molecular dynamics simulation of nitrogen adsorbed on graphite. Mol. Phys., 51, 1331-56. 5. Talbot, J., Tildesley, D.J., and Steele, W.A. (1986). Molecular dynamics simulation of fluid N 2 adsorbed on a graphite surface. Faraday Disc. Chem. Soc., 80, 91-105. 6. Talbot, J., Tildesley, D.J., and Steele, W.A. (1986). A molecular dynamics simulation of the uniaxial phase of N 2 adsorbed on graphite. Suif. Sci., 169, 71-90. 7. Allen, M.P. and Tildesley, D.J. (1987). Computer Simulation of Liquids. Oxford University Press.

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8. Frenkel, D. and Smit, B. (2002). Understanding Molecular Simulation, From Algorithms to Applications, 2nd edna Academic Press. 9. Haile, J.M. (1992). Molecular Dynamics Simulations: Elementary Methods. J. Wiley and Sons. 10. Balbuena, P.B. and Seminario, J.M. (eds) (1999). Molecular Dynamics, From Classical to Quantum Methods. Elsevier. 11. Bruch L.W., Cole, M.W., and Zaremba, E. (1997). Physical Adsorption: Forces and Phenomenon. Clarendon. 12. Steele, W.A. (1973).The physical interaction of gases with crystalline solids. I. Gas-solid energies and properties of isolated adsorbed atoms. Surf. Sci., 36, 317-52. 13. Steele, W.A. (1978).The interaction of rare gas atoms with graphitized carbon black.]. Phys. Chem., 82, 817-21. 14. Watts, R.O. and McGee, I.J. (1976). Liquid State Chemical Physics. Wiley. 15. Maitland, G.C., Rigby, M., Smith, E.B., and Wakeham, W.A. (1987). Intermolecular Forces: Their Origin and Determination, Tables A3.1 and A3.2. Clarendon, pp.565-66. 16. Steele, W.A. (1974). The Interaction of Gases with Solid Surfaces. Pergamon Press. 17. Murthy, C.S., Singer, K., Klein, M.L., and McDonald, I.R. (1980). Pairwise additive effective potentials for nitrogen. Mol. Phys., 41, 1387-99. 18. Bojan, MJ., van Slooten, R., and Steele, W.A. (1992). Computer simulation studies of the storage of methane in microporous carbons. Separation Sci. Technol., 27, 1837-56. 19. Vernov, A.V. and Steele, W.A. (1986). Computer simulation of the multilayer adsorption of fluid N 2 on graphite. Langmuir, 2, 219-27. 20. Bojan, M.J., Vernov, A.V., and Steele, W.A. (1992). Simulation studies ofadsorption in rough-walled cylindrical pores. Langmuir, 8, 901-8. 21. Martinez-Alonso, A. Tascon, J.M.D., and Bottani, EJ. (2001). Physical adsorption of argon and CO 2 on C 60 fullerene.]. Phys. Chem. B, 105, 135-9. 22. Stan, G., Bojan, M.J., Curtarolo, S., et al. (2000). Uptake of gases in bundles of carbon nanotubes. Phys. Rev. B, 62, 2173-80. 23. Calbi, M.M., Gatica, S.M., Bojan, MJ., and Cole, M.W. (2001). Phases of neon, xenon, and methane adsorbed on nanotube bundles.]. Chem. Phys., 21, 9975-81. 24. Maddox, M.W. and Gubbins, K.E. (1995). Molecular simulation offluid adsorption in buckytubes. Langmuir, 11, 3988-96. 25. Kim, H.Y. and Cole, M.W. (1987). Three-body contribution to the adsorption potential of atoms on graphite. Phys. Rev. B, 35, 3990-4. 26. Roth, M.W. (1998). Bond-orientational structure and melting signature in krypton physisorbed onto graphite at complete coverage. Phys. Rev. B, 57, 12520-9. 27. Bojan, M. J., and Steele, W. A. (1993). Computer simulation studies of diffusion in physisorbed monolayers. Mater. Res. Soc. Symp. Proc., 290, 127-34. 28. Kolafa. J. (1988). On optimization of Monte Carlo simulations. Mol. Phys., 63, 559-79. 29. Norman, G.E. and Filinov, V.S. (1969). Investigations of phase transitions by a Monte Carlo method. High Temp. (USSR), 7, 216-22. 30. Bojan, MJ., Bakaev, V.A., and Steele, W.A. (1999). Smart Monte Carlo algorithm for the adsorption of molecules at a surface. Mol. Simul., 23, 191-201. 31. Jiang, S. and Gubbins, K. E. (1995).Vapor-liquid equilibria in two-dimensional Lennard-Jones fluids: unperturbed and substrate-mediated films. Mol. Phys., 86, 599-612.

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32. Cracknell, R.F., Nicholson, D., Parsonage, N.G., and Evan, H. (1990). Rotational insertion bias: a novel method for simulating dense phases of structured particles, with particular application to water, Mol. Phys., 71, 931-43. 33. Ulberg, D.E. and Gubbins, K.E. (1994). Monte Carlo implementation on the Connection Machine 2; water in graphite pores. Mol. Simul., 13,205-19. 34. Bottani, E., Bakaev, V.A., and Steele, W.A. (1994). A simulation/experimental study of the thermodynamics properties of CO 2 on graphite. Chem. Eng. Sci., 49, 2931-9. 35. Avgul N.N. and Kiselev A.V. (1970). In Chemistry and Physics of Carbon, Vol. 6, p. 65 (P. Walker, ed.). Marcel Dekker. 36. Matties, M.A. and Hentschke, R. (1996). Molecular dynamics simulation of benzene on graphite. 1. Phase behavior of an adsorbed monolayer. Langmuir, 12, 2495-500. 37. Matties, M.A. and Hentschke, R. (1996). Molecular dynamics simulation of benzene on graphite. 2. Phase behavior of adsorbed multilayers. Langmuir, 12, 2501-4. 38. Steele, W.A., Vernov, A., and Tildesley, DJ. (1987). Studies of the adsorption of N 2 on the graphite basal plane by computer simulation. Carbon, 25, 7-17. 39. Evans, DJ. and Morriss, G.P. (1983).Isothermal isobaric molecular dynamics ensemble. Chem. Phys., 77, 63-6. 40. Nose, S. (1984). A molecular dynamics method for simulations in the canonical ensemble. Mol. Phys., 52, 255-68. 41. Hoover, W. G. (1985). Canonical dynamics: equilibrium phase-space distributions. Phys. Rev. A, 31, 1695-7. 42. Nose, S. (1984). A unified formulation of the constant temperature molecular dynamics methods.]. Chem. Phys., 81, 511-19. 43. Kim, H.-Y. and Steele, W.A. (1992). Computer-simulation study of the phase diagram of the CH 4 monolayer on graphite: corrugation effects. Phys. Rev. B, 45, 6226-33. 44. Kofke, D.A. (1993). Gibbs-Duhem integrations: a new method for direct evaluation of phase coexistence by molecular simulations. Mol. Phys., 78, 1331-6. 45. Kofke, D.A. (1993). Direct evaluation of phase coexistence by molecular simulations via integration along the coexistence line.]. Chem. Phys., 98, 4149-62. 46. Widom, B. (1963).Some topics in the theory offluids.]. Chem. Phys., 39, 2802-12. 47. Finn, J .E. and Monson, P.A. (1988). Adsorption equilibria in an isobaric ensemble. Mol. Phys., 65, 1345-61. 48. Paredes, J.I., Suarez-Garcia, F., Villar-Rodil, S., et al. (2003). N 2 physisorption on carbon nanotubes: computer simulation and experimental results.]. Phys. Chem. B, 107,8905-16. 49. Martinez-Alonso, A. Tasc6n, J.M.D., and Bottani, EJ. (2000). Physisorption of simple gases on C 60 fullerene. Langmuir, 16, 1343-8. 50. Panagiotopoulos, A.Z. (1987). Direct determination ofphase coexistence properties of fluids by Monte Carlo simulation in a new ensemble. Mol. Phys., 61, 813-26. 51. Panagiotopoulos, A. Z. (1987). Adsorption and capillary condensation of fluids in cylindrical pores by Monte Carlo simulation in the Gibbs ensemble. Mol. Phys., 62,701-19. 52. G6zdz, W.T., Gubbins, K.E., and Panagiotopoulos, A.Z. (1995). Liquid-liquid phase transitions in pores. Mol. Phys., 84, 825-34. 53. Pierce, M. and Manousakis, E. (1998). Phase diagram of second layer of 4He adsorbed on graphite. Phys. Rev. Lett., 81, 156-9.

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54. Pierce, M. and Manousakis, E. (1999). Path-integral Monte Carlo simulation of the second layer of 4He adsorbed on graphite. Phys. Rev. B, 59, 3802-14. 55. Pierce, M. and Manousakis, E. (1999). Monolayer solid 4He clusters on graphite. Phys. Rev. Lett., 83, 5314-17. 56. Nho, K. and Manousakis, E. (2002). Submonolayer molecular hydrogen on graphite: a path integral Monte Carlo study. Phys. Rev. B, 65, 115409-1-12. 57. Nho K., and Manousakis, E. (2003). Commensurate-incommensurate transitions in quantum films: submonolayer molecular hydrogen on graphite, Phys. Rev. B, 67, 195411-1-7. 58. Wang, Q. and Johnson, J.K. (1998). Hydrogen adsorption on graphite and in carbon slit pores from path integral simulations. Mol. Phys., 95, 299-309. 59. Wang, Q. and Johnson, J.K. (1999). Molecular simulation of hydrogen adsorption in single-walled carbon nanotubes and idealized carbon slit pores.]. Chern. Phys., 110, 577-86. 60. Wang, Q. andJohnson,J. K. (1999). Computer simulation of hydrogen adsorption on graphitic nanofibers.]. Phys. Chern. B, 103,277-81. 61. Challa, S.R., Sholl, D.S., and Johnson, J.K. (2002). Adsorption and separation of hydrogen isotopes in carbon nanotubes: multicomponent grand canonical Monte Carlo simulations.]. Chern. Phys., 116,814-24. 62. Gatica, S.M., Stan, G., Calbi, M.M., et al. (2000). Axial phase of quantum fluids in nanotubes.]. Low Temp. Phys., 120,337-59. 63. McGreevy, R.L. and Pusztai, L. (1988). Reverse Monte Carlo simulation: a new technique for the determination of disordered structures. Mol. Simul., 1, 359-67. 64. Pikunic, J., Clinard, C., Cohaut, N., et al. (2002). Reconstruction method for the characterization of porous carbons. Stud. Suif. Sci. Catal., 144, 19-26. 65. Pikunic, J., Clinard, C., Cohaut, N., et al. (2003). Structural modeling of porous carbons: constrained reverse Monte Carlo method. Langmuir, 19, 8565-82. 66. Thompson, K.T. and Gubbins, K.E. (2000). Modeling structural morphology of microporous carbons by reverse Monte Carlo. Langmuir, 16, 5761-73. 67. Pikunic, J., Pollen, J.-M., Thompson, K.T., et al. (2001). Improved molecular models for porous carbons. Stud. Suif. Sci. Catal., 132, 647-52.

MODELS OF POROUS CARBONS Henry Bock, Keith E. Gubbins, and Jorge Pikunic Department of Chemical and Biomolecular Engineering, North Carolina State University, Raleigh, NC, USA

Contents 5.1 Introduction 5.2 Experimental Probes

1°3 1°4

5.3 Molecular Models of Carbons 5.4 Adsorption, Diffusion, Reaction 5.5 Conclusions Acknowledgments References

106

5.1

121 127 128 128

INTRODUCTION

Except for the fullerenes, carbon nanotubes, nanohorns, and schwarzites, porous carbons are usually disordered materials, and cannot at present be completely characterized experimentally. Methods such as X-ray and neutron scattering and high-resolution transmission electron microscopy (HRTEM) give partial structural information, but are not yet able to provide a complete description of the atomic structure. Nevertheless, atomistic models of carbons are needed in order to interpret experimental characterization data (adsorption isotherms, heats of adsorption, etc.). They are also a necessary ingredient of any theory or molecular simulation for the prediction of the behavior of adsorbed phases within carbons - including diffusion, adsorption, heat effects, phase transitions, and chemical reactivity. Because the chemical and physical processes involved in the synthesis of disordered porous carbons are not well understood, attempts to develop mimetic modeling procedures, in which theory or simulation methods are used to mimic Adsorption by Carbons ISBN: 978-0-08-044464-2

© 2008 Elsevier Ltd. All rights reserved.

103

Chapter 5 Models of Porous Carbons

1°4

the complete synthesis, are difficult or impossible. There have been a few attempts to use ab initio or semiempirical methods to study some particular part of the synthesis route (see Section 5.3.3.2 below). Nevertheless, the great majority of attempts to model porous carbons can be classified as reconstruction methods, in which an atomistic model of the carbon is constructed that is consistent with available experimental structure data, usually X-ray scattering or transmission electron microscopy (TEM). The simplest reconstruction models are single-pore models, of which the slitpore model is the most widely used. The pore structure is represented as a collection of single, nonconnected pores of varying width, and in some cases varying wall thickness or wall heterogeneity. In the slit-pore model, the pores have parallel walls composed of graphene sheets; frequently these are treated as smooth and structureless. This model is widely used to estimate the pore size distribution, feR), where H is pore width, by assuming that the adsorption isotherm is a linear combination of isotherms calculated for pores of different sizes. While convenient, the slit-pore model neglects many important features of real disordered carbons, including pore connectivity, wall roughness, curved and defective graphene sheets, pores of wedge, and other shapes. These neglected features are known to play an important role in many processes in adsorbed phases, such as diffusion, phase changes, and chemical reactions. More recently, more sophisticated atomistic modeling methods have been proposed for disordered carbons that take these features into account at the cost of increased complexity and the need for more experimental data. In this chapter we give an account of the most useful and promising current methods for modeling porous carbons (Section 5.3). For completeness of the discussion we also include (Section 5.2), a brief account of the most important experimental methods for characterizing carbons. Following the section on models, we provide a review ofsome ofthe recent work on predicting the behavior of adsorbed phases within such model carbons (Section 5.4), including adsorption, heats of adsorption, diffusion, and chemical reactions. A more comprehensive review of the types of carbons, experimental methods for studying them, and molecular models has appeared [1] and covers the literature up to 2000.

5.2

EXPERIMENTAL PROBES

In 1917 Debye and Scherrer performed the first powder X-ray scattering experiments on diamond, graphite, and several amorphous carbons (chars) [2]. From their experimental results, Debye and Scherrer concluded that amorphous carbons consist of small graphitic units of about 30 atoms. Scattering is sensitive to the distance between the scattering particles. If a certain distance, d, appears in a periodic fashion, we find constructive interference of the scattered radiation of wavelength, A, at an angle, 2fJ with respect to the incident radiation following Bragg's law, d = A/2sin fJ. The scattering pattern of carbon blacks and activated

5.2 Experimental Probes

105

carbons consist of the (002) three-dimensional (3D) peak and several (hk) twodimensional (2D) peaks. The (002) 3D peak indicates stacking of individual graphitic layers and allows the determination of the inter layer distance, d = 0.32-0.38 nm; 0.3354 nm is found for graphite. The absence offurther 3D peaks is caused by horizontal distortion of the individual graphene sheets within the stack, i.e., by turbostratic ordering. The 2D peaks provide information about the ordering within the graphene sheets and the carbon-carbon distance (0.1415 nm for graphite). Porous carbons generally show less inlayer ordering than graphite and usually a larger interlayer spacing, d002 . The dimensions of the graphene stacks can also be determined from the scattering data. For activated carbons, a stack height of 1 nm (2-3 layers) and a stack width of 1-3 nm is found. Strong scattering but no peaks in small-angle X-ray scattering (SAXS) (2fJ < 15°) indicate the existence of a nonperiodic pore network at length scales beyond the interlayer spacing [3]. Information about pore morphology and topology, i.e., about the relative position and orientation of the graphitic crystallites and their connectivity is accessible using TEM or HRTEM. The basic principles of TEM are similar to those of conventional light optical microscopy. The contrast in TEM originates from scattering of electrons on the atoms of the porous carbons. Scattered electrons do not pass through the small opening of the objective aperture, thus denser regions of the carbon appear darker in the TEM image since they cause more scattering. In TEM, only the direct beam passes trough the aperture; while in HRTEM also diffracted beams contribute to imaging. This results in a higher resolution and allows not only the determination of qualitative information such as shape and orientation of the pores but also quantitative information such as pore size distributions. It is even possible to obtain the interlayer distance, d002 . Since the graphene sheets in activated carbons are finite and have defects, as seen from X-ray scattering, it is obvious that they are terminated by heteroatoms, such as H, 0, N, S, and P. These atoms generate heterogeneities in the walladsorbate interaction and thus their inclusion is essential for the adsorption properties of carbon materials. To include heteroatoms in models of amorphous carbons, we must know which and how many functional groups a specific carbon material contains and where they are located. Table 5.1 lists a number of methods which can be used to identify these functional groups. The Boehm titration is a wet chemical method where a sequence of bases with increasing basicity (pKa ) is used to titrate (neutralize) substances having a pKa less or equal to that of the base. Thus it is a reliable method to obtain general information about the surface acidity. Modern potentiometric titration significantly improves the pKa resolution compared to the Boehm titration. The usage of nonaqueous solvents as in calorimetric titration increases the pKa range that can be probed. All titration methods are, however, insensitive to the chemical nature of the functional groups, only their acidity is measured. X-ray photoelectron spectroscopy (XPS) uses X-rays to eject core electrons (ls) from carbon, oxygen, nitrogen, or other heteroatoms. The binding energy

Chapter 5 Models of Porous Carbons

106

Table 5.1 Methods for the characterization of activated carbons (Adapted from Ref. [1].)

Small-angle X-ray scattering X-ray diffraction Transmission electron microscopy Gas adsorption Boehm titration Potentiometric titration Calorimetric titration Temperature-programmed desorption (TPD) Fourier transform infrared spectroscopy X-ray photoelectron spectroscopy Immersion calorimetry Flow adsorption Inverse gas chromatography

Total surface area (open and closed pores) mean pore size Mean crystallite size, carbon-carbon pair correlation function 2D images of the pore structure, matrix correlation function Porosity, pore size distributiona , surface area a pKa of functional groups, their number pKa of functional groups, their number pKa of functional groups, their number Type of oxygen functional groups (strong or weak acids)/their number Type of functional groups (number) Type of functional groups, amount of heteroatoms (number of groups) Number of primary adsorption centers (oxygenated groups) Average polarity Average acidity

aThe introduction of an approximate model or a theory is needed to extract this data from the experiments.

of the core electron is measured. Thus XPS is sensitive to the atom type and to the way this atom is bound to its environment. Fourier transform infrared spectroscopy (FTIR) probes molecular vibrations. FTIR spectra are usually analyzed qualitatively by comparison with FTIR spectra of known organic compounds. Gas adsorption is sensitive to various properties of carbons, such as pore size, surface area, and porosity. Thus, it can be used itself to analyze carbon materials. However, the data interpretation relies on appropriate models to connect the adsorption results to properties of the carbon material (see Section 5.3).

5-3

MOLECULAR MODELS OF CARBONS

5.3.1 Regular Porous Carbons Regular porous carbons are carbon materials with a simple pore geometry; they include carbon nanotubes, fullerenes, and schwarzites. If carbon nanotubes are considered for sensor applications, ab initio models are necessary to test whether adsorption of a certain molecule (e.g., N0 2 ) generates a change of the electron density of the nanotube that is large enough to use the nanotube in a sensor [4].

5.3 Molecular Models of Carbons

107

Classical models of carbon nanotubes can be subdivided into two groups: explicit geometric and mean-field models [1]. An explicit model for a single-wall nanotube is obtained by rolling-up a graphene sheet (see Section. 5.3.2) to form a cylindrical surface. Geometric constraints determine possible nanotube diameters, unit cells, and symmetries (zigzag or armchair) [5, 6]. For the carbon atom-adsorbate atom potential [6] the Lennard-Jones (LJ 12-6) potential is often used. If the adsorbate is not sensitive to the atomistic details of the nanotube, e.g., the adsorbate atoms are much bigger than the carbon atoms, a mean-field model can be derived [7]. The mean-field potential is obtained by representing the nanotube wall by an areal density of carbon atoms (LJ 12-6) rather than their explicit positions and integrating along the azimuthal and longitudinal direction (see also Section 5.3.2). The resulting potential depends only on the (normal) distance between the adsorbate and the nanotube. The integration can also be performed numerically, which might be advantageous if more complicated nanotube structures are considered [8]. The extension to multiwall nanotubes and bundles or ropes is straightforward. One obtains the total adsorbate-nanotube potential by superposition of the individual single-wall nanotube potentials. Especially in heterogeneous bundles it is necessary to find the equilibrium configuration of the bundle [9]. In the case of explicit models the relative orientation (rotation) of the individual walls of multiwalled nanotubes and the relative orientation (rotation) of individual nanotubes in a bundle must be decided too [1]. Another interesting polymorph of carbon is fullerene. Although adsorption on individual fullerene molecules and on the surfaces offullerene crystals is not widely studied, explicit [10] as well as mean-field [11] models are available for individual fullerene molecules. The fullerene crystal can be modeled by placing individual (model) fullerene molecules on the sites of an fcc lattice, to match the symmetry and density ofthe real solid [12] or to match equilibrium structures obtained from computer simulations offullerene crystals [10]. A model for a defective crystal can be obtained by removing some ofthe fullerene molecules [13]. Besides fullerenes, nanotubes, and graphite, which are finite or (quasi) infinite in one or two dimensions, regular carbon materials that are infinite in three dimensions, called schwarzites, exist. Schwarzites can be synthesized inside zeolites or other ordered porous silica materials [14]. Thus, their topology and morphology is similar to that of the template, i.e., they consist of an extended network of channels and cages, each one being separated from a neighboring one by a graphene-like wall comprising five- and eight-membered rings. Explicit models for several schwarzites are available in the literature [14].

5.3.2 Disordered Porous Carbons: Simple Geometric Models The evolution of molecular models for disordered porous carbons is strongly connected with the advance of experimental techniques such as diffraction methods and electron microscopy. First, X-ray studies on carbon blacks revealed that these materials consist of a wealth of small graphitic crystallites.

108

Chapter 5 Models of Porous Carbons

The spatial arrangement of these graphitic crystallites determines the pore structure, i.e., the pore morphology and topology. As a consequence, all simple models of porous carbons are based on stacks of graphene sheets representing the pore walls. As in the case of nanotubes discrete as well as mean-field models of single graphene sheets or stacks of them are available. In several cases, both descriptions have been combined in hybrid models. A discrete model of a graphene sheet is obtained by placing (model) carbon atoms on a - 2D hexagonal lattice with lattice constant (carbon-carbon bond length) e. The values of e measured in disordered carbons are usually very similar to that of graphite. Thus, the carboncarbon bond length of graphite, e = 0.1415 nm, is usually used to construct the simple models discussed here. Carbon atoms as well as the adsorbate molecules are often modeled by the LJ 12-6 potential, (5.1) where Gfc and O"fc are the fluid-carbon energy and distance parameters, l respectively, and r is the distance separating two atoms or molecules. The total fluidwall interaction energy of an adsorbate molecule, j, with the graphene sheet is given by the sum, Li cP L] (rij) , which runs over all wall (carbon) atoms, i. This readily defines an explicit model for adsorption on a single graphene sheet. If we can disregard the atomistic nature of the graphene sheet, the sheet is sufficiently characterized by an areal carbon density. A mean-field model is obtained by replacing the sum over individual carbon atoms by an integral of the LJ potential over the area of the graphene sheet. If the sheet is assumed to be infinite in lateral dimensions one obtains the well-known Steele (10-4) potential [15] (5.2) where Psd is the areal number density of carbon atoms in the graphene layer. (Since the structure of graphite is known, the number density of carbon atoms in graphite can be calculated: Ps =2.0/(d12 J'3(3/2)) ~ 114nm- 3 .) With similar integration methods one obtains mean-field potentials for graphene sheets that are finite in one or more directions [1]. A model for a finite stack of graphene layers is obtained by summing over individual graphene layers modeled as described above. The spacing between the layers, d, is usually assumed to be that of graphite, d = d002 = 0.3354 nm. 1

Parameters for LJ potentials between unlike particles are usually obtained from the LJ potentials for the like-like interactions using Lorentz-Berthelot mixing rules, Ore = ,J0ffOee and arc = 1/2 (aff + aeJ. For graphite 0ee ~ 38.7 x 10- 23J and ace ~ 0.34 nm. A list of adsorbate parameters can be found in Ref [15].

5.3 Molecular Models of Carbons

1°9

For simple models this is reasonable, since deviations from this value measured for activated carbons are usually smaller than 0.03 nm and structural simplifications may be more serious. In explicit models ofgraphene stacks the registry ofadjacent layers has to be considered. The thermodynamically stable polymorph ofgraphite is hexagonal graphite having an ABA stacking. The position of the B layer with respect to an A layer can be obtained by starting from a perfectly aligned system (AAA) and displacing every second layer along an arbitrary bond by one bond length. In hybrid models the structure of the first few layers is considered explicitly, while for all other layers a mean-field description is adopted. To derive an even simpler description of a semi-infinite graphite substrate that is infinite in all directions but semi-infinite in the direction perpendicular to the graphene layers, the substrate is represented by a 3D carbon density. Volume integration gives the Steele (9-3) potential [15],

(5.3) Another mean-field potential, which is often used, is obtained by areal integration over the first layer of a semi-infinite graphite substrate and volume integration over all others. This gives the well-known (10-4-3) Steele potential [15],

U z (

) -

211'8

fcPc

[2

10

4

4]

afc a 2 d - -afc - -afc fc 5( z ) ( z) 3d(z+O.61d)3

(5.4)

These different wall models can now be assembled such that they confine some spatial region which represents the pore. The simplest and most widely used case is the slit pore. A slit pore of width, H, is created by placing two mutually parallel and laterally infinite graphene stacks at a distance, H, apart. Pores shaped like rectangular prisms are obtained by placing four graphene stacks at the side faces of the prism. To avoid overlap the graphene stacks are laterally finite or semi-infinite in the dimension perpendicular to the long axis of the prism [16, 17]. TEM images of many specimens reveal that the pore walls are usually not parallel. Because of this observation, a model for pores shaped like triangular prisms has been developed [18]. It is important to notice that the latter two models differ from the slit-pore model not only by pore morphology but also by the appearance of high-energy sites at the edges, generated by proximity of the two walls. Hybrid models are usually used to study defective surfaces. In these models the internal surfaces of a slit pore, defined by a stack of mean-field layers, are "coated" by one or more graphene layers with explicit atomic structure. To generate defects one or more carbon atoms are removed from one or more explicit graphene layers [19, 20]. All models discussed in this section are single-pore models describing the morphology of a single pore. The topology of the disordered material,

110

Chapter 5 Models of Porous Carbons

i.e., connectivity of pores, as well as the variety of pore sizes is completely disregarded, which significantly limits the predictive capabilities of these models. In recent years experimental techniques have been improved, providing much more detailed information of carbon materials. As described in the following section, this information is used together with sophisticated theoretical and simulation methods to obtain more detailed and more reliable models for disordered porous carbons.

5.3.3 Disordered Carbons: More Realistic Models 5.3.3.1 Reconstruction methods The goal of reconstruction methods is to build model pore structures that match experimental structure data (including surface chemistry data) for the real materials, at least in a qualitative way. For example, models can be constructed that match the experimental structure factor, Seq), or TEM data, by reverse Monte Carlo (RMC), off-lattice reconstruction, or other methods. Reconstruction methods can in principle be used to build a model for any type of porous material. However, considerable care and thought is needed in applying such methods, since the experimental data does not correspond to a unique molecular structure. For example, a range of atomic structures could give rise to the same S( q) curve or TEM data. This ambiguity can be reduced by incorporating constraints into the model development, so that unphysical structures cannot result, and by using more than one kind of experimental data in the fitting process. The simple geometric models mentioned above (see Section 5.3.2) can be thought of as the most basic form of reconstruction methods, in which the pore topology is based on electron micrographs of the material (e.g., cylindrical, slit-shaped), and the structure of the pore walls is assumed to be that of graphite. In the case of activated carbons, it is common to use a slit-pore model with graphitic pore walls. The only adjustable parameter is then the pore size, which may be estimated from electron micrographs. This model may be refined by including a distribution of pore sizes. The porous material is then modeled as a collection of independent and unconnected slit-shaped pores with graphitic pore walls, and a pore size distribution is determined so that the calculated adsorption isotherm matches the experiment [21]. There have been several improvements to the slit-pore model and the description based on the concept of a pore size distribution. These improved models are also constructed by making detailed observations of the experimental data (electron micrographs, X-ray diffraction, adsorption isotherms, etc.), extracting more relevant features of the pore topology and the structure of the pore walls, and including these features in the models. For example, a 2D distribution of pore size and pore-wall thickness may be used, instead of a pore size distribution [22]. Most of these improvements are described in detail in a recent review [1].

5.3 Molecular Models of Carbons

111

The recent trend, driven by the increase in computing power, is to build all-atom models of porous carbons by solving a multidimensional inverse problem. The atomic positions in a system of carbon atoms, and perhaps other species, are stochastically changed to match experimental structure data. The RMC procedure [23] is useful to produce configurations that match a target structure factor, S(q), or pair correlation function, g(r). Target structure factors are usually obtained from X-ray diffraction. In addition, SAXS may be used to extend the structure factor to lower values of q, provided that X-ray diffraction and SAXS can be performed for an overlapping range of angles [24]. Target pair correlation functions may be obtained by taking the inverse Fourier transform of the structure factor. This operation, however, is particularly vulnerable to the limitations of the experimental data [25, 26], e.g., truncation errors. It is thus preferable [27] to use an alternative method, such as the so-called MC g(r) [26]. The idea of this inverse procedure is to stochastically modify a pair correlation function until its Fourier transform matches the experimental structure factor. The procedure is analogous to a lD RMC. Since the numerical pair correlation function can be generated for arbitrarily large r-values (limited only by the experimental q resolution), truncation errors are avoided in the Fourier transform. The resulting pair correlation function may be used as the target function in the RMC procedure, instead of the experimental structure factor, significantly reducing the computational cost and thus allowing the study of larger systems. In RMC, random moves, i.e., changes in the configuration of the system, are performed as in the metropolis MC algorithm. Random moves are accepted or rejected so that the difference between the calculated and target S( q) or g(r) is minimized. If g(r) is used as the target function, the parameter to be minimized is: nexp

L X2 =

[gsim (rJ -

gexp

(rJ]2

i=l

- - n -- - - - - - ex p

L

(5.5)

[gexp (rJt

i=l

where nexp is the number of experimental points, gsim (ri ) is the simulated g(r) and gexp (ri) is the experimental g(r) evaluated at rio The moves are accepted with probability:

Pace

= min [ 1, exp { -

;x (X~ew - X~ld) }]

(5.6)

where the subscripts old and new indicate before and after the move, respectively, and Tx is a weighting parameter or effective temperature. It is important to note that, although the parameter Tx does not have a thermodynamic meaning, it behaves like temperature. The parameter X is therefore minimized when the effective temperature is close to zero. The original RMC procedure prescribes that T x should be proportional to the variance of the target function.

112

Chapter 5 Models of Porous Carbons

However, assuming that the error in the target function is relatively low, any arbitrarily low value would be appropriate. An alternative is to change the effective temperature in the frame of the simulated annealing method [28] to increase the chances of finding the global minimum of the parameter x, instead of a local minimum. Simulated annealing has been successfully used in RMC modeling of carbons [27, 29]. As mentioned above, a set of experimental data does not necessarily correspond to a unique molecular structure. Moreover, even unphysical structures may be consistent with a set of experimental data. It is therefore necessary to carefully choose a set of constraints to limit the number of possible structures. The uniqueness theorem of statistical mechanics [30, 31] provides a guide to the number and type of constraints that should be applied in the RMC method in order to get a unique structure [32]. For systems in which only two- and three-body forces are important, the uniqueness theorem states that a given set of pair correlation function and three-body correlation function determines all the higher correlation functions. In other words, assuming that only two- and three-body forces are important, the RMC method must be implemented along with constraints that describe the three-body correlations [27]. One way ofimplementing constraints is in a rigid way. For example, Thomson and Gubbins [33] have modeled an activated mesocarbon microbead with RMC along with the following constraints: (1) any atom can only have two or three neighbors, (2) all the carbon-carbon bond lengths are 1.42 A, and (3) all the bond angles are 120 The advantage of doing this is that when these three constraints are applied together, basic carbon units, or plates, can be defined. These plates are rigid aromatic sheets of Sp2-bonded carbon, which resemble the structure of graphene segments. Many-atom moves that accelerate the convergence process can then be applied. For example, Thomson and Gubbins included three types of stochastic moves: (1) plate translation-rotation, (2) ring creation-annihilation, and (3) plate creation-annihilation. Only those moves that improve the fit to the experimental radial distribution function are accepted, i.e., the effective temperature was set to zero. In their resulting models, the graphene segments are roughly aligned (see Fig. 5.1) but their shape, size, and relative angles of tilt are different. The match between the simulated and the experimental g(r) is excellent for interatomic distances greater than 5 A (see Fig. 5.1). However, deviations occur at smaller distances. Two possible reasons for this discrepancy are (1) truncation errors in the Fourier transform of the experimental structure factor to obtain the radial distribution function, producing unphysical features in the target radial distribution function, and (2) overly rigid constraints on the RMC platelet shape. While the constraints applied by Thomson and Gubbins are reasonable for many graphitizable carbons, the use of graphene microcrystals as the basic units fails to account for ring defects and nonaromatic rings that are important in many activated carbons used in adsorption applications. A better match to the target g(r) may be obtained by allowing the formation of defects in the form of nonaromatic rings and by including heteroatoms [34]. 0

•

5.3 Molecular Models of Carbons

113

(a)

(b) 10

5 ~


"'-

0

~ ~

---Target -5

-10

- - - - . Simulated - - _ . Initial 0

5

10

15

20

Angstroms

Figure 5.1 Activated mesocarbon microbead RMC model. (a) Structural representation of the converged structure. The spheres represent carbon atoms that are shown at a scale much less than their van der Waals radii for reasons of clarity. (b) C-C radial distribution functions (RDF). The experimental RDF (solid line), the simulated, converged RDF (long-dashed line), and the initial simulated RDF (dotted line) are shown. The numbers indicate the different peaks of the RDF. (Adapted from Ref. [33].)

Chapter 5 Models of Porous Carbons

114

Pikunic et al. [27] have implemented a set ofjlexible constraints in the RMC procedure. Assuming that most carbon atoms have Sp2 hybridization, they constrain the coordination number of carbon atoms and the bond angles using a set of simple expressions:

(5.7) and

ifJ2

= -1

no

L n8

i=l

[

cos (OJ) -

COS

(2.-!!... )]2

(5.8)

3

where N 3 /N is the fraction of carbon atoms with carbon coordination number of 3, i.e., the fraction of carbon atoms that are bonded to three other carbon atoms. The target value ofN3 /N is estimated from the experimental composition data (H/C and OIC ratios) [27]. In graphite, for example, the fraction would be equal to one (Ji are the different bond angles in radians, and no is the total number of bond angles. This expression is based on the assumption that the angular contribution to the potential energy is proportional to the sum over all C-C-C bond angles of the squared difference between the cosine of the actual bond angle and the cosine of the equilibrium bond angle, which are 21T/3 radians for Sp2 hybridization. This dependence of the potential energy with bond angle is consistent with bond-order potentials (e.g., Tersoff and Brenner potentials) [35-37]. The reconstruction method, termed constrained reverse Monte Carlo (CRMC), consists of simultaneously minimizing three order parameters: the usual X2 , along with 82, and 0/ 2. The procedure allows building configurations of carbon atoms that have the same pair correlation function as the real material, as well as bond angles and carbon coordination number consistent with the experimental composition and the assumption of Sp2 hybridization. The acceptance probability prescribed in the original RMC method is replaced with

The parameters TifJ/Tx and Ts/Tx ' which determine the relative weight of the three order parameters, are kept fixed. Pikunic et al. [27] found that the resulting structures are not very sensitive to the specific values of the weighting parameters. RMC simulations are performed using this expression for the acceptance probability, in the frame of simulated annealing. Pikunic et al. [27] modeled two carbons manufactured by pyrolysis of saccharose at up to 400°C and at up to 1000°C. The resulting cokes are termed

5.3 Molecular Models of Carbons

115

CS400 and CS1000, respectively. The inputs to the reconstruction procedure, described above, were the compositions (H/C and OIC ratios), skeletal densities obtained by mercury porosimetry, and pair correlation functions from X-ray diffraction and SAXS. The pair correlation functions of the converged models, shown in Fig. 5.2 (dashed line), are in excellent agreement with the target functions. The fact that the agreement is better for CS400 seems to indicate that the minimization method is more effective for more disordered and less dense materials. Snapshots of the CRMC converged structure for cokes CS400 and CS1000 are shown in Figures 5.3 and 5.4 respectively. Pikunic et al. also developed a simple method to simulate TEM of simulated structures. They assume that the material is quasi-amorphous. Diffraction contrast due to crystalline registry is therefore negligible compared to mass-thickness (a)

6..,.----------------------."

5'+--tt--------------------I '-

3'

0>

~--~.

- ----------------------1

2

0 0

2

4

8

6

10

12

14

r(A) (b) 6

5

4 :; 3 0>

2

o ,'t--...-r"',,···,.....,.....·--,,·,""""~·,·,'·'''·'l'·'''··'''w'''f·'''·''''',.

o

2

4

....'If·,....,·>W·"",··,,....·..••.. y ..··,..•.. ,·..·.,·....,.., ..,·..~..·•.. • ..•••.... 1'..·,.....·•......·"'..........·......·"'..•·....·......-1

6

8

10

12

14

r(A)

Figure 5.2 Pair correlation functions of the saccharose-based carbons (a) CS400 and (b) CS1000: target (solid line) and converged CRMC structure (dashed line). (Adapted from Ref. [27].)

116

Chapter 5 Models of Porous Carbons

Figure 5.3 Snapshot of the CRMC converged structure for CS400. The simulation box is separated in four sections for clarity. The gray cylinders represent C-C bonds. (Adapted from Ref. [27].)

contrast, which can be calculated using Beer-Lambert's law. Experimental and simulated TEM micrographs for CS400 are shown in Fig. 5.5. It is important to note that many features of the experimental imaging procedure are not included in the simulations, e.g., scattering, transfer function of the microscope, sample thickness. Therefore, the contrast of the simulated images is not quantitatively comparable with that of the experimental images. However, most structural features observed in the experiments, highlighted in Fig. 5.5, are also present in the simulated images. Moreover, topological changes of the material upon heat treatment, as revealed by comparison of the experimental TEM images of CS400 and CS1000, are also observed in the simulated images (see Ref [27]). Although the comparison is qualitative, it is reassuring that the structural models are consistent with experimental structure data that is independent from the method's inputs. These models have also been geometrically characterized and tested against adsorption data (see Section 5.4); the predicted heats of adsorption are in excellent agreement with experiment.

5.3 Molecular Models of Carbons

117

Figure 5.4 Snapshot of the CRMC converged structure for CS1000. The simulation box is separated in four sections for clarity. The gray cylinders represent C-C bonds. (Adapted from Re£ [27].)

Further improvements to RMC-based reconstruction methods include implementing more sophisticated procedures than simulated annealing for finding the global minimum of the order parameters, such as parallel tempering. Improvement efforts may also be aimed at refining the constraints to describe three-body correlations. One alternative is to use a semiempirical interatomic potential [35, 36] as the three-body constraint. The reconstruction method would be equivalent to a biased MC simulation in the canonical ensemble. This idea has been implemented recently to model the local structure (not the porosity) of an industrial char [38] by using the environment dependent interaction potential [39] to describe three-body interactions. The resulting models resemble disordered and buckled graphitic structures, with a small number of five- and seven-atom rings. An alternative is to generate an initial structure using RMC, and subsequently relax it by performing MC or molecular dynamics simulations with a realistic Hamiltonian, e.g., semiempirical potentials or tight binding. Finally, improvements may also be aimed at replacing the RMC procedure with one recently developed by Rutledge [40], which incorporates the target function

Chapter 5 Models of Porous Carbons

118

(a)

Experiment

Simulations

(b)

Experiment

Simulations

(c)

Experiment

Simulations

Figure 5.5 Experimental TEM micrographs of CS400 (left) and simulated images for three beam directions (right). The 5 nm scale applies for the four images. (a) HigWighted are examples ofdot-like segments, (b) short segments, and (c) stacks of short segments. (Adapted from Re£ [27].)

5.3 Molecular Models of Carbons

119

into a semigrand Me simulation by introducing a generalized, polydisperse composition space. The advantage of this method is that it retains the character of a thermodynamic system; the target function and semiempirical potential can be handled together without adjustable parameters.

5.3.3.2 Ab Initio and mimetic simulation methods Semiempirical and ab initio approaches

Because of their computational intensity and the chemical complexity of the synthesis of porous carbons, a full mimetic simulation using ab initio (i.e., from the beginning, or first principles) methods is not yet feasible. Nevertheless, some ab initio and semiempirical calculations have been reported that throw some light on parts of the synthesis process, at least for idealized systems. Ab initio or first principles methods seek to describe the electrons of a chemical system through solution of the many-body Schrodinger equation (Hamiltonian), and so do not require any experimental input [41]. In semiempirical methods, the many-electron problem is simplified in some way, and then some parameters obtained from experiment or higher level ab initio calculations are included in order to get good results. Semiempirical methods are not true ab initio methods, since they make use of experimental information, but they are particularly useful for dealing with large systems where more computationally demanding methods are impossible to apply. Pappano et al. [42] have used a semiempirical method to study the polymerization of phenanthrene and anthracene, relevant to the carbonization process. The resulting polymerized phenanthrene material contained holes and curvature induced by the presence of five-membered rings, whilst the polymerized anthracene system contained little curvature. Chen and Yang, in a series of studies at both the semiempirical [43] and, more recently, ab initio [44] levels, have studied the gasification of graphite by CO 2 , H 2 0, and 2 , which is of relevance to activation. They considered both uncatalyzed systems and those catalyzed by alkali and alkaline metals, indicating under what conditions catalytic effects are likely to prevail and suggesting reaction mechanisms. Ma et al. [45] used a semiempirical method to study the inhibitive effects of boron on gasification, whilst Kyotani and Tomita [46] used an ab initio method to consider the reaction of carbon with NO and N 2 0. Because they are so computationally intensive, ab initio and semiempirical studies are limited to models that are about 10 rings or less. In order to study more realistic carbon structures, approximations in the form of the Hamiltonian (i.e., Schrodinger equation) are necessary. The tight-binding method, in which the many-body wave function is expressed as a product of individual atomic orbitals, localized on the atomic centers, is one such approximation that has been successfully applied to amorphous and porous carbon systems [47]. Charlier et al. [48] used the tight-binding model to study distorted stacking of graphene layers, termed pregraphitic or turbostratic carbon. The turbostratic structure was obtained by generating an amorphous cluster of graphene plates that

°

120

Chapter 5 Models of Porous Carbons

contained 24 graphene layers and 35 736 carbon atoms. The disordered packing was found to more closely resemble the Bernal stacking of graphite (ABAB) in density and shape. The tight-binding method has also been applied to amorphous carbons, with an emphasis on studying the electronic structure [49, 50]. Wang et al. [51] used tight-binding molecular dynamics (TBMD) to simulate a high-temperature quench of liquid carbon at various densities to produce a porous carbon. Forces were calculated through a combination of the tightbinding orbitals and the Coulomb repulsion of the carbon nuclei. Different initial carbon densities were found to lead to different bonding arrangements. A high initial density resulted in diamond-like carbon characterized by a large fraction of Sp3 bonding sites (72 %). Low carbon density resulted in an amorphous carbon structure with curved graphene sheets, containing many nonaromatic five-, six-, and sevenfold carbon rings. An approach that is attractive and that can be applied to a wide range of types of carbons is to combine the tight-binding method with RMC to determine carbon structures and properties. In this approach the RMC method is first used in conjunction with experimental structure data (usually in the form of smalland wide-angle X-ray or neutron scattering data) to determine a molecular structure for the carbon that is a good approximation to the true structure, and includes longer range structural features. Tight-binding calculations are then carried out to relax the structure and to incorporate local bonding and interactions into the framework. Rosato et al. [29] carried out such a procedure for amorphous carbons by applying the RMC method to experimental radial distribution function data from scattering, followed by TBMD to capture shortrange bonding configurations. More recently, Pellenq et al. [52] have used a similar approach, using tight binding Me in place ofTBMD, to develop realistic models of several microporous carbons based on carbonization of saccharose. Such approaches are quite flexible and should be able to provide reasonably realistic molecular structures at both short and longer ranges for a wide variety of carbons. Probabilistic approaches

Because of the computational intensity of the deterministic approaches described above, several attempts have been made to develop stochastic-based mimetic models. The gasification of polyaromatic molecules has been modeled by Kyotani et al. [53] using a MC process where the probability of a carbon reacting is determined using Huckel molecular orbital (HMO) theory [54]. It should be possible to extend this approach to more complex structures, given the simplicity of HMO theory. Stochastic approaches have been used to model coal devolatilization using the DVC (depolymerization, vaporization, and crosslinking) model (e.g., Refs [55-57]). In one such approach [57], the precursor is modeled by sites representing molecular fragments of varying molecular weight and chemistry connected by labile links that may be broken with a probability defined by their reactivity. It may be possible to extend such methods to study the carbonization of other precursors, in addition to coal.

5.4 Adsorption, Diffusion, Reaction

5.4

121

ADSORPTION, DIFFUSION, REACTION

One of the main purposes of developing structural models of porous solids is to predict the effects of confinement on the properties of adsorbed phases, e.g., adsorption isotherms, heats of adsorption, diffusion, phase transitions, and chemical reaction mechanisms. Once a structural model for a particular porous solid has been chosen or developed (see Section 5.3), it is necessary to assume an interaction potential between the solid (adsorbent) and the confined fluid (adsorbate), as well as a fluid-fluid potential, and to decide on a theory or simulation method to calculate the property of interest [58]. A great many such studies have been reported in the literature, particularly for simple pore geometry models, and we do not attempt to review them here. Instead we present a few examples of such studies, with emphasis on those involving more realistic pore models. It is common to assume a LJ 6-12 potential (Eqn (5.1)) to model the repulsive and dispersion interactions between a carbon atom and a nonpolar adsorbate atom, e.g., argon, xenon. For polar fluids, such as water and nitrogen, it may be necessary to include charges explicitly or a dipole or quadrupole [31]. An alternative approach is to model the adsorbate as a LJ 6-12 fluid. This approach, although somewhat simplistic, may be suitable for nonpolar adsorbates with low quadrupole moment, e.g., nitrogen. The adsorbent-adsorbate potential parameters are usually obtained from ab initio calculations or by fitting to lowcoverage adsorption properties such as the Henry's constant, on ideal, nonporous adsorbents, e.g., graphite [59, 60]. The application of statistical thermodynamic theories, such as density functional theory, and classical models to gas adsorption has been recently reviewed [21, 61]. These methods are usually restricted to simple geometric models (Section 5.3.2). Molecular simulation, on the other hand, can be used to predict adsorption properties in any porous carbon model, including those described in Section 5.3.3. The most widely used simulation method for studying adsorption behavior is GCMC [59, 62, 63]. These simulations can be routinely performed today on personal computers for systems of several nanometers, allowing the estimation of adsorption isotherms and heats of adsorption. Provided that the structural models are realistic, and that the adsorbate-adsorbent interaction parameters are carefully determined from experiment or ab initio calculations, excellent predictions can be obtained. An example is shown in Fig. 5.6. The lines show experimental isosteric heats of adsorption of argon in two disordered porous carbons obtained from pyrolysis of saccharose at 400°C (CS400) and 1000°C (CS1000). Structural models for these two materials were obtained using a CRMC method [27] (see Section 5.3.3.1). These models were subsequently used in GCMC simulations [64], with argon-carbon interaction parameters obtained in an independent study [65]. The predicted isosteric heats of adsorption are in excellent quantitative agreement with experiment. It is important to note that the models of CS400 and CS1000 were obtained from

122

Chapter 5 Models of Porous Carbons

20

(5

16

E

-~~

..~~

12

_ ~ ,

8

4+----,.-----r--------,---~------I

0.0

0.2

0.4

0.6

0.8

1.0

Figure 5.6 Isosteric heat of adsorption of argon at 77 K. Experiment: CS400 (dashed line) and CS1000 (solid line). Simulations: CS400 (circles) and CS1000 (squares). (Adapted from Ref. [64].)

experimental structure data, and no parameters were adjusted to match the adsorption data. The "true" pore size distribution obtained geometrically, from atomic positions, is shown in Fig. 5.7(a). It is obvious that CS400 and CS1000 have very similar pore size distributions. However, the potential energy of an adsorbate atom confined in these two models is quite different (Fig. 5.7(b)). Moreover, as evidenced in Fig. 5.8, the nitrogen adsorption isotherm obtained in a collection of slit pores with the same pore size distribution differs from those in CS400 and CS1000 [66]. These differences are likely due to the nongraphitic structure of disordered porous carbons as well as topological differences. It has been shown that different degrees of curvature alone, in carbonaceous materials, may cause differences of tens ofkJ/mol in zero-coverage isosteric heats of adsorption [67]. These results indicate that characterization methods based on the slit-pore model and the concept of a pore size distribution are not suitable to describe disordered porous carbons. A strong test of the realism of a molecular model of a porous carbon is the study of diffusion of the confined adsorbate molecules. Pikunic [68] has used molecular dynamics simulation to study self-diffusion of argon in the CRMC models of the saccharose-based microporous carbons CS400 and CS1000, with pore size and energy distributions shown in Fig. 5.7. He found ballistic motion (mean squared displacement proportional to (2, where ( is the elapsed time) at very short times, follovved by a transition to single-file diffusion (mean squared displacement proportional to (0.5) at longer times. There was no Fickian regime (mean squared displacement proportional to t). This prediction has not yet been confirmed by experiment. There have been a number of simulation studies of the adsorption of water in carbon slit pores [69] and in carbon nanotubes [70]. Segarra and Glandt [71] were the first to study water adsorption using a more realistic model of the porous

5.4 Adsorption, Diffusion, Reaction

123

(a) 1.2 - - - - - - - - - - - - - - - - - - - - - ,

0.8

-_J:

0.6

Q..

0.4

0.2

....

04---.....,..--..L~r___--_r_--.....,..~~::-.,.._--

2

3

4

5

7

6

8

H(A) (b) 0.7 - . - - - - - - - - - - - - - - - - - - - - - - - - ,

A

·,.-,:'. ·- .: ·. ·... ·.

0.6 0.5

•

S

·.

~ Q..

I

·. ···: .... ......

0.4 0.3

0.2

.'

:

r ·:

0.1

~.

0........,......,..-r--p~..,....,._._.,........_;;..."'I"""'"'r'...........'1"""1". . .~..,.....~_r_~~r--.-......._i

o

5

10

15

20

25

30

-U(KJ/mol)

Figure 5-7 (a) Pore size distribution ofthe models ofCS400 (solid line) and CS1000 (dashed line). The test particle is a simple model of nitrogen. (b) Adsorbent-adsorbate potential energy distribution for a single nitrogen molecule in the models of CS400 (solid line) and CS1000 (dashed line) at 77 K. (Adapted from Ref. [28].)

carbon. The model consisted of randomly oriented platelets of graphite, with a dipole uniformly distributed over the edge of the platelets to mimic the activation. The SPC (simple point charge) model was used for the water interaction. Although these calculations gave adsorption isotherms that were qualitatively similar to the experimental results, subsequent work [72] suggest that their model of the surface sites is not sufficiently inhomogeneous to predict the correct trends in low adsorption data and in heats of adsorption. McCallum et al. [73] studied water adsorption in a Norit-activated carbon derived from peat moss and oxidized using 30 % hydrogen peroxide. The activated carbon was modeled as being

12 4

Chapter 5 Models of Porous Carbons

0.8 0.6

~

~

0.4 0.2

O.....-=::;;... . . . . . . . . . . . . . .==:IIIL--...-----...----........ 1.0E-12

1.0E-Q9

1.0E-Q6

1.0E-Q3

1.0E+00

P/PO

Figure 5.8 Nitrogen adsorption isotherms at 77 K in an assembly of independent graphitic slit pores with a pore size distribution equal to that shown in Fig. 5.7(a) (solid line), and in two realistic models of porous carbon: CS400 (squares) and CS1000 (circles). Fractional filling is shown as a function of relative pressure. (Adapted from Ref. [68].)

made up of noninterconnected slit pores having a distribution of pore widths that approximated the experimental material, and whose surfaces are decorated with model OH groups at a site density of 0.675 sites per square nanometer, as estimated from experiment. H-bonding sites on water molecules and OH groups were modeled as square well sites, and the one H-bond site parameter on the OH groups was fitted to low-pressure adsorption data. The predicted isotherm from GCMC simulations was in generally good agreement with experiment (Fig. 5.9). Brennan et al. [74] used GCMC simulations to study the adsorption ofwater in a

0.03

.

,'."

'

.

'

N

-€ (5

0.02

E

Sen

en Q)

0

x

Q)

0.01

~

0.00 ~zm:al_e==:..i.~-+----+-----+---~ 1.0 0.4 0.6 0.8 0.2 0.0

P/Po

Figure 5.9 Adsorption of water from experiment and simulation at 298 K. The solid line and open circles represent the experimental data; the dashed line and filled circles show the simulated isotherm obtained using simulated isotherms for discrete pore widths together with the experimental pore size distribution. (Adapted from Re£ [73].)

5.4 Adsorption, Diffusion, Reaction

12 5

more realistic model of an activated mesocarbon microbead sample from Osaka Gas Company. The carbon model was prepared by the RMC procedure of Thomson and Gubbins [75], by matching the model structure to the experimental structure factor, and consists of connected slit-like pores between graphene microcrystals. The pores were decorated with oxygenated surface sites placed randomly on the edge carbons of the graphene microcrystals; these sites were taken to be CO groups, and their interaction was modeled using the OPLS (optimized potentials for liquid simulations) model. For the water interaction a point charge model due to Errington and Panagiotopoulos [76] was used, with potential parameters that were optimized for vapor-liquid coexistence properties. A range of site densities, from zero to 2.25 CO per square nanometer were studied, covering the entire experimentally accessible range. The adsorption behavior was found to be strongly dependent on the site density, with significant uptake of water occurring at lower pressures for higher-site densities. For a typical oxygenated site density of 0.65 site/nm2 , the presence of adsorbed water was found to dramatically decrease the connectivity of the available pore space (Fig. 5.10). This pore-blocking effect due to water clusters forming around oxygenated sites provides an explanation of the large decrease in capacity and selectivity observed in industrial adsorbers due to humidity in the gases entering the adsorber. Confinement in porous carbons can have a large effect on chemical reactions, changing the yield, reaction rate, and even the reaction mechanism in some cases. Strong effects occur due to increased density of the adsorbed phase, selective adsorption of reactants or products, strong electronic interactions between the reacting species and the pore walls that can change the potential energy surface of the reaction and bond strengths, reduced dimensionality, etc. The effect on equilibrium yield is most easily studied, since it depends only on the initial reactants and final products, and not on the reaction path or mechanism. The reactive MC method [77], in which trial forward and backward reaction

(a)

(b)

(c)

Figure 5.10 Available pore space when water is present in an activated carbon. The sequence of figures represent different amounts of water present: (a) P/Po = 0, (b) P/Po = 0.10, (c) P/Po = 0.14. Carbon atoms, surface sites, and water molecules have been removed to enhance visualization of the pore space. (Adapted from Re£ [74].)

Chapter 5 Models of Porous Carbons

126

moves are incorporated, has been successfully used to study several reactions in slit-pore carbons and carbon nanotubes, including the reactions 2NO = (NO)2 [78, 79], N 2 + 3H2 =2NH 3 [78, 79], and the esterification reaction [80] CH3 COOH + C 2H sOH = C 2H sOOCCH 3 + H 20. In each of these cases, the yield is increased due to confinement within the carbon. The effect is particularly dramatic for the case of the nitric oxide dimerization reaction. The simulations predict an increase in yield of the dimer by one to two orders of magnitude at lower (liquid range) temperatures, the effect being larger in carbon nanotubes than in slit pores due to the additional confinement (Fig. 5.11). In the simulations, the increase is primarily due to the increased density of the adsorbate phase. Even larger increases are observed in the experimental studies [81, 82], possibly due to a change in the bonding energy of the dimer due to interaction with the walls (an effect that was not taken into account in the simulations). For the ammonia synthesis and esterification reactions, which are carried out at higher temperatures, a smaller but significant increase in yield (up to a factor of 2) is predicted, and in these cases it is due to selective adsorption. No experimental studies are available for these reactions, so these results cannot be verified. Fewer studies of the effect of confinement in carbons on reaction mechanism and rates are available. By assuming that confinement has no influence on the reaction path or transition state, it is possible to use reactive MC simulation to determine the equilibrium concentration of the transition state species, and then use this together with transition state theory to predict the effect of confinement on reaction rates. This was the basis of a study by

1.0 2NO=(NO)2 0.8 C\I

0

~

15

0.6

c 0

:u ~

0.4

Q)

(5 ~

....--.2.5aNO 0--03.0aNO . - - . 3.5aNO

¢--¢ 4.0aNO ~4.5aNO

0.2

4o--
BULK 0.0 115.0

125.0

135.0

145.0

155.0

165.0

Temperature/K

Figure 5.11 Mole fraction of dimers for the pore phase at a constant bulk pressure of 0.16 bar, for various pore widths expressed as multiples of aNO' where aNO is the LJ diameter for the NO molecule (0.3172 nm). (Adapted from !-te£ [78].)

5.5 Conclusions

127

Turner et al. [83] of the HI decomposition reaction, 2HI = H 2 + 12 , in carbon slit pores and carbon nanotubes. Large increases occurred (by up to a factor of 60) in the reaction rate, due to selective attraction of the transition state species to the pore walls. This selective attraction arises because the transition species is larger than other molecular species in the reaction mixture and has a stronger dispersion interaction with the carbon wall. More rigorous and complete calculations require the use of a dual scale approach, involving ab initio methods to determine the potential energy surface of the reaction, and atomistic molecular dynamics simulations to determine reaction rates [41].

5.5

CONCLUSIONS

The structural models available for porous carbons can be roughly divided into two classes: simple geometric models, such as collections of slit- or wedgeshaped pores, and more complex models in which pore connectivity, tortuosity, and curved and defective carbon sheets are included. The simple geometric models are easy to apply, and can give a good account of adsorption when the pore size distribution is fitted to experimental data. Such models are now incorporated into the software of most sorptometers, and are used to estimate surface areas and pore size distributions. However, such models omit many important features of porous carbons, including pore connectivity, tortuosity, variations in pore shape, and chemical heterogeneity of the surfaces. Such models may give poor results even for adsorption if extrapolated to temperatures or adsorbate gases far from the region of fit. They are particularly poor in representing diffusion in carbons, where connectivity, tortuosity and surface heterogeneity have a large influence on the diffusive flux. Diffusion rates calculated using slit-pore models can be in error by an order of magnitude or more. In recent years, several more realistic models have been proposed, which attempt to include connectivity, variations in pore morphology, defective ring structures, curved carbon plates, and so on. These more complex models include the virtual carbon model, the chemically constrained model and RMC models. None of these models are yet fully developed or tested, but they offer the prospect of considerably more sophisticated and accurate modeling of carbons. What is needed, are carefully designed efforts to test and refine these models through collaborative research programs involving complementary, experimental, and modeling studies. Eventually, it should be possible to replace the simple geometric models by the more complex models in practical applications, such as predictions of adsorption, separations, and diffusion rates. The existing structural models are overwhelmingly of the reconstructive type, in which the model is constructed based on experimental structural data. This is a result of the complex and poorly understood synthesis of the carbons. Mimetic simulation methods, in which the synthesis is modeled using molecular or ab initio simulations, have been successfully used for some other porous materials,

Chapter 5 Models of Porous Carbons

128

e.g., porous glasses [84] and MCM-41 [85]. Such approaches are desirable since they can produce unique and physically realistic structures. Moreover, they offer insight into the synthetic route itsel£ and may suggest ways to improve it. Some attempts to model a part of the synthetic process using mimetic ab initio methods have been made (see Section 5.3.3.2). At first sight it would seem hopeless to attempt mimetic methods to simulate the entire synthetic process for activated carbons. However, reasonably successful intermolecular potentials exist for carbon (e.g., Ref [35]). These cannot be expected to produce realistic structures for activated carbons via direct simulations. The synthetic process involves many chemical reactions, the details of which are largely unknown, and the final carbon structures are not equilibrium ones. However, it may prove possible to improve the models by incorporating the potential in the reconstruction in some way. While the principal stumbling block remains the development of more realistic models, improvements in experimental techniques are also needed. In the measurements of structure by diffraction or TEM, higher resolution and accuracy are desirable to provide a clearer picture of the atomic and surface structure. In the case of TEM measurements, the development of methods to obtain 3D structures, as opposed to the 2D thin-film structures currently possible, would provide a major advance. In the surface chemistry studies, further resolution of both the location and species of surface groups is needed.

ACKNOWLEDGMENTS We thank the National Science Foundation (grant no. CTS-0211792) and Department of Energy (grant no. DE-FG02-98ER14847) for support of this research and the National Partnership for Advanced Computational Infrastructure for providing computing time.

REFERENCES 1. Bandosz, T.J., Biggs, M.J., Gubbins, K.E., et al. (2003). Molecular models of porous carbons. In Chemistry and Physics of Carbons (L.R. Radovic, ed.). Marcel Dekker, pp. 41-228. 2. Debye, P. and Scherrer, P. (1917). Interferencen an regellos orientierten Teilchen im Rontgenlicht III. Physik Zeitschr., XVIII, 291-301. 3. Ruike, M., Kasu, T., Setoyama, N., et al. (1994). Inaccessible pore characterization of less-crystalline microporous solids. J. Phys. Chern., 98, 9594-600. 4. Peng, S., Kyeongjae, C., Pengfei, Q., and Hongjie, D. (2004). Ab initio study of CNT N0 2 gas sensor. Chern. Phys. Lett., 387, 271-6.

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27. Pikunic, J., Clinard, C., Cohaut, N., et al. (2003). Structural modeling of porous carbons: constrained reverse Monte Carlo method. Langmuir, 19, 8565-82. 28. Kirkpatrick, S., Gelatt, Jr, C.D., and Vecchi, M.P. (1983) Optimization by simulated annealing. Science, 220, 671-80. 29. Rosato, V., Lascovich, J.C., Santoni, A., and Colombo, L. (1998). On the use of the reverse Monte Carlo technique to generate amorphous carbon structures. Int. ]. Mod. Phys. C, 9, 917-26. 30. Henderson, R.L. (1974). Uniqueness theorem for fluid pair correlation-functions. Phys. Lett., 49A, 197-8. 31. Gray, C.G. and Gubbins, K.E. (1984). Theory cifMolecular Fluids. Clarendon Press, p.178. 32. Evans, R. (1990). Comment on Reverse Monte Carlo simulation. Mol. Simul., 4, 409. 33. Thomson, K.T. and Gubbins, K.E. (2000). Modeling structural morphology of microporous carbons by Reverse Monte Carlo. Langmuir, 16, 5761-73. 34. Pikunic, J., Pellenq, RJ.-M., Thomson, K.T., et al. (2001). Improved molecular models for porous carbons. Stud. Suif. Sci. Catal., 132, 647-52. 35. Brenner, D.W. (1990). Empirical potential for hydrocarbons for use in simulating the chemical vapor deposition of diamond films. Phys. Rev. B, 42, 9458-71. 36. TersofL J. (1988). Empirical interatomic potential for carbon, with applications to amorphous carbon. Phys. Rev. Lett., 61, 2879-82. 37. Horsfield, A.P., Bratkovsky, A.M., Fearn, M., et al. (1996). Bond-order potentials: theory and implementation. Phys. Rev. B, 53, 12694-712. 38. Petersen, T., Yarovsky, I., Snook, I., et al. (2004). Microstructure of an industrial char by diffraction techniques and Reverse Monte Carlo modelling. Carbon, 42, 2457-69. 39. Marks, N. (2001). Generalizing the environment-dependent interaction potential for carbon. Phys. Rev. B, 63, 35401-1-7. 40. Rutledge, G.C. (2001). Modeling experimental data in a Monte Carlo simulation. Phys. Rev. E, 63, 021111-1-5. 41. For a review of ab initio and semi-empirical methods see: Santiso, E. and Gubbins, K.E. (2004). Multi-scale molecular modeling of chemical reactivity. Mol. Simul., 30, 699-748. 42. Pappano, P.J., Mathews, J.P., and Schobert, H.H. (1999). Structural determination of Pennsylvanian anthracites. 24th Biennial Conference on Carbon Extended Abstracts, American Carbon Society, pp. 202-3. 43. Chen, S.G. and Yang, R.T. (1997). Unified mechanism of alkali and alkaline earth catalyzed gasification reactions of carbon by CO 2 and H 2 0. Energy Fuels, 11, 421-7. 44. Chen, N. and Yang, R.T. (1998). Ab initio molecular orbital study of the unified mechanism and pathways for gas-carbon reactions.]. Phys. Chem. A, 102,6348-56. 45. Ma, X., Wang, Q., Chen, L.Q., et al. (1997). Semi-empirical studies on electronic structures of a boron-doped graphene layer - implications on the oxidation mechanism. Carbon, 35,1517-25. 46. Kyotani, T. and Tomita, A. (1999). Analysis of the reaction of carbon with NO/N 2 0 using ab initio molecular orbital theory.]. Phys. Chem. B, 103,3434-41. 47. For a review of the tight-binding method see: Goringe, C.M., Bowler, D.R., and Hernandez, E. (1997). Tight-binding modeling of materials. Rep. Prog. Phys., 60, 1447-512.

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48. Charlier, J.C., Michenaud, J.P., and Lambin, P. (1992). Tight-binding density of electronic states of pregraphitic carbon. Phys. Rev. B, 46, 4540-3. 49. Lee, C.H., Lambrecht, W.R.L., Segall, B., et al. (1994). Electronic-structure of dense amorphous-carbon. Phys. Rev. B, 49, 11448-51. 50. Stephan, U., Frauenheim, T., Blaudeck, P., andJungnickel, G. (1994). Pi-bonding versus electronic-defect generation - an examination of band-gap properties in amorphous-carbon. Phys. Rev. B, 49, 1489-501. 51. Wang, C.Z., Qui, S.Y., and Ho, K.M. (1997). O(N) tight-binding molecular dynamics study of amorphous carbon. Compo Mater. Sci., 7, 315-23. 52. Pellenq, R.J.-M., Bichara, C., Jain, S.K., et al.(2005). paper in preparation. 53. Kyotani, T., Ito, K., Tomita, A., and Radovic L.R. (1996). Monte Carlo simulation of carbon gasification using molecular orbital theory. AIChE J., 42, 2303-7. 54. Stein, S.E. and Brown., R.L. (1987). Pi-electron properties of large condensed polyaromatic hydrocarbons.]. Am. Chem. Soc., 109,3721-9. 55. Solomon, P.R. and Fletcher, T.H. (1994). 25th Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, pp. 463-74. 56. Jones, J.M., Pourkashanian, M., Rena, C.D., and Williams, A. (1999). Modeling the relationship of coal structure to char porosity. Fuel, 78, 1737-44. 57. Mathews, J.P., Hatcher, P.G., and Scaroni A.W. (1998). Devolatilization, a molecular modeling approach. Am. Soc. Preprints, 43, 136. 58. Nicholson, D. and Parsonage, N.G. (1982). Computer Simulation and the Statistical Mechanics of Adsorption. Academic Press. 59. Steele, W. A. (1974). The Interaction of Gases with Solid Surfaces. Pergamon Press. 60. Bruch, L. W., Cole, M. W., and Zaremba, E. (1997). Physical Adsorption: Forces and Phenomena. Clarendon Press. 61. Lastoskie, C.M. and Gubbins, K.E. (2000). Characterization of porous materials using density functional theory and molecular simulation. Stud. Surf. Sci. Catal., 128,41-50. 62. Allen, M.P. and Tildesley, D.J. (1987). Computer Simulation of Liquids. Clarendon Press. 63. Frenkel, D. and Smit, B. (2002). Understanding Molecular Simulation, 2nd edn. Academic. 64. Pikunic, J., Llewellyn, P., Pellenq, R.J.-M., and Gubbins, K.E. (2005). Argon and nitrogen adsorption in disordered nanoporous carbons: simulation and experiment. Langmuir 21, 4431-40. 65. Steele, W.A. (1978). Interaction of rare-gas atoms with graphitized carbon-black. ]. Phys. Chem., 82, 817-21. 66. Coasne, B., Pikunic, J.P., Pellenq, R.J.M., and Gubbins, K.E. (2003). Comparison between adsorption in pores of a simple geometry and realistic models of porous materials. Mater. Res. Soc. Symp. Proc., 790, 53-8. 67. Jiang, J., Wagner, N.J., and Sandler, S.I. (2004). A Monte Carlo simulation study of the effect of carbon topology on nitrogen adsorption on graphite, a nanotube bundle, C60 fullerite, C168 schwarzite, and a nanoporous carbon. Phys. Chem. Chem. Phys., 6, 4440-4. 68. Pikunic, J.P. (2003). Ph.D. Dissertation, North Carolina State University. 69. For a review of work up to 2000, see: Brennan, J.K., Bandosz, T.J., Thomson, K.T., and Gubbins, K.E. (2001). Water in porous carbons. Colloids Surf. A, 187-8, 539-68.

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70. Striolo, A., Chialvo, A.A., Gubbins, K.E., and Cummings, P.T. (2005). Water in carbon nanotubes: adsorption isotherms and thermodynamic properties from molecular simulation. J. Chern. Phys. 122, 234712. 71. Segarra, E.l. and Glandt, E.D. (1994). Model microporous carbons microstructure, surface polarity and gas-adsorption. Chern. Eng. Sci., 49, 2953-65. 72. Gordon, P.A. and Glandt, E.D. (1997). Adsorption of polar gases on model silica gel. Langmuir, 13, 4659-68. 73. McCallum, C.L., Bandosz, TJ., McGrother, S.C., et al. (1999). A molecular model for adsorption of water on activated carbon: comparison of simulation and experiment. Langmuir, 15, 533-44. 74. Brennan, J.K., Thomson, K.T., and Gubbins, K.E. (2002). Adsorption of water in activated carbons: effects ofpore blocking and connectivity. Langmuir, 18,5438-47. 75. Thomson, K.T. and Gubbins, K.E. (2000). Modeling structural morphology of porous carbons by reverse Monte Carlo. Langmuir, 16, 5761-74. 76. Errington, J.R. and Panagiotopoulos, A.Z. (1998). A fixed point charge model for water optimized to the vapor-liquid coexistence properties. J. Phys. Chern. B, 102, 7470-5. 77. Johnson,J.K., Panagiotopoulos, A.Z., and Gubbins, K.E. (1994). Reactive canonical Monte Carlo: a new simulation technique for reacting and associating fluids. Mol. Phys., 81, 717-33. 78. Turner, C.H., Johnson, J.K., and Gubbins, K.E. (2001). Effect of confinement on chemical reaction equilibria: the reactions 2NO=(NO)2 and N 2+ 3H2 = 2NH3 in carbon micropores.J. Chern. Phys., 114, 1851-9. 79. Turner, C.H., Pikunic, J., and Gubbins, K.E. (2001). Influence of chemical and physical surface heterogeneity on chemical reaction equilibria in carbon micropores. Mol. Phys., 99, 1991-2001. 80. Turner, C.H. and Gubbins, K.E. (2003). Effects of supercritical clustering and selective confinement on reaction equilibrium: a molecular simulation study of the esterification reaction. J. Chern. Phys., 119, 6057-67. 81. Kaneko, K., Fukuzaki, N., Kakei, K., et al. (1989). Enhancement of NO dimerization by micropore fields of activated arbon-fibers. Langmuir, 5, 960-5. 82. Byl, 0., Kondratyuk, P., and Yates, J.T. (2003). Adsorption and dimerization of NO inside single-walled carbon nanotubes - an infrared spectroscopic study. J. Phys. Chern. B, 107, 4277-9. 83. Turner, C.H., Brennan, J.K., Johnson, J.K., and Gubbins, K.E. (2002). Effect of confinement by porous materials on chemical reaction kinetics. J. Chern. Phys., 116,2138-48. 84. Gelb, L.D. and Gubbins, K.E. (1998). Characterization of porous glasses: simulation models, adsorption isotherms, and the BET analysis method. Langmuir, 14, 2097-111. 85. Siperstein, F.R. and Gubbins, K.E., (2001). Synthesis and characterization of templated mesoporous materials using molecular simulation. Mol. Simul., 27, 339-52; Siperstein, F.R. and Gubbins, K.E. (2003). Phase separation and liquid crystal self-assembly in surfactant-inorganic-solvent systems. Langmuir, 19, 2049-57.

THE REASONS BE-HIND ADSORPTION HYSTERESIS Timur S. Jakubov Department of Applied Chemistry, Royal Melbourne Institute of Technology, Melbourne, Australia

Contents Introduction Capillary Condensation Hysteresis and the Kelvin Equation Hysteresis and Adsorption-Induced Strain of Adsorbents Low-Pressure Hysteresis Pore Network and Interconnectivity Some Peculiarities of the Adsorption Hysteresis for Carbonaceous Adsorbents References

6.1 6.2 6.3 6.4 6.5 6.6

6.1

133 135 136 137 137 138 140

INTRODUCTION

The phenomenon of hysteresis is widespread in nature. Behavior of many systems in physics [1], chemistry [2], biology [3], social science [4, 5], and interdisciplinary sciences [6] exhibit hysteresis. The most general reason for existing of these phenomena is as follows: if we reverse the path in the control variables space, we do not necessarily reverse the path in state variables space. Physically it means that there are two or more different local minima and only one corresponds to the thermodynamic equilibrium state, the others must be metastable. These persisting metastable states are responsible for the origin of hysteresis. Among these systems adsorption hysteresis stands out because of its direct and close connection with a number of other complicate phenomena and relevant Adsorption by Carbons ISBN: 978-0-08-044464-2

© 2008 Elsevier Ltd. All rights reserved.

133

134

Chapter 6 The Reasons Behind Adsorption Hysteresis

functions, which in turn are a real challenge to a researcher. Among them are capillarity, criticality of confined fluids, surface phase transition, wettability and contact angles, curvature of interface and surface tension, influence of external potential fields, etc. Physical experiment, molecular simulation, and density functional theory approach are the dominant tools in studies of behavior of confined fluid at present. The first experiment in which adsorption hysteresis was observed was reported [7] in 1897. However, it took several decades before the status of the phenomenon of hysteresis in adsorption science was conclusively established. During this period a large body of experimental evidence was provided first and foremost in thorough studies by Zsigmondy [8], Anderson [9], Lambert and coworkers [10-15], Rao [16], and several others. In succeeding years, a number of new experimental investigations [17-23] was performed using a more advanced technique. The discussion of the works prior to 1967 can be found in the excellent Everett's review [24]. Beginning in 1993, a series of experiments [25-41] has been performed on ordered mesoporous adsorbents with a wellcharacterized pore structure such as MCM-41 with cylindrical and SBA with cage-like pores. In the context of present-day knowledge the adsorption hysteresis originates from the following main reasons: capillary condensation in the pores with specific geometry (however, it should be noted that, if the overlap of surface forces of the opposite walls in the fine pores takes place, a capillary condensation hysteresis may be developed, which is not connected with particular geometry of the pores [42]); elastic and plastic deformations of adsorbents during adsorption process; surface phase and structural phase transitions; kinetic effects associated with the existence of the potential energy barriers at the points of entrance into and egress from the fine pores; superposition of the several effects. According to modern classification, recommended by IUPAC [43], four general types of hysteresis loops designated by the symbols Hl, H2, H3, and H 4 are distinguished. Their shapes below are shown schematically in Fig. 6.1. Below we consider the most important occurrences of the adsorption hysteresis related to the most common reasons.

c:: -0 (J.) .c

oen

"C

ro

E ~

o

E


Relative pressure, p/Po

Figure 6.1 Four general types of adsorption hysteresis.

6.2 Capillary Condensation Hysteresis and the Kelvin Equation

6.2

135

CAPILLARY CONDENSATION HYSTERESIS

AND THE KELVIN EQUATION

According to deduction the classical Kelvin equation [44], which describes the dependence of the saturated vapor pressure on the curvature of interface in two-phase system, is rigorous one, when it is employed for the free (not confined) liquid because this equation takes into consideration only the action of the surface tension forces at the liquid-vapor interface. The present-day refined form of Kelvin's equation may be expressed as [45]

(6.1)

where lIi is the molar volume of the liquid, (j is the liquid/vapor interfacial tension, rm is the mean radius of curvature of the liquid/vapor interface, p and Poo are the saturated vapor pressures over curve and plane interfaces, respectively, and T and R have their usual meanings. To this must be added that (j and lIi depend on radius of curvature and pressure, respectively. However, in actual practice, the Kelvin equation is of frequent use in description of fluids confined in small pores or capillaries of solid. In this case the role of potential field of solid is not only comparable to the surface tension forces, but in some situations it predominates the contribution of the surface tension and the employment of the classical Kelvin equation becomes questionable and is limited by sufficiently large size of capillary [46]. Furthermore, the liquid layer with cylindrical shape, for instance, without the external potential field of cylindrical symmetry cannot exist, as absolutely unstable and nonequilibrium state. Consequently, the Kelvin equation can be used for description of the behavior of the liquid in the small pores or capillaries, only if it is generalized so that the impact of solid wall potential is taken into account. In the presence of the potential field the confined liquid behavior changes qualitatively. Just the wall potential define a limiting thickness of stable liquid layer in pore. Only if the size of pore is relatively large and the limiting thickness is less than radius of pore a capillary condensation may occur, otherwise, it does not take place [40, 47]. Thus, without considering the influence of wall potential the Kelvin equation can be only improved, but not generalized. Historically, however, considerable attention has been given to corrections to the Kelvin equation arising from the thickness of adsorbed layer and the dependence of surface tension on curvature of interface. The first problem was initially considered as monolayers by Foster [48] and more recently as a function of equilibrium pressure of the system by Cohan [49], Derjaguin [50], Foster [51], and Brockhoff and de Boer [52,53]. The initial approaches of Foster and Cohan

Chapter 6 The Reasons Behind Adsorption Hysteresis

136

reduced the radius R in cylindrical capillary to R-t, where t is the thickness of the adsorbed film. However, as it was shown by Derjaguin [50], that correction to the Kelvin equation depends on the attractive part of the solid-fluid potential function and replacing R by R - t is not generally valid. Derjaguin recognized that the interface contained a transition zone between the wetting adsorbed film on the solid surface and the meniscus of the confined fluid, where surface forces and capillary forces act simultaneously. This early result was recovered more recently from a modern density functional approach by Evans et al. [54]. Regarding to surface tension, after Gibbs' original formulation [55] the first results were obtained by Tolman [56], Koenig [57], and Buff [58] who derived the differential equation linking surface tension with radius of curvature. However, the integration of this equation is entail rough assumption regarding the Tolman length 8 - the distance between the Gibbs surface of tension and the equimolar surface - which was considered as constant and equal 8 (the planar limit of 8). Recently, the validity of Tolman's assumption has been evaluated [59, 60] in terms of the dependence of magnitude and sign of 8 on droplet size. It was shown that the planar limit is valid, if droplet contains more than 106 atoms, that is R > 22.5 nm - almost upper limit of mesopores (by argon at 90 K). The sorption potential of a confined fluid in a long open-ended cylindrical capillary was calculated by Barrer et al. [61] and subsequently by Nicholson [62] both of whom employed a sorption potential, which included elliptical integrals of the first and second kind. Integrals were evaluated numerically by fitting to a ninth-order polynomial function. Saam and Cole [63] expressed the attractive part of a cylindrical wall potential in terms of a hypergeometric function and calculated substrate potential as a function of inner radius of capillary. The potential energy profiles for atoms adsorbed in slit-like as well as in cylindrical pores in the Henry's law region are presented in the work of Everett and Powl [64]. The effective one-body potential as well as the wall-fluid potential has been calculated by Evans et al. [65] and Peterson et al. [66] in further studies to detail adsorbed phase behavior in cylindrical and slit-like pores. More recently Tja~opoulos et al. [67] obtained the expression for the interaction potential for the test fluid molecule with a monolayer surface forming a cylindrical pore wall also in terms of a hypergeometrical function. Then summing the interaction potential over 10 cylindrical surfaces with the same spacing, surface number density and Lennard-Jones parameters, authors reproduced the potential energy graphs obtained by numerical integration of this potential function. 00

6.3

HYSTERESIS AND ADSORPTION-INDUCED STRAIN

OF ADSORBENTS

Some dimensional changes of solid adsorbents accompany any adsorption process. However, the strain of adsorbents is not always responsible for adsorption hysteresis. For instance, the adsorbents with sufficiently small pores do not

6.5 Pore Network and Interconnectivity

137

exhibit hysteresis [40, 47], whereas deformation of the adsorbents occurs. Often the strain is merely the attendant phenomenon, but it nonetheless has an impact on quantitative characteristics of the hysteresis loop. For instance, the strain of the porous solid affects on contact angle and surface tension of confined fluid and consequently on capillary condensation. This problem was studied in particular by Lester [68] and Rusanov [69, 70]. In the absence of the other reasons sorbent's strain produces an adsorption hysteresis if either the deformation of solid is irreversible or the relaxation time of sorbent is essentially greater than the time necessary for establishment of the adsorption equilibrium. In these cases, the adsorption and desorption isotherms do not have a common reversible part. In the former case the hysteresis usually disappears in the repeat experiments. Recently, the simultaneous measurements of the adsorption - desorption isotherms, associated deformation curves and heat of adsorption for a number of systems were performed by Tvardovski et al. and reported in a series of papers [71-75]. Although the authors advocated that deformation ofsorbent is the universal cause of adsorption hysteresis, in actually, their experiments lend support to our outlined point of view.

6.4

LOW-PRESSURE HYSTERESIS

As is known [24] the hysteresis loop may persist to the lowest pressure in absence of a hysteresis closing point. This phenomenon referred to, as low-pressure hysteresis (LPH) is more frequent for microporous adsorbents particularly for active carbon. LPH has been the subject of some purposeful experimental investigations and theoretical hypotheses [76-80]. Not counting the systems with irreversible sorbent's deformation when hysteresis loop is observed in all range of relative pressure, the LPH has its origin above all in the kinetic effects associated with overcome the potential barrier at the open end of fine pores. As was shown in the work by ]akubov and Mainwaring [81], the behavior of the potential field at the open end of sufficiently narrow pores always exhibits the existence of potential barriers not only for inward diffusion, but also for outward diffusion. In addition, these barriers, generally, are unequal in magnitude. Moreover, the contraction of adsorbent that often occurs at low relative pressure may gives birth to the barrier for outward diffusion for pores, which have not had the barrier for inward diffusion.

6.5

PORE NETWORK AND INTERCONNECTIVITY

Finally, it is worth mentioning briefly of such a factor as interconnectivity of the pores, which significantly complicated theoretical studies ofthe adsorption systems with hysteresis. The investigation of this problem dates back to the

138

Chapter 6 The Reasons Behind Adsorption Hysteresis

pioneering work of Fatt [82] and since then has been intensively studied by many other researches. Basically, two kinds of the models for interconnected pore networks have been advanced and developed: structurally regular lattice models of the various complexity [62, 83-85] and the random or stochastic models [86-89]. In regard to methods and approaches used for examination of these models, the main method is the application of percolation theory [90-95] where critical percolation probabilities have been calculated by Monte Carlo methods [96] or probabilistic methods [84]. Numerous studies (we referred to just a small number of these works) lead to the general conclusion: capillary phenomena in such porous materials can produce irreversibility arising from pore-blocking effect [96-101]. Thus, the interconnectivity of pores is one more contributor of the adsorption hysteresis phenomena.

6.6

SOME PECULIARITIES OF THE ADSORPTION

HYSTERESIS FOR CARBONACEOUS ADSORBENTS

In the closing section we will enlarge on the distinctive characteristics of adsorption hysteresis, which are typical for porous carbonaceous adsorbents. The peculiarities associated with adsorption on active carbon, in particular, with hysteresis phenomenon owe its origin to two major factors. The first one lies in the fact that porous carbon adsorbents, as a rule, are structurally labile, especially the carbon of steam-gas activation. Every adsorption-desorption cycle involving a thermal treatment leads to the irreversible changes of adsorbents, and only after several training cycles the adsorbent reaches a stable state. The second factor is related to the surface chemical structures on active carbons, in particular, with their ability to oxidize easily and form the oxide adsorption centers such as hydroxyl, carbonyl or carboxyl groups. As a result the energetics and wettability of the surface changes that influences essentially on the adsorption isotherm and hysteresis. The difference between adsorptiondesorption isotherms for oxidized and reduced adsorbents is clearly demonstrated in Fig. 6.2. It should be noted that the range of relative equilibrium pressure in the hysteresis area is the same for both isotherms, whereas the amounts adsorbed are significantly different. Furthermore, the mechanism of adsorption of the nonpolar hydrocarbon (benzene) and polar adsorbate (water) on active carbon differs greatly. This difference is well represented in Fig. 6.3. In particular, the curves in Fig. 6.3 show that the hysteresis area of benzene corresponds to the adsorption in mesopores, and results from capillary condensation, whereas the hysteresis area of water corresponds to the adsorption in micropores, and thus cannot result from capillary condensation. Dispersion interaction, plays a dominant role in the case of benzene, but is not significant for water. The main mechanism of water adsorption by carbonaceous adsorbents includes the formation of hydrogen bounds

6.6 Some Peculiarities of the Adsorption Hysteresis for Carbonaceous Adsorbents

139

40

Ci

32

0 0

,.-....

~ "'0

24

Q)

.0

0 en

"'0

ctI

16

'E ::::J

0

E

«

8

PVDC-600 (degassed 10000 C) 0

0

0.2

0.4

0.6

0.8

1.0

Relative vapor pressure • Adsorption • Desorption

Figure 6.2 Adsorption-desorption isotherms of water on PVDC carbon before and after outgassing at 1273 K (Reprinted from Ref. [102] with permission from Elsevier).

0.4

2 0.3

:§

M

E 0.2

~

s:

0.1

o

0.5

pips Figure 6.3 Adsorption-desorption isotherms of benzene (1) and water (2) at 293 K on active carbon. AG-2 (Wo = 0.322 cm3 /g, Eo = 18.1 kJ/mole) (Reprinted from Re£ [103] with permission from the Editorial office of "Russian Chemical Bulletin").

Chapter 6 The Reasons Behind Adsorption Hysteresis

between water and oxygen complexes on the surface of adsorbent, as well as between the molecules of water.

REFERENCES 1. Pippard, A.B. (1985). Response and Stability. Cambridge University Press. 2. Vidal, C. and Pacault, A. (eds) (1981). Nonlinear Phenomena in Chemical Dynamics. Springer. 3. Lotka, A.J. (1925). Elements of Mathematical Biology. William and Wilkins. 4. Elster, J. (1976). A note on hysteresis in the social sciences. Synthese, 33, 371-91. 5. Franz, W. (ed.). (1990). Hysteresis Effects in Economic Models. Physica-Verlag. 6. Scott, A.C. (1977). Neurophysics. John Wiley & Sons. 7. van Bemmelen, J .M. (1897). Die adsorption. Das wasser in den kolloiden, besonders in dem gel der kieselsaure. Z. Anorg. Chem., 13, 233-356. 8. Zsigmondy, R. (1911). Ober die struktur des gels der kieselsaure. Theorie der entwasserung. Z. Anolg. Chem., 71, 356-77. 9. Anderson, J.S. (1914). Die struktur des gels der kieselsaure. Z. Physik. Chem., 88, 191-228. 10. Lambert, B. and Clark, A.M. (1929). Studies of gas-solid equilibria. Part II. Pressure-concentration equilibria between benzene and (a) ferric oxide gel, (b) silica gel, directly detennined under isothennal conditions. Proc. R. Soc. Lond. A, 122, 497-512. 11. Lambert, B. and Foster, A.G. (1931). Studies of gas-solid equilibria. Part III. Pressure-concentration equilibria between silica gel and (a) water, (b) ethyl alcohol, directly detennined under isothermal conditions. Proc. R. Soc. Lond. A, 134, 246-4. 12. Lambert, B. and Foster, A.G. (1932). Studies of gas-solid equilibria. Part IV. Pressure-concentration equilibria between ferric oxide gels and (a) water, (b) ethyl alcohol, (c) benzene, directly determined under isothennal conditions. Proc. Roy. Soc. Lond. A, 136, 363-77. 13. Foster, A.G. (1934). The sorption of methyl and ethyl alcohols by silica gels. Proc. R. Soc. Lond. A, 146, 129-40. 14. Foster, A.G. (1934). The sorption of vapours by ferric oxide gel. I. Aliphatic alcohols. Proc. R. Soc. Lond. A, 147, 128-40. 15. Foster, A.G. (1935). The sorption of propyl and butyl alcohols by silica gels. Proc. R. Soc. Lond. A, 150, 77-83. 16. Rao, K.S. (1941). Hysteresis in sorption.]. Phys. Chem., 45, 500-39. 17. Amberg, C.H., Everett, D.H., Ruiter, L.H., and Smith, F.W. (1957). Studies in the thermodynamics of adsorption and adsorption hysteresis. In Proceedings of the 2nd International Congress Surface Activity, Vol. II Schulman, ed.). Butterworths, pp. 3-16. 18. Dubinin, M.M., Bering, B.P., Serpinsky, V.V., and Vasil'ev, B.N. (1958). The properties of substances in the adsorbed state: studies of gas adsorption over a wide temperature and pressure range. In Surface Phenomena in Chemistry and Biology a.F. Danielli, K.G.A. Pankhurst and A.C. Riddiford, eds). Pergamon Press, pp. 172-88.

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Chapter 6 The Reasons Behind Adsorption Hysteresis

38. Kruk, M.,Jaroniec, M., and Sayari, A. (1997). Application oflarge pore MCM-41 molecular sieves to improve pore size analysis using nitrogen adsorption measurements. Langmuir, 13, 6267-73. 39. Kruk, M., Jaroniec, M., and Sayari, A. (2000). Nitrogen adsorption study of M CM-41 molecular sieves synthesized using hydrothermal restructuring. Adsorption, 6, 47-51. 40. Kruk, M. andJaroniec, M. (2000). Accurate method for calculating mesopore size distribution from argon adsorption data at 87 K developed using model MCM-41 materials. Chem. Mater., 12, 222-30. 41. Long, Y., Xu, T., Sun, Y., and Dong, W. (1998). Adsorption behavior on defect structure of mesoporous molecular sieve MCM-41. Langmuir, 14,6173-8. 42. Derjaguin, B.V. and Churaev N.V. (1976). Polymolecular adsorption and capillary condensation in narrow slit pores. J. Colloid Interface Sci., 54, 157-75. 43. Sing, K.S.W., Everett, D.H., Haul, R.A.W., et al. (1985). Reporting physisorption data for gas/solid systems with special reference to the determination of surface area and porosity. Pure Appl. Chem., 57, 603-19. 44. Thomson, W. (1871). On the equilibrium of vapour at a curved surface of liquid. Phil. Mag., 42, 448-52. 45. Rowlinson, J.S. and Widom, B. (1982). Molecular Theory of Capillarity. Clarendon Press. 46. Fisher, L.R. and Israelachvili, J.N. (1981). Experimental studies on the applicability of the Kelvin equation to highly curved concave menisci. J. Colloid Interface Sci., 80, 528-41. 47. Dacey,J.R. and Thomas, D.G. (1954). Adsorption on saran charcoal. A new type of molecular sieve. Trans. Faraday Soc., 50, 740-8. 48. Foster, A.G. (1934). The sorption of vapours by ferric oxide gel. 1. Aliphatic alcohols. Proc. R. Soc. Lond. A, 147, 128-40. 49. Cohan, L.H. (1938). Sorption hysteresis and the vapor pressure on concave surfaces. J. Am. Chem. Soc., 60, 433-35. 50. Derjaguin, B.V. (1940). Theory of capillary condensation and other capillary phenomena with allowance for the disjoining action ofpolymolecular liquid films. Acta Physicochim. USSR, 12, 181-90. 51. Foster, A.G. (1952). Sorption hysteresis. Part II. The role of the cylindrical meniscus effect. J. Chem. Soc. Lond. Part II, 1806-12. 52. Broekho~ J.C.P. and de Boer, J.H. (1967). Studies on pore systems in catalysis. IX. Calculation of pore distributions from the adsorption branch of nitrogen sorption isotherms in the case ofopen cylindrical pores. A. Fundamental equations. J. Catal., 9, 8-14. 53. Broekhof£ J.C.P. and de Boer, J.H. (1968). Studies on pore systems in catalysis. XII. Pore distributions from the desorption branch of a nitrogen sorption isotherm in the case of cylindrical pores. A. An analysis of the capillary evaporation process. J. Catal., 10, 368-76. 54. Evans, R. and Marini Bettolo Marconi, U. (1985). The role of wetting films in capillary condensation and rise: influence of long-range forces. Chem. Phys. Lett., 114,415-22. 55. Gibbs, J.W. (1961). The Scientific Papers, Vol. 1. Dover Publications. 56. Tolman, R.C. (1949). The effect of droplet size on surface tension. J. Chem. Phys., 17,333-7.

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THE SURFACE HETEROGENEITY OF CARBON AND ITS ASSESSMENT James P. Olivier Micromeritics Instrument Corp., Inc., Norcross, GA, USA

Contents 7.1 Introduction 7.2 Theoretical Background 7.3 The Application of Density Functional Theory 7.4 Results for "Nonporous" Carbons 7.5 Activated Carbons 7.6 Conclusions References

7.1

147 15 1 153 156 160 165 165

INTRODUCTION

Today, there is probably universal agreement that virtually all real adsorbents are energetically heterogeneous; that is, they display a distribution of adsorptive potentials. Carbons as a class encompass a very wide range of such heterogeneity, from virtually uniform graphites to extremely heterogeneous carbon blacks and microporous activated carbons. Each of these categories presents its own challenges for the quantitative assessment of heterogeneity. 7.1.1

The Adsorptive Potential

In the context of this discussion, surface heterogeneity will be expressed in terms of the adsorptive potential of the material. The adsorptive potential is a measure ofthe net attraction between a solid surface and an adsorbed probe molecule. For physical adsorption, these forces arise chiefly from London-type dispersion interactions (van der Waals forces) resulting from induced-dipole/induceddipole and higher multipolar attractions which in turn depend on the size, Adsorption by Carbons ISBN: 978-0-08-044464-2

© 2008 Elsevier Ltd. All rights reserved.

147

Chapter 7 The Surface Heterogeneity of Carbon and Its Assessment

polarizability, and magnetic susceptibility of the interacting particles (atoms or molecules). Additional contributions may come from coulombic interactions, or from induction forces brought about by the operation of a surface electric field on induced or permanent dipoles of resident molecules. The net potential due to these forces acting on an adsorbed molecule is generally short ranged and is the summed effect from all nearby surface atoms. The contribution of the dispersion forces to the total potential can be well approximated by the Lennard-Jones (LJ) equation for pairwise interaction [1]; (7.1) In Eqn (7.1), cP is the potential, B the depth of the potential well, s the molecular separation, and (J" the separation at which cP = O. For an adsorptive molecule at the adsorbent surface, the total dispersion potential, U LJ , is the sum of its pairwise interactions with each atom of the solid: (7.2) In Eqn (7.2), Su is the distance from the adsorbed molecule to the solid atom j having energy parameter Bj . It is readily seen from Fig. 7.1 that over 90 % of the value of U LJ is provided by the surface atoms within 3-4 molecular diameters of the adsorbed molecule. It is clear that any irregularity in the local chemical composition, density, or geometry of the surface will cause a variation in the adsorptive potential at that point. If the surface topography is locally re-entrant, so as to constitute a fine pore of molecular dimensions, then the

2~---------------------'-----,

<5

E

..........

~

o

i.. ~

:~,.:_.--.:.:..:.:.:.:,.:.~~

~-

=:3

::>

co E (1) (5

a.

-2-1

-4

-//,

I

············•·

··········•

···

·1

I

en

(1)

c o """')

1

-6

U Cii

c c

(1)

.....J

-10

+----i-----T-------T-----,-------r----1

o

234

5

6

Relative distance from surface

Figure 7.1 The potential experienced by a molecule near a solid surface according to Eqn (7.2). The parameters chosen represent nitrogen near a graphite slab.

149

7.1 Introduction

adsorptive potential can be more than doubled. Since the effects of surface chemical heterogeneity and the effects of porosity on the adsorption isotherm are both expressed through the same adsorptive potential, we can anticipate some difficulty in separating the two causes. We shall see that such a separation is possible when the smallest pores in the material to be characterized are large enough to have negligible effect on monolayer formation. However, for microporous adsorbents such as activated carbon, this is not possible and other assumptions must be made. 7.1.2

Thermodynamic Meaning of the Adsorption Potential

In the preceding section, we have presented the idea that real surfaces can be, and usually are, "energetically heterogeneous" in that they provide regions of varying attractive potential to physically adsorbed molecules. In describing a surface energy characteristic, an energy function that is independent of temperature and concentration is desirable. Such a quantity is conveniently defined by the potential energy difference between the lowest energy state of the adsorptive molecule in the gas phase and its lowest energy state in the adsorbed phase, both at infinite dilution [2]. In this way we obtain a quantity that is independent of the kinetic states of the molecule in either phase and that measures most directly the adsorptive potential of the system. The adsorptive potential, Ua, is therefore defined for a homotattic suiface [2] as

ua =

a

pads -

a

E vib

(7.3)

a

where a pads is the potential energy per mole lost by an isolated molecule in moving from a distant point to its equilibrium adsorbed position. The second term on the right is the zero-point vibrational energy of the adsorbed molecule with respect to the surface. While a pads corresponds to the depth of the potential well in Fig. 7.1, we should note that a pads may differ from ULJ if mechanisms other than dispersion forces are at work. When a molecule is adsorbed, the process is accompanied by the liberation of heat that may be measured calorimetrically. The experimentally measured heat can be related to a thermodynamic quantity, the differential heat of adsorption, by relationships that depend on the specifics of the calorimeter used [3]. The differential heat of adsorption, qdiff, on a homotattic surface at any isotherm point is related to Ua by q diff

= Uo (a E vib _ a E aVib ) _

dE tr _ dErot

+a pia

(7.4)

where the term CE vib - aE~ib) is the thermal vibrational energy per mole of adsorbate in excess of the zero-point energy, dE tr and dErot are the kinetic energy changes on adsorption due to loss in translational and rotational degrees of freedom, and apia is the energy of interaction with all neighboring adsorbed molecules. This latter term is clearly dependent on surface concentration and could be estimated by an equation analogous to Eqn (7.2).

Chapter 7 The Surface Heterogeneity of Carbon and Its Assessment

150

Another thermodynamic quantity, qst, the isosteric heat of adsorption, can be calculated from the temperature dependence of the adsorption isotherm by obtaining the slope of the adsorption isostere and is defined by (7.5a)

where na is the moles adsorbed, and g V and a V are the molar volumes of the gas and adsorbed phases, respectively. Neglecting the molar volume of the adsorbed phase relative to the gas phase and assuming the gas phase is ideal gives the more familiar expression

Slnp) t ( 8(1/1) na = qS /R

(7.5b)

It can be shown that the differential and isosteric heats are related by (7.6)

The importance of Eqn (7.4) is that it expresses the differential heat of adsorption in terms of a number of concepts that have a readily visualized physical basis; it reasserts and emphasizes that the differential heat of adsorption contains inter alia separate expressions for the adsorbate-adsorbent interaction and the adsorbate-adsorbate interaction; and since all the other experimentally determined heats of adsorption are related to qdiff, the same conclusion also holds true for them. The quantity Va' expressing as it does the adsorbate-adsorbent interaction stripped of all other incidental energy changes such as lateral (fluidfluid) interaction, work terms, and kinetic and vibrational energy changes, is

-----....-------+---

Bulk phase

~

e> (J) c:

(J)

~

0

-------t

+--~--t-----t--&------t==......

C (J) (5

a..

a _.....-+-_--1.--

0.0

Evib

aEovib

0.5 1.0 1.5 2.0 2.5 3.0 3.5 Distance from surface (molecular diameters)

4.0

Figure 7.2 A schematic diagram of the various energy changes taking place on adsorption.

15 1

7.2 Theoretical Background

more suitable than any of the experimentally measured heats as an index of the fundamental "affinity" of a solid surface for adsorbing a particular gas molecule. The relation of the various heats of adsorption to the adsorptive potential is shown schematically in Fig. 7.2. It should be noted that while heat lost from a system is thermodynamically a negative quantity, it is a custom of long-standing to employ a positive sign in adsorption science. This is frequently confusing to newcomers to adsorption studies. For a more complete and detailed discussion of the thermodynamic quantities ofinterest in physical adsorption, the reader is referred to Chapter III of Ref [3].

7.2

THEORETICAL BACKGROUND

7.2.1 The Integral Equation of Adsorption

Although the concepts are somewhat older, the most widely used model for describing adsorption on an energetically heterogeneous surface was first explicitly stated by Ross and Olivier [4, 5]. The model postulates that the surface' of a real solid is composed of small patches of different adsorptive potential that adsorb independently of one other. The distribution of adsorptive potentials, Uo, among these patches may be represented by a continuous distribution function:

1 da fa= AdU. =f(Uo)

(7.7)

°

where fa is the patch (or site) frequency per unit energy interval on a surface of area A. The distribution function must normalize to unity, as was pointed out by Hill [6], since we are dealing with a surface of finite extent; that is, !(Uo)dUo = 1, over the range of energies considered significant. At any equilibrium pressure p under isothermal conditions, the quantity adsorbed per unit area, q, on a given surface patch will depend only on the adsorptive potential of that patch according to a function: or more generally q = q (P, Uo)

(7.8)

The observed total amount adsorbed, Q at pressure p is then the sum of the contributions from each patch of surface, i.e., (7.9) Equation (7.9) is therefore the general form for any adsorption isotherm and corresponds to equation IV-4 ofRef [3]. Equation (7.9) is now often referred to as "the integral equation of adsorption" or "the generalized adsorption integral." The function q(p,Uo) is called the kernel function or the local isotherm. The local isotherm can take various forms, depending on the geometry of the system that Eqn (7.9) is being used to describe.

Chapter 7 The Surface Heterogeneity of Carbon and Its Assessment

7.2. 2 Solving and Using the Integral Equation of Adsorption 7.2.2.1 Analytic solutions

Referring to Eqn (7.9), we see that in any treatment of surface heterogeneity, we have to deal with three functions, any two of which, if known, assumed or determined can be used in theory to obtain the third. Equation (7.9) represents a Fredholm's integral of the first kind. The solution of equations of this type is well known to present an ill-posed or ill-conditioned problem. For our purposes, this means that the data, Q(P), can be "well represented" by many function pairs in the integrand; hence, simply fitting the data does not guarantee that the kernel function or the distribution are individually "correct." In addition, the mathematical difficulties of handling Eqn (7.9) analytically have severely restricted the number of possible variations that have been published and these are now only of historical interest. No analytic solution of Eqn (7.9) has yet been made based on reasonable models of multilayer adsorption incorporating adsorbate-adsorbate interaction; such a solution may not be possible. 7.2.2.2 Numerical solutions

Unlocking the utility ofEqn (7.9) has been a challenge for decades. The period of renewed adsorption research activity in the decade of the 1950s happened at a time when high-speed electronic computing was just becoming available to researchers in this field. This made the numerical solution of Eqn (7.9) a feasible undertaking. For the first time, it was possible to at least calculate the numerical values of Q(P) from the integral equation of adsorption using more theoretically sophisticated kernel functions that incorporated adsorbate-adsorbate interaction, together with a reasonable distribution function. Equation (7.9) can be rewritten in discrete form as a summation over all significant adsorptive potential patches: (7.10) where we have replaced Ua with the less specific equivalent, B i . The first such solutions were carried out by Ross and Olivier [4, 5] and are tabulated in Ref [3]. Using Gaussian distributions of adsorptive potential of varying width, they computed tables of model isotherms using kernel functions based on the Hill-de Boer equation for a mobile, nonideal two-dimensional gas. It was not actually possible to fit data to the computed models using numerical methods in 1957, so Ross and Olivier developed a technique to find the best fitting model for an experimental isotherm data set by means of graphical overlays. They found that excellent fits to the experimental data could be obtained provided that the degree of heterogeneity was not too great. As pointed out above, a good fit to the data does not in itself verify a kernel

7.3 The Application of Density Functional Theory

153

function or the distribution. However, as the adsorbent becomes more and more homotattic, its isotherms should approach agreement with the kernel function. This was shown to be the case for adsorption measurements on a series of carbons graphitized at increasing temperatures, culminating in the highly graphitized carbon black, P-33, whose isotherms of argon and nitrogen at 77 K and 90 K are closely fitted by the Hill-de Boer equation in the monolayer region. By also correctly describing the heat of adsorption as a function of quantity adsorbed for heterogeneous surfaces, this work confirmed Eqn (7.9) as a powerful tool for investigating surface heterogeneity and the validity of the two-dimensional nonideal gas model for the kernel function. In later work, Ross and Morrison [7, 8] were able to make several advances. The van der Waals equation of state for real gases, which is the basis of the Hill-de Boer equation, is known to be rather inaccurate. Ross and Morrison based their kernel function on a two-dimensional form of the much better virial equation of state. But more importantly, advances in computing resources made it possible to solve Eqn (7.10) for the unknown distribution function using a nonnegative least squares method, rather than assuming a form a priori [9]. Again, it was found to be difficult to fit uniquely isotherm data for surfaces that were more than moderately heterogeneous. The major limitation lies in the fact that the kernel functions used were only models for monolayer adsorption, yet it is well known that adsorption proceeds to multilayers as pressure is increased. To ensure that the more strongly adsorbing portions of the surface remained in the monolayer range, only the lowest pressure portion of the isotherm can be used. This means that the low adsorptive energy portions of the surface contribute little to the total amount adsorbed, making their estimation uncertain. If higher pressure data are included in Q(P), then multilayers exist on some surface patches, which are then not correctly modeled by the monolayer kernel function. Further advances had to await the theoretical development of an improved kernel function.

7.3

THE ApPLICATION OF DENSITY FUNCTIONAL THEORY

While good descriptions of adsorption on uniform surfaces in the submonolayer region have been available for decades, only since the 1990s has accurate calculation ofthe whole isotherm, including the multilayer region, been demonstrated [10]. These calculations use a modified nonlocal density functional theory (MNLDFT). The first use of multilayer local isotherms calculated by MNLDFT in obtaining a measure of surface energetic heterogeneity for several solid adsorbents was reported in 1996 [11]. The formalism of density functional theory (DFT) has received considerable attention as a way to describe the adsorption process at the fluid-solid interface. The older approach was to treat the adsorbate as a separate, two-dimensional phase existing in equilibrium with the bulk gas phase. This model works well

154

Chapter 7 The Surface Heterogeneity of Carbon and Its Assessment

in the monolayer region, but at higher surface concentrations the formation of multilayers requires adopting some sort of three-dimensional model in order to account for increasing adsorbate-adsorbate interaction and the diminishing adsorption potential contribution. Using density functional theory, the adsorptive can be treated as a single, inhomogeneous fluid phase. The fluid varies in density from that of the bulk gas to a much higher value at the adsorbent surface in response to the strength and configuration of the surface adsorptive forces. In this paradigm, there is no separate adsorbed phase; indeed, the concept of a monolayer capacity, fundamental to the two-phase paradigm has disappeared as well. The benefit of this approach is that the isotherm can be modeled from the Henry's law region through to saturation, and even above the adsorptive's critical temperature. In particular, the ability with DFT to model physical adsorption in a pore space of slit-like or cylindrical geometry has led to potentially useful methods for extracting surface area and pore size distribution information from experimental adsorption isotherms [12, 13]. The predictions of density functional theory have been reported to compare well with the results of simulations [14, 15] using Monte Carlo or molecular dynamics methods. Stringent comparisons to real data have been made by us [10] for the adsorption of nitrogen and argon on the near-homotattic surface of a highly gr~phitized carbon, Sterling FT-G(2700). In performing such comparisons, the only unknown intensive parameter is the LJ pairwise interaction energy X f between the adsorbate and adsorbent atoms. Using the customary Tarazona [16] prescription (with corrected weight functions [17]) for the free-energy density functional, we have found that the experimental isotherm data in the monolayer region of coverage can be moderately well described by DFT calculations; however, in the multilayer region of the isotherm, the quantity adsorbed per unit area is significantly over predicted. Later work [10] has shown that a modification to the mean field approximation used to calculate the attractive component of the configurational chemical potential leads to theoretical isotherms that agree closely with experiment over a six-decade range of pressure. An example is shown in Fig. 7.3, along with the results of the unmodified NLDFT of Tarazona [17].

7.3.1 The Deconvolution Method The integral equation of adsorption, Eqn. (7.9), can be rewritten in specific units as

Q(P)

=

f deq(p, e)j(e)

(7.11)

where Q(P) is the total quantity of adsorbate per gram of adsorbent at pressure p, q(p,X) , the kernel function (the local isotherm), describes the adsorption

isotherm for an ideally homotattic surface characterized by an interaction energy e as quantity of adsorbate per square meter of surface, and f(e) the surface area distribution function with respect to e. The quantity e(Eqn. 7.1)) as we

7.3 The Application of Density Functional Theory

0.5

~

g:

-r-----------------~_:r_'1

-0-

0.4

(J)

155

Data

--- MNLDFT --- NLDFT

('I)

E

~

0.3

-0

Q)

-eo ~

0.2

ECO

0.1

CO ~ :::J

o

0.0 ..................~~-........_--,.__--r__--.....__-___4 1e-6 1e-5 1e-4 1e-3 1e-2 1e-1 1e+0 Relative pressure

Figure 7-3 A comparison of experimental data for nitrogen adsorbed at 77 K on Sterling FT-G(2700) graphite with the modified nonlocal density functional theory [10] (MNLDFT) and unmodified [1 7] nonlocal density functional theory (NLDFT).

shall see is closely related to the adsorptive potential and can be equated to the quantity a pads in Eqn. (7.3) and in Fig. 7.2. While DFT allows us to calculate values for q(p, 8), it of course provides no analytic form for the function, and in general the form of f(8) is also unknown. However, by using carefully designed numerical methods, model isotherms calculated by MNLDFT can be used in carrying out the inversion of the discrete form of the integral equation of adsorption. In this way one can determine the effective adsorptive potential distribution of the adsorbent from the experimental adsorption isotherm. The method used can be expressed by (7.12) where Q(P) is the experimental adsorption isotherm interpolated onto the vector p of pressure points, q(p, 8 ij ) a matrix of quantity adsorbed per square meter, each row calculated by MNLDFT for a value of 8 at pressures p, andf(8J a vector of positive or null values whose terms represent the area of surface in the sample characterized by energy Xi' The total surface area of the sample is given by

The solution values desired are those positive numbers that most nearly, in a least squares sense, solve Eqn. (7.12). Additional constraints on the solution may be required to stabilize the deconvolution process [18, 19]. The formulation and solution of Eqn. (7.12) differs from previous work in an important way. In previous attempts, Q(P) was the amount adsorbed at the

Chapter 7 The Surface Heterogeneity of Carbon and Its Assessment

experimental pressures, p. This required that q(p, XJ be calculated for that specific set of pressures, and that the size ofJ (XJ be no greater than the number of experimental points. Not only does this result in a large computing task for each data set, it causes the evaluation ofJ(XJ to be subject to a varying bias, depending on how many and where on the pressure scale the isotherm points were measured. The automatic adsorption equipment available today permits a large number of experimental points to be measured and the resulting isotherms can be interpolated accurately onto a predetermined optimized set of pressures. Hence, the vector p can be chosen to best represent the kernel function over the wide pressure range required by the set of Xi. If we consider m members of the set of X and a vector p of length n, it is clear that n X m must hold. If n = m, the solution vector J (X) can be "noisy" because of even small imperfections in the data or model. For n > m, the solution is smoother because of the additional data constraints. Various other regularization techniques have been proposed to mitigate the inversion problem; in this work we use the method of co-minimization of the second derivative of f(X) together with an overdetermined matrix for which n > 2m.

7.3.1.1 Parameters of the model matrix For use with Eqn.(7.12), a model matrix was calculated by the MNLDFT method [10] using the parameters suitable for nitrogen at 77.3 K. For convenience, the values of X were specifically the values of X sf / k used to calculate the wall potential V(z) of that reference, and ranged from 20 to 100 K in steps of 2.0 K (approximately 1/2RT). Relative pressure points were chosen in geometric progression from 1 x 10-6 to 0.6 with 40 points per pressure decade. Model isotherms were normalized to 1 m 2 of surface.

7.4

RESULTS FOR "NONPOROUS" CARBONS

Synthetic and natural graphites and carbon blacks are arguably nonporous, though the small spaces between primary particles in a carbon black agglomerate may act as pores in some materials. Additionally, the prismatic surfaces of natural graphite may display "missing" graphene planes that in effect become shallow slit-like pores. If such pores have a width less than about 1 nm, they will report as very high energy regions in the adsorptive energy distribution. The data reported here were obtained using a Micromeritics ASAP 2010 equipped with optional 10- and 1-torr pressure transducer. Low-pressure data were corrected for thermal effusion.

157

7.4 Results for "Nonporous" Carbons

7.4.1 Synthetic Graphitic Carbons Heating a graphitizable thermal carbon black to high temperature in an inert atmosphere produces some of the most energetically uniform surfaces known. One reason for this lies in the shape of the particles formed. Electron micrographs [3] reveal that the individual particles are doubly truncated polygonal (principally hexagonal and octagonal) bipyramids consisting of minute radiating crystals. The exposed surface of each crystal is the graphite basal plane. The surface of the whole faceted particle is therefore entirely composed of the carbon layer plane of crystalline graphite with no exposed prismatic surface. To confirm the deconvolution algorithm, we show in Figs. 7.4(a) and (b) the result of applying Eqn. (7.12) to the experimental data contained in Fig. 7.3. Since this data set was used in developing the MNLDFT model, we would expect to recover a monomodal energy distribution with esf / k = 57.0 K, as used in the fit shown in Fig. 7.3. The best fit contained contributions from the classes representing esf / k = 56 and 58, with an area weighted mean of 56.7 K, which is satisfactory agreement. The total surface area obtained is 12.4m2 jg. The BET (stands for Brunauer, Emmett, and Teller) area of this certified reference material is 11.1 m 2 j g. Because the MDFT model ignores the slight corrugation of the wall potential, the commensurate film transition seen at 0.008 relative pressure is not reproduced. Figure 7.5 , (a) and (b), illustrates the application of Eqn. (7.12) to the nitrogen isotherm obtained with Vulcan 3-G(2700). While graphitized at the same temperature as the Sterling FT, Vulcan has previously been reported as less uniform than the Sterling material [14]. As additional evidence, note that the commensurate film transition near 0.008 Pre! seen in Figs. 7.3 and 7.4 is not

(a) 6 - r - - - - - - - - - - - - - - - - - , -

f

(b) 10 . , . . . . . - - - - - - - - - - - - - - - ,

5 •

~

en 4

-

Experimental data MNLDFT fitted

8

ME

()

:;; 3 Q)

.c

~

"'C

2

eel

~1 c: eel

2

::J

o

0

1e-6 1e-5 1e-4 1e-3 1e-2 1e-1 1e+0 Relative pressure

0+--.,.----r------..LL1r----r---r--------l o 20 40 60 80 100 120 csf/k (K)

Figure 7.4 (a) The expe9mental data (points) of Fig. 7.3 fitted by Eqn (7.12) using the deconvolution method (solid line). (b) The adsorptive potential distribution for the Sterling graphite.

Chapter 7 The Surface Heterogeneity of Carbon and Its Assessment

(a) 40 - r - - - - - - - - - - - - - - - - , 1 E " " " 1 (b) 40 - , - - - - - - - - - - - - - - - ,

~ 0..

~ (f)

•

35 -

Experimental data DFTfitted

~ S

30

,£.

Q)

u

"0

~ 20

~ 20

o

::J CIJ

CIJ

~

«;

15

'E Q)

~

~

E ~

10

::J

o

30

co co ~

ME 25

10

(.)

E

5

o -+-------r::::y;.;...=..---r-----r-----r----.----f 1e-6

1e-5

1e-4

1e-3

1e-2

1e-1

1e+0

O-t----.,.---20 40

80

100

Relative pressure

Figure 7.5 (a) A comparison of experimental data for nitrogen adsorbed at 77 K on Vulcan 3-G(2700) (points) with the fit given by the modified nonlocal density functional theory (MNLDFT) models (line). (b) The adsorptive potential distribution for the Vulcan 3 graphite.

experimentally detected on the Vulcan surface. The area weighted mean value ofXsf / k is 56.1 K, and the total reported surface area is 80.78 m 2 I g. The surface area by BET is 73.5 m 2 /g.

7.4.2 Natural Graphites Natural graphites differ from those described above chiefly in their morphology. While equally crystalline, virtually all possible growth, cleavage, and fracture surfaces are present along with the extended basal surfaces. Interest in characterizing these materials has grown because of their importance in batteries for light-weight energy storage. The performance of a graphite anode in a lithium ion battery is known to be strongly related to the graphite's surface properties, in particular to the surface area and to the relative extent of basal plane and prismatic crystallite surfaces exposed to the electrolyte [20]. The presence of prismatic surface is necessary to allow the intercalation of the Li+ ion into the bulk of the graphite. In principle, therefore, graphites with a higher ratio of prismatic to basal surfaces should yield superior performance. We illustrate this in Fig. 7.6, (a) and (b). We see that the fine-grinding procedure has the expected result of increasing the total surface area, from 6.28 to 25.78 m 2 I g. In addition, the adsorptive potential distribution has been broadened. If we consider the central peak in these distributions, between say 50 to 60 K, to represent the graphite basal plane, we see that the fraction of basal plane has been reduced in the ground material, which indeed gives superior anode performance.

159

7.4 Results for "Nonporous" Carbons

KS75

(a)

Area =6.28 m2/g

20

(b)

40 60 80 Adsorptive potential (K)

100

120

KS75KM

6........----------------------. Area = 25.76 m2/g 5

O-+----~­

o

20

40 60 80 Adsorptive potential (K)

100

120

Figure ].6 (a) The adsorptive potential distribution of a natural, low surface area graphite. (b) The same material after a fine-grinding procedure, showing a slightly broadened distribution and increased surface area.

7.4.3 Carbon Blacks An example of a much more heterogeneous surface is shown in Fig. 7.7. The adsorbent in this case is a carbon black designated C4, used by ASTM committee D24 as a reference reinforcing black. Again we see that the MNLDFT models provide an excellent fit to the adsorption data. The total surface area by the present method is 138.69 m 2 /g; the BET method gives 129.63 m 2 /g. The weighted mean value ofXsf/k is 53.61 K. The central mode of the distribution is seen to be somewhat lower than that for the graphites.

Chapter 7 The Surface Heterogeneity of Carbon and Its Assessment

160

(b) 12 - r - - - - - - - - - - - - - - - - ,

(a) 50 • -

Experimental data Fitted MNLDFT models

-

~

10

5

m

8

(ij (ij

'E Q) E Q)

~

6

4

2

0-+---r------,r-----r---r----,--~__1

1e-7 1e-6 1e-5 1e-4 1e-3 1e-2 1e-1

Relative pressure

1e+0

o -+-----r--

o

20

40

60

80

100

120

Adsorptive potential (K)

Figure 7-7 (a) A comparison of experimental data for nitrogen adsorbed at 77 K on ASTM carbon black C4 (points) with the fit given by the modified nonlocal density functional theory (MNLDFT) models (line). (b) The adsorptive potential distribution for the carbon black.

7.5

ACTIVATED CARBONS

The carbons discussed up to this point display a range of adsorptive potentials created chiefly by their surface roughness and chemistry; thus, their isotherms can be quite accurately modeled by a system of free, homogeneous surfaces of varying adsorptive potential. Their heterogeneity is then described by the area distribution of those potentials. Activated carbons cannot be energetically characterized by this method. These materials have a much more complex structure, providing many possible sources of energetic heterogeneity. As in developing any characterization method, one wishes to define and use the simplest model that yields reasonable and useful results.

7-5-1 Assumed Structure Activated carbons are usually visualized as an assemblage of graphitic planes arranged in a near-parallel fashion, thus creating a microporous solid having approximately slit-like pores of molecular dimensions. The resulting overlapping wall potentials produce greatly enhanced adsorptive potentials, so one may argue that the energetic heterogeneity of the material is to a large extent controlled by the distribution of its pore widths rather than the detailed nature of the pore walls themselves. Several current characterization methods are based on this simple model. However, within the slit pore structure, the pore walls may be of different and varying thickness, from a single carbon layer to essentially graphitic (more than five layers) and can also be of varying lateral extent. The graphene planes within a wall unit may have some crystalline stacking order, i.e., as in

161

7.5 Activated Carbons

hexagonal (aba ... ) or rhombohedral (abca ... ) graphite or may be completely turbostratic, with no discernable relationship. In addition, a wall unit may carry certain functional groups, typically containing oxygen, nitrogen, or sulfur, on its surface or especially at its periphery. Locally, a number of wall units may be ordered in a parallel fashion, creating a domain having a slit pore structure. At longer range, the orientation of these locally ordered domains is probably uncorrelated, leading to the possibility of interdomain pore spaces of indeterminate geometry and with perhaps a larger average width than that of the slit pores within the more ordered domains. In addition, it is by no means clear that such a structure is totally rigid. That is, it is possible that dilation and/or contraction of domains may occur as a result of the pressure tensors within the pore system [21, 22]. While still greatly simplified, the above picture leads to several sources of differing adsorptive potential. In estimated order of importance, these are as follows: 1. 2. 3. 4. 5.

The The The The The

distribution of pore widths distribution of wall potentials distribution of wall unit and domain size or area form and distribution of interdomain porosity quantity of functional groups

At the time of this writing, commercially available software includes only the first of these.

7.5.2 Example Applications of the Simple Model The commonly used DFT-based methods for characterizing activated carbon assume that the pores are geometrically slits with smooth, unterminated graphitic walls of constant wall potential. The experimental data are then modeled as a system of homogeneous, confined slits of varying width. The energetic heterogeneity of the material is therefore completely expressed in terms of its distribution of pore widths. The integral equation of isothermal adsorption, Eqn (7.12), for the case of pore-size distribution can be written as the convolution

Q(P)

=

f dH q(p, H)j(H)

(7.13)

where Q(P) is the total quantity of adsorbate per gram of adsorbent at pressure p, q(p, H), the kernel function, describes the adsorption isotherm for an ideally homoporous material characterized by pore width H as the quantity of adsorbate per square meter of pore surface, and j(H) is the desired pore surface area distribution function with respect to H. The kernel function is calculated by DFT for a confined fluid [10, 14, 15] and Eqn (7.13) solved by the methods already discussed.

Chapter 7 The Surface Heterogeneity of Carbon and Its Assessment

162

Isotherms for argon at 87 K adsorbed on typical activated carbons are shown in Figs 7.8 and 7.9, along with the reconstructed isotherm resulting from the pore width distributions shown. While the fit to the data is satisfactory in both cases, inspection of the pore width distributions obtained for these and many other activated carbon samples reveals a disturbing similarity: they all show deep minima at regular multiples of the probe molecule diameter, particularly near 1 nm (3xXo) [21,23]. This can be traced to packing effects inherent in the kernel function models that seem to be missing in the real data. Figure 7.10 shows how the pore fluid density as calculated by DFT varies with pore width, with density maxima near the pore width distribution minima. (a)

~

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.

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Relative pressure

100

Figure 7.8

(a) A comparison of experimental data for argon adsorbed at 87 K on Carbosieve G activated carbon (points) with the fit given by the nonlocal density functional theory (NLDFT) models (line). (b) The pore width distribution for the carbon. (a)

700

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600

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(b) Experimental data NLDFT fitted isotherm

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Relative pressure

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100

Pore width (A)

Figure 7.9 (a) A comparison of experimental data for argon adsorbed at 87 K on activated carbon RH572 (points) with the fit given by the nonlocal density functional theory (NLDFT) models (line). (b) The pore width distribution for the carbon.

7.5 Activated Carbons

0.040

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Figure 7.10 The average pore fluid density in pores of various widths as calculated by nonlocal density functional theory (NLDFT). Note the periodic nature of the density, with density maxima near the positions of the minima in the distributions shown in Figs 7.8 (b) and 7.9(b).

7.5.3 Advanced Activated Carbon Models The simple model ofan activated carbon, pictured as a set of homogeneous graphitic planes arranged in a parallel fashion so as to form slit-like pores, needs to be developed further. From the above enumerated list of factors causing heterogeneity, the variation in wall potential is next in importance to variation in pore width. Remembering that the distribution of adsorptive potentials is totally reflected in the adsorption isotherm of a given material, we realize that a decrease in assumed average wall potential will result in a decrease in the deduced average pore width in order to compensate. With two distributed variables to contend with, one is faced with a choice of assuming a priori that the two variables are correlated in some fashion, or they are totally uncorrelated. Bhatia [24] has advanced convincing arguments that, in order to account for the observed surface areas, the pore wall units in an activated carbon must have thicknesses primarily in the range of one to three graphene planes, leading to significantly lower wall potentials than assumed in the simple model discussed above. The adsorptive potential of a wall unit composed of n graphene planes can be calculated by integrating Eqn (7.1) for the case of an adsorptive molecule and a set of graphene planes of infinite extent: (7.14) where ¢ft(z, n) is the potential acting on a single adsorptive molecule at distance z from the surface of a stack of n planes separated by a distance ~ for graphite. The quantity Ps is the area density of carbon atoms in the graphene sheet (0.382 A-i), (Tft for the LJ separation, and eft the LJ potential well depth. In Fig. 7.11,

Chapter 7 The Surface Heterogeneity of Carbon and Its Assessment

-5

(5

.§ ...,

---1Iayer ................... 2 layers - - - - - - 3 layers _ .. _ .. _ .. - 4 layers - - - Slayers

-6

~

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-1 0 -+-----,-----'T""'"-----r------"T----r----~ 0.85 0.90 0.95 1.00 1.05 1.10 1.15

Relative distance from surface

Figure 7.11 The adsorptive potential between nitrogen and a pore wall of different thicknesses near the potential minimum as calculated by Eqn (7.14).

we show plots of Eqn (7.14) for values of n from 1 to 5. The effect of wall thickness on adsorptive potential is seen to be quite significant for less than four layers. At five layers, the wall acts like an infinitely thick slab. By assuming that the wall thickness is distributed randomly, following a Poisson distribution, and that the average wall thickness is correlated with pore width, Bhatia is able to solve Eqn (7.13) by the usual means without introducing new parameters. The results yield both a pore width distribution and a wall thickness distribution. Compared with the simple model, this method yields pore width distributions that are shifted toward smaller widths, as expected. However, the distributions are similarly multimodal, showing periodic minima notably near 1 nm pore width. A second advanced approach currently under development has been reported by Ustinov and Do [23]. These workers make no assumptions about possible correlations between wall thickness and pore size. Indeed, they assume that the pore wall adsorptive potentials are variable without assuming a specific source and have an energy distribution independent of pore width. The adsorption integral can then be written as a double convolution. The kernel function is first convolved over the distribution of pore wall energies, then over the pore width distribution to match the experimental data. The model isotherms for the range of energies and pore widths are calculated by DFT in the usual way. Surprisingly, the solution of the equation is a reasonably straightforward iterative task and not overly time-consuming on modern equipment. The first reports using this method are quite encouraging. The pore width distributions obtained are significantly less complex than given by the simple model, without the anomalous periodicity, and the fit to the data is notably supenor.

References

This model, however, implicitly assumes that the behavior of a locally heterogeneous pore can be modeled as the linear sum oflocally homogeneous pores of the same width having different wall potentials. This would seem to be justified only if the pore widths are small compared with the scale of the locally uniform patches or domains within a given pore. This would be expected to be the case in activated carbon micropores. However, the equation would not be applicable to mesopores, for instance, where the range of the local heterogeneity is small compared with the pore dimensions [25].

7.6

CONCLUSIONS

We have seen that carbon materials encompass a very wide range of energetic heterogeneity as expressed through the variation in adsorptive potential. When the material is essentially nonporous, it can be characterized in a straightforward fashion by the deconvolution of the appropriate adsorption integral with interaction energy as the distributed parameter. The complex structure of activated carbon requires a different approach. In this case, the geometric heterogeneity of the micropore structure is best expressed primarily in terms of the micropore size distribution, although this simplest model is not entirely free from artifacts in the calculated distribution. Recognition of the inherent heterogeneity of the pore wall unit itself has, in early work, shown hope ofproviding a major advance in characterizing activated carbon structures.

REFERENCES

1. Lennard-Jones, J.E. and Dent, B.N. (1928). Cohesion at a crystal surface. Trans. Faraday Soc., 24,92-107. 2. Sanford, C. and Ross, S. (1954). Homostatic surface: A suggested new word. J. Phys. Chern., 58, 288-8. 3. Ross, S. and Olivier, J.P. (1964). On Physical Adsorption. New York: Interscience. 4. Ross, S. and Olivier, J.P. (1961). On physical adsorption. 12. Adsorption isotherm and adsorptive energy distribution of solids. J. Phys. Chern., 65, 608-15. 5. Olivier, J.P. and Ross, S. (1962). On physical adsorption. 16. Physical interaction of H 2 , D 2 , CH 4 , and CD 4 with graphite. Proc. R. Soc. (London), 265A, 447-54. 6. Hill, T .L. (1949). Statistical mechanics of adsorption. 6. Localized unimolecular adsorption on a heterogeneous surface. J. Chern. Phys., 17, 762-71. 7. Ross, S. and Morrison J.D. (1975). Computed adsorptive-energy distribution in the monolayer (CAEDMON). Surf. Sci., 52, 103-19. 8. Morrison, J.D. and Ross, S. (1973). The second and third virial coefficients of a two-dimensional gas. Suif. Sci., 39, 21-36.

166

Chapter 7 The Surface Heterogeneity of Carbon and Its Assessment

9. Sacher, R. S. and Morrison, J.D. (1979). An improved CAEDMON program for the adsorption isotherms of heterogeneous substrates. J. Coil. Interface Sci., 70, 153-66. 10. Olivier, J. (1995). Modeling physical adsorption on porous and nonporous solids using density functional theory. J. Porous Mater., 2, 9-17. 11. Olivier, J. (1996). The determination of surface energetic heterogeneity using model isotherms calculated by density functional theory. In Proceedings of the Fifth International Conference on Fundamentals of Adsorption (M.D. LeVan, ed.). Boston: Kluwer Academic Publishers, pp. 699-707. 12. Seaton, N.A., Walton, J.P.R.B., and Quirke, N. (1989). A new analysis method for the determination of the pore size distribution of porous carbons from nitrogen adsorption measurements. Carbon, 27, 853-61. 13. Olivier, J.P., Conklin, W.B., and Szombathely, M.V. (1994). Determination of pore-size distribution from density-functional theory - A comparison of nitrogen and argon results. In Characterization of porous solids III (COPSIII), Studies in Surface Science and Catalysis, Vol. 87 O. Roquerol et aI., eds). Amsterdam: Elsevier, pp. 81-9. 14. Lastoskie, M., Gubbins, K.E., and Quirke, N. (1993). Pore size heterogeneity and the carbon slit pore: A density functional theory model. Langmuir, 9, 2693-702. 15. Lastoskie, C.M., Gubbins, K.E., and Quirke, N. (1993). Pore size distribution analysis of microporous carbons: a density functional theory approach. J. Phys. Chem., 97, 4786-96. 16. Tarazona, P. (1985). Free-energy density functional for hard-spheres. Phys. Rev. A, 31, 2672-9. 17. Tarazona, P., Marconi, U.M.B., and Evans, R. (1987). Phase-equilibria of fluid interfaces and confined fluids - nonlocal versus local density functionals. Mol. Phys., 60,573-95. 18. Lawson, C.L. and Hanson, RJ. (1974). Solving Least Squares Problems. Englewood Cliffs, NJ: Prentice Hall. 19. Jaroniec, M., Kruk, M., Olivier, J.P., and Koch, S. (2000). A new method for the accurate pore size analysis ofMCM-41 and other silica based mesoporous materials. COPS V. In Studies in Surface Science and Catalysis 128 (K.K. Unger et aI., eds). Amsterdam: Elsevier, pp. 71-80. 20. Winter, M., Moeller, K.C., and Besenhard, J.O. (2003). Carbonaceous and graphitic anodes: basic aspects. In Science and Technology of Advanced Lithium Batteries (G.A. N azri and G. Pistoia, eds). New York: Kluwer Academic Publishers, Chapter 5, pp. 144-94. 21. Olivier,J.P. (1998). Improving the models used for calculating the size distribution of micropore volume ofactivated carbons from adsorption data. Carbon, 36, 1469-72. 22. Reichenauer, G. and Scherer, G.W. (2001). Effects upon nitrogen sorption analysis in xerogels. J. Coil. Interface Sci., 236, 385-6. 23. Ustinov, E.A. and Do, D.D. (2004). Application of density functional theory to analysis of energetic heterogeneity and pore size distribution of activated carbons. Langmuir, 20, 3791-7. 24. Bhatia, S.K. (2002). Density finctional theory analysis of the influence of pore wall heterogeneity on adsorption in carbons. Langmuir, 18, 6845-56. 25. Maddox, M.W. Olivier, J.P., and Gubbins, K.E. (1997). Characterization of MCM-41 using molecular simulation: heterogeneity effects. Langmuir, 13(6), 1737-45.

WETTING PHENOMENA William A. Steele Department of Chemistry, The Pennsylvania State University, University Park, PA, USA

Contents 8.1 Introduction 8.2 Wetting on Carbon 8.3 Conclusions References

8.1

167 175 180 181

INTRODUCTION

The wetting of solid surfaces by liquids has been studied for many years, both theoretically and experimentally. Useful reviews of this work include those by de Gennes [1], Dietrich [2], Adamson (Chapters 10, 13, and 16 in [3]), and Sullivan and Telo de Gama [4]. Before beginning a discussion of this phenomenon in the case of vapors condensed onto solid carbons, it is helpful to summarize some general features of wetting. Thus, the characteristics of the wetting of solids by liquids will be briefly described in this introductory section, to be followed by a discussion of some of the experimental and simulation studies of vapors on carbon surfaces. The first point to note is that there are two distinctly different approaches to this problem: one, which will be called macroscopic, is based primarily on interpretations of the measured contact angles for a liquid droplet on a surface. The contact angle is generally defined as the angle between two lines, one tangent to the liquid surface and the other to the solid surface, meeting at the point where the droplet surface touches the solid. Observations of this angle are often interpreted using Young's equation [5] that relates the contact angle Ow to the surface tensions of the three phases involved, namely, Ylv' Yls' and Ysv' Adsorption by Carbons ISBN: 978-0-08-044464-2

© 2008 Elsevier Ltd. All rights reserved.

167

168

Chapter 8 Wetting Phenomena

the surface tension at the liquid-vapor, the liquid-solid, and the solid-vapor interface, respectively. A calculation of the work for an infinitesimal increase of the liquid-solid contact area yields Young's equation: (8.1) Evidently, the two quantities that determine the contact angle are Yls - Ysv and Ylv. The physically relevant values of contact angles are limited by the fact that cos Ow must be less than 1 and greater than -1. A value of Ow = 0 corresponds to complete wetting of the surface by the liquid, i.e., to the situation where the droplet has spread into a thin layer covering the entire solid surface. The other limit of 180 corresponds to no wetting (=drying) , i.e., a droplet that has not spread at all and thus is in touch with the surface only at the point of contact between the nearly spherical liquid drop and the planar solid. If the surface tensions are such that the calculated cos Ow becomes greater than + 1, the system is said to undergo a wetting transition where the surface is completely wet for all calculated values of cos Ow > 1; on the other hand, if the calculated values of wetting angle become less than -1, a drying transition occurs. The surface tension to be substituted in Eqn. 8.1 consists of a liquid-vapor tension which has the usual value modified by the presence of significant gas-solid interactions for the molecules in a very thin layer of fluid (in contrast to that for the bulk liquid which is often used in the calculation of this quantity). The surface tensions involving the solid are more problematic. For instance, it is implied that the solid surface is planar and homogeneous in the derivation, which is frequently not the case for real surfaces of interest. 0

There are several complicating factors that tend to reduce the utility of this

macroscopic approach. First, one often finds that values of observed contact angles depend upon whether the droplet is spreading or contracting, which indicates that the system is not in thermodynamic equilibrium as is implicit in the derivation of Young's equation. Second, most solids have rough or nonplanar surfaces especially in pores or powders, or the surfaces may be chemically heterogeneous. Both these factors complicate the calculation of contact angle from Young's equation. However, statistical mechanical expressions for the elements of the pressure tensor Pxx ' Pyy, and Pzz are well known (chapter 3 in [6], Section 4d in [7], [8]). Here x and yare taken to be parallel to the surface and z is perpendicular to the surface. Since Pzz does not depend upon z, it is essentially the vapor pressure of the spreading liquid. However, P xx and Pyy are dependent upon z and approach Pzz at large distances from the surface. An integration of (Pxx + Pyy )j2 - Pzz over x, y, and z will give the area times the surface tension of the gas-liquid interface. The theoretical expressions for the pressure tensor give the explicit relationship between the molecular interactions and the computed (or measured) surface tensions. The interactions involved are those for the molecules in the fluid near the surface interacting with each other (gasgas energies) and with the underlying solid (gas-solid energies). This approach to surface tension usually involves computer simulations to obtain the pressure tensor and from them the values of the surface tension of the liquid adsorbate.

8.1 Introduction

1.0 ....-------------------.---~

,

,,

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, '" ,, "

0.5

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Figure 8.1 Cosines ofthe contact angles for a Lennard-Jones (LJ) fluid on a graphitic surface

e:,

are plotted versus the ratio of the gas-solid interaction well depth to the gas-gas well depth. The fluid-solid interaction was evaluated using a simplified interaction potential and the resulting curves are shown for two values of the reduced temperature T= kT/ egg. The dashed parts of the curves are estimates reflecting the fact that unreasonably long simulation runs were required to obtain reliable results in this region. At the upper and lower boundaries of the figure, the slopes of the curves change discontinuously to zero, corresponding to complete wetting (for increasing along the upper boundary) or complete drying (for along the lower boundary). decreasing

e:,

e:,

Such simulations also allow one to evaluate the adsorption isotherm for a given set of molecular interactions so that the simulation of wetting behavior via the adsorption isotherm is related to the contact angle through simulation of the elements of the pressure tensor. Figure 8.1 shows simulated contact angles [9] for a fluid with LennardJones (LJ) gas-gas interactions interacting with a 9-3 wall (a simplified version of the gas-solid potential for a graphitic solid) with repulsive and attractive interactions varying as Z-9 and Z-3, respectively, where z is the fluid atom-solid surface distance). The contact angles were evaluated for several temperatures and potential functions by substituting simulated surface tensions into Young's equation. The figure shows the angles obtained for two temperatures (T* = kTj egg) as a function of the energy well-depth ratio e: defined above. The curves shown all have discontinuous changes in slope (to zero) at the limits of + 1 and -1. This is associated with a first-order transition from partial wetting to either complete wetting of the wall-fluid interface when the calculated values of cos (J become greater than +1, or complete drying when the value becomes less than -1. Evidently, the intermediate values of cos (J shown in the figure correspond to partial wetting as a function of the energy ratio

e:.

Chapter 8 Wetting Phenomena

170

An alternative theoretical approach to the evaluation ofthe solid-liquid surface tension which is particularly useful at low pressure and coverage is based on an integration of the Gibbs adsorption equation (Eqn 2.60 in [7]) that can be written as (8.2) where na is the number of moles adsorbed, A is the area, and Pb and Pb are the density and pressure of the bulk gas, respectively. As will be discussed below, this expression is particularly useful for calculations of the solid-fluid surface tension denoted here by y. For example, suppose the coverage is small enough for Henry's law to be valid. Then the coverage na will be given by (8.3) If the surface coverage is small enough for Eqn 8.3 to be valid, an integration of Eqn 8.2 gives RTP K

H y = - - -b - -

(8.4)

A

In Fig. 8.2, the points are the results obtained by evaluating the transverse component of the pressure tensor obtained from Monte Carlo simulation and the line is the result of an integration of the Gibbs adsorption isotherm using the simulation data. The vertical dashed line shows the saturation vapor pressure.

0.5

0.4

0.3

-'"'/ 0.2

0.1

0.0 0

10

5

15x 10-3

p*

Figure 8.2 Solid-fluid surface tension y* = ya 2 / e for the Ar-C0 2 system [10] at kT/ e = 0.88, where e and a are the Ar-Ar well-depth and size parameters for a LennardJones (LJ) potential (elk = 120 a = 3.4 A) plotted as a function of the reduced pressure 0

,

3

p* = pa Ie.

17 1

8.1 Introduction

14

12 10 8 6

Nonwetting Partial wetting Wetting Prewetting Monolayer

._...-+...._.

4

0.2

0.4

0.6

0.8

Figure 8.3 Isotherms are shown for the types of adsorption that can occur for simple gases on a flat homogeneous adsorbent surface. With the exception of the prewetting isotherm, the nature of the interactions that produce these isotherms is discussed in the text.

Clearly, any isotherm equation that gives a good representation of na as a function of Pb can be used in the Gibbs equation to evaluate the solid-fluid surface tension as a function of coverage. In the so-called microscopic approach, one obtains wetting properties from the adsorption isotherms for a vapor on a solid. Here we show how the isotherms can vary from drying to wetting as the interaction potentials are changed. These isotherms show coverage () = na / nmono as a function of x = PI Po, where na is the number of moles adsorbed, nmono the number of moles in a monolayer, and Po the bulk vapor pressure at a fixed T. Figure 8.3 shows the following: (i) For very weak interactions, the adsorbed phase is essentially a twodimensional ideal gas; thus, a plot of () versus x will be linear with a small slope given by the Henry's law. The theoretical expression for K H is well known:

KH = _1 kT

f

[exp( -us(z)/kT) -l]dz

(8.5)

where z is distance from the surface and us(z) is the gas-solid interaction for a flat homogeneous surface. If na remains small for pressures over the entire range up to the condensation pressure Po, gas-gas interactions have a negligible effect on the isotherm so that one has a "drying" system. (ii) When the attractive gas-gas interactions become strong enough to significantly affect the isotherm, it takes on the characteristics of what is known

172

Chapter 8 Wetting Phenomena

as "partial wetting." In this case, the isotherm is moderately curved upward to lie above the Henry's law straight line and intersects the PI Po = 1 line at a moderately small coverage. The virial isotherm equation (p. 107 in [6]) is one way to introduce the effect of (weak) gas-gas interactions. Thus, it gives the isotherm that was used to construct the curve shown in Fig. 8.3. Partial wetting isotherms are known as Type VI or Type VII in the usual classification scheme (p. 534 in [3]). (Although calculations of the contact angles associated with such isotherms do not appear to have been performed in sufficient detail to fill in the quantitative aspects of this picture, there seems to be no great difficulty in making such calculations, at least for simple model surfaces.) (iii) A "wetting" isotherm that shows the usual "knee" at the completion of the monolayer plus a steep increase as PI Po approaches unity is also shown. (It is known as a Type II isotherm (p. 534 in [3]).) Gas-solid interaction energies that are strong compared to the experimental value of kT lead to steep rises in the amount adsorbed at submonolayer coverages. As is well known, when the amount adsorbed approaches monolayer coverage, the effect of the repulsive gas-gas interactions at high 2D densities is to make the isotherm flatten out and thus produce the knee. (iv) An isotherm that exhibits the thin-to-thick vertical jump known as a "prewetting" transition is also shown [11, 12]. In common with the wetting isotherm, the prewetting isotherm also shows a steep increase as PI Po approaches unity. An extensive literature exists that deals with questions concerning changes in wetting behavior with changing temperature [13-22]. For example, what is the order of the thermodynamic transition from partial to complete wetting or drying that take place at various values of T? Theory indicates that these transitions are indeed first order below a wetting critical temperature T we. Figure 8.4 is a temperature-density phase diagram for a system made up of a gas plus fluid in contact with a uniform solid surface [13, 23]. Drying, wetting, and prewetting lines as well as the wetting critical temperature (denoted by T e in this figure) are all shown. In addition to the computer simulations of the wetting of atomic adsorbates on simple, planar homogeneous surfaces [10, 24-32], the theory of wetting on heterogeneous [33-39] surfaces has been considered. In particular, Cassie's law [33] was proposed over 50 years ago to deal with planar surfaces that consist of patches of chemically heterogeneous surface. This law was obtained from the simple assumption that the surface excess free energy is the sum of distinct contributions for each of the chemically different regions. Swain and Lipowsky [34] and Henderson [35] have derived a statistical generalization of this law and the deviations from it because of the dependence of the local surface tension upon position or shape of the boundary. Frink and Salinger [36] have presented a numerically more complex theory of this problem and have calculated both contact angles and surface-phase transitions for chemically heterogeneous surfaces. Computer simulations [37-39] were carried out for gases adsorbed on surfaces

173

8.1 Introduction

T

p

Figure 8.4 Schematic phase diagram for an adsorption system exhibiting prewetting. The solid curve shows the coexistence of gas and liquid phases in contact with the surface and is nearly the same as the curve for the bulk material, somewhat modified because of the effects of the gas-solid interactions upon the adsorbate phases. The adsorbate gas-liquid critical temperature (denoted by T c in this figure) depends upon the gas-solid potential but is not very different from that for the bulk. (A simulated value of 0.94 was obtained for a truncated LJ 12-6 potential [23], compared with the bulk T c: of1.23 for the same model.) The dashed curve is the prewetting line where thin and thick films can coexist and Tic is the prewetting critical temperature where the difference between thick and thin films vanishes.

of slit pores with walls consisting of alternating strongly and weakly interacting strips. A few of the results are shown in Fig. 8.5 where reduced units were used so that dimensionless energies and distances were defined by dividing by Egg and reduced distances by (Tgg' where gg denoted well depth and size parameters for the LJ fluid adsorbate. In some cases, liquid bridges were formed by stratified liquid stabilized by the strong strips. Figure 8.5 shows local densities p(x, z) obtained for surfaces made up of parallel strips separated by reduced distances sz/ {Tgg. The fluid-solid energies of adsorbate atoms were given by sums over the solid of 12-6 pair energies with parameters that made surfaces with strips of alternating strongly and weakly attractive solid atoms. For kT/ B gg = 1, the figure shows strong alternations in density with the weakly attracting surface showing negligible adsorption over much of its area, and moderate adsorption in the form of molecular strata between the strong strips at the smaller strip separations. Phase diagrams were obtained for some of these model systems and compared favorably with those for a mean-field lattice.gas model. [40, 41]. Thus, these systems can exhibit wetting that is very different from that described earlier. Other theoretical work on this problem is that of Henderson [42], who considered the properties of a fluid adsorbed in a parallel-walled pore with grooved walls; Bryk et al. [43] simulated a gas adsorbed on a number of rough surfaces created by placing a disordered quenched layer of hard spheres on a substrate interacting with the adsorbed atoms via a LJ 9-3 potential. Simulations showed that the system exhibits wetting, prewetting, and partial wetting for

I

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ena Phenom Wetting 8 r te p a Ch

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a rbed o n as a d s o s g a h J) t a (L Sz th ones nnard-J are d e n o te d b y e L (c) a r ips d fo simulate ons b e tw e e n str c e d units. p (x , z) u ti d s ra e a ie r p it e s in s n it h Sz . The cal de 8.5 Lo striped surface 7.2, 7.5, 8.2, w ulation ally n, of l chemic o t h e r sim n the to p d o w n e A th . r m e o r lay ed o alues, f r ] is bas gh o u t e a -4

4

lly r o u ces [44 ace o f atomica us surfa the (100) surf order o e e n th e f g o o r ickness o n hete atoms o n o r i n d to be a first- by easing th i n g properties t n bed eare e b r o ads ett h a t app y p e r t u r toms f w tl w o h f g e o n v li o s a y g ti d a ly le ulations n o r de t was on ns (one o r t w o r o d u c t i o l solid. T h e sim erfect solid tha o ti c e f r sta impe e p rfect cry ansition for th ncentration o f tr o c g r e w e t t i n c t i o n o f a small du h e i n t r o u n i t cell). surface

I I I

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175

8.2 Wetting on Carbon

8.2

WETTING ON (ARBON

The various forms of solid carbon provide an important group of adsorbents for wetting studies. They can be graphitized to exhibit chemically and physically homogeneous surfaces that are characterized by relatively strong gassolid interactions for nonpolar adsorbates such as the rare gases. To illustrate some of these ideas, Table 8.1 summarizes the well depths of the gas-graphite interaction potential for most of the rare gases on graphite. Here, 8 gs is the well depth for an isolated gas-atom interacting with the solid, 8 gg is the well depth is the ratio of the two well depths, for gas atoms with LJ pairwise interactions, and Ter is the rare gas critical temperature, shown here to indicate the temperature range in which one might study wetting behavior of these systems. Note that the values of gas-gas well depths shown here are for the effective interaction of a pair of atoms in the dense liquid phase and differ somewhat from those obtained from second virial coefficients measured in the gas. The well depths (in energy units divided by the Boltzmann constant) have been obtained from the experimental Henry's law constants for these adsorption systems. A comparison of the energy ratios in Table 8.1 for the rare gas-graphite systems with the data of Fig. 8.1 illustrates the fact that all these gases can wet the graphite surface. The experiments that established this are those of Thomy, Duval, and coworkers, published over 30 years ago. [47-49], for krypton, xenon, and methane (among others) adsorbed on exfoliated graphite. Roughly 20 years later, Morrison and coworkers [50, 51] extended these studies by measuring isotherms to considerably higher coverages and over a range of (low) temperatures for Kr, Xe, and CH 4 and showed that the complete wetting behavior indicated in the earlier work actually appears to be partial wetting when the range of coverage of the measurements is sufficiently extended. Plots of the isotherm data given

8:

Table 8.1 Well depths of the gas-graphite interaction potential for rare gases on graphite -

,

.;;)

Neon Argon Krypton Xenon

;~ 340 959 1255 1932c

0: /

,-

C"

34 120 160 221

-

-

cr t

v

_

l:S¥

--

44.5 157 209 290

10 8 8

9

aThese values were obtained by fitting experimental Henry's law constants to the theoretical expression for potentials obtained by assuming that the gas-solid interaction energy is given by a pairwise sum over the carbon atoms of LennardJones (LJ) inverse 12-6 functions of separation distance [45]. bFrom fits of experimental liquid state data to simulations of the LJ liquid [46]. CCorrected value.

Chapter 8 Wetting Phenomena

---r-----r----..,..-----r-----....--

25,...----......

~

Ii

,

N 15 E .......... <5 E

~

•

70K + 75K )( 80 • vap70K - vap 75 K ---._vap 80 K •._.•.•..

20

-+

Ii .i

~

•

~

.sas

j(

c:: 10

~

J

1+ +1.

.l

!

• i; ! I

~ )C)q

I

)(

+ +

5

. •

i

x

)(

)(

)/C

x·

•

)(

•

xX

•

•

•

•

0 0

0.5

1.5

2

2.5

3

Pressure (torr)

Figure 8.6 Experimental isotherm data for Kr at three temperatures on graphitized carbon black.

in Ref [50] for Kr at three temperatures are shown in Fig. 8.6 and indicate partial wetting. The coverages at which these Kr isotherms meet the bulk vapor pressure lines are estimated to be 9.2 ± 0.3 (70K), 11.6 ± 0.3 (75K), and 17.3 ± 0.5 (80 K), in units of micromoles per square meter. Denoting coverages by na , the authors fitted the results for all three gases at several temperatures to an equation of the form (8.6) where k is an arbitrary constant and Tw is the temperature for wetting-partial wetting. The analysis gives Tw/Tcr = 0.40 for each gas, where T cr is the bulk critical temperature. This result might lead one to guess that the films are sufficiently thick (over five layers) at the transition to partial wetting to give properties that are no longer sensitive to the gas-solid interactions. In contrast to the strong interactions and consequent wetting often observed for nonpolar gases on graphite, the nonchemical interactions of these gases with metals can be quite weak compared with their gas-gas interactions. For example, calculations of the ratios of the gas-solid to the gas-gas well depth for the inert gases and hydrogen on alkali metals give values that are much smaller than those summarized in Table 8.1, varying from 2.0 to 0.9 as the metal atomic number increases [52]. Clearly, the wetting properties of these systems will differ considerably from those for the rare gases on graphite. Polar gases on graphite will be nonwetting if the dipolar interactions in the adsorbed phase are sufficiently strong. Water on graphitized carbon black is a

177

8.2 Wetting on Carbon

well-known example because the water dipoles make quite small contributions to the water-graphite interaction compared to the dipolar (i.e., H-bond) part of the fluid energy. Similar considerations may apply to other dipolar molecules. Consequently, the experimentalist must take great care to exclude partial oxidation of the substrate that gives rise to polar centers near the points of oxidation. (A few of the large number of papers reporting experiments on these systems are cited in Refs. [53-63].) Such sites will interact strongly with polar adsorbates to form clumps of polar adsorbed molecules in the vicinity of the imperfections on or in the adsorbent surface. (Nitrogen also appears to interact strongly with polar sites on carbon surfaces, probably due to the interaction of its quadrupole moment with the electrostatic fields associated with polar imperfections.) It is believed that adsorbed clumps will serve as nuclei for droplet formation, thus facilitating wetting. The picture presented here would lead to the conclusion will produce quite that inclusion of strongly polar gas-gas interactions in small values of this parameter for such gases on highly purified graphite, which is thus a rationale for their nonwetting behavior. The dipole moment JL and polarizability a (a major factor in determining attractive part of the "van der Waals" energy) are summarized in Table 8.2 for a few simple molecules; these polarizabilities can be compared with the values shown for a couple of nonpolar molecules. In addition to isotherm measurements, other experimental probes used in the studies cited here include determinations of the coverage dependence of the heats of adsorption on carbon, particularly for water. For example, a microcalorimetric study [55] of the heats of adsorption of water on several chemically modified high-surface-area carbons found some heats greater than 50 kJ/mole (compared to 44 kJ/mole for the condensation of pure water) the large heats were ascribed to chemical adsorption and are most likely due to the reaction of water with strongly polar groups on the carbon surfaces; as the adsorption proceeded, heats were observed that were roughly equal to the water heat of condensation, and finally heats less than 42 k]/mole that presumably

e:

Table 8.2 Selected dipole moments and polarizabilities a

HF H 20 NH3

CH 3 0H C 2 H s OH CH 3 Cl Ar

N2 a Polarizabilities

1.91 1.85 1.47 1.71 1.69 1.71

o o

2.46 1.48 2.22 3.23

5.10 4.53

1.66 1.76

for nonspherical molecules are averages over the three principal axes.

Chapter 8 Wetting Phenomena

came from physical adsorption on the relatively nonpolar hydrophobic parts of the surfaces. When these carbons were reacted with H 2 at 950°C, the heats of water adsorption were small enough to indicate hydrophobicity; subsequent oxidation at 150°C showed significant increases in the amount adsorbed and the heat of adsorption of water on the surfaces. In a different study [57], ozone treatment of graphite produced dramatic increases of the heats of adsorption of water, thus changing the surface from hydrophobic to hydrophilic. Although water-water interaction potentials are well understood by now, the molecular water-graphite interaction potential remains the subject of extensive studies. Reviews of previous work on this problem have been published by Werder et al. [64] and by Pertsin and and Grunze [65] in conjunction with their theoretical-simulational paper. A considerable number of simulation studies of water on carbon surfaces and in carbon pores have been reported. The conclusions reached were primarily that the thermodynamics and structure of water-graphite system are extremely sensitive to the range and orientation dependence of the water-graphite interaction potential. In fact, the adsorbed water molecules in the monolayer are found to be highly oriented, even when using orientation-independent water-graphite potential models. This orientation dependence is ascribed to the tendency of the water molecules to maximize the H-bonding to their neighbors in the adsorbed film by minimizing the number of H-bonds oriented toward the graphite surface. Much work in the theoreticalsimulational area remains to be done on this system (particularly, simulations over an extended temperature range are needed). Jaffe et al. [66] have summarized the calculations of the contact angle for nanometer-scale droplets of water on graphite using various model potentials for the water-graphite interaction. It was noted that experimental measurements of this angle [67, 68] are not all in agreement, but it was concluded that values of 85° ± 2° and 42° ± 7° are reasonable. The simulations are for nanometer-size droplets and thus are not fully compatible with the experiments. Simulated values obtained run from 0° to 111 °C but Jaffe et al. list five water-graphite potentials that yield simulated contact angles close to their recommended value of85-89°. The simulations also give angle-averaged minimum interaction energies in the range -5.8 to -7.0 kJ/mole for isolated water molecules on graphite. In simulations of the watergraphite or water-carbon pore systems [64-66, 70-75], it is straightforward to evaluate the average number of H-bonds per water as a function of separation distance between the water and the solid surface. For instance, Walther et al. [71] find that the average number of bonds per molecule in the contact layer is 3.1 and 3.5 for the adsorption in pure water, and Shevade et al. [75] obtained results of 2.9 and 3.7 for the water in a 50:50 mixture of water and methanol. Other simple polar molecules (see Table 8.2) whose adsorption on graphite has been studied include ammonia [76-80], methanol [81, 82], and ethanol [81, 83-85]. An interesting difference between water and the alcohols is that the dipolar bonding (H-bond) network is three dimensional in bulk water but two dimensional in the alcohols where linear chains are formed. It appears that this network is disrupted in monolayer films of water, but not of the alcohols. This

8.2 Wetting on Carbon

179

is one of the reasons for the difficulty of water wetting on graphite, but its ease for the alcohols. The interactions of methanol and ethanol with active carbons having varying degrees of oxidation have been studied by Stoekli and coworkers [81]. They showed that measured energies of interaction were larger for ethanol than methanol, and that the energies increased linearly for both molecules as the oxygen content of the solid adsorbent increased, similar to water adsorption. Thus, both the hydrocarbon parts of the alcohols and their dipoles make important contributions to their interaction with partially oxidized carbon adsorbents. The temperature dependence of the isotherms of ammonia on graphite has been carefully studied in conjunction with neutron diffraction measurements [76]. Figure 8.7 shows that this system exhibits several types of behavior ranging from partial wetting at the two lowest temperatures studied, to what may be prewetting at the three intermediate temperatures. However, prewetting jumps are generally larger than those shown in Fig. 8.7 and an alternative explanation would be that the rise is just monolayer completion, moved to an unusually high value of plpo because of relatively weak gas-solid interactions for a polar gas in contact with the nonpolar graphite surface. In a study of the structure of monolayer films of carbon dioxide on graphite, Morishige [86] observed that carbon dioxide does not wet the graphite surface at temperatures below 104 K. It is likely that the electrostatic quadrupole inter-

T(K)

Isotherm feature

Microscopic status

<172

No step

Bulk crystallites (BC)

172-195

Single step (0.5 < PIPo < 0.95)

X < 21iquid film (LF) X>2LF+BC

Single step

PIPo-O.S)

X<2LF X> 2 LF + bulk liquid

Step disappears

Complete wetting?

50

ii:'

ren

C')

~

195-212

40

E

>212

~ "'C Q)

.c 30

o en

"'C

ctS

Q)

E

"

20

:J

J9

(3

>

10

•

x

• •

".

9

...

•

0.6

0.7

0.8

0.9

PIPo Figure 8.7 Adsorption isotherms of ammonia on graphite [76]. From left to right, the isotherm temperatures are 244.0, 212.1, 183.0, 172.1, 170.3, and 161.0 K, respectively. The table in the inset summarizes the wetting regimes for each.

Chapter 8 Wetting Phenomena

180

actions, which are relatively strong for this molecule, stabilize the bulk solid in preference to the surface layer where the electrostatic part of the moleculesurface interaction is not strong. A class of adsorbing solids which is currently receiving much attention is that of the so-called buckytubes that consist of graphite planes, which have, in essence, been rolled into cylindrical tubes of diameter equal to a few angstrom. The relatively small atoms and molecules that can enter these tubes tend to form quasi-one-dimensional phases. Their wetting properties are greatly affected by their geometry, i.e., a molecule that fits snugly into a tube of circular cross section will have a considerably enhanced gas-solid interaction. If the sizes are such that this interaction is attractive, wetting will be favored; furthermore, the gas-gas interactions with the two neighbors in a quasi-one-dimensional array will be less important than with the six neighbors on a flat surface, which further enhances the likelihood of wetting in a buckytube. These tubes are known to close-pack into bundles of parallel tubes, and the nature of the adsorption in the interstices and on the external surfaces of these bundles is discussed in Chapter 15 by Calbi et al. in this book. Complications occur because of the fact that the tube walls can be oxidized at certain points during their formation, sometimes to the extent of burning holes in the tube walls [59-63]. This process often involves the creation of polar groups in the vicinity of the defects, which can enhance the wetting of dipolar molecules in such tubes. Current studies are only now beginning to provide answers to some of the questions concerning the properties of buckytube adsorbents.

8.3

CONCLUSIONS

It has been argued here that the surfaces created from carbon are providing an extremely useful platform for studying the structures and thermodynamic properties of monolayer and thin multilayer films of a wide variety of adsorbates. Particularly useful are those that are graphitic in nature: they are chemically quite stable and can be prepared in a variety of useful forms - the classic case is exposed basal planes, but more recently, the surfaces of fullerenes and carbon nanotubes have become excellent choices for studies of adsorption in confined volumes or on simple planar substrates. Thus, for example, measurements and simulations of the structures and the phase equilibria of solid monolayer films have been studied for a wide range of materials [87] with the goal of gaining a better understanding of the role of intermolecular forces in determining the properties of two-dimensional matter and how this role changes as the monolayer films are thickened in a gradual approach to three-dimensional matter. The graphite substrate on which the adsorption occurs is a nearly perfect choice for the experimental and theoretical work: it is almost planar with a small periodically varying component to the gas-solid energy whose effects on the properties of an overlayer film are minor and can readily be included in the description of

References

181

these adsorption systems. The chemical and structural purity of the solid surfaces is high and can be maintained at a high level or varied in a controlled fashion. Studies of adsorbed phases in carbon nanotubes are still in their early stages but offer the opportunity for extensive determinations of the behavior of matter in strongly restricted volumes. Viewed in this way, wetting behavior on such surfaces is another important way of demonstrating how gas-gas and gas-solid interactions determine the temperature and layer-thickness dependence of the structure and thermodynamic properties of molecularly thin layers on inert, nearly planar surfaces. Furthermore, the controlled introduction of chemical impurities on carbon surfaces produces a whole new set of adsorbing solids with interesting and practically significant properties. The goals of this chapter have been to show how fundamental wetting theory is illuminating simulations and experiments on highly purified carbon surfaces as well as on the materials with moderate impurity levels.

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Chapter 8 Wetting Phenomena

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Chapter 8 Wetting Phenomena

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77. Bomchil, G., Harris, N., Leslie, M., et al. (1979). Structure and dynamics of ammonia adsorbed on graphitized carbon black. Part 1. Adsorption isotherms and thermodynamic properties.]. Chem. Soc. Faraday Trans. 1,75, 1535-41. 78. Gamlen, P.H., Thomas, R.K., Trewern, T.D., et al. (1979). Structure and dynamics of ammonia adsorbed on graphitized carbon black. Part 2. Neutron diffraction.]. Chem. Soc. Faraday Trans. 1,75, 1542-52. 79. Gamlen, P.H., Thomas, R.K., Trewern, T.D., et al. (1979). Structure and dynamics of ammonia adsorbed on graphitized carbon black. Part 3. Neutron quasielastic and inelastic spectra.]. Chem. Soc. Faraday Trans. 1, 75, 1553-69. 80. Tabony, J., Bomchil, G., Harris, N.M., et al. (1979). Structure and dynamics of ammonia adsorbed on graphitized carbon black. Part 4. Nuclear magnetic resonance spectra.]. Chem. Soc. Faraday Trans. 1,75, 1570-86. 81. Lopez-Ramon, M.V., Stoekli, F., Morenos-Castilla, C., et al. (2000). Specific and nonspecific interactions between methanol and ethanol and active carbons. Langmuir, 16, 5967-72. 82. Morishige, K., Kawamura, K., and Kose, A. (1990). X-ray diffraction study of the structure of a monolayer methanol film adsorbed on graphite.]. Chem. Phys., 93, 5267-70. 83. Kiselev, A.V. and Kovaleva, N.V. (1995). Izv. Akad. Nauk SSSR, Ser. Khim., 989. 84. Herwig, K.W. and Trouw, F.R. (1992). Ethanol on graphite: the influence of hydrogen bonding on surface melting. Phys. Rev. Lett., 69, 89-92. 85. Morishige, K. (1992). Structure and melting of a monolayer ethanol film on graphite.]. Chem. Phys., 97, 2084-9. 86. Morishige, K. (1993). The structure ofa monolayer film of carbon dioxide adsorbed on graphite. Mol. Phys., 78, 1203-9. 87. Steele, W.A. (1996). Monolayers of linear molecules adsorbed on the graphite basal plane: structures and intermolecular interactions. Langmuir, 12, 145-53.

ADSORBED GASES IN BUNDLES OF CARBON NANOTUBES: THEORY AND SIMULATION M. Mercedes CalbP, Milton W. Cole 2 , Silvina M. Gatica 2 , Mary J. Bojan 3 and J. Karl Johnson 4 1 Department of Physics, Southern Illinois University, Carbondale, IL; 2Department of Physics, Pennsylvania State University, University Park, PA; 3Department of Chemistry, Pennsylvania State University, University Park, PA; 4Department of Chemical and Petroleum Engineering, University of Pittsburgh, and National Energy Technology Laboratory, Pittsburgh, PA, USA

Contents 9.1 Introduction 9.2 Endohedral Adsorption 9.3 Adsorption in Interstitial Channels 9.4 External Surface Acknowledgments References

9.1

187 19 0 19 8 202 206 206

INTRODUCTION

The discovery of carbon nanotubes [1, 2] has led to extensive investigation of adsorption on these remarkable substrates. Much of this effort has been directed toward potential applications, such as gas storage and separation, which exploit the fact that every carbon atom of a single-wall carbon nanotube (SWNT) can provide two surfaces, inside and outside of the tube, for Adsorption by Carbons ISBN: 978-0-08-044464-2

© 2008 Elsevier Ltd.

All rights reserved.

187

188

Chapter 9 Adsorbed Gases in Bundles of Carbon Nanotubes: Theory and Simulation

potential gas adsorption; this corresponds to a specific area of order 2500 m 2 / g. Early claims of extraordinary hydrogen uptake (e.g., six H 2 molecules per C atom) stimulated a particularly intense effort to achieve practical amounts for storage applications, but those results have not been confirmed by any subsequent experiments. More modest uptake (0.5 molecule per C atom) of H 2 has been found to occur in some experiments and that may suffice for storage and other applications [3-9]. This chapter focuses on basic scientific questions concerning the structural, dynamical, and thermal properties of gases adsorbed in the environment shown in Fig. 9.1, a nanotube bundle. Much of the research to date has assumed that these bundles are ideal, consisting of identical, perfect, and parallel collections of tubes. More realistic analyses are based on simulations derived from distributions of tube radii (R) in typical laboratory samples [10, 11]. The role of such disorder should be taken into account when comparisons are made with the data. Figure 9.1 exhibits the various adsorption sites accessible, in principle, to an adsorbate. The external surface region includes the so-called groove between pairs of nanotubes, an energetically favorable site because of the high coordination number of C atoms; the binding energy is typically a factor 1.7 times as large as that on graphite. Between a triad of nanotubes within the bundle lie "interstitial channels" (ICs). If not blocked at the end, the ICs are accessible to small atoms or molecules. Finally, there exists the "endohedral" region inside the individual tubes; access to this region usually requires chemical treatment to open the tube [12-15]. The subsequent sections of this chapter are organized by site.

Figure 9.1 Simulation of adsorption of methane at 159.88 K and 0.05 bar on monodisperse and polydisperse distributions of nanotubes within bundles. (Adapted from Re£ [11].)

9.1 Introduction

This chapter describes results obtained from theoretical and simulation studies of adsorption in these geometries. Chapter 15 discusses the specific case of hydrogen adsorption, emphasizing the problems of gas storage and isotope separation. Chapter 17 deals with the results from experimental studies and compares these with relevant calculations. We confine our description to the results of the research and ignore the detailed assumptions and methods used in the calculations. At the outset, we note that most studies employ simplified model adsorption potentials, such as continuum versions of the tubes, rather than atomistic descriptions. This approach may be justified by our lack of knowledge of the geometry (e.g., polydispersity), on the one hand, and by the absence of reliable theories of adsorption potentials for the nanotube array, on the other. When we know the potential better than we do now, more sophisticated modeling will be possible (and probably necessary) for explaining experimental data. A significant fraction of the research literature is focused on SWNTs having radius R of order 0.7 nm. This is exemplified by a particular variety of tube, the so-called (10,10) "armchair" nanotube; the general (n, m) designation refers to the lattice vector of the graphene sheet identifying a line perpendicular to the hypothetical cutout employed to construct the tube. For this (10,10) species, the lattice vector is bent into a circumferential curve that is locally parallel to the C-C bonds of the tubes. This curve can pass through 20 C nuclei per revolution and corresponds to R = 0.68 nm. Much of the research literature makes the simplifying approximation that the tube consists ofsmeared-out helium, ignoring atomicity. Calculations indicate that this is usually a good approximation inside the tubes, where the coordination number of an atom is high, but it is less accurate for exohedral adsorption [16]. Nanotubes in the laboratory often exhibit an aspect ratio ofl0 000, i.e., length L approximately in microns. From the fundamental perspective, an important stimulus of this research is the realization that such a linear geometry provided by small R nanotubes yields one-dimensional (lD) phases ofmatter; that description is certainly true from the phase transition perspective (since only one dimension approaches infinity in the thermodynamic limit). The subject of lD matter has been studied as an academic problem for many years [17, 18]. An intriguing aspect of the subject is that no phase transitions occur in a strictly lD system at finite temperature (T). In the nanotube environment, however, lD lines of adsorbed molecules can interact with neighboring lines of molecules, resulting in a 3D transition at finite T. To this date, in fact, predictions have been made of lD, 2D, 3D, and even 4D phases of matter in this novel environment [19, 20]. All such regimes will be discussed, to some extent, in this chapter and Chapter 15. The rich variety of phenomena has made theoretical study both enjoyable and rewarding. The outline ofthis chapter is as follows: Section 9.2 discusses adsorption within the tubes; Section 9.3 addresses the subject of IC adsorption; and Section 9.3 describes adsorption on the external surface.

Chapter 9 Adsorbed Gases in Bundles of Carbon Nanotubes: Theory and Simulation

190

9.2 9.2.1

ENDOHEDRAL ADSORPTION

General Remarks

This section deals with adsorption inside the nanotubes. Access of molecules to this region requires a sample preparation technique that leaves open the ends or the walls of the tubes, because molecules cannot tunnel through the close-packed, graphene-like tube wall (interatomic spacing 0.14nm). The other possibility is that the tube forms around the molecules, as is likely to be the case for endohedral C 60 (the system nicknamed "peapods" [21 ]). The interior of a tube is usually more attractive to an adparticle than the exterior because of the larger effective coordination experienced inside. This difference is exemplified in Fig. 9.2 for the case ofXe in a tube of radius 0.7 nm. One may consider a wide variety of adsorbed molecules and nanotube sizes. The morphology of the adsorbed film depends on the relationship between the particle diameter (u) and the diameter, 2R, of the tube. This dependence stems from the potential energy function; an example is shown in Fig. 9.3 for the case of a C 60 molecule in nanotubes of different sizes [23]. Note that the energy minimum occurs on the axis, i.e., radial distance r = 0, for the smaller tube, while it lies near r = 0.37 nm for the larger tube. In the case of a Lennard-Jones (LJ) type of pair potential describing the molecule-C pair interaction, with hard-core parameter u int ' the transition between these two types of behavior occurs at tube radius ~rans = 1.212uint [24], where u int is the LJ hard-core diameter of the gas-C interaction. Typically, an arithmetic combining rule is used to relate the lengths involved in the problem:

u int =

(U+Uc ) 2

3000 2000 1000

g

0

S ~

-1000 -2000 -3000

/ 0

2

4

10

12

14

16

r(A)

Figure 9.2 Xe atom's interaction with a (10,10) nanotube.The left curve shows the interior region and the right curve shows the exterior region. (Adapted from Re£ [23].)

9.2 Endohedral Adsorption 6 ...-----,.----,.--

4

> ~

---r---.,.---r-------,.---.,...-"T""I,

,! , ,

- (10,10) ._. (15,15)

j ! !

,

2

i

~

!

0>

CD

c

w

,.

0

i

I

._._._._._._.,.,. -2

-4

0

0.1 0.2 0.3 0.4 Distance from tube center/tube radius

Figure 9.3 Potential energy of a C 60 molecule as a function of relative distance from the axis of two different nanotubes. (Adapted from Re£ [23].)

Here, (I is the diameter of the gas-gas interaction and (Ie is that ofC, typically taken to have a value (Ie = 0.34 nm for C atoms of graphene-like surfaces, a value based on the interlayer separation of graphite planes [25]. For the case of C 60 , this analysis predicts a crossover value ~rans = 0.8 nm. The potentials of Fig. 9.3, calculated by Hodak and Girifalco, are consistent with this finding. For a (10,10) tube, R = 0.68 nm; hence, the C 60 molecule is localized near the axis; its motion at room temperature is limited to a domain of relative extent rlR < 0.01. The behavior of an ensemble of many C 60 molecules is then well described by a lD model, which has been employed by several authors [26-30]. In the case ofa (15,15) tube, instead, R = 1.02nm > ~rans' so that the potential minimum lies away from the axis. As seen in the figure, the molecule's radial motion extends over a relative range dr/ R "'-'0.01 near r = 0.37 nm. Such a system of C 60 molecules at low coverage and temperature might be well described by a 2D model, where the azimuthal motion provides the second dimension (in addition to the motion parallel to the z axis of the tube). Both continuum and lattice gas descriptions of this problem have been evaluated [29-36]. Figure 9.4 depicts the kind of interesting behavior that has been seen in simulation studies by Hodak and Girifalco [23]. At low T, the system consists of two parallel strands of C 60 molecules in nearly perfect registry. These strands disorder as T increases, but the fluctuations appear to be small at 50 K. Above 100 K, instead, the system resembles a poorly defined lD chain of molecules. It is interesting that such a low temperature has a dramatic effect on a system for which the characteristic energy scales (gas-gas and gas-surface) are of order several tenths of an electron volt, which corresponds to T "'-' 1000 K. We attribute this unstable behavior to the one-dimensionality of the peapod system, which precludes truly long-range order at any finite T. The issue of radial localization and "effective dimensionality" is somewhat different in the quantum case [16, 24, 37], as exemplified in Fig. 9.5, for the

19 2

Chapter 9 Adsorbed Gases in Bundles of Carbon Nanotubes: Theory and Simulation

Figure 9.4 Monte Carlo snapshot configurations of molecules inside a (15,15) nanotube at various temperatures and fIXed density. (Adapted from Ref. [23].)

case (J" /(2R) = 0.26. Note that the ground-state wave function of a He atom is relatively delocalized, extending over a region ~r / R rv 0.2 because of zeropoint motion. In the quantum description, single-particle wave functions are of the form

\fJmk(r)

= R(r) exp[i(m

Here R(r) is the ground-state radial wave function,

cP is the azimuthal angle,

m is the azimuthal quantum number, and k is the wave vector parallel to the z axis of the tube. The figure also shows wave functions of a "helical" excited

state (with m = 1) and a radial excited state. The latter states are of such high energy that they are often ignored. An interesting consequence of this spectrum is the specific heat, C N (1), shown in Fig. 9.6. In the classical case of low density depicted there, C N / N equals Boltzmann's constant kB times the (D/2), where D is the dimensionality. In the present case, the behavior of the system is observed to be effectively lD at low T and 2D at higher T. The crossover temperature (rv l K) is determined by the azimuthal (centrifugal) excitation energy; this varies as < r > -2, where < r > is the mean value of the radial coordinate [24].

193

9.2 Endohedral Adsorption 20 __---...---..,..--........--,,---....--.r-"":"'"---w

~

1

~,I

r:I)

."

I

Q:I

10

++~\ ! ++++

"

+

-10

----

+ ~++

I----~~-----L . -.....

.................

I

_-_ .. _-_ .. _..,I

I

I

-------- '--20 & . . . - - - - ' - -.......- -........- -.......- -.......0.4 0.2 0.0

.........

0.6

rlR

Figure 9.5 Potential energy (dashed curve) and simplified model potential (full curve) for a 3He atom in a tube of radius 0.5 nm. The energies of the ground state and lowest azimuthally and radially excited states are shown as horizontal lines along with the corresponding wave functions (squares, circles and crosses, respectively). (Adapted from Ref. [37].)

1.5

....----~---~---~-------,

---------;r---------20

0.5

-------;r--------------------10

0.0 1...-..----'--------'--------'--------' 0.0 1.0 2.0

T(K)

Figure 9.6 Heat capacity per atom, in units of Boltzmann's constant, as a function of T for a noninteracting gas of 4He atoms within a tube with R = 0.5 nm The low T limiting behavior is that of a lD gas, while the high T limit is that of a 2D gas. (Adapted from Re£ [24].)

One can study tubes of larger radius than those mentioned above. In such cases, adsorption occurs in a set of cylindrical shells. This kind of behavior has been explored as a general model of adsorption in porous media, using a wide variety of techniques [38-44]. For lack of space, we ignore such large-pore behavior in the remainder of this chapter.

194

9.2.2

Chapter 9 Adsorbed Gases in Bundles of Carbon Nanotubes: Theory and Simulation

Axial-Phase Transition

If the pore radius lies in an appropriate range, relative to (T, there can occur a so-called axial-phase transition. The term refers to capillary condensation in the case when a "shell" phase, bound to the wall, is gradually augmented by the appearance of a 1D "axial phase," localized near r = O. This transition is exemplified by the simulation results for H 2 in Fig. 9.7. One observes that at low chemical potential p., the film is localized at r = 0.39 nm, at close approach to the C cylindrical surface. As p., is increased above a threshold value, the axial phase appears rather abruptly. This behavior is demonstrated further in Fig. 9.8, which separates the total coverage into axial and shell contributions. At saturation, their ratio is about 6.9. Since this transition is essentially a configurational phenomenon, similar behavior is expected for the case of a classical gas. Figure 9.9 shows an adsorption isotherm in such a case, computed with a lattice gas model in which seven "shell" sites near the tube wall surround each axial site. The figure compares results from mean field (MF) theory and Monte Carlo calculations [31, 32]. The axial "transition" is spread over a range of p., in both calculations since the temperature is above that of the MFaxial-phase condensation. Although the MF results are qualitatively correct, they exhibit a spurious shell-filling transition at low T, seen in the figure as a coverage discontinuity near the reduced chemical potential p., * = 2.2. Similar spurious transitions arise in virtually all density functional studies of this problem, as these employ an MF approximation of the effective potential experienced by the particles; the effect of omitted fluctuations is particularly acute in 1D systems [42-44].

12

-

p,=-419 K p,=-354 K ---- p,=-322 K -_...............

:§' 10 'c

M

::J

.ci

~ ~

:.0 (lj

.0

e0.

~

"00

8

III

'~'I'

1"11\

.,1 \'_ 6

4

c

Q)

-.:~

~

i~t\\ ~"i '

0

'\,. \

2

0

)\

\\\

~" \ ~

c'\'o...._ 0

2

3

4

Radius (A)

Figure 9.7 Dependence on chemical potential JL of H 2 film density in a pore with R= O.7nm at 10K. (Adapted from Re£ [34].)

195

9.2 Endohedral Adsorption

0.04 0.3

0.03

~
0.2

~

0.02 0.1 0.01 o~+-'-~~~,..."..'------'------'~---'------'~--&---'o -500 -450 -400 -350 -300 -250 fL (K)

Figure 9.8 Adsorption isotherms for the case shown in Fig. 2.6; left ordinate (upper curve) depicts the shell areal density (J, while right ordinate (lower curve) shows the linear density NIL of the axial phase. (Adapted from Ref. [34].) 8

.-

.... .. "

I

~.

6

.:

I'-

,.

."

;::;,:: .........

-

;,'

~-

I: ." I

,

I

I I

2

~

I

,,'

.. ..•.•

r::~'

,.;

• .(//1'

"

•••

.' .

..: o'

I"

:

.-. -••••

T=O.5,MC T=1, Me T=O.5, MF T=1, MF

O'--_ _......!!!!!:==..:l-_ _--i.._ _-..l._ _ -23 -22 -21

_

---l~

__J

-20

Figure 9.9 Adsorption isotherms for a lattice gas model consisting of shell and axial sites at the indicated temperatures (reduced by the pair interaction well depth) and various values of the reduced chemical potential. While mean field (MF) results exhibit a discontinuous shell-filling transition at T == 1, essentially exact Monte Carlo (MC) results show a near discontinuity there. (Adapted from Re£ [31, 32])

Figure 9.10 shows the specific heat at half-filling for this lattice model [31, 32]. The low T peak is due to a quasitransition of the shell phase, whereas the high T peak is due to promotion of atoms from the shell to the axial phase; the latter is analogous to heat capacity peaks on planar surfaces due to layer promotion [45, 46]. Qualitatively similar behavior was seen in a simulation of CO 2 in a (10,10) tube

19 6

Chapter 9 Adsorbed Gases in Bundles of Carbon Nanotubes: Theory and Simulation

0.5

]l ~

~

0.25

4

6

T*

Figure 9.10 Specific heat (left scale) at half-fuling for the lattice gas model shown in Fig. 9.9. Right scale denotes the contribution to eNdue to promotion of atoms from shell to axial sites. (Adapted from Refs [31, 32].)

by Matranga et al. [14] (see Fig. 11 of that article), which shows a similar energy increase attributed to gas evaporation from the shell phase.

9.2.3 Other Endohedral Transitions In a bundle, lD lines of molecules confined within one tube can interact with neighboring lines within parallel tubes. As a result, the system can undergo 3D transitions even though the molecular motion is essentially lD. Two kinds of transition have been explored for this highly anisotropic problem. One is condensation of the vapor phase into a liquid [30, 47-50] and the other is crystallization of that liquid [51, 52]. Because these parallel lines of atoms experience weak interchannel interactions (compared with the intrachannel interactions), the transitions occur at very low temperature. Figure 9.11 exemplifies this phenomenon for the case of C 60 molecules, for which the intermolecular potential has a well depth of order 3000 K. When confined inside a bundle, the transition is manifested as van der Waals loops appearing below 500 K. When the anisotropy is so large, the analysis is simplified, so that an analytic limiting expression can be derived. One asymptotic result of Fisher [53] has proved to be particularly useful for understanding the results of numerical calculations [30, 47-51]. The Fisher expression yields the critical temperature of an anisotropic lattice gas model, as follows:

KBY c

=

2J1 {In(l/c) -In[ln(l/c)]}

Here Jl is the longitudinal interaction and c = Jt/Jl is the ratio of the transverse to longitudinal interactions, where c < < 1. The lD limit Tc = 0 is approached only gradually (logarithmically) as c goes to zero. Equivalently, the strictly lD

9.2 Endohedral Adsorption

197

30 ...----------.,.....-------r-----"T--r-I1'"1

1300K 1000K 20

10

<' ..........

~ Q..

0

-10

-20 0

0.02

0.04

0.06

0.08

0.1

1/a (A-1)

Figure 9.11 1D line pressure as a function of linear density 1/a for C 60 molecules, taking into account interactions between molecules in different tubes. Note the van der Waals loop below 570 K, signaling a phase transition. (Adapted from Ref. [30].)

system is very sensitive to weak interchannel interactions, a consequence of the divergent correlation length of the 1D system at low T. Figure 9.12 depicts the results of Carraro [51, 52] for showing a crystallization transition of similarly coupled 1D chains of molecules. As T increases, at fixed 4.0 3.5 3.0

0

o

2.5

o 2.0 1.5 1.0 0.5 0.0 0.00

0.05

0.10

0.15

0.20

0.25

T

Figure 9.12 Density and inverse particle displacement function, in reduced units, as described in text, as a function of reduced temperature showing crystallization of a system of coupled parallel chains of molecules. (Adapted from Refs [51, 52])

198

Chapter 9 Adsorbed Gases in Bundles of Carbon Nanotubes: Theory and Simulation

pressure, melting occurs at reduced temperature 0.15; this is manifested as a divergence of < u 2 >, the mean-square fluctuations of the particles about their equilibrium sites. Note that the transition is of higher than first order, because the density is continuous across the transition. The latter property also occurs in the 2D Kosterlitz-Thouless transition [54].

9-3

ADSORPTION IN INTERSTITIAL CHANNELS

When nanotubes gather spontaneously into bundles, they tend to pack into a hexagonal lattice leaving narrow ICs between the tubes where small atoms and molecules can be adsorbed. For example, in a typical (10,10) tube bundle, the distance between the center of the tubes is around 1.7 nm and the radius of the ICs is approximately 0.3 nm. The possible realization of lD matter when gas is adsorbed in these channels motivated the study of lD and quasi-1D phases of several gases. For classical gases, the lD equation of state is particularly convenient because there exists an analytical solution for the classical 1D equation of state for an arbitrary pair potential [17, 18]. There is one caveat: interactions beyond the nearest neighbor are neglected in that solution of the problem. These interactions, however, are weak and can be easily evaluated with perturbation theory, if necessary [55]. For quantum fluids, i.e., He and H 2 , lD studies require numerical methods. The ground-state and zero-temperature equation of state of such gases are of particular interest as these small adsorbates are the most likely to be adsorbed in the ICs [56]. In the case of 4He, the lD ground state (minimum of the energy per atom, BIN) is an extremely weakly bound liquid [57-59] (Fig. 9.13); the cohesive energy is less than 3 mK; this value may be the lowest value for any many-body physical system ever studied. This situation is a consequence of the large zero-point energy. The liquid has a very low equilibrium density, corresponding to a mean interatomic spacing of about 2.5 nm. These results [59], obtained with the "exact" diffusion Monte Carlo (DMC) method, employ an empirical potential derived from 3D experiments [60]; if the conventional LJ He-He interaction were used instead, the system would not be bound at all (as is the case, incidentally, for lD 3He). In reality, we do not know what interaction potential is appropriate for fluids adsorbed in the bundle environment. One study [61] has shown that the neighboring C atoms provide some reduction in the long-range attraction, in which case the real ground state may well be a lD gas, rather than a low-density liquid. We note in passing that 2D liquid 4He has a binding energy of order 0.9 K, a factor "J3 000 greater than the lD result and eight times smaller than the 3D result [62]. A similar behavior was predicted for linear phases ofH 2 and D 2 • A system ofH2 molecules in a strictly lD array and inside a narrow tube (radius "J0.34 nm) was studied using the DMC method [63]. The lD calculation shows the existence of a self-bound state at T = 0 with a binding energy of 4.8 K. Very similar results

199

9.3 Adsorption in Interstitial Channels

102

,.0'

x

.0'

15

g

10

1

0'

,tf

10°

Lv

.".0' JIt.'

10-1 10

q

S

~ ••Q

10-2

x

0.1

tu

0.2

0.3

p(A-1)

5

0.4 x

o

Ref. [11] x This work 0

0.00

0.02

0.04

0.06

0.08

0.10

p(A-1)

Figure 9.13 Energy per 4He atom as a function of lD density from the diffusion Monte Carlo (DMC) calculation (circles and full curve) of Boninsegni and Moroni [58]. Crosses are hypemetted chain results of Krotscheck and Miller [57]. Analogous DMC results were obtained by Gordillo, Boronat, Casulleras [59].

are obtained in the quasi-1D case of H 2 inside the tube where small transverse displacements (perpendicular to the tube axis) are allowed. Studies of the lD quantum gases at high density reveal the gradual development of strong interparticle correlations, manifested in the radial distribution function, corresponding to a nearly periodic structure [59, 63]. In that case, a quasicontinuous T = 0 liquid to solid transition was predicted. If the corrugation of the external potential is taken into account, a transition from a commensurate to an incommensurate state can also occur as the density increases [64]. An analysis following the ideas of Carraro [51, 52] would yield a genuine crystal if coupling between particles in neighboring grooves were included. Such a model calculation has not yet been undertaken however. As discussed in Section 9.2.3, despite the apparent 1D nature of matter filling the channels, atoms in adjacent ICs of a bundle can interact with each other. In that case, a fully 3D condensation transition with a nonzero critical temperature can happen where the final condensed state is an anisotropic liquid [47-49]. This state is much more stable than the 1D liquid; for example, the binding energy of a He system [47, 48] increases from 2 to 16 mK. Although the interchannel interaction is very weak compared with the gas-gas interaction inside the channels, its presence is enough to drive the transition. On the

200

Chapter 9 Adsorbed Gases in Bundles of Carbon Nanotubes: Theory and Simulation

other hand, the critical temperature is mainly determined by the intrachannel interaction and weakly dependent on the strength ofthe interchannel interaction. Another peculiar aspect of the adsorption in the ICs is the possibility that the adsorbed gas expands the lattice and/or deforms the tubes. Such changes in the structure of the bundle would happen provided the adsorption energy gain in the new environment overcomes the energy cost for deforming the lattice. In that respect, a theoretical study recently showed that hydrogen adsorption in the ICs may increase the separation between the tubes in a bundle, making the channels much more favorable for adsorption [65]. Figure 9.14 shows the dramatic effect of a small dilation (1 %) in the potential and ground-state energy of a single hydrogen molecule within an IC. In that work, it is assumed that the tubes (all with the same diameter) form a perfect hexagonal lattice, and a uniform linear density of hydrogen is filling infinitely long and straight ICs. The total energy of the system, which includes the gas-gas, gas-tubes, and tube-tube interactions, is minimized to find the ground state (Fig. 9.15). It is found that the hydrogen can greatly increase its binding energy (from 280 K to 480 K) by slightly widening the ICs so that the gas condensation in the ICs at T = 0 involves an expansion of the bundle. This many-body effect can also be thought as a consequence of an "effective interaction" between the molecules that results from the gas-gas interaction mediated by the dilation of the lattice.

8~-----------------'

dilated 4

o~--------_-=...::r=--=-t---.,......

-400 /'

---- ----- --~- ----------~

-800

-1200

o

,..,/

0.2

0.4

r(A)

Figure 9.14 Probability density (top panel) and potential energy of H 2 (bottom panel) as a function of perpendicular distance from the center of the interstial channels (Ie). Dotted lines indicate the ground state energies. (Adapted from Ref. [65].)

9.3 Adsorption in Interstitial Channels

201

•••••••••••••••••••••• . . . . . ... ... -",NT-NT

o

._--*-~-~

g <: iJJ

-300

-600

Figure 9.15 Energy contributions to the total energy per particle (full curve) as functions of the linear density of H 2 . The ground state happens at Pc = 0.277 A-1. (Adapted from Ref. [65].)

The large increase in binding energy suggests the presence of a strong "effective interaction" that would lead to a high critical temperature for this transition. In the case of Hz, the critical temperature was estimated to be around 400 K. A less dramatic effect is found for smaller atoms such as He or Ne as in these cases the size of the ICs is near the optimal one. On the other hand, it is predicted that larger particles like Ar or CH 4 would be adsorbed in the ICs only if this dilation occurs. More recently, the results of this model have been tested using DMC techniques yielding a rather good agreement [66]. At this point, it is important to briefly review the experimental results concerning interstitial adsorption. This topic has been one of the most controversial issues in the study of gas adsorption in carbon nanotubes probably because the accessibility of the ICs may be different in different samples. For He, the ICs provide the most attractive sites of the bundle and there is at least some evidence that the atoms enter the channels [67-70]. The most recent one is based on a very high value of the isosteric heat obtained at very low coverage that can only be explained with the interstitial adsorption [71]. The case of Hz is somewhat different since the binding energy in the grooves is greater than in the ICs (at least 100 K larger considering a lattice dilation). Here, a determination of the isosteric heat of adsorption of Hz and D z at low coverage shows a considerable isotopic effect, a difference of about 200 K that has to be originated by a high confinement of the gas like the one that happens in the ICs [72]. Another piece of evidence comes from adsorption isotherms of Hz measured at 90 K. In that case, a kink and an abrupt slope in the isotherm at nearly 40 atm seems to show a transition to higher coverage states. The authors attribute this behavior to Hz permeating between the tubes that separate to allow

Chapter 9 Adsorbed Gases in Bundles of Carbon Nanotubes: Theory and Simulation

202

the interstitial adsorption [73]. Although somewhat indirect, this work would confirm the presence of the dilation-induced adsorption explained above. In addition, shifts in the Raman spectra of H 2 adsorbed in the bundles seem to indicate the population of the ICs [74]. With respect to some other gases, recent neutron scattering measurements have shown no lattice dilation when Ar or CH 4 is adsorbed in the bundle [75, 76]. However, to explain the adsorption isotherms, the authors still claim that there could be some interstitial adsorption if one considers that the adsorption happens in heterogeneous bundles (where the tubes have different diameters) of flexible tubes. In this case, the tubes would deform to accommodate these larger adsorbates [76]. In fact, a similar conclusion has been drawn from a recent computer simulation study of CH 4 adsorption on heterogeneous bundles, without considering the flexibility of the tubes [11]. On the other hand, another experimental study of gas adsorption concluded that Ne, CH 4 , and Xe were not adsorbed in the ICs [77] . We note that the T = 0 K theory predicts IC adsorption of heavy gases only at very high jL, far above the threshold for groove adsorption on the external surface. For smaller gases such adsorption seems a logical concomitant of current potential models. Different kinds of novel phenomena have been predicted when gases are adsorbed in the ICs. Among them is the possibility of using these channels as quantum sieves for separating isotopic mixtures [78]. This effect, discussed in Chapter 15, is based on the difference in binding energies of the isotopes that results from the difference in their zero-point kinetic energy that arises in confined environments. Another intriguing prediction involves the possibility of observing an unusual Bose-Einstein condensation of H 2 adsorbed in the ICs. In this case, a 4D behavior is expected for this system if tubes of different sizes are considered within a bundle [79].

9.4

EXTERNAL SURFACE

The external surface of a nanotube bundle is accessible to any adsorbate and for many gases that is the only region that needs to be considered. Such is the case of closed tubes and either blocked ICs or medium- to large-size molecules that do not fit in the ICs. Molecules in the groove region, between two tubes, experience an attraction provided by two neighboring tubes. In that case, the heat of adsorption is nearly twice the value on graphite [56, 80-86]; the ratio is somewhat less than 2 because the tubes are convexly curved, reducing the effective coordination number of an adatom (relative to the planar surface value), and because graphite includes many underlying layers that increase the binding energy on a planar surface. Further adsorption occurs on the remainder of the external surface, which is somewhat less attractive than the surface of graphite for the same two reasons.

9.4 External Surface

Q)

... ()

203

10

100

·c

C> .........

:J

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E E

Q; c.. 1\

<: v

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50

O~_..I.--_....L-_---I.&.,;.----L.-."-E;"",.L...---'-_----.L_---J

-32

-28

-24

-20

-16

-12

-8

-4

Log (P[atm])

Figure 9.16 Ne isotherms at temperatures shown, depicting step-like growth and hysteresis at monolayer completion (N 70). Coverage scale is defined in the text. (Adapted from Ref. [81].) r-.J

The groove is a region of particular importance for fundamental reasons. Several studies of strictly lD matter (see Section 9.3) have been undertaken in order to describe this regime ofadsorption. On the other hand, simulation studies have been undertaken to describe classical adsorption on the external surface [11, 83-85]. The results tend to have common features, differing only in detail as a consequence of variable adsorption potentials. Experimental measurements have confirmed these findings for several gases [86]. As an example, Ne adsorption isotherms and density are shown in Figs 9.16 and 9.17. In these data, the ordinate N refers to the number of atoms per groove within one simulation cell, of length 3 nm. Then, about N = 9 atoms corresponds to close-packing for lD Ne. The isotherms show the gradual formation of the lD film within the groove, for N < 9. This regime of low J..L is followed by a coverage jump to a so-called three-stripe phase, with N = 27. The meaning of this name is evident from the density plot, i.e., the system consists of three parallel lines of Ne atoms, symmetrically arranged above the groove. The next jump in the isotherm, which shows hysteresis, is to the complete monolayer phase. The hysteresis arises from the existence of two distinct phases, seven-stripe and eight-stripe, which have nearly equal free energies; these are seen in the density plot. Above the monolayer regime there occurs a step, of height fiN = 9, in the isotherm that is clearly seen in the density profile as a "second-layer groove phase." Even this feature was seen in the experimental isotherm data of Migone's group [82, 87]. These simulation results were obtained using a simplification of the geometry: the surface was assumed to be an infinite, periodic array of parallel tubes lying on a flat surface. If a more realistic description of a nanotube bundle were used, the abrupt transitions appearing above would all become rounded. This can be seen in Fig. 9.18 for the case of CH 4 .

204

Chapter 9 Adsorbed Gases in Bundles of Carbon Nanotubes: Theory and Simulation

15

15

12

12 o~

y[A]

9

•

6

y[A]

fj\

•

9

~

8/ ~

~

~

•

6

3

3 3

6

9

12

15

3

6

9

12

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x [A]

x [A]

15 12 P y[A]

@

9

0

~

•

12

15

~

fil

6

e>

Ii'I

3 3

6

9

x [A] Figure 9.17 Density ofNe at T= 12K and log P (atm) = -19, -16, and -9, from top to bottom. The middle curve superimposes results for nearly degenerate seven-stripe and eight-stripe phases of the monolayer. (Adapted from Re£ [84].)

These classical simulation results are not quantitatively reliable below the Debye temperature due to the onset of quantum effects. The extreme example is He, described earlier, which does not condense above T = O. The other noble gases and CH 4 are of considerable experimental interest; these exhibit quantum effects below about 100 K in 3D. A number of phonon analyses have been undertaken for these gases, beginning with work of Siber [88]. Figure 9.19 shows typical data for the case of the three-stripe phase of CH 4 . As this phase includes three atoms per unit cell, the spectrum includes nine branches. At low T, the mode denoted Ll is the only one excited. It is seen to correspond closely to the lD phonon mode (at the same density) at long wavelengths but exhibits an avoided crossing with another longitudinal mode (L2) near phonon wavelength equal to 10 times the lattice constant, i.e., about 4nm. Thus, the thermal behavior is essentially that of a lD system (C proportional to T) only below about 15 K [89]. The approach to fully 3D behavior (i.e., C N ~ 3/2NkB ) appears for all gases studied to date somewhat above 50 K and that classical limit

20 5

9.4 External Surface

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, &

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18

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0.01

0.02

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0.04

CH 4/C (mol/mol)

Figure 9.18 Isosteric heat of adsorption for CH4 from experiments (circles) and simulations. The diamonds (squares) are for adsorption onto heterogeneous (homogeneous) bundles. (Adapted from Ref. [11].) 20

153

18

137

16

122

14

107

12

92

a,....

10

76

3

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61

6

46

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I"

Cf)

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-

0.2

0.4

0.6

0.8

1.0

g .c

IJ.JQ.

0

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Figure 9.19 Phonon dispersion relation (angular frequency vs. relative wave vector) for the three-stripe phase ofCH4 on the external surface of a bundle. L1, L2, and L3 are longitudinal branches, Le., molecular motion parallel to the groove. The dotted curve is the result for a 1D adsorbate at the same density. The remaining curves correspond to the dispersion relation of transverse modes. (Adapted from Ref. [89].)

206

Chapter 9 Adsorbed Gases in Bundles of Carbon Nanotubes: Theory and Simulation

is achieved above 100 K. The predictions of these phonon theories are amenable to testing with both low T specific heat and inelastic or quasielastic neutron scattering measurements.

ACKNOWLEDGMENTS This research has been informed and stimulated by discussion with many colleagues including F. Ancilotto, M. Bienfait, M. Bonigseni, C. Carraro, V. Crespi, S. Curtarolo, P. Eklund, L. Girafalco, K. Gubbins, R. Hallock, S. Hernandez, M. Hodak, M. Kostov, A. Migone, G. Stan, W.A. Steele, F. Toigo, A. Trasca, O. Vilches, and]. Yates. We are grateful to the National Science Foundation for its support.

REFERENCES 1. Iijima, S. (1991). Helical microtubules of graphitic carbon. Nature, 354,56-8. 2. Sinnott, S.B. and Andrews, R. (2001). Carbon nanotubes: synthesis, properties, and applications. Crit. Rev. Solid State Mater. Sci., 26, 145-249. 3. Dillon, A.C. and Heben, MJ. (2001). Hydrogen storage using carbon adsorbents: past, present and future. Appl. Phys. A Mater., 72, 133-42. 4. Dresselhaus, M.S., Williams, K.A., and Eklund, P.C. (1999). Hydrogen adsorption in carbon materials. P. C. MRS Bull., 24, 45-50. 5. Simonyan, V.V., Diep, P., and Johnson, J.K. (1999). Molecular simulation of hydrogen adsorption in charged single-walled carbon nanotubes. J. Chern. Phys., 111, 9778-83. 6. Wang, Q.Y. andJohnson,J.K. (1999). Optimization of carbon nanotube arrays for hydrogen adsorption. J. Phys. Chern. B, 103, 4809-13. 7. Wood, J .R. and Wagner, H.D. (2000). Single-wall carbon nanotubes as molecular pressure sensors. Appl. Phys. Lett., 76, 2883-5. 8. Wang, Q.Y., Challa, S.R., Sholl, D.S., andJohnson,J.K. (1999). Quantum sieving in carbon nanotubes and zeolites. Phys. Rev. Lett., 82, 956-9. 9. Mao, Z.G. and Sinnott, S.B. (2001). Separation of organic molecular mixtures in carbon nanotubes and bundles: molecular dynamics simulations. J. Phys. Chern. B, 105, 6916-24. 10. Migone, A.D. and Talapatra, S. (2003). Encyclopedia of Nanoscience and Nanotechnology. American Scientific Publishers. 11. Shi, W and Johnson, J.K. (2003). Gas adsorption on heterogeneous single-walled carbon nanotube bundles. Phys. Rev. Lett., 91, 015504 1-7. 12. Kuznetsova, A., Yates, J.T., Jr, Liu, J., and Smalley, R.E. (2000). Physical adsorption of xenon in open single walled carbon nanotubes: observation of a quasi-onedimensional confined Xe phase. J. Chern. Phys., 112, 9590-8.

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13. Kuznetsova, A., Mawhinney, D.B., Naumenko, V., et al. (2000). Enhancement of adsorption inside of single-walled nanotubes: opening the entry ports. Chern. Phys. Lett., 321, 292-6. 14. Matranga, C., Chen, L., Smith, M., et al. (2003). Trapped CO 2 in carbon nanotube bundles.]. Phys. Chern. B, 107, 12930-41. 15. Pradhan, B.K., Harutyunyan, A., Cole, M.W., et al. (2002). Large cryogenic storage of hydrogen in carbon nanotubes at low pressures.]. Mater. Res., 17,2209-22. 16. Stan, G. and Cole, M.W. (1998). Hydrogen adsorption in nanotubes.]. Low Temp. Phys., 110, 539-44. 17. Takahashi, H. (1966). Mathematical Physics in One Dimension (E.H. Lieb and D.C. Mattis eds). Academic Press, pp. 25-7. 18. Takahashi, M. (1999). Thermodynamics of lD Solvable Models. Cambridge University Press. 19. A review of these phases is in Calbi, M.M., Gatica S.M., Bojan, MJ., et al. (2001). Condensed phases of gases inside nanotube bundles. Rev. Mod. Phys., 73, 857-65. 20. Ancilotto, F., Calbi, M.M., Gatica, S.M., and Cole, M.W. (2004). Bose-Einstein condensation of helium and hydrogen inside bundles of carbon nanotubes. Phys. Rev. B, 70, 165422 1-11. 21. Smith, B.W., Monthioux, M., and Luzzi, D.E. (1998). Encapsulated C 60 in carbon nanotubes. Nature, 396, 323-4. 22. Simonyan, V.V., Johnson, J.K., Kuznetsova, A., and Yates, J.T. Jr. (2001). Molecular simulation of xenon adsorption on single-walled carbon nanotubes.]. Chern. Phys., 114,4180-5. 23. Hodak, M. and Girifalco, L.A. (2003). Systems of C-60 molecules inside (10, 10) and (15, 15) nanotube: a Monte Carlo study. Phys. Rev. B, 68, 085405. 24. Stan, G. and Cole, M.W. (1998). Low coverage adsorption in cylindrical pores. Surf. Sci., 395, 280-91. 25. Steele, W.A. (1973). The physical interaction of gases with crystalline solids. I. Gas-solid energies and properties of isolated adsorbed atoms. Surf. Sci., 36, 317. 26. Hodak, M. and Girifalco, L.A. (2001). Quasi-one-dimensional system of molecules inside carbon nanotubes: exact solution for the lattice gas model and its application to fullerene-filled nanotubes. Phys. Rev. B, 64, 035407 1-9. 27. Hodak, M. and Girifalco, L.A. (2001). Fullerenes inside carbon nanotubes and multi-walled carbon nanotubes: optimum and maximum sizes. Chern. Phys. Lett., 350, 405-41. 28. Hodak, M. and Girifalco, L.A. (2002). Cohesive properties of fullerene-filled nanotube ropes. Chern. Phys. Lett., 363, 93-8. 29. Girifalco, L.A. and Hodak, M. (2003). One-dimensional statistical mechanics models with applications to peapods. Appl. Phys. A, 76, 487-98. 30. Calbi, M.M., Gatica, S.M., and Cole, M.W. (2003). Statistical mechanics of interacting peapods. Phys. Rev. B, 67, 205417 1-6. 31. Trasca, R.A., Calbi M.M., and Cole, M.W. (2002). Lattice model of gas condensation within nanopores. Phys. Rev. E, 65, 061607 1-9. 32. Trasca, R.A., Calbi, M.M., Cole, M.W., and Riccardo, J.L. (2004). Lattice-gas Monte Carlo study of adsorption in pores. Phys. Rev. E, 69, 011605 1-6. 33. Simonyan, V.V., Diep, P., and Johnson, J.K. (1999). Molecular simulation of hydrogen adsorption in charged single-walled carbon nanotubes.]. Chern. Phys., 111.9778-83.

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Chapter 9 Adsorbed Gases in Bundles of Carbon Nanotubes: Theory and Simulation

34. Gatica, S.M., Stan, G., Calbi, M.M., et al. (2000). Axial phase of quantum fluids in nanotubes. J. Low Temp. Phys., 120, 337-59. 35. Ohba, T., Murata, K., Kaneko, K., et al. (2001). N-2 adsorption in an internal nanopore space of single-walled carbon nanohorn: GCMC simulation and experiment. Nano. Lett., 1, 371-3. 36. Tanaka, H., El-Merraoui, M., Steele, W.A., and Kaneko, K. (2002). Methane adsorption on single-walled carbon nanotube: a density functional theory model. Chem. Phys. Lett., 352, 3-41. 37. Stan, G., Gatica, S.M., Boninsegni, M., et al. (1999). Atoms in nanotubes: small dimensions and variable dimensionality. Am. J. Phys., 67, 1170-7. 38. Steele, W.A. and Bojan, MJ. (1998). Simulation studies of sorption in model cylindrical micropores. Adv. Coli. Interface Sci., 77, 153-78. 39. Gatica, S.M., Hernandez, E.S., and Szybisz, L. (2003). Heat capacity of helium in cylindrical environments. Phys. Rev. B, 68, 144501. 40. Maddox, M.W. and Gubbins, K.E. (1995). Molecular simulation offluid adsorption in buckytubes. Langmuir, 11, 3988-96. 41. Maddox, M.W. and Gubbins, K.E. (1997). A molecular simulation study offreezing/melting phenomena for Lennard-Jones methane in cylindrical nanoscale pores. J. Chem. Phys., 107, 9659-67. 42. Gelb, L.D., Gubbins, K.E., Radhakrishnan, R., and Sliwinska-Bartkowiak, M. (1999). Phase separation in confined systems. Rep. Prog. Phys., 62, 1573-659. 43. Evans, R. (2001). Liquids and Interfaces (J. Charvolin,J.F.Joanny, andJ. Zinn-Justin, eds). Elsevier. 44. Ravikovitch, P.I., Vishnyakov, A., and Neimark, A.V. (2001). Density functional theories and molecular simulations ofadsorption and phase transitions in nanopores. Phys. Rev. E, 64, 011602. 45. Elgin, R.L. and Goodstein, D.L. (1974). Thermodynamic study of the 4He monolayer adsorbed on Grafoil. Phys. Rev. A, 9, 2657. 46. Dash, J.G., Schick, M., and Vilches, O.E. (1994). Phases of helium monolayerssearch and discovery. Surf Sci., 299, 405-14. 47. Cole, M.W., Crespi, V.H., Stan, G., et al. (2001). Anisotropic condensation of helium in nanotube bundles. Phys. Rev. Lett., 84, 3883. 48. Gatica, S.M., Calbi, M.M., and Cole, M.W. (2003). Universal anisotropic condensation transition of gases in nanotube bundles. J. Low Temp. Phys., 133, 399. 49. Radhakrishnan, R. and Gubbins, K.E. (1997). Quasi-one-dimensional phase tran\sitions in nanopores: pore-pore correlation effects. Phys. Rev. Lett., 79, 2847. 50. Brualla, L. and Gordillo, M.C. (2003). Liquid-gas transition of neon in quasi-onedimensional environments. Phys. Rev. B, 68, 075423. 51. Carraro, C. (2002). Existence and nature of a freezing transition inside threedimensional arrays of narrow channels. Phys. Rev. Lett., 89, 115702. 52. Carraro, C. (2000). Ordered phases of atoms adsorbed in nanotube arrays. Phys. Rev. B, 61, R16 351. 53. Fisher, M.E. (1967). Critial temperatures of anisotropic ising lattices. II. General upper bounds. Phys. Rev., 162, 480-5. 54. Kosterlitz, J.M. and Thouless, DJ. (1978). Progress in Low Temperature Physics, Vol. 7B. North-Holland, p. 371. 55. Bakaev, V.A. and Steele, W.A. (1997). Hard rods on a line as a model for adsorption of gas mixtures on homogeneous and heterogeneous surfaces. Langmuir, 13, 1054-63.

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56. Stan, G., Bojan, M.J., Curtarolo, S., et al. (2000). Uptake of gases in bundles of carbon nanotubes. Phys. Rev. B, 62, 2173-80. 57. Krotscheck, E., Miller, M.D., and Wojdylo, J. (1999). Properties of He 4 in one dimension. Phys. Rev. B, 60, 13028-50. 58. Boninsegni, M. and Moroni, S. (2000). Ground state of He 4 in one dimension. ]. Low Temp. Phys., 118, 1-6. 59. Gordillo, M.C., Boronat, J., and Casulleras, J. (2000). Quasi-one-dimensionaI 4 He inside carbon nanotubes. Phys. Rev. B, 61, R878-81. 60. Aziz, R.A., Nain, V.P.S., Carley, J.S., et al. (1979). An accurate intermolecular potential for helium.]. Chern. Phys., 70, 4330-7. 61. Kostov, M.K., Cole, M.W., Lewis, J.C., et al. (2000). Many-body interactions among adsorbed atoms and molecules within carbon nanotubes and in free space. Chern. Phys. Lett., 332, 26-34. 62. Whitlock, P.A., Chester, G.V., and Krishnamachari, B. (1998). Monte Carlo simulation of a helium film on graphite. Phys. Rev. B, 58, 8704-15. 63. Gordillo, M.C., Boronat, J., and Casulleras, J. (2000). Zero-temperature equation of state of quasi-one-dimensional H 2 . Phys. Rev. Lett., 85, 2348-51. 64. Boninsegni, M., Lee S., and Crespi V.H. (2001). Helium in one-dimensional nanopores: free dispersion, localization, and commensurate/incommensurate transitions with nonrigid orbitals. Phys. Rev. Lett., 86, 3360-3. 65. Calbi, M.M., Toigo, F., and Cole, M.W. (2001). Dilation-induced phases of gases adsorbed within a bundle of carbon nanotubes. Phys. Rev. Lett., 86, 5062-5. 66. Gordillo, M.C., Boronat,J., and CasullerasJ. (2003). H-2 in the interstitial channels ofnanotube bundles. Phys. Rev. B, 68,125421 1-6. 67. Teizer, W., Hallock, R., Dujardin, E., and Ebbesen, T. (1999). He-4 desorption from single wall carbon nanotube bundles: a one-dimensional adsorbate. Phys. Rev. Lett., 82, 5305-8; Phys. Rev. Lett., 2000, 84, 1844 (E). 68. Kahng, Y.H., Hallock, R.B., Dujardin, E., and Ebbesen, T.W. (2002). He-4 binding energies on single-wall carbon nanotube bundles.]. Low Temp. Phys., 126, 223-8. 69. Kahng, Y.H., Hallock, R.B., and Dujardin, E. (2003). Competitive adsorption of He-4 and H-2 on single-wall carbon nanotube bundles. Physica B, 329, 280-1. 70. Wilson, T. and Vilches, O.E. (2003). Adsorption of He 4 on carbon nanotube bundles. Physica B, 329, 278-9. 71. Wilson, T. and Vilches, O.E. (2003). Helium adsorbed on carbon nanotube bundles: one-dimensional and/or two-dimensional solids. Low Temp. Phys., 29, 732-5. 72. Wilson, T., Tyburski, A., DePies, M.R., et al. (2002). Adsorption ofH-2 and D-2 on carbon nanotube bundles.}. Low Temp. Phys., 126, 403-8. 73. Ye, Y., Ahn, C.C., Witham C., et al. (1999). Hydrogen adsorption and cohesive energy of single-walled carbon nanotubes. Appl. Phys. Lett., 74, 2307-9. 74. Williams, K.A., Pradhan, B.K., Eklund, P.C., et al. (2002). Raman spectroscopic investigation ofH-2, HD, and D-2 physisorption on ropes of single-walled, carbon nanotubes. Phys. Rev. Lett., 88, 165502. 75. Bienfait, M., Zeppenfeld, P., Dupont-Pavlovsky, N., et al. (2003). Adsorption of argon on carbon nanotube bundles and its influence on the bundle lattice parameter. Phys. Rev. Lett., 91, 035503. 76. Johnson, M.R., Rols, S., Wass, P., et al. (2003). Neutron diffraction and numerical modelling investigation of methane adsorption on bundles of carbon nanotubes. Chern. Phys., 293, 217-30.

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Chapter 9 Adsorbed Gases in Bundles of Carbon Nanotubes: Theory and Simulation

77. Talapatra, S., Zambano, A.Z., Weber, S.E., and Migone, A.D. (2000). Gases do not adsorb on the interstitial channels of closed-ended single-walled carbon nanotube bundles. Phys. Rev. Lett., 85, 138-41. 78. Wang, Q.Y., Challa, S.R., Sholl, D.S., andJohnson,J.K. (1999). Quantum sieving in carbon nanotubes and zeolites. Phys. Rev. Lett., 82, 956-9. 79. Ancilotto, F., Calbi, M.M., Cole, M.W., et al. (2004). Intriguing examples of inhomogeneous broadening. Isr.]. Chern., 43, 229-34. 80. Talapatra, S. and Migone, A.D. (2002). Adsorption of methane on bundles of closed-ended single-wall carbon nanotubes. Phys. Rev. B, 64 045416. 81. Zambano, A.J., Talapatra, S., and Migone, A.D. (2001). Binding energy and monolayer capacity of Xe adsorbed on single-wall carbon nanotubes. Phys. Rev. B, 64, 075415 1-6. 82. Talapatra, S., Rawat, D.S., and Migone, A.D. (2002). Possible existence of a higher coverage quasi-one-dimensional phase of argon adsorbed on bundles of single-walled carbon nanotubes.]. Nanosci. Nanotechnol., 2, 467-70. 83. Calbi, M.M. and Cole, M.W. (2002). Dimensional crossover and quantum effects of gases adsorbed on nanotube bundles. Phys. Rev. B, 66, 115413-1-12. 84. Calbi, M.M., Gatica, S.M., Bojan, M.J., and Cole, M.W. (2001). Phases of neon, xenon and methane adsorbed on nanotube bundles.]. Chern. Phys., 115,9975-81. 85. Gatica, S.M., Bojan, M.J., Stan, G., and Cole, M.W. (2001). Quasi-one and twodimensional transitions of gases adsorbed on nanotube bundles.]. Chern. Phys., 114,3765-9. 86. Talapatra, S. and Migone, A.D. (2001). Existence of novel quasi-one-dimensional phases ofatoms adsorbed on the exterior surface ofclose-ended single wall nanotube bundles. Phys. Rev. Lett., 87, 206106 1-4. 87. Talapatra, S., Krungleviciute, V., and Migone, A.D. (2002). Higher coverage gas adsorption on the surface of carbon nanotubes: Evidence for a possible new phase in the second layer. Phys. Rev. Lett., 89, 246106 1-4. 88. Siber, A. (2002). Phonons and specific heat of linear dense phases of atoms physisorbed in the grooves of carbon nanotube bundles. Phys. Rev. B, 66, 235414. 89. Kostov, M.K., Calbi, M.M., and Cole, M.W. (2003). Phonons and specific heat of neon and methane on the surface of a nanotube bundle. Phys. Rev. B, 68, 245403.

ENERGETIC TOPOGRAPHY EFFECTS Antonio J. Ramirez-Pastor,l Jose L. Riccardo,l and Giorgio Zgrablich 1,2 1 Laboratorio de Ciencias de Superficies y Medios Porosos, Universidad Nacional de San Luis, CON/CET, San Luis, Argentina; 2 Departamento de Qufmica, Universidad Aut6noma Metropolitana/ztapalapa, Mexico

Contents Introduction The Adsorptive Energy Surface 10.3 Generalized Gaussian Model 10.4 Simulations on Ideal Heterogeneous Systems 10.5 Comparison Test for the GGM 10.6 Bivariate Model and Simulation Method 10.7 Adsorption Results 10.8 Scaling Behavior and Temperature Dependence 10.9 Conclusions Acknowledgments References 10.1

211

10.2

21 4 216 221 223 225 227 230 233 234 234

10.1 INTRODUCTION

The role of the adsorptive surface characteristics in many processes ofpractical importance is a topic of increasing interest in surface science. Adsorption, surface diffusion, and reactions on catalysts are some of the phenomena that are strongly dependent upon surface structure. Most materials have heterogeneous surfaces that, when interacting with gas molecules, present a complex spatial dependence of the adsorptive energy. This is specially the case for activated carbons, where many defects and impurity atoms and molecules are incorporated Adsorption by Carbons ISBN: 978-0-08-044464-2

© 2008 Elsevier Ltd. All rights reserved.

211

212

Chapter 10 Energetic Topography Effects

in the graphitic pore walls. It is of substantial interest to attempt a complete characterization of such heterogeneity. Through the last 50 years physical adsorption has been used for determining energetic properties of heterogeneous substrates, but this still remains an open problem in many aspects [1-4]. For a very long time in the history of the studies of heterogeneous adsorbents, the adsorptive energy distribution (AED) was considered as the only important characteristic to be known in order to describe the behavior ofadsorbed particles, and much effort was dedicated to its determination by inverting the integral equation [5]:

OCT, j.t) = f OCT, j.t, e)f(e)de

(10.1)

where () is the mean total coverage at temperature T and chemical potential /-L, () is the local coverage (usually called the local isotherm) corresponding to an adsorptive energy 8, andf(8) is the AED. It should be noticed that Eqn 10.1 is strictly and generally valid only for noninteracting particles, which is a quite unrealistic case. If adsorbed particles interact with each other, then the local coverage at a point with a given adsorptive energy depends on the local coverage on neighbor points with different adsorptive energies and, in general, Eqn 10.1 should be replaced by a much more complex one, like [6]:

where now () depends not only on the adsorptive energy at a single point on the surface but also on the adsorptive energy at (in general) M neighbor points, and fM(8 1 , ••• ,8 M ) is a multivariate probability distribution that specifies how adsorptive energies are spatially distributed, or in other words, the energetic topography of the surface. We remark that, even for interacting particles, Eqn 10.2 reduces to Eqn 10.1 for two extreme topographies: (1) random sites topography (RST), where adsorptive energies are distributed totally at random among adsorbing sites, and (2) large patches topography (LPT) , where the surface is assumed to be a collection of homogeneous patches large enough to neglect border effects between neighbor patches with different adsorption energies. Of course, the local adsorption isotherm will be different for these two extreme topographies. It is by now clear that RST and LPT are particular limiting cases (occurring only rarely in real systems) of heterogeneous surfaces with more general topographies, and that the topography strongly affects many molecular processes occurring on such surfaces, like adsorption, surface diffusion, and reactions [6-12], thus making the simple determination of the AED not enough to characterize the heterogeneity. It is then necessary to obtain the multivariate probability distribution, or at least the AED plus the spatial correlation function. At this point we can precisely see the difficulties involved in the characterization of a general heterogeneous surface. As is well known, Eqn 10.1 for the

10.1

Introduction

2 13

simple cases of the two extreme topographies is an ill-posed problem for the determination of the AED f (e) due to the form of the kernel of the integral equation determined by the local isotherm. The determination of the AED from experimental adsorption isotherms requires elaborate computational methods, which have been developed with much effort in many years [5]. When treating with more general topographies, Eqn 10.2 must be used, where the local isotherm is a much more complex equation (if available at all) and we must deal with a multiple integral on the energy, and the unknown quantity to be calculated is the multivariate AED. Even in the simplest case in which the topography could be described by a two-point correlation function, the problem cannot be solved by inverting the multidimensional integral equation. It is then of great importance to develop simple models capable of describing the energetic topography on the basis of a few parameters and to study the effects of these parameters on several surface processes, with the hope that, in such a process, methods to obtain the relevant parameters from experimental data will be envisaged. These models can be of two kinds: continuum models or lattice-gas models. The former are more suited to mobile adsorption, generally physisorption, and then more closely related to the surface energetic characterization problem, whereas the latter are more suited to localized adsorption (e.g., chemisorption) . In this chapter we address the two kinds of theoretical approaches. On the one hand, we review the Generalized Gaussian Model (GGM), a continuum model based on a bivariate energy distribution with spatial correlations, extend it to deal with particles interacting through Lennard-Jones (LJ) potential, and compare its predictions to Monte Carlo simulations of mobile adsorption on solids with well-controlled heterogeneity. In Section 10.2 the basic concept of the Adsorptive Energy Suiface (AES) is introduced on the basis of a simple example and the characteristics determining the topography are discussed. In Section 10.3 the GGM is reviewed and extended to deal with LJ interacting particles. A Monte Carlo simulation method to obtain adsorption isotherms for solids with well-characterized heterogeneity is then developed in Section 10.4. Results from simulations and from the model are presented and compared in Section 10.5. On the other hand, we refer to the bivariate model, a lattice-gas model based on the concept of bivariate surfaces, i.e., surfaces composed of two kinds of sites, say weak and strong sites with adsorptive energies eland G2' respectively, arranged in patches of size I. Recent developments in the theory of adsorption on heterogeneous surfaces, like the supersite approach [13], and experimental advances in the tailoring of nano-structured adsorbates [14, 15], encourage this kind of study. A special class of bivariate surfaces, with a chessboard structure, has been observed recently to occur in a natural system [16], although it was already intensively used in modeling adsorption and surface diffusion phenomena [17-21]. Bivariate surfaces may also mimic, to a rough approximation, more general heterogeneous adsorbates. Just to give a few examples, we may mention the surfaces with energetic topography arising from a continuous distribution

Chapter 10 Energetic Topography Effects

21 4

of adsorptive energy with spatial correlations, like those described by the Dual Site-Bond Model [8], or that arising from a solid where a small amount of randomly distributed impurity (strongly adsorptive) atoms are added [9]. In both cases the energetic topography could be roughly represented by a random spatial distribution of irregular patches (with a characteristic size) of weak and strong sites. Accordingly, the scope of the present work is to determine, via Monte Carlo simulation, the general properties of the adsorption of interacting particles on model bivariate surfaces with a characteristic correlation length, l, and find out to what extent this length scale could be determined from adsorption measurements. In Section 10.6 we present the bivariate adsorption model and simulation method. The behavior of relevant quantities, like adsorption isotherms and isosteric heat of adsorption, is discussed in Section 10.7. Section 10.8 is dedicated to the determination of general scaling properties leading to power-law behavior and to the discussion of its implications in the determination of 1 from experimental measurements. Finally, general conclusions are given in Section 10.9.

10.2 THE ADSORPTIVE ENERGY SURFACE In order to base our analysis on a well-defined simple system, let us consider a heterogeneous solid consisting of a regular crystal of atoms A (e.g., an hcp crystal) where a small fraction is substituted by impurity atoms B. We move a probe atom P on the (X, Y) surface of the crystal; the probe interacts with atoms A and B with a LJ potential:

(10.3) where S stands for the substrate atom, A or B, and Band II are the usual energy depth and particle-diameter parameters, respectively. At each point i = (X, Y) the total interaction energy of the probe atom is calculated as a function of Z by summing up all pairwise interactions with the substrate's atoms within a cutoff distance rc = 40-PS: (10.4)

Then, by finding the minimum in the coordinate Z, we obtain the equilibrium height Zo and the adsorptive energy at position (X, Y) on the surface. What we get in this way is the AES seen by the probe atom, defined as E{X, Y, Zo) = minz{E{X, Y, Z)}. Figure 10.1 shows this energy surface for a crystal with 20 % of impurity atoms with BpA/kB = 160 K, BpB/kB = 320 K, and o-ps = 0.35 nm; darker regions represent stronger adsorptive energy, while brighter ones correspond to weaker

10.2

The Adsorptive Energy Surface

2 15

Figure

10.1 Adsorption Energy Surface (AES) for a crystal of atoms A with 20 % impurity of atoms B. Adapted from Ref. 25.

adsorptive energy. Significant correlation is seen to be present, in the sense that strong adsorptive regions appear to be quite larger than one lattice size in spite of the low density of impurity atoms, reflecting the fact that the probe atom interacts with many atoms of the substrate at once. As a first rough approximation, the energy surface could be considered as a collection ofirregular patches of different strengths. However, the energetic topography shows a quite greater complexity and such a picture could lead to an oversimplified model not reflecting important behaviors in molecular processes occurring on the surface. The cuts on the borders of the sample give the adsorptive energy profiles along X and Y directions, reinforcing the idea of a high complexity. The problem is how to model in a simple, and still realistic, way such a complex behavior? In other words, which are the characteristic (and relevant) quantities necessary to construct simple models capable of reproducing in a statistical sense the main topographic features? In a very general way, we can say that the AES is mathematically described by a stochastic process [22, 23], i.e., a random function depending on some parameter. In our case, the adsorptive energy is a random function of the position on the surface, H(R), where the symbol (A) indicates a random quantity and R is the position vector on the surface whose components are (X, Y). A particular realization of the stochastic process H(R) is the function E(X, y) represented in Fig. 10.1 (we can drop the dependence with Zo). The statistical description of such a stochastic process could be very complex. However, some simplifying assumptions, based on physical grounds, may greatly reduce this complexity. In fact, it is reasonable to assume that the surface is statistically

Chapter 10 Energetic Topography Effects

216

homogeneous, i.e., any macroscopic portion of the surface has all the meaningful information, and that the AED can be approximately described by a multivariate Gaussian distribution depending on the distance between pairs of points on the surface. This approach leads to the GGM [6, 12], which is capable of describing the energetic topography on the basis of the mean and the dispersion of the adsorptive energy, and a correlation function depending on the distance on the surface.

10.3 GENERALIZED GAUSSIAN MODEL

The GGM was introduced and developed in Refs [6, 12] for particles interacting through a square-well potential. Here we extend it for LJ interacting particles. We start by assuming the validity of the statistical homogeneity hypothesis: (10.5) where < . .. > denotes average over an ensemble of many realizations of the surface. The most general statistical information for a continuous stochastic process is given by its generating functional. If we assume that the AES is a Gaussian stochastic process, then its generating functional is given by [22, 23]:

F(a) == (exp {f d2 Ra(R) [E(R) - E]})

= exp [~f where H(R,

f d Rd R'a(R)H(R, R') a(R')] 2

2

(10.6)

R') = ([E(R) - E][E(R') - E]) is the covariance function and E =

(E(R»).

From the generating functional, the multivariate probability density distribution for the adsorptive energies at n points on the surface is obtained as:

where, by virtue of the condition (10.5), the covariance matrix (10.8)

10.3

2 17

Generalized Gaussian Model

is a function of the relative position vector between two points. Here n is the adsorptive energy dispersion and C the correlation function. If furthermore the surface is statistically isotropic, C is only a function of the distance r between two points. In this model the mean value of any macroscopic quantity of interest depending on the AES could then be evaluated by knowing E, 0, and C(r). The correlation function C(r) carries all the useful information about the energetic topography and should, in principle, be determined from the geometric and chemical structure of the adsorbent (even though the methodology to achieve this has not been developed so far). However, we could simplify the model even more by proposing for C(r) a simple Gaussian decay like:

(10.9)

where ro is the correlation length. This expression, which we do not intend to take as a realistic correlation function valid for any surface, simply stresses that the spatial correlation between adsorptive energies at points separated by a distance r < Yo is very high (close to 1) while for r > ro it is very low (close to 0). Thus the present model becomes very attractive in the sense that the energetic topography is characterized by a single parameter, the correlation length, and this opens the possibility for the determination of the three simple parameters of the model (E, fl, and ro) by, for example, fitting experimental adsorption isotherms. It is worthwhile to remark that the present model is a continuous one and not a lattice model of adsorption sites. This is an appealing feature, since, as we can see from Fig. 10.1, adsorption sites hardly form a regular lattice and furthermore many of them are so shallow that an adsorbed particle will most probably be quite mobile on appreciably large regions. To obtain a manageable equation for the adsorption isotherm in this model, without loosing the generality of a continuous model, we make use of a virial expansion for the two-dimensional spreading pressure 4J of the adsorbed phase [24]:

(10.10)

where p is the adsorbate surface density and Bn (1) is the nth two-dimensional virial coefficient. If the adsorbed phase is in equilibrium with an ideal gas phase whose density is Po and whose pressure is p, then making use of Gibbs equation Pod4J = pdp, the adsorption isotherm equation is given by:

p = K(1)pexp

[E

_n_

n~2 n-l

Bn (1) pn-l]

(10.11)

Chapter 10 Energetic Topography Effects

218

where K( 7) is an integration constant. By assuming that the potential energy of the system of adsorbed particles is the sum of the interparticle potential

Ugg

(IR

i -

R1 1), and the gas-solid potential [1]

(10.12) and that the stochastic process E(R) has the distribution given by Eqn. 10.7, the coefficients in Eqn. 10.11 are obtained as [12]: (10.13)

(10.14) where

S~,2 =112 = expl-Ugg (IR i - ~D IkB TJ -1 S~,2,3 = ftJtJ;3 S~,2,3,4

=ftJt~J;J;J;4 + 6ftJt~J;Jh4 + 3ftJ;.JhJt4 and so on.

It is clear that the calculation of gas-solid virial coefficients is very difficult, so that only the first few of them could be evaluated. This means that the model will be useful only at low values of the adsorbed phase density. But on the other hand, the most important effects of heterogeneity can be seen for the low-pressure part of the adsorption isotherm. In order to study how the first few virial coefficients depend on the energetic topography, we assume an interparticle interaction given by a LJ potential: (10.15) where (J is the particle diameter and kB Tgg is the depth of the potential. For the LJ potential, Eqn. 10.15, and introducing the notation E = -kB T a and n = kB T:, we obtain (see detailed calculations in Ref [25]): B2 (7)

= ~ + rg n { E

i [ -

(

~y exp ( -l (~r) ]-E

00

B3 (7)=- (2;)2

[10

00

tgt dt - 3 10

i [ -

(

~ r]}(10.16)

~~g2dt+310 ~lg~dt- 10 ~~dt] 00

00

(10.17)

10.3

21 9

Generalized Gaussian Model

where

gi(t) =

fa

b

drFi(r)Vo(tr)

(10.18)

r

F(r) = exp {4; [(~Y2 - (~r]} exp [ (~ e-H~)2] i

F2 (r)

= exp [ (~

'I' = 1T

fa

r

exp ( -liz

(~r)]

(10.19)

(10.20)

b

rFi (r)dr

(10.21)

and E i is the exponential integral function. The integrals involved in B 2 and B3 can be evaluated numerically. B4 could also be evaluated numerically within reasonably large computer time, but it would not be worth the much greater effort, because already at very low adsorbed phase density topography effects could be appreciated. Adimensional virial coefficients can be defined as B: = Bn/ (7TU 2 /2)n. The 2nd and 3rd coefficients are shown in Fig. 10.2 as a function of T/Tgg for Ts/Tgg = 2.0 (which represent a reasonably high heterogeneity with respect to interparticle interactions) and different values of roo As can be seen, the sensitivity of the virial coefficients with respect to the correlation length Yo is very high at low temperatures and is still appreciable even at a relatively

4

Ts/Tgg

=2.0

4

2

- 0 - '0=0 ____ '0 =0.20-

3

B;

'0=0-

0

B; -0-

----

-2

'0=

2

00

'0= 0 '0= 0.20-

---0- '0=0~

-4

'0=

00

0 0

(a)

2

3

4

T/Tgg

5

6

7

0

(b)

234

5

6

7

T/Tgg

Figure 10.2 Normalized gas-solid virial coefficients for a Lennard-Jones potential, as a function of the reduced temperature TITgg' for different values of the correlation length TO and for a given value of the standard deviation of the adsorptive potential kB T s ' Adapted from Re£ 25.

Chapter 10 Energetic Topography Effects

220

high temperature. As T:/Tgg decreases (figures not shown here), the effect of topography becomes weaker and practically disappears for T:/Tgg < 0.5. It is interesting to analyze the adsorption process to understand the peculiar behavior of B2 at low temperatures. For Yo = 0 (completely random topography) and Yo --+ 00 (macroscopic homogeneous patches) the relative positions of adsorbed particles are not dictated by the adsorption energy topography but rather by the interparticle potential, with prevalence of the attractive region, then making the integrand in Eqn. 10.14 preferentially positive, and therefore B2 --+ +00 as T --+ O. For 0 < Yo < 2(J, on the contrary, adsorbed particles are forced by the adsorptive energy topography to be close enough so that the repulsive part of the interparticle potential makes the prevailing contribution to the integrand in Eqn. 10.14, and B2 --+ -00 as T --+ O. As can be easily understood, the virial coefficients for Yo greater than a few particle diameters will behave approximately as for Yo = 00. Once the virial coefficients have been evaluated, the adsorption isotherm for low pressure is obtained through (10.22) (10.23) The constant K (T), known as the Henry's constant, representing the slope of the adsorption isotherm at a very low pressure, depends not only on the

TiTgg

0.3

--0-

-------D-

0.2

--atr-

= 2.0

'0 = 0 '0 =0.2a '0 = a '0 = 00

P

0.1

0.0

-+-~~~-r-r-"T""TTT~"'T""""""T""'T""TTT1rrr--,..-r-T"TTTI~""""""rTTTT-rr--T""""T""'1rTTTTrr-r-r-J"TTTT'Ii

1E-3

0.01

0.1

1

10

100

1000

10000

p/K(T)

Figure 10.3 Adsorption isotherms calculated from the GGM for Lennard-Jones interacting particles, for TITgg = 2.0 and different values of the correlation length. Adapted from Re£ 25.

10.4

Simulations on Ideal Heterogeneous Systems

221

mean adsorptive energy, E = -kB Ta, as classically believed [3], but also on the adsorptive energy dispersion 0 = kB Ts • Adsorption isotherms calculated from the above equations for Ts/Tgg = 2, T/ T gg = 2, and different values ofthe correlation length ro are shown in Fig. 10.3. The effect of the correlation length can be clearly appreciated as a considerable decrease in adsorption density as ro increases. Theoretical adsorption isotherms could be fitted to experimental ones obtaining the parameters K(T), ~, and ro, characterizing the AES for a given real gas-solid system. In what follows, however, we point to a quite stronger test of the GGM, namely, we produce artificial (computer-made) heterogeneous adsorbents with well-controlled energetic topography, determine the AED and the correlation function corresponding to the gas-solid system, then simulate the adsorption process in the continuum, and finally compare the observed behavior with the predictions (not data fitting) of the GGM.

10.4 SIMULATIONS ON IDEAL HETEROGENEOUS SYSTEMS A collection of solids is prepared as explained in Section 10.2, corresponding to different concentrations of impurity atoms, and their AES are generated. We can then study the statistical properties of these AES, like the AED and the spatial correlation function C(r). These statistical properties for a set of ideally prepared heterogeneous solids are shown in Figs. 10.4 and 10.5. As the concentration of impurity atoms increases, the mean value of the adsorption energy distribution (Fig. 10.4) shifts toward lower energy values (stronger adsorption) and its dispersion also increases. At the same time, the spatial correlation function (Fig. 10.5) presents an attenuated oscillatory behavior, with the decaying being slower for higher concentrations of impurity atoms. Once the ideal heterogeneous solids are prepared, the adsorption process is simulated through a continuum space Monte Carlo method in the grand canonical ensemble [26, 27]. The simulation method can briefly be outlined as follows. (a) A value of the pressure, p, and temperature, T, is fixed. (b) An arbitrary initial state with N adsorbed particles, S[y, is established (e.g., by adsorbing N particles at randomly chosen positions on the solid surface) and its energy is calculated as

(10.24)

222

Chapter 10 Energetic Topography Effects

-15.0

-12.5

-10.0

-7.5

-15.0

-12.5

-10.0

-7.5

U/Cgs

U/Cgs

(b)

(a)

Figure 10.4 Adsorptive energy distributions (AED) for ideal heterogeneous solids with different concentrations of impurity atoms. Adapted from Re£ 25.

-0--_____

'0=5.030 % '0 =3.5 70/0

--0--

0.8

'0=3.0 1 %

'0 =0.0

0%

0.4

0.0

-0.4

o

4

8

12

([A]

Figure 10.5 Comparison between "real" spatial correlation functions and those assumed by the GGM. Adapted from Re£ 25.

10.5

Comparison Test for the GGM

223

(c) One of the following three processes is randomly chosen with equal probabilities:

• Particle Displacement. A particle is chosen at random and a change in its position by a displacement vector Sis attempted. The modulus of the displacement vector is fixed but its direction is randomly chosen. The energy of the final state of the system (if the displacement were accepted), is calculated and the transition is accepted with probability

U(Sj),

W(S~ ---+ S;)

= min {1, exp [- (

U(Sj)k-TU(S["»)] }

(10.25)

B

• Particle Adsorption. A position on the surface is chosen at random and the adsorption of a new particle at that position is attempted. The transition is accepted with probability

m(S!'J~SN+l)=min{l I

'f

'

pA ex kB T( N + 1) P

[_(U(S[+l)-U(S["»)]} kB T

(10.26)

• Particle Desorption. An adsorbed particle is randomly chosen and its desorption is attempted. The transition is accepted with probability

W(S~ ---+ S;-l)

TN [(U(SN-l)-U(SN»)]} = min { 1, k~A exp 'f k T j

B

(10.27) where A is the area of the solid surface sample in the simulation. Step (c) is repeated until thermodynamical equilibrium is reached, and then further Monte Carlo steps (MCS) are executed to obtain the mean value of adsorbed particle density. By changing the value of p, the adsorption isotherm can be obtained.

10.5 COMPARISON TEST FOR THE

GGM

We now compare the predictions of the GGM with the behavior observed through simulations for the ideal heterogeneous systems As we can see from Fig. 10.4, the AED could be qualitatively described by a Gaussian distribution, as assumed by the GGM, whose dispersion increases as the concentration of impurity atoms increases. The case corresponding to 0 % concentration of impurity atoms is the less favorable, but it is also true that a

Chapter 10 Energetic Topography Effects

224

distortion of the AED in the high-energy region (weak adsorption energy) is not important for adsorption at low pressure, where the deeper adsorptive energy regions are preferentially occupied by adsorbed particles. It is to be expected that for more general heterogeneous solids, where heterogeneity could be due not only to impurity atoms but also to a number of defects, or even to the presence of amorphous structures, the AED would be even more similar to a Gaussian distribution. On the other hand, for the spatial correlation function, the Gaussian decay assumed by the GGM is also qualitatively acceptable, as can be seen from Fig. 10.5, where black symbols represent the Gaussian decay for different correlation lengths and the open symbols represent the spatial correlation function obtained from the AES for different concentrations of impurity atoms. In fact, even if the "real" correlation function presents the oscillatory structure induced by the periodic character of the solid lattice, these oscillations are not relevant to the adsorption of molecules, whose size is usually larger than the solid lattice spacing. What is important is the attenuation of the oscillations. Visual inspection of Fig. 10.1 suggests the importance of the size of the dark and bright regions, rather than the small grains within these regions. The important fact then is that the GGM provides a simple correlation function, which takes into account such a decay with only one parameter, the correlation length roo We now choose more or less appropriate (by visual comparison) AED and correlation length values for different samples of heterogeneous solids, and compare adsorption isotherms obtained by the GGM with simulated isotherms for those samples. This comparison is shown in Fig. 10.6, where black symbols represent simulated isotherms, whereas full curves represent GGM predictions. As

0.08

0.04

.: .'.•... 'a =2 '

. " ·.···'0=2.5 70/0

~~~~""""'L..--

1E-4

1E-3

1%

0.01

'a =3.5 30%

---+- 0.00

0.1

p[bar] Figure 10.6 Comparison between adsorption isotherms simulated on ideal heterogeneous solids (black symbols) and those predicted by the GGM (full lines), for three different samples. Adapted from Ref. 25.

10.6

Bivariate Model and Simulation Method

225

we have already mentioned, the comparison can only have significance at low pressure, given that we only use the virial expansion up to the 3rd coefficient. In this region, and considering that this is not the result of a parameter fitting procedure, we may say that the predictions of the model are satisfactory.

10.6 BIVARIATE MODEL AND SIMULATION METHOD

We now turn to a completely different kind of approach. We assume that the substrate is represented by a two-dimensional square lattice of M = L x L adsorption sites, with periodic boundary conditions. Each adsorption site can be either a "weak" site, with adsorptive energy E 1 , or a "strong" site, with adsorptive energy E 2 (E 1 < E 2 ). Weak and strong sites form patches of different geometry: (1) Square patches of size I (l = 1, 2, 3, ... ), which are spatially distributed either in a deterministic alternate way (chessboard topography), Fig. 10.7(a), or in a nonoverlapping random way (random topography), Fig. 10.7(b); (2) strips of transversal size I (l = 1, 2, 3, ... ), which are spatially distributed either in an

(a)

:::: ::::.... ........:::: .... ....:::: ............ ........:::: ........:::: .........:::: ... ....:::: :::: :::: :::: :::: .... ::::....::::....::::....:::: :::: :::: :::: . .:::: .... .... .. :::: .... :::: :::: ::::. . .... .. SSSS;;;;SSSS;;;;SSS

(c)

:::: ::::

mi .... .... ::::

.... :::: .... .... .... .... .... ....

:::: :::: ....

.... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... ....... ... ... ... ...... ... ... .... .... .... .... ..... ...

(b)

i;;;;iiis;;;;

.... .... .... .... .... .... .... ...... ... ... ..... ... ..... ... ...... ... ...... ... ... ...... ... ... ...... ... ... ...... ... ... ... .... .... . .... .... ... .... .... ... ....... ... .... .... ..... ... .... ... ..... ... .... ..... ... ...... ... ... ....... ... ... ...... ... ... .... .... ... ..... ...

(d)

.... .... ... ... .... .... .... .... .... .... . . ............ ............ ............ ............ ............ ............ ............ ............ :::::::: :::: :::::::: :::::::: ........ :::: ........ ........ ........ :::: ........ .... .... .... :::: . ........ . . ........ . . ........ . . ..... ... ............ .... :::::::::::: .... .... .... .... .... .... .... imim····imm~ .... .... . . .... .... . . .... . . ::::

.... .... .... .... .... .... .... .... .... .... .... .... :::: :::: :::: .... .... .... .... .... :::: .... .... .... .... :::: ....

............ :::::::::::: iiiiiiiiiiii :::::::::::: ............ ............ ............ ............ ............ :::::::::::: ............ ............ :::::::::::: ............ ............ ............ ............ ............ :::::::::::: ............ ::::::::::::

Figure 10.7 Schematic representation of heterogeneous bivariate surfaces with chessboard, (a), random square patches, (b), ordered strips, (c) and random strips, (d), topography. The patch size in this figure is 1== 4.

226

Chapter 10 Energetic Topography Effects

ordered alternate way, Fig. 10.7(c), or in a nonoverlapping random way (random topography), Fig. 10.7(d). In order to easily identify a given topography, we introduce the notation Ie for a chessboard topography of size 1 and, similarly, IR for random square patches, los for ordered strips, and IRS for random strips. Then, in Fig. 10.7(a)-(d), the topographies are 4e , 4R , 40s , and 4RS ' respectively. We also use the notation "bp" to refer to the extreme case ofbig patches topography (1-+ (0), i.e., a surface with one-half of weak sites and one-half of strong sites. The substrate is exposed to an ideal gas phase at temperature T and chemical potential J-L. Particles can be adsorbed on the substrate with the restriction of at most one adsorbed particle per site and we consider a nearest neighbor (NN) interaction energy w among them (we use the convention w > 0 for repulsive and w < 0 for attractive interactions). Then the adsorbed phase is characterized by the hamiltonian: H

= -M [ (8 1 01 + 82 ( 2 ) -

J-LO] + w

L ninj

(10.28)

(i,j)

where 0 = 01 + O2 is the total surface coverage (summing the coverages on weak and strong sites), ni is the site occupation number (=0 if empty or =1 if occupied) and the sum runs over all pairs of NN sites (iJ). Without any loss of generality, we can consider that all energies are measured in units of kB T, and that 8 1 = 0 and 8 2 = 8 1 + iiE, in such a way that the adsorptive energy is characterized by the single adimensional parameter iiE. The adsorption process is simulated through a Grand Canonical Ensemble Monte Carlo (GCEMC) method [26, 27]. For a given value of the temperature T and chemical potential j.L, an initial configuration with N = M /2 particles adsorbed at random positions is generated. Then an adsorption-desorption process is started, where a site is chosen at random and an attempt is made to change its occupancy state with probability given by the Metropolis rule, P = min {1, exp(-iiiHlkB T)}, where f1 iH = Hf - Hi is the difference between the hamiltonians of the final and initial states. A MCS is achieved when M sites have been tested to change its occupancy state. The approximation to thermodynamical equilibrium is monitored through the fluctuations in the number N of adsorbed particles; this is usually reached in 104 to 105 MCS. After that, mean values of thermodynamic quantities, like the surface coverage 0 and the internal energy U, are obtained by simple averages over m configurations. Then, o= < N > I M and U = < H > - J-L < N > where the brackets denote averages over statistically uncorrelated configurations. By changing the value of J-L, the adsorption isotherm at a given temperature can be obtained. Furthermore, from the simulation results, the differential heat of adsorption qd as a function of the coverage is calculated as qd = a < U> lao [28]. In our calculations we have used M ~ 104 and m = 105 . With this size of the lattice (L ~ 100, in such a way that it is a multiple of 1) we verified that finite size effects, which affect the isotherms in the case of repulsive interactions at much smaller sizes, are negligible.

10.7

Adsorption Results

227

10.7 ADSORPTION RESULTS We treat separately the cases of repulsive and attractive interactions. 10.7.1

Repulsive Interactions

Given that all energies are being measured in units of kB T, all results will be independent of the temperature and, furthermore, because the critical temperature for the appearance of a c(2 x 2) ordered phase in a zero-field Ising model is given by kB Te = 0.567w [29], there will be a critical NN interaction, we = 1.763668, above which the formation of the ordered phase is possible at (J = 0.5. In order to understand the basic phenomenology, we consider in the first place a chessboard topography with I = 4 (size of each homogeneous patch). Figure 10.8 shows the behavior of adsorption isotherms, (a), and qd((J), (b), for different square patches topographies for w = 4 and ~E = 24. It can be seen that all curves are contained between two limits: the one corresponding to Ie and the other corresponding to bp. For chessboard topographies, four different adsorption processes can be visualized, separated by shoulders in the adsorption isotherm and by steps in qd: (i) strong site patches are filled up first to (J = 0.25, where a c (2x2) structure is formed on them (in this region qd = 24); (ii) since 4w < ~E, the filling of strong site patches is completed up to (J = 0.5 (in this region qd decreases continuously from 24, zero-occupied NN, to 8, fouroccupied NN); processes (iii) and (iv), corresponding to the regions 0.5 < (J < 0.75 and 0.75 < () < 1, respectively, are equivalent to processes (i) and (ii) for

30

1.0 dE=24 0.8

20

w=4

0.6

---

10

()

--0- 3c

qd 0

----- 1R --.-2R

-10

---------- 3R ---._-- 4R

-----1 R f/" f;?:'___ 1c - - 2 R

0.4

. ~: .: ----I:s- 2c ---------- 3R - D - 3c ------- 4R

0.2

---.---- bp

--0- 4c -------- bp 0.0

-20 -30

-20

-10

0

10

20

0.0

0.2

0.4

0.6

0.8

1.0

()

{l

(a)

1c

- D - 2c

(b)

Figure 10.8 Adsorption isotherm, (a), and differential heat of adsorption, (b), for different topographies and repulsive interactions in regime I. Adapted from Re£ 30.

Chapter 10 Energetic Topography Effects

228

1.0

i1E= 12 -------- 1R

8

0.8

__ 2

w=4

R

------. 4 R

0.6

............. bp

o

()

0.4

-------- 1R

0.2

../(----- 1c - - 2 R --L::s- 2 -----. 4 R

_____ 1

-8

c --L::s- 2 c

c -D-4 ············· b p c

- D - 4c

-16

0.0 -20

-10

0

10

20

0.0

0.4

0.6

0.8

1.0

e

J-l (a)

0.2

(b)

Figure 10.9 Adsorption isotherm, (a), and differential heat of adsorption, (b), for different topographies and repulsive interactions in regime II. Adapted from Re£ 30.

weak site patches. Random topographies are seen to behave in a similar way with a particularly interesting feature: the behavior of a random topography of size 1 seems to approach that of a chessboard topography with an effective size Ieff > 1. As can be easily understood, as long as the condition w/ ~E :s 1/4 is satisfied, the adsorption process is similar to the one described above, i.e., strong site patches are filled first and weak site patches are filled after. We call this feature Regime 1. Figure 10.9 shows the behavior of adsorption isotherms, (a), and qd((}), (b), for different square patches topographies for w = 4 and ~E = 12. In this case, where w/ ~E 2: 1/3, the adsorption process follows a different regime, which we call Regime II: (i) the strong site patches are filled until the c(2 x 2) ordered phase is formed on them; (ii) the weak site patches are filled until the c(2 x 2) ordered phase is formed on them; (iii) the filling of the strong site patches is completed; (iv) the filling of the weak site patches is completed. It should be noticed that Regimes I and II are disconnected. In between, i.e. 1/4< w/ ~E < 1/3, the system behaves in a mixed transition regime changing continuously from one to another. Strip topography presents a similar behavior as square patches topography (not shown here), with the feature that ordered strips behave like chessboard square patches with a higher Ieff and random strips behave like random square patches also with a higher Ieff . A more detailed behavior of adsorption isotherms and differential heat of adsorption can be found in Refs [30, 31]. 10.7.2

Attractive Interactions

In the case of attractive interactions only Regime I is possible, i.e., for all values of ~E and w, strong patches fill first and weak patches fill last. Figures 10.10 and 10.11 show the typical behavior for square patches and

10.7

Adsorption Results

229

16

1.0

- e - bp

w=-1

0.8

- o - 4c

12

LiE=12

--0-- 2c

----*-

0.6 f)

qd 0.4

- - 4R - - - - 2R

0.2

- - - - .. 1R

1c

8

-e-bp - o - 4c

4

--0--2 c

w=-1 LiE=12

---*"-1 c

0.0

0 -18

-12

-6

0

0.0

0.2

0.4

J-l

0.6

0.8

1.0

f)

(a)

(b)

Figure 10.10 Adsorption isotherm, (a), and differential heat of adsorption, (b), for square patches topographies and attractive interactions. Adapted from Re£ 31.

1.0 16

w=-1 0.8

w=-1

12

LiE=12

LiE=12 0.6 f)

qd 0.4

-e-gp - 0 - 608

8

-0---2 08

-e-gp - 0 - 608

--*-1 08

4

-0---2 08

0.2

--*-1 08 0 0.0 -18

(a)

-12

-6

J-l

0

0.0

(b)

0.2

0.4

0.6

0.8

1.0

f)

Figure 10.11 Adsorption isotherm, (a), and differential heat of adsorption, (b), for strips topographies and attractive interactions. Adapted from Re£ 31.

for strips, respectively. In the last case only the ordered strips topography has been represented, as the density of curves is already high. The plateau in the isotherms and the corresponding abrupt drop in the differential heat of adsorption indicate that the strong patches are being filled before adsorption starts on the weak patches.

Chapter 10 Energetic Topography Effects

230

Again we observe that all curves vary between the bp topography and the Ie topography and that random topographies behave like the ordered ones with a larger effective size.

10.8 SCALING BEHAVIOR AND TEMPERATURE DEPENDENCE

The fact that both adsorption isotherm and heat of adsorption curves for different topographies, characterized by a length scale 1, vary between two extreme curves, suggests that we should search for some appropriate quantity to measure the deviation among these curves and study the behavior of such quantity as the length scale is varied. The quantity we found most suitable is the area between a given curve and a reference curve. For adsorption isotherms, this quantity, Xa' is defined as (10.29) where (JR(J-L) is the reference adsorption isotherm. A similar quantity, Xh' can be defined for adsorption heat curves. By taking as a reference curve the one corresponding to the bp topography, we obtain the plot of Xa as a function of 1 for different topographies corresponding to Regime I as shown in Fig. 10.12. Here we can see that Xa behaves as a power law in 1with an exponent a ~ - 2. Exactly the same behavior is also found for Xh' It is interesting to note that the

102 10°

101

L1E=12 w=-1

X 10-1 10-2

'0.

10°

X

..•...

·D.

.... ..•.. .... ....

10-1

D chessboard (5 = 1)

a

ordered strips (5=2)

. ~.

..•.

"0.

..•. ··A..

• random square patches (5= 2) .. random strips (5= 4)

(a)

....0.

Jeff

'0..

10-2

10-3

'0,

."

'0.

10-3

'0 .

··A.

".

..... D "'0.

..... D chessboard (5= 1)

a

10°

101

Jeff

'0.

. "'Q..

'0 ..

"Q..

.

'0 .

'".. '. 'a,. ..... li

ordered strips (5=2)

.

• random square patches (5=2) .. random strips (5=4)

(b)

Figure 10.12 Power law behavior of the quantity Xa showing the collapse of data for different topographies on a single curve when the effective length scale It1J is used: (a), repulsive interactions in Regime I; (b), attractive interactions.

10.8

Scaling Behavior and Temperature Dependence

231

exponent a is the same for repulsive (corresponding to Regime I) and attractive interactions and for all topographies, i.e., chessboard, random square patches, ordered strips, and random strips, as logarithmic plots are parallel. Straigthforward calculations demonstrate that the curves for X (either Xa or Xh) corresponding to the different topographies should collapse on the same curve as a function of an effective length 5cale (representing an effective patch size), leff' given by leff = 51, where 5 = 1 for chessboard topography, 5 = 2 for random square patches and for ordered strips, and 5 = 4 for random strips. The insets in Fig. 10.12 (a) and (b) show that this is indeed what happens. For repulsive interactions and for values of dE and w corresponding to Regime II, we find similar results, except that the exponent now has a different value, a ~ -3. Then, Xa behaves as a power law in the effective length scale, of the form In X = const + alnleff . This power law is valid over the whole range of energies, with different values of the exponent a. Figure 10.13 condenses the behavior of the scaling exponent for kB T = 1. We found that this behavior can be expressed as:

a a

= a l = -1.952±0.053;

for w/dE ~ 1/4

= a 2 + [12(1/3 - w/ dE)]I3(a l - ( 2 ); for 1/4 ~ w/ dE ~ 1/3 a = a 2 = -3.049±0.065; for w/dE ~ 1/3

(10.30)

with (3 = 0.42 ± 0.04 for repulsive interactions while a = a l = -1.9526 ± 0.053 for attractive interactions. As the temperature is changed, we find that the scaling exponent does not change for Regime I, whereas for Regime II its value tends toward that corresponding to Regime I as temperature increases [32]. This can be appreciated in Fig. 10.14(a), where hollow square symbols stand for a l and hollow circles -1.0

~-r--I----r----'--~-----"I---.:---r----rl--r---r-I-_

.-

Regime I --..'

:. -

Regime II

--..

-1.5 -

-

.. .

---ll------ft------~---- t, : : -2.5-2.0

a

• square patches, w> 0 -3.0 -

~ ~i~p~,e~:~hes, w < O ~----------Q-----------e------~

strips, W < 0

-3.5 -4.0

~

AE=4w

1

1

'\~

~/

AE=3w

-t---r--I----r---,I,...--+--,.I--I.....;....,----r'--r---r-,--f

0.1

0.2

0.3

0.4

0.5

Iwl/AE

Figure 10.1] Universal behavior of exponent a as a function of the adimensional variable willE for kB T= 1.

23 2

Chapter 10 Energetic Topography Effects

Regime I

Regime II

-2.0 ks T/!J.E= 1.20

-2

ks T/!J.E=0.33

-2.4

ks 77!J.E=0.16 ks T/!J.E=0.08

-3 -2.8

0.0

0.2

0.4

0.6

0.8

0.1

kBT/~E

(a)

0.2

0.3

0.4

0.5

w/~E

(b)

Figure 10.14 Dependence ofthe scaling exponent a on temperature. (a) Variation of a with k B T / LlE for Regime I (squares) and Regime II ( circles). Error bars represent Monte Carlo statistical errors. The solid line curve represents the fitting for Regime II given by Eqn. 10.31. (b) Overall behavior of a for different temperatures, represented through k B T / LlE. Curves for the intermediate regime are obtained by application of Eqn. 10.31 to Eqn. 10.30, while circles represent Monte Carlo results for wiLlE = 0.3. Adapted from Ref. 32.

symbols for a 2 • The full line represents a least squares fitting to the variation of a 2 given by

u 2 (kT/LlE) = -2-1.612exp(-S.2174kT/LlE)

(10.31)

If we assume this same variation for the values of the scaling exponent for the intermediate regime between Regimes I and II, we then obtain the general behavior represented in Fig. 10.14(b), where symbols in the intermediate regime correspond to Monte Carlo calculations. It is found that the scaling exponent a presents universality properties, in the sense that its behavior is identical for any value of LlE, for the different topographies considered, for different thermodynamical quantities (i.e., adsorption isotherm and differential heat of adsorption) and for different reference curves, even a theoretical one expressed, for example, through a mean field approximation for the bp topography like: (10.32) The corresponding reference curve for qd can be found by numerical differentiation through the general thermodynamical relation qd = (af.1/alnT)(} - kB T. This last universality property is extremely useful for practical applications, since if e 1 , e 2 , and w could be independently determined, as will be discussed

10.9

Conclusions

233

below, then the power law and the scaling exponent given by Eqns. 10.30 and 10.31 can be used to obtain Ieff from an experimental adsorption isotherm. These results suggest a method to solve the problem of the characterization of the energetic topography of heterogeneous substrates, which can be approximated by bivariate surfaces, through adsorption measurements of particles experimenting repulsive interactions. Adsorption measurements that are strictly necessary are the variation of the differential heat of adsorption as a function of coverage, qd (8), which can be obtained by using microcalorimetric techniques, and the adsorbate-adsorbate interaction energy, w, which can be obtained by low-energy electron diffraction (LEED) or scanning tunneling microscopy (STM) measurements at different temperatures to determine the critical temperature for the formation of the ordered c(2 x 2) structure. In the case of attractive interactions w can be estimated from adsorption measurements at very low pressures. With this, and since qd (0) = 8 2 and qd (1) = 8 1 + 4w, it is possible to determine 8 1 , 8 2 , and dE. Then, given the value of wi dE, the value of a can be obtained from Eqns 10.30 and 10.31. Finally, by choosing an appropriate theoretical approximation as a reference curve for qd (8), the value of Xh can be calculated allowing Ieff to be obtained from In X = const + aln leff' Note that the measurement of adsorption isotherms is not necessary for repulsive interactions, though it would be convenient to get an alternative value of Ieff to check the accuracy of the result.

10.9 CONCLUSIONS Several conclusions can be drawn from the present contribution. On the one hand, we have addressed the mobile adsorption (i.e., more suited to physical adsorption) of gases on heterogeneous surfaces at a low pressure. We have stressed the importance of the adsorptive energy topography, which can be taken into account by a theoretical model like the GGM, and we have extended such a model by calculating the 2nd and 3rd gas-solid virial coefficients for particles interacting through a LJ potential. The GGM turns out to be quite an attractive model due to its simplicity; in fact in this model the AES is statistically described by only three parameters: the mean value of the AED, kB T a , and its dispersion, kB I:, and the correlation length, roo The last parameter is the most relevant one describing the topography. The gas-solid virial coefficients were shown to depend strongly on the topography and, consequently, so does the adsorption isotherm at a low pressure. The only way to test the validity of such a model is to compare its predictions with the behavior of a system whose AED properties are well specified, and this is the case when adsorption is simulated on ideally constructed heterogeneous solids, as done here. The test turned out to be satisfactory for adsorption at a low pressure. From the above, we may say that the present form of the GGM can be used to fit experimental adsorption isotherms of physically adsorbed gases on heterogeneous solids at a low pressure,

Chapter 10 Energetic Topography Effects

234

obtaining in this way the parameters characterizing the heterogeneity. We may expect that the model would work better with substrates presenting a rough AES, because of either chemical impurities or roughness in the physical surface, such as in the case of activated carbons. Finally, since virial coefficients are found to be more sensitive to the correlation length at lower temperature, the appropriate adsorbates should be selected in such a way as to obtain experimental low-density adsorption isotherms at the lowest possible temperatures to ensure good sensitivity in the fitting parameters. On the other hand, we have studied by Monte Carlo simulations the adsorption of particles, interacting through a NN interaction w, on heterogeneous bivariate surfaces characterized by different energetic topographies. The heterogeneity is determined by two parameters: the difference of adsorptive energy between strong and weak sites, fiE, and an effective correlation length, Ie£[, representing the length scale for homogeneous adsorptive patches. Unique scaling properties and power-law behavior have been established for relevant adsorption quantities, such as the adsorption isotherm and the differential heat of adsorption. Two distinct filling regimes, Regime I and Regime II, separated by an intermediate mixed regime, are clearly identified in the adsorption process. The scaling exponent a as a function of wi fiE is found to follow a universal behavior. Its value is constant with temperature for Regime I, whereas it increases with temperature for Regime II and the intermediate regime toward the value corresponding to Regime I. This temperature dependence is given as an empirical equation obtained by Monte Carlo data fitting. These findings provide for the first time a method to characterize the energetic topography (i.e., obtain the parameters from experimental measurements) of a class of heterogeneous surfaces that can be approximately represented as bivariate surfaces.

ACKNOWLEDGMENTS

We gratefully acknowledge financial support from CONICET of Argentina and CONACYT of Mexico, which made possible the development of the present research.

REFERENCES

1. Steele, W.A. (1974). The Interaction of Gases with Solid Suifaces. Pergamon. 2. Jaroniec, M. and Madey, R. (1988). Physical Adsorption on Heterogeneous Suifaces. Elsevier.

References

235

3. Rudzinski, W. and Everett, D.H. (1992). Adsorption of Gases on Heterogeneous Surfaces. Academic Press. 4. Rudzinski, W., Steele, W.A., and Zgrablich, G. (1997). (eds). Equilibria and Dynamics of Gas Adsorption on Heterogeneous Solid Surfaces. Elsevier. 5. Jaroniec, M. and Brauer, P. (1985). Recent progress in determination of energetic heterogeneity of solids from adsorption data. Surf. Sci. Rep., 6, 65. 6. Riccardo, J.L., Chade, M.A., Pereyra, V.D., and Zgrablich, G. (1992). Adsorption and surface diffusion on generalized heterogeneous surfaces. Langmuir, 8, 1518. 7. Zgrablich, G., Mayagoitia, V., Rojas, F., et al. (1996). Molecular processes on heterogeneous solid surfaces. Langmuir, 12, 129. 8. Zgrablich, G., Zuppa, C., Ciacera, M., et al. (1996). The effect of energetic topography on the structure of the adsorbate. Surf. Sci., 356, 257. 9. Bulnes, F., Nieto, F., Pereyra, V., et al. (1999). Energetic topography effects on surface diffusion. Langmuir, 15, 5990. 10. Bulnes, F., Pereyra, V., Riccardo, J.L., and Zgrablich, G. (1999). Effects of the heterogeneous energetic topography on the collective motion of adsorbed particles. ]. Chem. Phys., 111, 1. 11. Gargiulo, V., Sales, J.L., Ciacera, M., and Zgrablich, G. (2002). Characterization of energetic topography of heterogeneous surfaces through the analysis of thermal desorption spectra. Surf. Sci., 501, 282. 12. Ripa, P. and Zgrablich, G. (1975). Effect of the potential correlation function on the physical adsorption on heterogeneous substrates.]. Phys. Chem., 79, 2118. 13. Steele, W.A. (1999). The supersite approach to adsorption on heterogeneous surfaces. Langmuir, 15, 6083. 14. Yang, M.X., Gracias, D.H., Jacobs, P.W., and Somorjai, G. (1998). Lithographic fabrication of model systems in heterogeneous catalysis and surface science studies. Langmuir, 14, 1458. 15. Lopinski, G.P., Wayner, D.D.M., and Wolkow, R.A. (2000). Self-directed growth of molecular nanostructures on silicon. Nature, 406, 48. 16. Fishlock, T.W., Pethica, J.B., and Eydell, R.G. (2000). Observation of a nanoscale chessboard superstructure in the Br-Cu (100) adsorbate system. Surf. Sci., 445, L47. 17. Nitta, T., Kuro-oka, M., and Katayama, T. (1984). An adsorption isotherm of multi-site occupance model for heterogeneous surface.]. Chem. Eng.]pn., 17,45. 18. Balazs, A.C., Gempe, M.C., and Zhou, Z. (1991). Polymer adsorption on chemically heterogeneous substrates. Macromolecules, 24, 4918. 19. Patrykiejew, A. (1993). Monte Carlo study ofadsorption on heterogeneous surfaces: finite size and boundary effects in localized monolayers. Langmuir, 9, 2562. 20. Nitta, T., Kiriyama, H., Shigeta, T. (1997). Monte Carlo simulation study for adsorption of dimers on random heterogeneous surfaces. Langmuir, 13, 903. 21. Nieto, F. and Uebing, C. (1998). Diffusion of adsorbates on random alloy surfaces. Eur. Phys. ]., Bl, 523. 22. Feller, W. (1971). An Introduction to Probability Theory and Its Applications, Vol. II, 2nd edn. Wiley. 23. Gardiner, C.W. (1985). Handbook of Stochastic Methods, 2nd edn. Springer. 24. Hill, T.L. (1956). Statistical Mechanics. McGraw-Hill. 25. Nazzarro, M. and Zgrablich, G. (2003). Energetic topography effects on mobile adsorption on heterogeneous surfaces at low coverage. Langmuir, 19, 6737. 26. Binder, K. (1986). Monte Carlo Methods in Statistical Physics. Springer-Verlag.

Chapter 10 Energetic Topography Effects

27. Nicholson, D. and Parsonage, N.G. (1982). Computer Simulation and the Statistical Mechanics of Adsorption. Academic Press. 28. Bakaev, V. and Steele, W.A. (1992). Grand canonical ensemble computer simulation of adsorption of argon on a heterogeneous surface. Langmuir, 8, 148. 29. Yeomans, J.M. (1992). Statistical Mechanics of Phase Transitions. Clarendon Press. 30. Bulnes, F., Ramirez-Pastor, A.J., and Zgrablich, G. (2001). Scaling behavior in adsorption on bivariate surfaces and the determination of energetic topography. J. Chern. Phys., 115, 1513. 31. Bulnes, F., Ramirez-Pastor, A.J., and Zgrablich, G. (2002). Scaling laws in adsorption on bivariate surfaces. Phys. Rev. E, 65, 31603. 32. Roma, F., Bulnes, F., Ramirez-Pastor, A.J., and Zgrablich, G. (2003). Temperature dependence of scaling laws in adsorption on bivariate surfaces. J. Phys. Chern., 5,3694.

POROUS TEXTURE CHARACTERIZATION FROM GAS-SOLID ADSORPTION Duong D. Do, Eugene A. Ustinov, and Ha D. Do School

of Engineering,

University of Queensland, St Lucia, Qld, Australia

Contents 11.1 11.2 11.3 11.4 11.5 11.6 11.7

Introduction Potential Models Classical Methods for Pore Characterization Density Functional Theory Monte Carlo Simulations Additional Features Conclusions Acknowledgment References

239 24 0 246 253 257 262 263 264 264

11.1 INTRODUCTION

Characterization of porous activated carbon and its derivatives has been a subject of great interest for many decades. Various tools for equilibria characterization are available in the literature, and they can be broadly classified into two groups: One is based on classical approaches while the other has firm foundation on molecular interaction calculations. Scientists constantly develop new tools or refine existing methods to better characterize porous carbons as the structure has significant effects on equili~ria as well as kinetics. Adsorption by Carbons ISBN: 978-0-08-044464-2

© 2008 Elsevier Ltd. All rights reserved.

239

Chapter

11.1.1

11

Porous Texture Characterization from Gas-Solid Adsorption

Carbon Structure

Carbon-based materials usually have a bimodal pore size distribution with one dominant peak being less than approximately 2 nm and the other major peak usually greater than 50 nm. The classification of pore size established by IUPAC [1] reflects neatly the range of pore sizes exhibited by carbon-based materials, which is micropores (pore size less than 2 nm), macropores (greater than 50 nm), and mesopores (falling between micropores and macropores). Micropores in activated carbon are dominantly used for storage of adsorbed molecules. The potentials exerted by the confinement of small pores are so great such that molecules inside those pores are not free from the attractive forces exerted by both walls of the pore [2]. Micropores are usually modeled as slit pores although this is a gross idealization of real pores, which are known to be finite, contain functional groups, defects, and do not have perfectly flat graphite surface [3]. Although there are attempts to relax some of the above restrictions, the ideal model of perfectly flat slit pore of infinite extent is still the most popular model used in almost all characterization methods. The complexity and the extreme computation time of more structured models are such that the ideal model of slit pore is still the obvious choice for pore characterization. Advanced carbon materials, such as carbon nanotubes and nanohorns, have pores of cylindrical shape and as such cylindrical pore is suitable for adsorption analysis for these types of materials. Since the discovery of carbon nanotube by Iijima [4], carbon nanotubes have been used by many as the candidate pores to study fundamentally the adsorption mechanism in cylindrical pores. In the past four decades, we have witnessed the significant development of various methods to describe microporous solids because of their important contribution to improving of adsorption capacity and separation. Various models of different complexity have been developed [5]. Some models have been simple with simple geometry, such as slit or cylinder, while some are more structured such as the disk model of Segarra and Glandt [6]. Recently, there has been great interest in using the reverse Monte Carlo (Me) simulation to reconstruct the carbon structure, which produces the desired properties, such as the surface area and pore volume [7, 8]. Much effort has been spent on studies of characterization of porous media [9-15]. In this chapter we will briefly review the classical approaches that still bear some impact on pore characterization, and concentrate on the advanced tools of density functional theory (DFT) and MC, which currently have wide applications in many systems.

11.2 POTENTIAL MODELS

The success of various models rests on the correct choice of the pairwise potential energy equation. In this section we will address the potential equations commonly employed for adsorbates used in pore characterization.

11.2

Potential Models

11.2.1

Fluid-Fluid Potential Models

There are many potential models that have been proposed in the literature. Among the popular ones that are currently enjoying widespread applications are the Lennard-Jones (LJ 12-6) equation and the Buckingham Exp-6 equation. The parameters of these equations are usually obtained by matching the theory (i.e., DFT) or simulation results (e.g., MC simulations) against various experimental properties, e.g., second virial coefficient, viscosity, vapor pressure, saturated liquid density, or surface tension, at the temperature at which the adsorption is carried out. Depending on the complex structure of the adsorbate molecule, simple atoms or spherical molecules can be assumed to behave as one-center interaction particle, i.e., they contain only one interaction site that involves in the interaction with the other atoms or molecules. Some adsorbates such as nitrogen and carbon dioxide contain more than one interaction site on each molecule. 11.2.1.1

Single interaction site particle

When a particle contains only one interaction site, the interaction between it and another is calculated with an equation that relates the interaction potential energy and the distance between two particles. One such equation is the LJ 12-6 equation, which contains two parameters, the collision diameter (J and the well depth of the potential B: (11.1 ) The molecular parameters of common adsorbates used in the pore structure characterization are listed in Table 11.1. It should be noted that these values are not unique as there are many other combinations of collision diameter and well depth of the interaction energy that have been determined in the literature [16]. Also noted in the table are the different sets of values that are used in DFT and in MC simulation. The difference is due to the mean field approximation assumed in the DFT analysis.

Table 11.1 Molecular parameters for simple molecules treated as 1C-LJ center

3.405 3.6154 3.685 3.81

119.8 101.5 164.41 148.1

3.305 3.5746 3.630 3.6177

118.05 93.746 163.1 146.91

Chapter

11

Porous Texture Characterization from Gas-Solid Adsorption

The LJ 12-6 potential equation is very popular, but that two-parameter equation is not flexible enough to handle many compounds adequately. This is resolved with equations involving more than two parameters, e.g., the Buckingham Exp-6 equation. This equation attracts interest from many workers [17-20] because it contains an additional parameter a that controls the steepness of the repulsive part of the interaction potential energy profile. It has the following form, and parameters for some gases are listed in Table 11.2: Table 11.2

Ar

Nz CH 4

'P(r) = {

Parameters for the Buckingham Exp-6 equation

123.2 131.49 113.5 100 152.8 160.3

e 1-6ja

11.2.1.2

3.866 3.784 4.040 4.12 4.206 4.188

Hirschfelder et al. [16]

14 15 16.2 13.6 14 15

Hirschfelder et al. [16]

Jones and Gray [21] Hirschfelder et al. [16] Errington and Panagiotopoulos [20]

[(00

r)] -(r- )6}

{ -exp 6 a 1- a

rm

m

(11.2)

r

Multisite particles

In pore characterization of carbonaceous materials, nitrogen and carbon dioxide have been commonly used. Nitrogen is used because it is readily available, while carbon dioxide is used as a probing molecule for smaller pores because of its small linear dimension and it can be used at temperatures close to the ambient temperature. Because of their shape, we should consider each molecule as a particle composing of many interaction sites. Each site on one molecule will interact with all sites of another molecule. We write below the interaction energy between a site a on a molecule i with a site b on a molecule j with a LJ 12-6 equation. ~a.'b)

'PI,}

= 4e(a,b)

u(a,b)) _ _ 12 _ (u(a,b)) _ _ 6] (a,b) (a,b) [ ( r· . r· . I,}

(11.3)

I,}

The subscript is used for particle while the superscript is for site. Thus for a given intersite distance ri~;,b) to calculate the interaction energy 'P~~,b), we need to know the cross collision diameter a(a,b) and the cross well depth E(a,b). They can be determined by invoking the mixing rule due to Lorentz-Berthelot

11.2

Potential Models

243

J

(LB) , a(a,b) = [a(a,a) + a(b,b)] /2 and 8(a,b) = 8(a,a) 8(b,b). Knowing the site-site interaction, the interaction between two molecules is simply: M M 'Pi,j

= L...J L...J 'Pi,j(a,b) '"' '"'

(11.4)

a=lb=l

where M is the number of sites on each molecule. We have just addressed the interaction energy between two molecules where the interaction is due to a dispersive force. Although nitrogen and carbon dioxide have zero dipole moment, they both possess quadrupole, e.g., the quadrupole moments of nitrogen and carbon dioxide are -4.9 x 10- 40 and -14.9 x 10- 4°Cjm 2 , respectively. The effect of quadrupole can be accounted for in the intermolecular interaction by specifying the charges and their locations on each molecule. The interaction energy due to electrostatic force between a charge a on a molecule i and a charge b on a molecule j is determined via the Coulomb law of electrostatic interaction:

'Pq;i,j

ab

l

(a,b)

=

41T8

qi qj

o

.

(a,b) y..

(11.5)

l,}

where 8 0 is the permittivity of free space, yi:;,b) is the distance between two charges a and b on the molecules i and j, respectively, q~ is the value of the charge a on the molecule i and qJ is the value of the charge b on the molecule j. The electrostatic interaction between two molecules then takes the form with M q being the number of charges on the molecule: Mq Mq

'Pq; i,j

'"' '"'

= L...J L...J 'Pq;(a,b) i,j

(11.6)

a=lb=l

Nitrogen

Cracknell et al. [22] proposed a two LJ site and a four-charge model (M = 2 and M q = 4). The four charges lie on the molecular axis joining the centers of two nitrogen atoms and they are symmetrical with respect to the molecular~ center of mass. The distance between two positive charges of 0.373e is 1.694

A,

while that between two negative ~harges of -0.373e is 2.088 A.

The distance between the two LJ sites is 1.094 A, and the collision diameter and t?e well depth of the interaction energy for nitrogen atom are (J'(N,N) = 3.318 A and S(N,N) jk = 37.8K. Bottani and Bakaev [23] proposed a two LJ site and a three-charge model (M = 2 and M q = 3). One positive charge (0.910e) is at the center of the molecular axis joining the two centers of nitrogen atoms and the two syn:,metric negative charge (-0.405e) are on the same axis with a distance of 1.1 A from each other. The collision diameter and the well depth of the interaction energy

244

Chapter

11

Porous Texture Characterization from Gas-Solid Adsorption

~

of a nitrogen atom are a(N,N) = 3.32 A and e(N,N) /k = 36.4 K. The distance between the two LJ sites is the same as that between two negative charges (i.e., the charge is on the LJ site). This model is less computer-intensive than the Cracknell's model because of one less charge to compute the electrostatic interaction. Carbon dioxide The model proposed by Harris and Yung [24] for carbon dioxide is commonly used for pore characterization [25]. In this model, there are three LJ sites with charges centered on each site. The molecular parameters are given below:

= 2.757 A, B(C,C) /k = 28.129 K a(O,O) = 3.033 A, B(O,O) / k = 80.507 K f, = 1.149A; qC = 0.6512e; qO = -0.3256e a(C,C)

The parameter f, is the distance between the oxygen LJ site and the carbon LJ site. 11.2.2 Solid-Fluid Potential Energy

The solid-fluid potential energy can be calculated by performing a summation of pairwise interaction between all the sites on an adsorbate molecule with all the atoms on the surface. This corrugated surface is important if the collision diame;er of the adsorbate molecule is comparable to the carbon-carbon distance (1.21 A) on the graphite surface or if the temperature is very low, when the structural behavior of the contact layer is very sensitive to this effect. However, for adsorbates having large collision diameter and high temperature, the assumption of structureless surface is reasonable and the surface can be assumed to be a continuum and the solid-fluid potential energy can be obtained by simple integration. 11.2.2.1 Slit shape pore

In the case of a single atom, its interaction with a structureless homogeneous surface made-up by a number of graphite layers, can be calculated from the Steele 10-4-3 equation [26, 27]: u

z - 41TB

sEC ) -

2

sfPs

1 a sf 10 1 a sf 4 a sf 4] [ 5 ( - z ) - -2 ( - z ) - 6.i(z + O.61.i)3

a Ll sf

(11.7)

where Ps is the density of the carbon center (114 x 1027 / m 3 ) , Ll is the interlayer graphite spacing (3.35 x 10- 10 m), and a sf and B sf are fluid-solid molecular parameters. The variable z is the distance between the atom and the plane

11.2

245

Potential Models

passing through the centers of all atoms of the outermost layer of the pore wall. The solid-fluid molecular parameters are usually obtained by matching the following theoretical Henry constant against the adsorption data on nonporous graphitized thermal carbon black: K

=

1 kT

/00 {exp [U Z) ] - 1} dz ----;;y Sf

(

(11.8)

o

where K = f/P. Here f is the surface excess. If the Henry constant is not available experimentally, the fluid-solid molecular parameters can be estimated from the usual LB rule. For carbon, the following parameters are commonly used u ss = 0.34nm and sssik = 28K. Equation (11.7) is the fluid-solid interaction energy for either atoms such as noble gases or lC-LJ molecules. For a polyatomic molecule with M centers of LJ type, the solid-fluid interaction energy can be determined the same way as we have presented earlier for fluid-fluid interaction. The interaction potential energy between a site a of the molecule i and the homogeneous flat solid substrate is calculated by the same 10-4-3 Steele potential [26, 27]: qJ(a)

= 41TP

I,S

e(a,s) [ a(a,s)Y C

Ll

1 (u(a,s)) 10 1 (u(a,s)) 4 [U(a,s)]4 } _ _ _ _ _ _ ----5 z 2 Z 6~(0.61~+z)3

1

(11.9) Knowing the interaction potential energy of the site a of the molecule i with the surface as given above, the solid-fluid interaction energy of the molecule i is 'Pi,s = L~l 'P~~. Once the solid-fluid potential energy for one wall is obtained, the potential energy between one molecule with a pore of slit shape and a width H is obtained from 'Pi, s(Z) + 'Pi , (H - z) 5

11.2.2.2

Cylindrical pores

The solid-fluid potential dealt with in the last section is for slit pores, and therefore it is applicable for solids such as activated carbon and activated carbon fibers. In the case of cylinder such as carbon nanotube, the interaction energy between a site a and the solid composing of Z concentric tubes is calculated from [28]:

'P~a) I,S

z

= 41TP C s(a,s) "L

{[u(a,s)]12 I n,6 _ [u(a,s)]6 I n,3 }

(11.10)

n=l

where I n,3 and I n,6 are calculated from the following integrals: (11.11)

Chapter 11 Porous Texture Characterization from Gas-Solid Adsorption

for m = 3 and 6. Here r is the distance of the interaction site a from the center of the tube. The variable an is the radius of the nth concentric shell, i.e., an = R + nli, where Ii is the spacing between two concentric shells, and R is the radius of the innermost carbon shell. This pore radius is defined as the distance from the pore center to the circular ring passing through all the carbon centers of the inner most shell. The integral of Eqn (11.11) can be expressed in terms of the hypergeometric function [29]. Knowing the interaction potential energy of the site a of the molecule i with the cylindrical pore as given in Eqn (11.10), the solid-fluid interaction energy of the molecule i and the pore is then calculated from 'Pi,s = L~l 'P~~. This potential energy equation has been used by a number of authors [30-34] in their analysis of solids having cylindrical pores, such as carbon nanotube and MCM-41.

11.3 CLASSICAL METHODS FOR PORE CHARACTERIZATION

Before discussing the two advanced methods for pore characterization, we would like to note that classical methods presented in the literature are applicable to mesoporous solids [35-38]. Among the early methods for characterizing microporous solids is the Hovarth-Kawazoe method [39] and it was later modified by a number of authors [40-44]. 11.3.1

Barrett, Joyner, and Halenda Method

The method devised by Barrett, Joyner, and Halenda (BJH) [35] is one of the earliest methods developed to address the pore size distribution of mesoporous solids. This method assumes that adsorption in mesoporous solid (cylindrical pore is assumed) follows two sequential processes - building up ofadsorbed layer on the surface followed by a capillary condensation process. Karnaukhov and Kiselev [45] accounted for the curvature in the first process, but Bonnetain et al. [46] found that this improvement has little influence on the determination of pore size distribution. The second process is described by either the Cohan equation (for adsorption branch) or the Kelvin equation (for desorption branch). 11.3.2

Broekhoff-de Boer Method

Among many classical approaches available in the literature, a method developed by Broekhoff and de Boer (BdB) [47-53] for description of vapor adsorption and desorption in cylindrical pores and slit pores is the most thermodynamically rigorous and elegant for more than 35 years. This method relies on a reference system, which is a flat surface having the same structure and surface chemistry as that of the adsorbent. The pores of the adsorbent can have either

11.3

Classical Methods for Pore Characterization

247

a cylindrical shape or slit shape. Their theoretical analysis rests on the following assumptions: • The adsorbed phase has the form of a liquid film whose density is equal to that of saturated bulk liquid. The liquid film-vapor interface is of zero extent. • The contribution of gas-like phase to the amount adsorbed is neglected. • The surface tension of the liquid film is the same as that for the macroscopic liquid and does not depend on the film thickness and the interface curvature. • The solid-fluid potential varies with the distance from the flat surface the same way as from cylindrical surface regardless of the surface curvature and from the pore wall of slit pore. All these assumptions do not exactly agree with results obtained from molecular simulations. However, errors resulting from these assumptions in the case of cylindrical pore and in the case of the reference flat surface may partly compensate each other. The advantage of the BdB method is that in the framework of their model all thermodynamic derivations are strictly correct. Details of this method can be found in the excellent papers by Broekhoff and de Boer.

11.3.3 Dubinin Methods The Dubinin-Radushkevich (DR) equation was originally devised as an empirical expression of the Polanyi adsorption potential theory, and due to its simplicity it has been widely used to correlate adsorption data in many microporous solids despite its failure in giving the correct Henry constant at extremely low pressures. This equation is based on the premise that adsorption in micropores follows a mechanism of pore filling rather than the molecular layering and capillary condensation as proposed for mesoporous solids. It has the form:

() =

W Wo

= exp [_ (RTln po/ p )2] Eof3

(11.12)

where WI W O is the fraction of the micropore volume that is occupied by adsorbate molecules, f3 is called the similarity constant (benzene is chosen as a reference, i.e., f3 = 1) and Eo is the characteristic energy and is related to the mean micropore size. The DR equation describes reasonably well, adsorption data of many vapors in carbonaceous materials that have a wide pore size distribution (PSD). For fine microporous solids having narrow PSDs, the Dubinin and Astakhov (DA) equation was proposed by replacing the exponent 2 in Eqn (11.12) by n, where n is usually referred as the heterogeneity factor. This factor usually falls in the range of 1.5-3.0, and it can be as high as 5-6 for fine microporous solids such as zeolites. To describe solids having a distribution in terms of either energy or pore size, Stoeckli [54] and Huber et al. [55] proposed to use the DR equation as a local isotherm in an integral equation to correlate adsorption isotherm of

Chapter 11 Porous Texture Characterization from Gas-Solid Adsorption

heterogeneous solids. This distribution is in the form of the micropore volume with respect to the parameter B (B = 1/ Eo~). Stoeckli [56] described the distribution in terms of the pore size rather than energy. To achieve this, they related the characteristic energy Eo in terms of the micropore size as given below.

10.8

H=----

(11.13)

Eo -11.4

where H is in nm and Eo is in kJ/mol. Using the DA equation with n = 3 as the local isotherm, the overall isotherm equation can be written in terms of an integral involving the micropore size distribution in the integrand. Fitting this overall isotherm against experimental data, the parameters involved in the micropore size distribution can be optimally derived, from which the micropore size distribution can be deduced.

11.3.4 Horvath-Kawazoe Method and its Modifications The Horvath and Kawazoe (HK) method [39] was developed to determine the PSD of active carbons from nitrogen adsorption isotherm. All pores are assumed to have slit shape. This method rests on the assumption that the adsorption state of a pore is either empty or completely filled. The demarcation pressure between these two states is called the pore-filling pressure, and it is a function of pore width. The equilibrium of a pore exposed to a bulk phase of constant chemical potential is obtained from the minimization of the following grand thermodynamic potential:

n=

(11.14)

F-nJL

where F is the Helmholtz free energy, n is the number of molecules adsorbed in the pore, and JL is the chemical potential. If the pore is empty, the grand thermodynamic potential n is zero. When the pore is completely filled, the grand potential is a function of chemical potential. It is positive for low chemical potentials and become negative at higher chemical potentials. The chemical potential at which this grand potential changes is zero, is the pore-filling chemical potential. Thus the pore-filling chemical potential is simply equal to the molar Helmholtz free energy of the adsorbed phase, i.e., (11.15)

ILf = F

The molar Helmholtz free energy of the adsorbed phase is simply the sum of the intrinsic Helmholtz free energy and the solid-fluid potential averaged over the adsorbed phase. Assuming a liquid-like behavior of the adsorbed phase, this free energy is given by H-lTs[

-F= [G - -POv ] L M

1

+--H 2(Ts[

f

udz

(11.16)

11.3

249

Classical Methods for Pore Characterization

Here G L = J.L (1) + kB T In Po is the molecular Gibbs free energy of the bulk liquid at the saturation pressure Po; u is the solid-fluid potential at a distance z from the pore wall. The chemical potential J.Lf in the bulk phase at the filling pressure Pf is J.L (1) + kB TIn Pf· Then combining Eqns (11.15) and (11.16) yields the following basic equation relating the pore-filling pressure Pf vs pore width: 0

0

H-asf

kB TIn (Pf) Po

=

1

H -2usf

f

udz

(11.17)

asf

Note that the solid-fluid potential energy in the above integrand is a function of H (e.g., the 10-4-3 Steele potential). Let us illustrate the HK method in the case of nitrogen adsorption in carbon slit pores at 77.35 K. For this system, the potential well depth ssf / kB is 56 K and the solid-fluid collision diameter u sf is 0.3488 nm. The pore-filling pressure vs the pore width, obtained from Eqn (11.17), is shown in Fig. 11.1. The solid line is calculated by the nonlocal density functional theory (NLDFT), which will be described to some detail in Section 11.4. As seen in the figure, the curve obtained with the HK method (dashed line) correlates with NLDFT much better than that calculated with the Kelvin equation (dash-dotted line). Knowing the pore-filling pressure as a function of pore width, for a given bulk-phase pressure p, the width of the pore that is just instantly filled at this pressure is denoted as H f . All pores having widths smaller than H f will be filled while those having widths greater than H f are still empty. Thus the overall 100

.------------._-._-.---.---._-._-.---.---._-._-.-------.=-~.

10-1

----

/.".-.

t·

i

10-2 10-3

;

;

10-4

;

;

~ 10-5

;

0: 10~

~

l

. I

! I !I

10-7 10-8

I I

10-9

I I

I

10-10

10- 11

/

-+-----.,.----lI-~-____r__-_____r----r--___r_--_r__-___I

o

2

3

4

Pore width (nm)

Figure 11.1 Pore-filling pressure dependence on the pore width for nitrogen adsorption in carbon slit pore at 77.35 K. (Solid line) NLDFT. (Dashed line) Horvath-Kawazoe method. (Dash-dot line) Kelvin equation.

Chapter

11

Porous Texture Characterization from Gas-Solid Adsorption

amount adsorbed is simply the total volume of those pores having the width smaller than H f multiplied by the liquid density. Hf(P)

a=PL

f !(Ht)dHt

(11.18)

The comparative accuracy and simplicity were the reasons why the HK method has enjoyed its popularity. This method was further extended to cylindrical [57] and spherical pores [40]. However, the pore-filling pressure is insufficiently accurate to predict pore size distribution with the same accuracy as that obtained with rigorous molecular approaches like grand canonical Monte Carlo (GCMC) simulations and NLDFT. Various attempts to improve the HK method have been made in the literature. One of such attempts is the method developed by Dombrowski et al. [43], who proposed a "weighted" version of the HK approach. They were guided by results obtained by DFT, in which the density profile across the pore exhibits an oscillational behavior with a period roughly equal to one collision diameter. This makes their modified HK method DFT-dependent. Analogous attempt to improve the HK method was made by Rege and Yang [41]. They considered layering of the adsorbed molecules with the assumption that each layer only interacts with adjacent molecular layers. However, both the attempts for improvement of the HK model rest on the same assumption of step-like local isotherm. It is known that the pore-wall wetting precedes the capillary condensation, resulting in quite involved shape of local isotherms, which strongly depends on the pore size. This shortcoming of the HK model was recently overcome by more rigorous thermodynamic analysis of adsorption in slit carbonaceous pores accounting for the dependence of surface tension on the adsorbed film thickness [44].

11.3.5 Enhanced Potential Method of Do and Coworkers Adsorption in mesopores is traditionally characterized by a mechanism of two sequential processes (e.g., the BJH method). Many attempts have been made to extend the applicability of the classical approach to smaller pores [58, 59]. With this allowance the range of applicability of the Kelvin equation could be extended only moderately. In the attempt to deal with micropores or pores of all sizes using the semiclassical approach, Do [60] introduced a concept of enhanced layering and enhanced potential. In the method of Do and coworkers [60-70], the mechanism is proposed in that the adsorption occurs by two sequential processes: (i) molecular layering and (ii) pore filling. At first, this method sounds like the same method that has been used in the last 60 years for the description of adsorption in mesopores and macropores. So what are the differences here? The differences lie in the enhancement in the adsorption affinity (due to the overlapping of potential exerted by opposite surfaces) and in the enhanced pore pressure in the core (due to the long-range interaction ofthe solid-fluid potential). Details of this method can be found in Do and Do [65]. We will only brief it here.

11.3

Classical Methods for Pore Characterization

The pore pressure used in the calculation of the adsorbed film thickness is calculated from Pp = Pexp (

-aC{) )

(11.19)

kT p

where 'P p is the mean solid-fluid potential energy in the inner core region. The parameter a is introduced because of the approximate nature of that equation. The mean solid-fluid potential energy 'P p is obtained as an average of the solidfluid potential energy profile over the domain of the inner core, 0, that is not occupied by the adsorbed phase. H/2

- f 'Pp(z)dzj f 'Pp =

n

n

f

'Pp(z)dz

dz = ( zo+t ) H/2-t-z

(11.20)

0

The pore pressure is directly responsible for the molecular layering and the pore filling. Having described the pore pressure, we now address the molecular layering process. This process can be described by any appropriate equation. If there is no or weak fluid-fluid interaction, we can use the BET-type equation, while if the fluid-fluid interaction is strong we can use the modified Hill-de Boer equation as suggested by Do and Do [63] to calculate the adsorbed film thickness t. In these equations the affinity constant is a function of pore size and the pressure involved in those equations is the pore pressure. Now we turn to the pore-filling process. We argue that this process is governed by the following equation, which is similar in form to the modified Kelvin equation: RTln

'VV p ) = _ 2 I M ( Po (H/2 - t - zo)

(11.21)

The difference between the above equation and the modified Kelvin equation is the use of the pore pressure. Substituting the pore pressure of Eqn (11.19) into the above equation gives H/2

f 'Pp(z)dz - YVM R Tin (pP ) = _zo+_t _ (H/2 t zo) o a

(11.22)

For large pores (mesopores and macropores), the contribution of solid-fluid potential is negligible (the first term in the RHS) and the above equation is reduced to the modified Kelvin equation. On the other hand, for small pores of molecular dimension the overlapping of potentials exerted by the two opposite walls is such that the overlapped potential outweighs the surface tension effect

Chapter

11

Porous Texture Characterization from Gas-Solid Adsorption

1.2 1.0 0.8 d

0.6 0.4 0.2 0.0 0

4

2

Figure 11.2 The dependence of Q' on the reduced pore width.

(i.e., the second term on the RHS is negligible). We see that the pore-filling process in small pores is dictated by the enhanced potential. First, we apply this method to calculate the pore-filling pressure vs pore width, i.e., the pore at which the pore is filled with adsorbates. The necessary parameter in the estimation of the pore pressure is a. We obtain the dependence of this parameter on pore width by matching the pore-filling pressure obtained by our method with the results of DFT and GCMC, and Fig. 11.2 shows this dependence for nitrogen and argon. It is interesting to note that this dependence on pore width is independent of adsorbate. The dependence of the pore-filling pressure vs pore width is shown in Fig. 11.3, where we observe good agreement between this method and DFT and GCMC.

10-10

+---':'~--+-----+--~----i------~------l

o

10

20

30

Pore width (A)

Figure 11.3 Reduced pore-filling pressure vs pore width.

40

50

11.4

253

Density Functional Theory

This method has been tested against the GCMC simulation [65], and the derived PSDs and the fitting of adsorption isotherm agree well with those obtained with the GCMC. It has also been applied to various activated carbons and is tested against the DFT theory for activated carbon processing pores of different size [69]. It has been found that for standard activated carbon, this method agrees well with the DFT while in purely fine microporous activated carbon, the two methods show some deviations. It is worthwhile to mention here that the DFT also disagrees with the MC simulations in small pores containing less than two molecular layers [71].

11.4 DENSITY FUNCTIONAL THEORY 11.4.1

Introduction of DFT

Density functional theory is a powerful tool to study many phenomena in physical chemistry and chemical engineering. It was popularized in the early 1960s by a number of authors [72-74]. But it is not until the 1980s that this theory had found widespread applications in many interfacial problems. Capillary condensation in pore was systematically studied [75], and the first paper [76] applying this technique to the problem ofPSD determination of carbon particle appeared in 1989. This work used a local DFT, and it is now superseded by the NLDFT, which was developed by Tarazona and Evans [77-79]. This is the method that is now widely used in the characterization of pore size distribution. 11.4.1.1

The NLDFT method

Application of NLDFT to adsorption of fluids in porous media is usually carried out at constant temperature and pressure (constant chemical potential). The equilibrium state of the grand canonical ensemble corresponds to the minimum of the following thermodynamic grand potential:

n=

(11.23)

F- nJL

where n is the number of molecules in the pore and is obtained from the integration of the local density over the volume of the pore n = p(r)dr. Here p(r) is the local density expressed in molecules per unit volume. In a confined space of a pore the density and the thermodynamic functions such as the Helmholtz free energy are distributed over the pore space. Letf(r) be the molecular Helmholtz free energy. Then the total Helmholtz free energy of the fluid confined in the pore is

J

F

f

= p(r)f(r)dr

(11.24)

Chapter 11 Porous Texture Characterization from Gas-Solid Adsorption

254

The system is said to be at equilibrium when the grand thermodynamic potential is a minimum. To perform this minimization, we need to determine the molecular Helmholtz free energy, and this is the crucial part of the DFT method as we shall show below. The molecular Helmholtz free energy f(r) may be expressed as a sum of four contributions: • • • •

the the the the

ideal part J:d (r) = kB T [In (A 3p(r)) - 1] excess repulsive part !ex [p (r)] attractive part of fluid-fluid intermolecular interactions uint (r) external part of solid-fluid interactions uext (r)

Here p(r) is the smoothed density; and A is the thermal de Broglie wavelength. The repulsive part of the Helmholtz free energy is usually calculated by the Carnahan-Starling equation derived for the hard sphere fluid [80]:

4- 3-2 (1 _Yj)2 '

r (-)-k T 17- 17 Jex

YJ -

B

(11.25)

where dHS is the equivalent hard sphere diameter. As we have mentioned earlier, there are different recipes for calculating the smoothed density, but in the case of a single component system the most popular prescription is that proposed by Tarazona et al. [79]:

p(r)

= f p (r') w (Ir -

r'l ,

P(r'» dr'

(11.26)

It was assumed that the weighting function could be approximated by a power serIes W

(Ir - r'l , P(r')) =

W o (Ir

- r'l) + Wi (Ir - r'l) per) + W 2 (Ir - r'l) [p(r)]2 (11.27)

The attractive part of the Helmholtz free energy is calculated via mean field approximation:

. uillt(r) = "21

J4> (Ir - r'l)

p (r') dr'

(11.28)

where ¢(r) is the attractive potential of two molecules. The factor 1/2 is because each molecule accounts for one half of ¢(r). This potential is expressed by the Weeks-Chandler-Andersen rw'CA) scheme [81] -Sf['

4>(r)

=

4cff [

(~ff y2 - (~£f

rl

r < rm

rill < r < rc

0, Here sf[ is the potential well depth, and rm

= 2i / 6

(Tf[.

(11.29)

11.4

Density Functional Theory

255

Table 11.3 Molecular parameters for Ar and N2 determined from bulk properties and surface tension

Ar N2

4.2712 (4.2617) 4.3405 (4.3155)

0.3380 (0.3380) 0.3581 (0.3575)

0.3318 (0.3305) 0.3537 (0.3575)

116.93 (118.05) 98.09 (94.45)

0.0125

34944

0.00888

28693

The condition of minimum of the grand thermodynamic potential requires its functional derivative ao/ap to be equal to zero. In the case of the onedimensional task it yields:

JL = kB TIn (A 3 p(z)) +!ex [p(z)]

+

f

int

p (z')i:x [p (z')] 'P (z, z') dz' + 2u (z)

+ uext(z)

where f:x is the derivative of!ex with respect to the smoothed density ') (

'P z, z

=

W o (Iz

(11.30)

p, and

- z'l) + P(z') Wi (Iz - z'l) + [p (Z,)]2 W 2(Iz - z'l) 1_ PI (Z') - 2p (Z') PZ (z') (11.31)

The increase of the bulk pressure at a small increment after achievement of the equilibrium density distribution allows obtaining the adsorption branch of the isotherm. If the pore is wide enough, the capillary condensation will occur, with the pressure of the condensation being corresponded to the vapor-like spinodal point. Similarly, desorption branch of the isotherm will be obtained at the decrease of pressure. In this case, the capillary evaporation will occur at a liquid-like spinodal point. The equilibrium transition pressure is obtained by comparing the grand thermodynamic potentials corresponding to the adsorption and the desorption branches of the isotherm. It corresponds to the equality of these values of the grand thermodynamic potential. In Table 11.3 we present molecular parameters for argon and nitrogen, determined by the approach discussed in this section. In parentheses we present the values reported by N eimark et al. [31]. The surface tension and the liquid-phase density for Ar and N 2 at their boiling points, at which the molecular parameters were obtained, are also presented in this table. 11.4. 2

DFT Applications to Pores (Slit and Cylinder)

Application of the DFT theory to argon adsorption on graphitized carbon black at 87.29 K [82] is shown in Fig. 11.4, where the solid line is from the DFT theory.

Chapter

256

11

Porous Texture Characterization from Gas-Solid Adsorption

_100 C\I

N E 100 ::::::

(a)

E

..........

(5

E

-6 "'C Q)

-6 ~

60

..c

..c

"'C ct1

"'C ct1

C 20 :::J

'E

CJ)

:::J

o E

0

E 0 0.0

10

(;

0 CJ) 40

cd::

(b)

o E

80

cd:: 0.1 1'-.......-r-...........-rrrr--.....--.-.........-T"~---r--"r-T'"T'"'I"'T'TTT"""--.-""T"""'T""T"T"T'T'I'T'"

0.2

0.4

0.6

0.8

1.0

0.0001

0.001

p/Po

0.01

0.1

p/Po

Figure 11.4 Argon adsorption isotherm on graphitized carbon black at 87.29 K in linear scale (a) and logarithmic scale (b). (Solid lines) correlation by NLDFT. (Dashed lines) correlation with nonadditivity factor a of 0.0183. Specific surface area is taken to be 13.26m2 jg.

The common feature observed in both DFT and GCMC simulations is that these results overpredict the amount adsorbed in the reduced pressure region greater than about 0.2. This seems to indicate that the fluid-fluid interaction energy is overestimated in the presence of a solid surface, and therefore the usual assumption of pairwise additivity of fluid-fluid and solid-fluid potential energies is questionable. One way of resolving this issue is the application of the following quadratic equation for the potential of one molecule [83]: (11.32)

u=--------

kT

Here a is a positive parameter accounting for the multibody interaction. The dashed lines in the figure present the correlation by the NLDFT with the parameter a equal to 0.0183. This quite simple modification of NLDFT leads to excellent fitting of experimental data with parameters listed in Table 11.4. The parameters presented in this table may be used in modeling of adsorption in slit and cylindrical pores. For illustration, we show in Fig. 11.5 the local isotherms for nitrogen adsorption at 77.35 K in slit pores of various pore widths. As seen in this figure the shape of the local isotherm depends on the pore width. Having this information on local isotherms for a wide range of pore widths, they can be used to determine the pore size distribution.

Table 11.4 Molecular parameters for Ar and N2 adsorbed on graphitized carbon black [71]

Ar 87.3K N 2 77K

118.05 94.45

0.3305 0.3575

0.338 0.3575

58.01 56.10

0.3353 0.3488

0.0183 0.0242

11.5

257

Monte Carlo Simulations

40~---------------------------'

32 M

E

~ (5

E

24

S

~

.~

16

c

Q)

o

8

O~=-.....;!:~-=--..,..--=:::::::;:_:::;;;;;;;..p::::;;""iiiiiiijiillIIIIiiiiii~=;:'-_~

10-10

10-9

10-8

10-7

10-6

10-5

10-4

_ _~-=--:;::::::"":""---1

10-3

10-2

10-1

10°

p/Po Figure 11.5 Set of nitrogen adsorption isotherms in slit pores at 77.3 K. Dashed lines correspond to narrow pores having width H (from right to left), nm: 0.60, 0.62, 0.64, 0.66. In this range, the increase of the pore width shifts isotherms toward lower pressures. (Solid lines) the pore width (from left to right), nm: 0.68, 0.72, 0.76, 0.80, 0.84, 0.88, 0.94, 1.0, 1.1, 1.2, 1.4, 1.6,2,2.4,3, 4.

11.5 MONTE (ARLO SIMULATIONS 11.5.1

Ensembles Used in Simulations of Adsorption

Monte Carlo has been increasingly applied to solve many adsorption of interest. This is greatly due to the increasing speed of personal computer and the greater arsenal of MC simulation methods that have been developed in the past few decades. Among these methods, the GCMC and the Gibbs ensemble Monte Carlo (GEMC) are particularly useful for pore characterization. We will discuss briefly these methods. More detailed exposition can be found in many excellent books [84, 85]. 11.5.1.1

Grand canonical Monte Carlo

In the GCMC simulation [86, 87], we specify temperature, volume (pore volume), and the chemical potential in the simulation box. This ensemble is ideal to study adsorption where a solid adsorbent (or a single pore) is exposed to a bulk fluid of constant pressure or chemical potential. Like all MC simulation methods, a Markov chain of molecular configurations is produced. Any properties of interest can be derived by averaging over this Markov chain. In GCMC, there are three different moves used to generate the Markov chain which is then composed of a series of molecular configurations. They are (i) displacement, (ii) creation, and (iii) destruction. We briefly describe them. The first move is the displacement of particle. This can be done by choosing a particle in

Chapter

11

Porous Texture Characterization from Gas-Solid Adsorption

random. This particle is displaced to a new position, and the acceptance or , rejection of this move will follow the rule of acceptance commonly used in MC simulation: (11.33)

where d U is the difference between the configurational energy after the displacement and that before the displacement (dU = Unew - Uo1d ). For the calculation of interaction energy, the nearest periodic image convention [85] is used. The two remaining moves in the GCMC are the creation and destruction of a particle. They are selected with equal probability. In the creation move, a particle is created at a random position within the simulation box that already contains N particles. The newly inserted particle is denoted as the (N + 1)th particle. The insertion has the following probability of acceptance:

. {1 P = nun

V exp { [JL - U(N + 1) + U(N)]}} , A3(N + 1) kT

(11.34)

where V is the simulation box volume. In the destruction move a particle is selected in random and removed from the box. The selected particle is assigned as the Nth particle, with no loss of generality. The probability of such removal is

. {A

3

N exp {-[JL+U(N-1)-U(N)]}} P = ffiln 1, - V kT

(11.35)

The GCMC, in principle, is easy to apply and its extension to mixture is straightforward.

11.5.1.2

Gibbs ensemble Monte Carlo

Another method that is very useful in determining isotherm is the GEMC simulation [88]. This method was first developed for studying adsorption in cylindrical pores. It was later applied to study adsorption in slit pores [89]. In this method, the coexistence of two phases can be simulated without the need to establish the interface between them. As such the method can be used to study the vapor-liquid equilibria, and the low and high densities in a pore (phase transition in pores). Another advantage of the method is that, there is no need for the explicit determination of the free energy or chemical potential of the two phases. The MC steps are designed so that at equilibrium there will be equality between pressure, temperature, and chemical potential between the two phases. Because there is no need to consider the interface joining

11.5

Monte Carlo Simulations

259

the two phases, the two coexisting phases can be simulated in two separate simulation boxes. One phase is simulated in box I, and the other phase is in box II. The system of two boxes is considered such that the total volume, total number of particles, and temperature are remained constant during the course of simulation. In this GEMC, like the case of GCMC, there are three basic moves. The first move is the displacement of particle. This can be done by choosing a box in random (with equal probability between box I and box II) and then a particle in that box is chosen randomly. This particle is displaced to a new position, and the acceptance or rejection of this move will follow the usual rule of acceptance commonly used in MC simulation, as we have described before for GCMC. The second type of move is the interchange of particle between the two boxes. In this move, a box is selected in random, say box II, and then a particle is selected in random in this box and moved from this box to box I at a random position. This move has the probability of acceptance as given in Eqn (11.33) with d U being given by (11.36) where dUi (i = I, II) is the energy change that occurs in simulation box i, and N i and ~ are the number of particles in and the volume of the box i, respectively. The number of attempts to perform this move is such that the success in interchange is about 2%. The third move in the GEMC is the volume exchange. Let d V be the volume change. A box is chosen in random, say box I, and its volume is decreased by d V (i.e., the volume of box II is increased by d V to maintain constant total volume). The positions of all particles in those two boxes are scaled linearly according to the change in the linear dimensions of the two boxes. For example, if the box lengths of box I before and after the change in volume are ~old and ~new, respectively, then the x-positions of all particles after the volume change are (the same applies for the y- and z-positions) xjnew = xjo1d (z;ew / ~old). The probability of acceptance for this move is given as in Eqn (11.33) with dU being given by

We have described the three basic moves for the GEMC simulation. They are for spherical molecules. For complex molecules, we have an additional move to displacement, which is the orientation of the molecule. The GEMC just described can be used to study the phase equilibria, e.g., vapor-liquid equilibria or either pure fluids or mixtures. For phase equilibria in pore, this method has been applied to cylindrical pore [88]. This method basically involves the simulation of two simulation boxes. If the two boxes are volumes within the pore (called pore-pore GEMC), the method provides

Chapter 11 Porous Texture Characterization from Gas-Solid Adsorption

260

directly the densities of the two phases, if the phase transition exists. Unfortunately, this pore-pore GEMC does not provide the chemical potential at which the transition takes place. It can be found by either applying the Widom method or using the phase densities obtained from the pore-pore GEMC in the GCMC simulation curve. Instead of using the pore-pore GEMC, the pore-fluid GEMC can be carried out to determine the equilibrium between pore and bulk phase directly [90].

11.5.2 Monte Carlo Simulation for Slit Pores

The GCMC simulation can be readily performed for a set of pores of various widths of interest. The result will be a set of local isotherms. Of interest in pore characterization are the local isotherms for argon at 87.3 K and nitrogen at 77 K. The figures in Fig. 11.6 typically show the local "isotherms of argon at 87.3 K for slit pores having width 8, 10, 20, and 30 A. These isotherms are presented as pore density (kmol/m3 ) vs pressure (Pa). The pore density is defined as the number of moles divided by the available volume for adsorbate molecules.

1.0 M

M~ 0.8 \.. ,.:":,,,~ '.,'.' ': ,..

a 0.8

~

~c 0.6

~ 0.6 C

~

< .• ,....•

,.,+

,;, \

I'

; •... ,.,.., .,

, "."i

'·','·i.····,··.··,·.. ·.·.·,;,·· . ' .. ' , ; ,' , ~

'.,.•,.,

;

".

"""'."1

o

.'

0..

] 0.2 +.. ,.,.~,.".:+ ....

0.0 1~1~1~1~1~1~1~1~1~1~ Reduced pressure

v .'" , ....

't ...., .. ··'·'·:"1

."~"":';;'::'" ...,..;.,,'~+ ...,.. '.,';"'+ ..,. "''''''''l-'''' ";"", ,": ....,..,·'·'··"1

0.0 +--'-'--'+--~""'IF-'--'-'-+--'-~---'---'"-T--'--'-"""+--'-~~ 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 10° 101 Reduced pressure

.

1.0 J\.. t-'r

a

<·,,~.

.. ,...• ,.. ;.,.•.,}

~ 0.4 + ..,.. ,..,."":,,....,. ·,····,•. '+···H· """o<,t ......, ........*,.... '.. <+'H:~ .. ·'.. ,·,·,.;:"....,..".:.••.,.",...<.. ,. ;.',.,~ ........, ":"<1

0.4

] 0.2

M

·..

~ ,.,.~

,.,.,.,.,..;. • ••

Q)

Q)

"0

o0..

I

,':v.,.,.'.;!

0.8

.~,...

~c 0.6 Q)

"0

~

o

0.4 ........

0..

~

-

] 0.2 0.0 10-6

.../ 10-5

10-4 10-3 10-2 Reduced pressure

10-1

10°

0.0 +---"-.....e4.....~-..E:::..;.-4------....-...r-----------+---'~...;.;.;f 10-5 10-4 10-3 10-2 10-1 10° Reduced pressure

Figure 11.6 Plot of pore density pu3 vs reduced pressure for argon at 87.3 K.

11.5

Monte Carlo Simulations

261

~

Here we see that for the 8 A pore, the change in density is continuous and this is due to the continuous filling of a single layer in that pore. A small jump in density at a reduced pressure of about 10-4 is due to the molecular arrangement to allow further s~all addition of molecules into the pore. The adsorption behavior in the loA pore is interesting. Here we observe a very sharp change in density at a reduced pressure of 2 x 10- 5 for adsorption branch and 1 x 10- 5 for desorption branch. This sharp change is the two-dimensional condensation of the two layers in that pore. ~The behavior of pore density vs reduced pressure in l~rger pores of 20 and 30

A is

typical of layering and pore filling. Take the

20 A for example, the behavior is that of layering for reduced pressure less than about 6 x 10-2 , at which the pore is instantly filled with adsorbed molecules. This is for adsorption branch. For desorption, the instantaneous evaporation occurs at about 2.5 x 10-2 • A clear hysteresis occurs between the adsorption and desorption branches.

11.5.3 Monte Carlo Simulation for Cylindrical Pores The methodology applied to cylindrical pores is identical to that presented earlier for slit pores. Figure 11.7 shows a set of local isothemls for argon adsorption at 87.3 K in cylindrical pores of various pore radii. The local isotherms in cylindrical pores in general exhibit general features that are the same as those for slit pores. Because the packing is better in slit pores, we do not see crossing of isotheffils in cylindrical pores and also the hysteresis is not as significant as in slit pores.

f-....

30

<5

E C Z" 20 "00

c

Q)

"'C

~ ~ 10

O+-:-...:...i...i.W~~~~~iIiiiiiii~:::::':"":"':..:.4-....:...i...:.':":'::+""":""':"~-":"":"'~

10-3

10-2

10-1

10 0

10 1

102

103

104

105

Pressure (Pa)

Figure 11.7 Adsorption of argC?n at 87.3 K in cylinders of various sizes (from left to right: 7, 8, 9, 10, 12, 15, 20, and 30 A).

262

Chapter 11 Porous Texture Characterization from Gas-Solid Adsorption

~ 11.6 ADDITIONAL FEATURES 11.6.1 Energetic Heterogeneity

The analysis we have dealt with in Sections 11.4 and 11.5 are applicable to energetic homogeneous surfaces. In reality, pores are heterogeneous and it should be considered in the modeling. The surface heterogeneity is modeled either by a periodic spatial variation of the solid-fluid potential [91-93], or in the framework of a patchwise model [94-96]. The latter is more general, and is often considered in the literature. 11.6.2 Pore Shape, Length, and Connectivity

Pores in solid adsorbent are usually assumed to have either slit or cylindrical shape. This is simply due to two factors. First is our lack of complete knowledge of the pore geometry, and the second factor is the complexity in the analysis of pore geometry other than slit and cylinder. Despite of these factors, many works [6, 97-105] have appeared in the literature to address these nonideal factors such as pore shape, pore length, and pore connectivity. 11.6.3 Numerical Inversion for Determining PSD

The pore size distribution function is an important characteristic of a porous solid. Given a pore size distribution j(H) and a set of local isotherms pCp, H) determined by any methods presented in Sections 11.3-11.5, the overall amount adsorbed is given by

a(p)

= f f(H)p(P, H)dlogH

(11.38)

The integral is defined with respect to logarithm of the pore width. Such a definition is preferable as the pore size usually varies over a wide range. Equation (11.38) is the Fredholm integral equation ofthe first kind, with pCp, H) being the kernel. The numerical inversion for determining PSD functionj(H) is achieved by discretizing the Fredholm equation as follows: N

a(p) == L Wi"kPk(P)

(11.39)

k=l

where N is the number of interval; w is the quadrature interval w = log (HN / H o) / N; H o and H N are minimal and maximal values of the pore width, respectively. Let a~XP = aexp(pi) be the experimental values of the amount adsorbed, measured in m points (1 ::s i ::s m). The PSD corresponds to the set of N values ofi"k, which should be chosen to provide the minimum of the residual 2 1{gj [a (Pj) - a~XP] } , where gj is a weighting coefficient.

L:::

11.7

Conclusions

11.6.3.1 Regularization method The numerical inversion belongs to the class of ill-posed problems. First, the distribution function is very sensitive to experimental errors, which may lead to artificial peaks and gaps in the PSD curve, sometimes producing even physically unrealistic negative values of the PSD function. Second, the result of inversion strongly depends on the kernel. If the model is not adequate and does not generate quite correct local isotherms, the PSD function might be very complex and partly negative. This problem may be overcome by smoothing the PSD function using the Tikhonov method of regularization [106-108]. This method, as applied to adsorption, has been comprehensively described in a number of papers [69, 109-112]. The idea of the regularization method is to introduce a "stabilizer" n to the residual: m

ffi =

L {gi [a (P;) -

a~] }

2

+ an

(11.40)

;=1

where a is a small positive parameter of regularization. There are different forms of the regularization function n, but the following form has been used in the literature [112, 113]: N-l

n = w- L 1

(h-1 - 2fTe +!k+l)2

(11.41)

k=2

Minimization of the residual min Eqn (11.40) cannot lead to the minimum of the root-mean-square deviation and the regularization function simultaneously. The regularization parameter a allows us to choose an appropriate compromise between smoothness of the PSD function and acceptable error norm. Of course, this choice is quite subjective and there are no universal recommendations. In most cases it is necessary to rely on experience and intuition. The DFT and GCMC methods have been increasingly applied by many to derive the effective PSDs for carbons [15,25, 114-131]. Most of these works use nitrogen at 77 K and argon at 87.3 K.

~ 11.7 CONCLUSIONS We have presented in this chapter a review of a number of advanced tools for pore characterization of carbon and its derivatives. Their method developments are presented briefly to higWight their importance in pore characterization.

Chapter 11 Porous Texture Characterization from Gas-Solid Adsorption

ACKNOWLEDGMENT This work is supported by the Australian Research Council.

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73. Kohn, W. and Sham, L. (1965). Self consistent equation including exchange and correlation effects. Phys. Rev. A, 140, 1133-8. 74. Mermin, N. (1965). Thennal properties of the inhomogeneous electron gas. Phys. Rev. A, 137, 1441-3. 75. Evans, R., Marconi, M.B., and Tarazona, P. (1986). Fluids in narrow pores: adsorption, capillary condensation, and critical points.]. Chem. Phys., 84(4), 2376-99. 76. Seaton, N.A., Walton, J.P.R.B., and Quirke, N. (1989). A new analysis method for the determination of the pore size distribution of porous carbons from nitrogen adsorption measurements. Carbon, 27, 853-61. 77. Tarazona, P. (1985). Free energy density functional for hard sphere. Phys. Rev. A, 31,2672-9. 78. Tarazona, P. (1985). Erratum: free energy density functional for hard sphere, Phys. Rev. A, 31, 2672 (1985). Phys. Rev. A, 32, 3148. 79. Tarazona, P., Marconi, U.M.B., and Evans, R. (1987). Phase equilibria of fluid interfaces and confined fluids. Non-local versus local density functionals. Mol. Phys., 60,573-95. 80. Carnahan, N. and Starling, K. (1969) Equation of state for non-attracting rigid sphere.]. Chem. Phys., 51, 635-6. 81. Weeks, J.D., Chandler, D., and Andersen, H.C. (1971). Role of repulsive forces in determining the equilibrium structure of simple liquids.]. Chem. Phys., 54, 5237-47. 82. Olivier, J. (1995). Modeling physical adsorption on porous and nonporous solids using density functional theory.]. Porous Mater., 2, 9-17. 83. Ustinov, E. and Do, D.D. (2003). Non-additivity of attractive potentials in modeling of N 2 and Ar adsorption isothenns on graphitized carbon black and porous carbon by means of density functional theory. Part. & Part. Sys. Charac.]. 21, pp. 161-9. 84. Frenkel, D. and Smit, B. (2002). Understanding Molecular Simulation. San Diego: Academic Press. 85. Allen, M. and Tildesley, D. (1987). Computer Simulation of Liquids. Oxford: Clarendon Press. 86. Nonnan, G.E. and Filinov, V.S. (1969). Investigation of phase transitions by a Monte Carlo method. High Temp. (USSR), 7, 216-22. 87. Adams, D.J. (1975). Grand canonical ensemble Monte Carlo for a Lennard-Jones fluid. Mol. Phys., 29, 307-11. 88. Panagiotopoulos, A. (1987). Adsorption and capillary condensation of fluids in cylindrical pores by Monte Carlo simulation in the Gibbs ensemble. Mol. Phys., 62,701-19. 89. Lastoskie, C., Gubbins, K.E., and Quirke, N. (1993). Pore size heterogeneity and the carbon slit pore: a density functional theory model. LAngmuir, 9(10), 2693-702. 90. Lastoskie, C.M., Quirke, N., and Gubbins, K.E. (1997). Structure of porous adsorbents: analysis using density functional theory and molecular simulation. In Studies in Surface Science and Catalysis, Vol. 104 (Equilibria and Dynamics of Gas Adsorption on Heterogeneous Solid Surfaces), Elsevier, Amsterdam, pp. 745-75. 91. Gac, W., Patrykiejew, A., and Sokolowski, S. (1997). Monte Carlo study of adsorption in energetically and geometrically nonunifonn slit-like pores. Thin Solid Films, 298, 22-32.

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108. Tikhonov, A.N. and Arsenin, V.Y. (1977). Solutions of nl-Posed Problems. New York: Wiley. 109. Mamleev, V. She and Bekturov, E.A. (1996). Improved method for analysis of energetic heterogeneity of surfaces from adsorption isotherms. Langmuir, 12,441-9. 110. Mamleev, V. She and Bekturov, E.A. (1996). Numerical method for analysis of surface heterogeneity in a case of finite diversity of adsorption sites. Langmuir, 12,441-9. 111. Bhatia, S.K. (1998). Determination ofpore size distributions by regularization and finite element collocation. Chem. Eng. Sci., 53, 3239-49. 112. Davies, G.M., Seaton, N.A., and Vassiliadis, V.S. (1999). Calculation of pore size distributions of activated carbons from adsorption isotherms. Langmuir, 15, 8235-45. 113. Jaroniec, M., Kruk, M., Olivier, J.P., and Koch, S. (2000). A new method for the accurate pore size analysis of MCM-41 and other silica based mesoporous materials. Stud. Surf. Sci. Catal., 128, 71-80. 114. Lastoskie, C., Gubbins, K.E., and Quirke, N. (1993). Pore size distribution analysis of microporous carbons: a density functional theory approach.]. Phys.Chem., 97, 4786-96. 115. Kruk, M., Jaroniec, M., and Bereznitski, Y. (1996). Adsorption study of porous structure development in carbon blacks.]. Colloid Interface Sci., 182, 282-8. 116. Choma, J. and Jaroniec, M. (1997). Influence of the pore geometry on the micropores size distribution function of active carbons. Adsorp. Sci. Techno I. , 15, 571-81. 117. Kruk, M.,Jaroniec, M., and Sayari, A. (1997). Application oflarge pore MCM-41 molecular sieves to improve pore size analysis using nitrogen adsorption measurements. Langmuir, 13,6267-73. 118. Kruk, M., Jaroniec, M., and Gadkaree, K. (1997). Nitrogen adsorption studies of novel synthetic active carbon.]. Colloid Interface Sci., 192, 250-6. 119. Li, Z., Kruk, M. Jaroniec, M., and Ryu, S. (1998). Characterisation of structural and surface properties ofactivated carbon fibres.]. Colloid Interface Sci., 204, 151-6. 120. Kruk, M.,Jaroniec, M., and Choma,J. (1998). Comparative analysis ofsimple and advanced sorption methods for assessment of microporosity in activated carbons. Carbon, 36, 1447-58. 121. Kruk, M., Li, Z., Jaroniec, M., and Betz, W. (1999). Nitrogen adsorption study of surface properties of graphitized carbon black. Langmuir, 15, 1435-41. 122. Kruk, M., Jaroniec, M., and Gadkaree, K. (1999). Determination of the specific surface area and the pore size of microporous carbons from adsorption potential distributions. Langmuir, 15 1442-8. 123. Ryu, Z., Zheng, J., Wang, M., and Zhang, B. (1999). Characterization of pore size distributions on carbonaceous adsorbents by DFT. Carbon, 37, 1257-64. 124. EI-Merraoui, M., Aoshima, M., and Kaneko, K. (2000). Micropore size distribution of activated carbon fibre using the density functional theory and other methods. Langmuir, 16, 4300-4. 125. Scaife, S. Kluson, P., and Quirke, N. (2000). Characterization of porous materials by gas adsorption: Do different molecular probes give different pore structures? ]. Phys. Chem., 104,313-18.

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POROUS TEXTURE AND SURFACE CHARACTERIZATION FROM LIQUID-SOLID INTERACTIONS: IMMERSION CALORIMETRY AND ADSORPTION FROM SOLUTION Renaud Denoyel, FrancQise Rouquerol, and Jean Rouquerol MADIREL, CNRS-Universite de Provence, Marseille, France

Contents 12.1 Introduction 12.2 Immersion Calorimetry of Carbons into Pure Liquids 12.3 Characterization of Carbons by Adsorption from Solution

References

273 274

289 297

>

12.1 INTRODUCTION

Characterization of carbons with help of liquids is especially interesting when the material is intended to be used in a liquid medium. This is in line with the following conclusion of the IUPAC Recommendations for the Characterization of Porous Solids [1] "The selection of a method of characterization must start from the material and from its intended use. The method chosen must indeed assess a parameter related as directly as possible to phenomena involved in the application of the porous material." It therefore makes sense using liquids to characterize carbons when they are to be used for instance in liquid purification, liquid-solid heterogeneous catalysis, or liquid suspensions (and not to rely only, in spite of its popularity, on the characterization by gas adsorption). Adsorption by Carbons ISBN: 978-0-08-044464-2

© 2008 Elsevier Ltd. All rights reserved.

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Chapter 12 Porous Texture and Surface Characterization from liquid-Solid Interactions

When one brings a carbon in contact with a liquid, the phenomena involved can be 1. the wetting ofthe carbon surface, which depends on the liquid used (hydrophobic, hydrophilic) and on the proportion ofpolar functions on the surface, 2. the penetration of molecules into micropores large enough to accommodate them (in case of a solution, the accessibility of a micropore may depend on the solute), and 3. the formation of a first layer with either special composition or/and special interaction with the solid surface. These phenomena, which, as we shall see, allow to assess information about the micropore size, the surface area, and some aspects of the surface chemistry, can be studied either with a pure liquid (immersion calorimetry) or with a solution (adsorption from solution). We shall successively deal with these two cases.

12.2 IMMERSION CALORIMETRY OF CARBONS INTO PURE LIQUIDS Two questions are raised by the title of this main section and deserve being answered immediately, i.e., (i) why are we dealing with calorimetry and (ii) is immersion calorimetry reserved to pure liquids? The answers are that (i) the heat exchanged on wetting is a precious data to be exploited, for sure (as we shall see), whereas (ii) the way devised to carry out a clean and precise immersion calorimetry experiment requests a pure liquid and is not adapted for the study of adsorption from solutions. In this section, we should certainly pay tribute to Zettlemoyer [2], who, with his coworkers, was the first to extensively apply immersion calorimetry for the study of adsorbents. 12.2.1 Experimental

In principle, nothing is as simple an immersion calorimetry experiment, for which the basic requirements are only a small quantity of powder, a liquid and a calorimeter. In reality, if it is easy to measure a "heat," it is more difficult to measure a reliable and meaningful change of a state function (energy or enthalpy). This requires indeed 1. A well-defined initial state, which involves both the nature and purity of the immersion liquid and, exactly as important, the extent of outgassing of the porous carbon. 2. A well-defined final state, which means a good, homogeneous wetting of the solid. 3. A procedure allowing to measure or calculate any exchange of heat or work taking place on immersion.

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Immersion Calorimetry of Carbons into Pure Liquids

275

The well-defined initial state requires to use high-purity liquids, specially when these are hydrocarbons (well-suited for carbons, which they easily wet); it was early shown indeed, by Harkins and Boyd [3], that very small amounts of a polar impurity like water dramatically increases the enthalpy of immersion, since the latter is preferentially and strongly adsorbed on the polar functions of the surface. Obtaining a reproducible state of outgassing for a microporous carbon is even more critical, specially for microporous carbons. Before deciding on the outgassing procedure, one should have in mind the following:

1. Immersion calorimetry requires a vacuum outgassing, in order to avoid the wetting of the pores to be partly prevented by the presence of a gas. 2. The goal of that vacuum outgassing is not to obtain a "perfectly clean" suiface or a "fully outgassed" material, with the danger of damaging it and changing for instance its extent of activation. The outgassed material should indeed be fully representative of the material in the state in which it will be used. 3. What one needs above all is a highly reproducible and well-defined outgassing thermal path. This means that the heat treatment is not only expected to be reproducible within a given laboratory, with a given setup and with a number of unknown conditions (like the partial pressures of the self-generated gases over the sample at any time of the heat treatment, like the temperature gradients within the sample, etc.) depending for instance on the sample mass and on the shape and size of the sample bulb. 4. An efficient and general solution to this problem is the use of Controlled Rate Outgassing [4] (a variant of the more general approach of controlled rate thermal analysis (CRTA) [5]). With this approach, a low, constant, outgassing rate can be selected, so as to lower at will any residual pressure or temperature gradient within the sample, whereas the residual pressure in the close neighborhood of the sample is continuously controlled and monitored. As a consequence, the parameters defining the "thermal path" followed by the sample are continuously controlled and recorded. A further interest of this outgassing method is that it is specially suited for very fine carbon powders since it allows to set the rate of gas evolution low enough to avoid any spurting of the powder out of the bulb and into the vacuum line. 5. The final outgassing temperature should be selected wisely, after carrying out a first, exploratory, CRTA or Thermogravimetry experiment; a good final outgassing temperature is one where most of the physisorbed water and CO 2 (and sometimes other organics) has left and where the porous structure and chemical nature of the sample remains untouched. Such a temperature most often corresponds to a clear inflexion point on the CRTA or TG curve. For porous carbons, this temperature usually lies between 120°C and 300°C. In the absence of any CRTA or TG information, a final outgassing temperature of 250°C is advisable in case the carbon is ultramicroporous. 6. Once a well-defined and reproducible state of outgassing is reached, it must be kept absolutely untouched until the time of the immersion which, in a microcalorimeter, cannot occur before several hours, for the sake of thermal

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Chapter 12 Porous Texture and Surface Characterization from Liquid-Solid Interactions

equilibrium. An efficient way to maintain the state of outgassing over hours is to avoid any transfer of the sample from an outgassing bulb to an immersion bulb (even in a glove box) and therefore to carry out the sample outgassing directly in the glass ampoule to be used in the immersion experiment.

The well-defined final state requires a good, homogeneous, wetting by a liquid of known composition. Such a good wetting is obtained with help of the vacuum that favors the intrusion ofliquid into the pores, whereas to be sure of the liquid composition in the close neighborhood of the adsorbent one has practically no choice: only a pure liquid must be used, as already pointed out in the introduction of this section on immersion calorimetry. This is indeed the only way, in the absence of any possible stirring, to avoid any unknown composition gradient in the close vicinity of the carbon surface. The procedure allowing to measure or calculate any exchange of heat or work taking place on immersion requires a careful analysis - and then, a careful control - of the events occurring during the immersion experiment. These events may include the breaking of the glass ampoule, the friction (against O-rings) of the rod used to produce the breakage, the vaporization requested to fill the previously evacuated void volume of the sample bulb, the continuous vaporization into the surrounding atmosphere (in case the experimental assembly is not tight), the work of the atmospheric pressure upon the surface of the liquid as its level is lowered during the immersion process and also, simultaneously, the simple loss of potential energy of the same liquid, as pointed out by Everett et al. [6]. In order to meet the requirements listed above, two different setups had to be devised for wetting and nonwetting systems, respectively.

12.2.1.1

Setup for wetting systems

A relatively simple setup could be designed for wetting systems [7], like carbons immersed into hydrocarbons, and is represented in Fig. 12.1. It operates as a closed system (to allow a close control of the immersion phenomenon) and includes the following elements: 1. A Tian-Calvet heat-flow microcalorimeter which, due to the 480 thermocouples of its thermopile, ensures all at once a good isothermicity of the experiment and a high sensitivity allowing to use a small sample (for an activated carbon, typically 50-100 mg) relatively easy to wet. 2. A glass bulb, containing the solid sample, with a tiny brittle end designed to give rise to a heat of breakage on the order of 5 mJ. This heat is small enough to allow some variations from one bulb to the other with no incidence on the final measurement. In case of a simple sphere, even thin-walled, the heat of breakage usually ranges between 0.5 and 2J, which is on the order of magnitude of the enthalpy of immersion to be measured and which is therefore not acceptable. The bulb is sealed after outgassing and before introduction into the microcalorimeter.

12.2

Immersion Calorimetry of Carbons into Pure Liquids

277

3. A glass rod used to depress and break the bulb and which tightly passes through O-rings in order to prevent any continuous vaporization of the liquid to the surrounding atmosphere. This tightness also avoids the atmospheric pressure to provide any work to the system when the liquid level is lowered on immersion. The various steps of the experiment with the above setup are the following: • a glass bulb is blown, with a brittle end in the bottom and an outlet open tube in the opposite side • the carbon sample is introduced and weighed in the bulb • a vacuum stopcock is fitted to the outlet tube and then connected to the outgassing CRT A system; when needed, it can further be connected to a chamber with a device providing a controlled vapor pressure in order to obtain the desired precoverage • the ampoule is sealed • it is placed in the calorimetric cell containing the liquid and left 2-3 h until a satisfactory thermal equilibrium is reached (which means that the sample and surrounding "isothermal block" temperatures are identical within better than 10-5 K) • the brittle end is broken • the heat-flow recording is carried out over 30-45 min

...- - - - - - - - Glass rod

- - - - - - - - - - - - O-ring

O-ring - - - - Thermopiles '.------ Liquid 0'------

Solid Isothermal block

Figure 12.1 Closed-system setup for immersion calorimetry of powders in a Tian-Calvet heatflow microcalorimeter. (Adapted from [7].)

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Chapter 12 Porous Texture and Surface Characterization from Liquid-Solid Interactions

The measured heat includes, together with the energy of wetting, the heat of breaking and the heat of vaporization (the major corrective term) which, fortunately, lend themselves to an easy evaluation from blank experiments with empty ampoules. Plotting indeed the measured heat as a function of the volume (or mass) of liquid which has filled the ampoule provides a straight line whose slope is proportional to the vaporization energy and whose intercept provides the mean value of the heat effect due to the breaking of the brittle end. This calibration curve simply requires, for application, weighing the bulb before and after each immersion experiment. It provides a corrective term which needs being divided by the weight of outgassed solid, itself derived from the difference between the weight of the stopcock and bulb assembly under vacuum, without sample, and the weight of the same assembly, but now including the sample, at the end of the outgassing procedure. Using modern isothermal calorimeters, experiments with a reproducibility better than 20 m] can be achieved. This is therefore the value one has to compare with the expected immersion energy in order to predict the feasibility of an experiment and to estimate the sample mass to be used. The immersion energies range between a few m]/m 2 (water/Teflon) and a few hundred m]/m 2 (specially carbons in organic solvents, but also inorganic oxides in water). Up to a few hundred milligrams of sample can be introduced in the bulb. One will notice that such a setup operates at constant volume (it is a closed system) rather than at constant pressure (expansion of the gas into the previously evacuated bulb lowers the starting pressure). Strictly speaking, this allows assessing an internal energy of immersion. Now, since this energy refers to an immersion process with only dense phases (only a liquid and a solid are involved in the definition of the energy of immersion), the change experienced by the p V term is negligible as compared to the change in internal energy. For this reason, the immersion enthalpy and the immersion energy can be used for each other, since they practically have the same value.

12.2.1.2

Setup for nonwetting systems

For nonwetting systems, like water with hydrophobic carbons, another approach had to be devised [8]. It is more expensive, but it can be applied to any systems (wetting or not) and does not need any glass blowing. The problem is that with a nonwetting system, i.e., with a contact angle higher than 90°, the wetting of a porous medium (either with intra- or interparticle pores) is not possible at a pressure lower than the saturation pressure. As a consequence, the immersion setup must be able to exert some controlled pressure to produce the intrusion of liquid into the pores. Its principle is represented in Fig. 12.2. The setup, which is all-metal, is able to withstand pressures up to 700 bar. It includes a high-pressure, high-accuracy, computer-controlled syringe pump and a stainless-steel, cylindrical, calorimetric cell.

12.2

279

Immersion Calorimetry of Carbons into Pure Liquids

Liquid supply

High-pressure syringe pump

Thermopile Isothermal block

Figure 12.2 High-pressure liquid intrusion calorimetry setup for the determination of energies of wetting for nonwetting systems. (Adapted from [39].)

The experiments are carried out in four steps: 1. The carbon sample is weighed in the calorimetric cell (out of the microcalorimeter) and then connected to vacuum for outgassing. 2. The cell is introduced into the microcalorimeter and left to reach thermal equilibrium. 3. The outlet valve of the syringe is open to let the vapor contact the carbon sample. 4. The pump is then slowly operated to introduce the liquid up to a predefined pressure of c. 1 bar. 5. Intrusion ofliquid into the porous medium is carried out stepwise, with fixed volume increments; extrusion is carried out in the same way. At each step, the total heat exchanged, the total volume intruded, and the final pressure are measured and recorded. The heat measured in step (3) corresponds to the adsorption of an unknown amount of vapor on the carbon surface. Now, in case of a wetting system, we know that the conditions are then fulfilled to have a multilayer adsorbed. This means that the heat measured in step (4) corresponds to the immersion energy of a precovered solid, so that it can be used for the surface area determination by the modified Harkins and Jura method [7]. The addition of the heats measured in steps (3) and (4) after suitable correction leads to the usual immersion energy. If the full wetting is not reached at saturation pressure it is then needed to proceed to step (5). More details about this procedure and the way to get experimental data are described elsewhere [9].

Chapter 12 Porous Texture and Surface Characterization from Liquid-Solid Interactions

280

12.2.2

Thermodynamics of Immersion

A summary of the main relationships which are needed for the processing of immersion calorimetry is proposed hereafter. More details may be found in the recent literature about their derivation [3, 9, 10]. The wetting state of a liquid-vapor-solid system depends on the value of the interfacial tensions y defined, for a given interface, as the free energy per unit area at constant volume and temperature:

y-

aF) (-aA

(12.1) TV

Since the term y depends on the nature of the phases on each side of the interface, these phases must be stated. Hence the following symbols generally used to denote the surface tension at various interfaces:

Ys at the solid-vacuum interface Ysv

at the solid-vapor interface

Ys1 at the solid-liquid interface Y1v

at the liquid-vapor interface

For the variation of the surface energy per unit area it can be shown [4] that

(-au) aA

(ay) aT

-y-TT V

(12.2) A

This equation is applicable to any interface, allowing the energies of extension per unit area of the solid-vacuum, solid-vapor, solid-liquid, and liquid-vapor interface to be defined (us' usv ' Us1' and U1v' respectively). Nevertheless, these energies as well as the interfacial tensions are rigorously measurable only in the case of the liquid-vapor interface. In conditions where a solid is in equilibrium both with a liquid and its vapor, a relation can be obtained through the Duprey oung equation between the three interfacial tensions and the angle () at the three phases contact line: Ysv

= Ys1 + Y1v cos ()

(12.3)

This equation is valid only for a flat solid surface. () is called the contact angle and its value is used to define the wettability of a surface: • for () = 0° the surface is completely wetted by the liquid • for 0° < () < 90° the surface is partially wetted • () > 90° is the situation of nonwetting These various situations can all be encountered with porous solids. However, because immersion calorimetry has been mainly used in the case of complete wetting the two following paragraphs are devoted to this situation. The case of nonwetting systems will be analyzed afterward.

12.2

Immersion Calorimetry of Carbons into Pure Liquids

281

In any thermodynamic experiment, including calorimetric, one needs well defined initial and final states in order to determine which state function may be derived from data. In the case of wetting, several types of experiments and definitions were proposed depending on the initial and final states [4, 11-15]: immersional wetting, adhesional wetting, spreading wetting, and condensational wetting. Adhesional wetting is a process where two starting interfaces (solid-gas and liquid-gas) are replaced by one (solid-liquid). It cannot be studied in the case of powders because the area of the starting liquid-gas interface is too small. Condensational wetting is the formation of a film by adsorption. Immersional wetting corresponds to a process where a solid-vacuum or solidvapor interface is replaced by a solid-liquid one. When starting from a solidvacuum inteiface, the free energy variation during the process is (per unit area)

ilF = 'Ysl- 'Ys

(12.4)

where 'Ysl and 'Ys are the solid-liquid and solid-vacuum interfacial tensions. The energy variation which is experimentally measured during this process (for example with the calorimetnc setups described above) is the "immersion energy." It can be related to the interfacial energies by using standard thermodynamic derivations, leading to (12.5) Now, when starting from a solid-vapor inteiface (i.e., a solid surface in equilibrium with a vapor at pressure P), the free energy variation is

ilF = 'Ysl - 'YSy(P)

(12.6)

where 'YSy (P) is the interfacial tension of the solid-vapor interface when the equilibrium pressure is P. The heat evolved during this process can be measured by the procedure proposed by Partyka et al. [7]. It allows determining the immersion energy of a precovered surface. An interesting application is the determination of the specific surface area by the modified Harkins and Jura method that will be described afterward. It can be written as follows: (12.7)

Spreading wetting corresponds to a process where a solid-vapor interface is progressively replaced by a solid-liquid interface. The corresponding free energy variation per unit area is (12.8) Provided the liquid-vapor interface area is not modified during the process. pO is the saturation pressure of the liquid. In fact this saturation pressure is fixed

282

Chapter 12 Porous Texture and Surface Characterization from Liquid-Solid Interactions

by the curvature of the liquid-vapor interface. Either for a small droplet or for a liquid front forced to penetrate into a pore, the equilibrium vapor pressure p+ is higher than the standard saturation pressure pO which is valid only for a flat liquid-vapor interface. The relationship between the actual vapor pressure p+ and pO may be given by the Kelvin equation = 2 ( P+) po r

RTln _

Ylv

(12.9)

k

where rk is the curvature radius of the liquid-vapor interface. From Eqn (12.8) the internal energy variation of this type of wetting process is (12.10)

This energy variation is measurable with the setup described in Fig. 12.2 when nonwetting porous systems are considered (() > 90°). When the contact angle is smaller than 90° it is very difficult to carry out a calorimetric experiments corresponding to spreading wetting because it is impossible to efficiently control any initial state where the powder would be unwetted, though in equilibrium with the saturating vapor:capillary condensation should occur between the particles.

12.2.3

Applications

Immersion energy is an integral quantity, which corresponds to the average interaction of the liquid with the entire solid. Each experiment only provides one figure, whereas, e.g., adsorption isotherms can discriminate between various kinds of successive interactions as the equilibrium pressure increases. Nevertheless, a careful analysis of the parameters contributing to the immersion energy allows to derive a most useful information about the solid surface. The immersion energy depends indeed on • The extent of the solid surface: for a given liquid-solid system, the immersion energy increases with the surface area (applications: measurement of the surface area either by comparison, using a reference material, or by applying a modified "absolute" Harkins and Jura method). • The chemical nature of the surface: for a given liquid, the immersion energy depends on the chemical nature of the surface: if the liquid is polar, the immersion energy increases with the polarity of surface chemical functions (applications: study of the influence of a heat treatment on the quality and amount of surface chemical functions, study of wettability). • The chemical nature of the immersion liquid: for a given surface, the immersion energy depends on the chemical nature of the liquid (applications: determination of the dipolar moment of surface sites by immersion in liquids of increasing polarities; analysis of the hydrophobic character).

12.2

Immersion Calorimetry of Carbons into Pure Liquids

• Porosity of the solid: if the solid is microporous, the molecules of the liquid may be too large to penetrate into all the pores (application: derivation of a micropore size distribution from the immersion energies in liquids of similar chemical nature but different molecular size). In the following paragraphs, we discuss the use of immersion calorimetry for the assessment of the surface chemistry, wettability, surface area and porosity of carbons. 12.2.3.1

Characterization of surface chemistry

The chemical nature of a solid determines its adsorptive and wetting properties. Now, the energy of immersion mainly depends on the surface chemistry but also, to some extent, on the nature of the bulk solid. For example, the interaction between water and silica has contributions from the bulk Si0 2 together with contributions from the silanol groups of the interface. Polar molecules are very sensitive to the local surface chemistry, whereas nonpolar molecules are more sensitive to the bulk composition. Interactions between a bulk liquid and a bulk solid through an interface are often described in terms of Hamaker constant [16]. Immersion calorimetry in apolar liquids was proposed to estimate the Hamaker constant [17]. The sensitivity of immersion calorimetry to the surface polarity has justified its use for characterising the surface sites. Dividing the energy of immersion into its various contributions leads to the following relationship: (12.11)

where E rep , stands for repulsive interactions at the interface, Ed is the contribution of dispersive forces (integrated over the entire volume) and Eo: is the energetic contribution of the polarity induced by the electric field at the interface. EJL is the contribution of the polar functional groups at the interface. It can be estimated from the average electric field at the interface F and the dipole moment JL of the liquid, as pointed out by Zettlemoyer et al. [18] or Morimoto and Suda [19]): (12.12)

where k is a constant which depends on the density of liquid molecules in the vicinity of the interface. This approach was validated by the nearly linear behavior observed when the immersion energy of a polar solid like titania is plotted as a function of polarity of the immersion liquid. It was also shown [18] that the immersion energy of a carbonaceous nonpolar surface is nearly independent of the immersion liquid. The slope allows one to calculate F, whereas the intercept at the origin provides the dispersive contribution. Numerous surface modifications were followed by immersion calorimetry. The energy of immersion and the kinetics of the process may help to distinguish between the removal ofphysisorbed water and the dehydroxylation as a function

284

Chapter 12 Porous Texture and Surface Characterization from Liquid-Solid Interactions

of outgassing temperature. Modifications making a carbon surface more or less hydrophobic were thus studied by immersion in water [20-22] but other polar molecules, like alcohols, were also useful to follow changes of polarity of carbon surfaces on oxidation [22-25]. Simple relationships were observed between the oxygen content, the acid-base properties and the immersion enthalpy of carbon surfaces in water [26-28]. The sensitivity to surface polarity also allowed to follow the regeneration of activated carbon surfaces [29]. In all above examples, the starting carbon was under vacuum. The result is averaged over all sites present on the surface. If information about the energetic distribution of surface sites is desired, it is necessary to carry out several immersion experiments after precovering the surface with the vapor of the immersion liquid up to various extents. This allowed Zettlemoyer et al. to plot "immersion isotherms", which are the fingerprint of the energetic distribution of the surface sites. Nevertheless, this is a time-consuming method which leads to the same information as that provided, in one experiment, by direct gas adsorption calorimetry, since the following equation holds [4]: (12.13) where d imm U( P) is the immersion energy after precoverage at the pressure P, d imm U the immersion energy under vacuum, uO" the molar surface excess energy and u1 the liquid molar energy. The difference uO" - u1 is assessed by gas adsorption calorimetry. In the case of porous solids, the main drawback of the immersion method is the filling of an unknown volume of pores during the precoverage step, unless the full adsorption isotherm of the vapor is previously known.

12.2.3.2

Characterization of wettability

Wettability is generally defined by the contact angle, which is the apparent result of the balance between interfacial free energies. Whereas it is relatively easy to "see it" and measure it on flat surfaces, its assessment on powders and porous solids is not straightforward. In the case of very hydrophobic porous solids (i.e., contact angles are >90°), it was shown by Gomez et al. [8] showed that both the pore size distribution and the contact angle can be assessed from a liquid intrusion experiment associated with calorimetry, like in the setup represented in Fig. 12.2. This approach is similar to mercury porosimetry, where the intrusion pressure and the intruded volume are continuously recorded, but, here, the extra measurement of the heat exchanged makes it possible, after appropriate correction for the compressibility of the liquid, to determine the variation of interfacial energy a,s the pore is progressively filled and therefore to evaluate the homogeneity of the surface. This interfacial energy only depends on the interfacial. tension and contact angle and it is involved in a process where

12.2

285

Immersion Calorimetry of Carbons into Pure Liquids

the solid-vapor interface is progressively replaced by a solid-liquid interface. For a reversible step, it can be shown [8] that

dU

=(T

dYlv

cos ( ) -

aT

d cos fJ + TYlv-- Ylv

aT

)

cos () dA

(12.14)

where () is the contact angle at equilibrium. Assuming that along the experimental intrusion path, be it reversible or not, the variation of interfacial energy is proportional to the wetted area, one can then plot the wetted area as a function of the pore size, which is a pore-size distribution curve. Its consistency was shown with the volume distribution obtained by applying the Washburn equation provided the (advancing) contact angle used for the calculation was constant. Also, the derived surface area compares reasonably well with the nitrogen-BET (BrunauerEmmett-Teller) surface area. This method therefore allows assessing, all at once, the pore size distribution, the contact angle and the homogeneity of the surface. If the advancing contact angle is lower than 90°, wetting is spontaneous inside the pores at a pressure equal or lower than the saturating pressure. Its measurement can be done by capillary rise. Nevertheless, this will only characterize the wettability of the external surface of the particles and not that of the internal surface of the pores. This is why, here again, calorimetric approaches were proposed to get an estimated value of the wettability in the case of powders. For example, Briant and Cuiec [30], showed that for a number of solid-liquid systems the following approximation holds: (12.15) This allows the ranking of a set of solids after their wettability by a given liquid, but only when the contact angle is zero. This approach was used to characterize the acid-base components of the surface tension [31, 32]. For values of the contact angle ranging from 0° to 90°, the method proposed by Spagnolo et al. [33] can be used. From the Young-Dupre equation and after integrating the Gibbs equation along the adsorption isotherm of the vapor, the following relations may indeed be derived:

-d imm U 1 -TIe - T [a (Ysl - Ys) / aT] cos () = - - - - - - - - - - - - - -

(12.16)

Ylv For solids of low energy, Spagnolo et al. [33] just keep the term which is evaluated to be 0.07 ± 0.02 from other sources [34]. Then cos () =

-~immu-0.07T

Ylv An equation of the form cos () =

-~immU

Ylv

+ TC

ays/aT, (12.17)

286

Chapter 12 Porous Texture and Surface Characterization from Liquid-Solid Interactions

where C is a constant, can be derived from Eqns (12.3) and (12.10) by assuming that the contact angle variation with temperature is independent of the nature of the system [10]. As stressed in the same paper, this equation is applicable only for systems with low value of immersion energy, which is precisely the case of carbons (and also, of course, of perfluorinated polymers). It should be pointed out that the methods used to evaluate wettability from calorimetric measurements have to be carefully used because they only lead to the energy part of the process and not to its free energy. Moreover, for contact angles above 90°, reliable experimental results, i.e., with full wetting, require the use of a high-pressure intrusion setup.

12.2.3.3 Characterization of surface area and porosity Theoretically, for a given chemical nature, the immersion energy of a nonporous solid should be proportional to the surface area and the corresponding coefficient should be available from a reference solid of known surface area. Nevertheless, the detailed surface composition and structure ofsolids with similar bulk composition and even crystallinity can be very different because of their chemical, mechanical or thermal history. Therefore, it would be unwise to use the relative measurement of surface area when both the surface and the immersion liquid are polar. Conversely, nonpolar liquids can be used for such a determination because the corresponding immersion energies are not sensitive to minute variations of the surface chemistry. This point will be addressed again later on in the case of microporous samples. Another way to derive a surface area is the Harkins and Jura "absolute method" [13], actually in its modified form by Partyka et al. [7]. The method is based on the "coating" of the solid particles by a water multilayer obtained at water saturating pressure and on the assumption that the liquid-vapor interface then surrounding each particle has the same area as the initially bare solid surface. This assumption usually does not hold because capillary condensation takes place and hides part of the initial area. The modification proposed lies on the observation that, when plotted as a function of either precoverage equilibrium pressure or adsorbed amount, the immersion energy of a nonporous solid in a wetting liquid drops down to a constant value once only 1.5-2 layers of water are preadsorbed. In these conditions, the area of the external water-vapor interface is closely comparable to that of the solid-water interface. Immersion of this system in water simply destroys the extemalliquid-water interface, whereas the energy of immersion is directly proportional to its area, after the following relationship:

dimmU = -A

( 'Ylv -

aYlV)

T aT

(12.18)

This equation is equivalent to Eqn (12.7), where ~sl - ~sv is replaced by ~lv· The method simply requires precovering the solid surface at a relative pressure corresponding to the plateau (a value slightly above 0.5 can be used safely

12.2

Immersion Calorimetry of Carbons into Pure Liquids

with water without any need for determining the whole graph of energy of immersion vs precoverage pressure). A surface area can then be determined without any assumption about the molecular cross section of the liquid. For a number of nonporous solids, the agreement was shown to be very good with the nitrogen-BET method. Nevertheless, one must keep in mind that the method requires the solid surface to be fully wetted by the liquid. In the case of carbons, a satisfactory wetting may require to use an alcane (like hexane) instead of water [13]. Furthermore, the method does not assess the surface area of micropores, which are filled during the precoverage process; in this case, it only assesses the "external" surface area, in a way similar to Sing's as method. We end this section with the characterization of microporou5 samples. An immersion experiment is a process where molecules initially in the bulk liquid are transferred to a solid-liquid interface. During this process, a number of liquidliquid bonds are transformed into liquid-solid bonds. The energetic balance, for the transfer of a molecule from the bulk liquid to a pore will depend very much on the relative size of the liquid molecule and the pore. If the pore size is such that only one molecule can penetrate, the enhancement of adsorbing potential will be of 2 and 3.68 for slit-shaped and cylindrical pores, respectively. Those calculations were performed by Everett and Powl [35] for the adsorption of one molecule interacting by only dispersive forces (Lennard-Jones type potential). Most interestingly, the above figures are very close to the ratio of the area covered by one molecule, in the corresponding pores, to its molecular cross section. These ratios are indeed 2 and 3.63, for slits and cylinders, respectively. It therefore looks appealing to extend this observation to any type of pore shape and to assume that, whatever it is, the immersion energy is simply proportional to the area accessible to the probe molecule [36] with a· coefficient which only depends on the solid-liquid system. This assumption can be checked, for pore sizes larger than a one molecular size, with help of the density functional theory (DFT). Because this is a thermodynamic calculation based on the minimization of the Grand Potential, the configurational energy is explicitly calculated with the DFT [37]. It is then possible to calculate the integral energy of adsorption. In the case of a porous system, the integral energy of adsorption up to completion of the pore filling can be related to the immersion energy by the following relationship:

where Llimmu is the immersion energy, Lladsu, the integral adsorption energy at saturation of the pore, na the amount adsorbed at saturation, and Llvapu the vaporization energy of the liquid. In Fig. 12.3, the integral adsorption energy per unit area calculated by DFT [38] is plotted as a function of the pore size, together with the corresponding immersion energy calculated by the preceding equation. This latter curve shows that the assumption ofproportionality between the surface area and the immersion energy holds for all pore size within ±10%. With a suitable nonporous standard of known surface area it is thus possible to determine the accessible surface area of any similar solid, even microporous.

288

Chapter 12 Porous Texture and Surface Characterization from Liquid-Solid Interactions

400 350 300

f

250

Integral energy of adsorption

"E' ;: 200 0)

CD

JJ

150 100

• • ••

•

Immersion energy

50

•

O+--------.------.---------r------.r----------,

o

5

10

15

20

25

Pore size (A)

Figure 12.3 Integral adsorption enthalpy and corresponding immersion enthalpy as a function of pore size, as calculated by DFT for the filling of a slit-shaped pore by a monoatomic fluid. (Adapted from [72].)

This method was shown to be well suited for microporous charcoals and immersed into organic liquids because of the absence of strong specific interactions [39, 40]. It is worth noting that for the smallest molecules used (benzene or methanol) the surface area provided by this method is, quite logically, higher than the nitrogen-BET equivalent surface area, since the BET method only takes into account one "side" of the molecule. Carrying out the same experiment for a set of liquids with different molecular sizes allows us to plot a graph of the accessible surface area as a function of pore width (Fig. 12.4). Assuming a pore shape, the next step is the derivation of a micropore width distribution, which can be compared to other approaches. One can indeed write d VCr)

= rdA(r) 2

where d V(r) and dA(r) are the pore volume and surface area in pores with sizes ranging between rand r + dr. For slit-shaped pores r is the aperture, whereas for cylinder r is the radius. The microporous volume between size a and b, is then given by

1

V

j 2

== -

b

rdA(r)

a

This integration can be performed on the curves in Fig. 12.4. The advantage of the method is that it gives a good assessment of the accessible pore volume by

12.3

Characterization of Carbons by Adsorption from Solution

1600 1400

0> .........

C\l

S

1200

C1

1000 C2

~

Q)

~

800

Q) ()

~

't:

600

:J

en

C3 400 - - . - - - - -.. C4

200 0 0.3

0.35

0.4

0.45

0.5

0.55

0.6

0.65

0.7

0.75

Pore width (nm)

Figure 12.4 Accessible surface area as a function ofpore width for a set ofactivated charcoals (activation increases from Cl to C4). The liquids used for immersion calorimetry are, in order of increasing size: benzene, methanol, isopropanol, cyclohexane, tertiary butanol, and a-pinene. (Adapted from [36].)

probing the solid at the temperature of interest, whereas the characterization of micropores by gas adsorption at 77 K may be limited by gas diffusion [4]. The immersion method was used for the study of zeolites [41] and it was recently extended to low-temperature immersion calorimetry, using nonspecific probes like liquid nitrogen, at 77 K, or liquid argon, at 87 K [42]. In some recent papers, immersion calorimetry is used in conjunction with gas adsorption (N2 or CO 2 ) to evidence gate effects that are observed when the pore entrance is partially blocked [43, 44].

12.3 CHARACTERIZATION OF CARBONS BY ADSORPTION FROM SOLUTION

Carbon materials are used in many industrial processes involving adsorption at a liquid-solid interface. Water purification by activated carbon, liquid chromatography, and stabilization of carbon black suspensions (inks, paints) are examples of such processes. The adsorption phenomena occurring at the solid-liquid interface are generally more complicated than those occurring at the solid-gas interface, simply because there is always competitive adsorption between at least two components. If the two components are miscible, the adsorption can be studied in the whole composition range (from 0 to 1 expressed in molar fraction).

290

Chapter 12 Porous Texture and Surface Characterization from Liquid-Solid Interactions

In the case of water solutions, the situation is extremely complex because water is itself a reactive solvent that is present under various forms (H 2 0, H+, or OH-) whose concentration depends on the pH. Moreover, adsorption is often studied in the presence of a salt, which also influences the adsorption process. Three species for water, two species for the salt in ionic form and one more for the solute then makes a minimum of six species involved in the adsorption process! As a consequence, a reliable study of adsorption from aqueous solution often requires to control or at least monitor pH, ionic strength, and temperature. Moreover, the concept of ionic strength may not be sufficient in the case where certain ions are specifically adsorbed. The reactivity of water with many surfaces, including carbon surfaces with polar groups, leads to the formation of a surface charge. The conditions of formation of the surface charge, its change with pH, ionic strength, and temperature were extensively studied in the case of nonporous minerals [15]. Another feature of adsorption from solution is the variety and complexity of molecules that may be involved in the processes. Indeed one can be interested either by a simple organic molecule, like benzene and its derivatives, or by much larger molecules like proteins, surfactants, or polymers, which bear many different chemical functions and may adopt a large number of conformations at the interface. For such molecules, a good knowledge of both the surface chemistry and the accessibility of porous materials are crucial to understand the adsorption phenomenon. In view of this complexity, here we shall focus our interest on aspects associated with the porosity of the solid. The first paragraph is about the basic concepts needed for such a kind of study. Examples are given in the second one. 12.3.1

Thermodynamics

In the field ofadsorption from solution, many discussions and reviews were published about the measurement of the adsorbed amount and the presentation of the corresponding data [14, 45-47]. Adsorption isotherms are the first step of any adsorption study. They are generally determined from the variation of macroscopic quantities which are rigorously measurable far away from the surface (e.g., the concentration of one species, the pressure, and the molar fraction). It is then only possible to compare two states: with or without adsorption. The adsorption data are derived from the difference between these two states, which means that only excess quantities are measurable. Adsorption results in the formation of a concentration profile near an interface. Simple representations are often used for this profile, but the real profile is an oscillating function of the distance from the surface [15, 16]. Without adsorption, the concentration should be constant up to the solid surface. Adsorption modifies the concentration profile of each component as well as the total concentration profile. It must be noted also that when the liquid is a pure component its concentration profile, i.e., its density, is also modified. Experimentally, the concentration can be measured at a large distance from the surface. The surface excess of component i is the

12.3

Characterization of Carbons by Adsorption from Solution

difference between the introduced amount ni and the amount calculated from the concentration measured far away from the surface c: and from a volume Vl,o which needs to be defined:

nC:1

= n. 1

c~1 VI,O

(12.19)

In the Gibbs representation, the volume V1,o is not limited by the solid adsorbent itself because the exact location of the adsorbing surface is actually unknown, so that this would introduce some uncertainty in the experimental data. Volume Vl,o is therefore limited by a fully theoretical surface (the Gibbs dividing surface, or GDS), which is precisely defined by the experimenter himsel£ although he usually tries to have it close to what he guesses to be the real adsorbing surface. What should not be forgotten when reporting liquid adsorption data (but which is rarely done) is therefore to state the exact way volume Vl,o was defined, in order to allow the reader to process the data with a different location of the GDS, which he may find more convenient to interpret the adsorption phenomenon. A way to avoid reporting this information is to eliminate Vl,o. This is possible after writing the preceding equation for each component or for the total amount of molecules, which leads to two possible ways to define and measure the surface excess: The relative suiface excess of 2 with respect to 1 (12.20)

the reduced suiface excess (12.21)

All surface excess amounts defined above usually refer to a unit mass or unit surface area (when available and when meaningful). The meaningfulness of the surface area requires being looked at thoroughly when porous solids like carbons are used for adsorbing large molecules from solution, because their surface areas were probably determined by gas adsorption of small molecules like nitrogen. By analogy with the characterization methods based on gas adsorption and on the shape of the isotherms, a classification of adsorption isotherms from liquid solution can be thought to be useful. The difficulties in establishing such a classification were underlined [9] .For dilute solutions Giles and Smith [48] proposed indeed 18 classes, Lyklema [15] simplified this down to 6, but we suggest retaining only 2 of them. Indeed, the shape of an adsorption isotherm from solution is the complex result of the balance between the solute-solute, solute-solvent, solute-surface, and surface-solvent interactions. Molecules do not only adsorb because they interact with the solid but also because the solvent may reject them. The surface is not itself a simple parameter because it is

292

Chapter 12 Porous Texture and Surface Characterization from Liquid-Solid Interactions

L

s

Figure 12.5 Two basic shapes of adsorption isotherms from dilute solutions. (Adapted from [9].)

generally heterogeneous. The presence of pores, of various crystalline faces or of different chemical sites influences the shape of the adsorption isotherm. It is only for a homogeneous surface that the relationship between the isotherm shape and the adsorption mechanism can be expected to be simple. One can then define two main shapes of isotherms (Fig. 12.5): L-type or S-type. The L-type, would follow the Langmuir model, which is site adsorption without any lateral interaction between the adsorbate molecules. The concavity of the curve, in normal scale, is always directed toward the concentration axis. The S-type would follow a more complex model in which lateral interactions between molecules are to be taken into account, using, e.g., the Bragg-Williams approximation [15]. A concavity of the adsorption isotherm directed toward the y-axis is a very strong indication of lateral interactions between molecules. If one looks at the IUPAC classification of gas adsorption isotherms [1], the same remark holds: this type of concavity is related with phenomena involving interactions between adsorbate molecules: capillary condensation, multilayer formation, 2-D phase changes, etc. Most experimental adsorption isotherms can be considered as a combination of these two "ideal" types. For heterogeneous surfaces, adsorption isotherms are often modeled as a combination of Land S adsorption isotherms corresponding to a distribution of patches [49, 50]. The many other shapes proposed in the preceding classifications [48] like stepwise, high affinity, or linear can be considered either as the combinations of S- and L-types or as a representation of the phenomenon for a limited range of concentration. For example, the highaffinity type is an extreme form of L-type. A linear adsorption isotherm (if it is not an artefact due to the penetration of the solute in the solid [15] may be the first portion of an L-type observed in the low concentration range. For the sake of characterization, only adsorption isotherms of simple shape may be used to provide safe interpretations. For example, to transform a surface excess amount into a surface area, a well-defined plateau is required, like in L-type isotherms for which a monolayer coverage can be assumed. If more complex shapes are obtained and if one wishes to extract from the data an

12.3

293

Characterization of Carbons by Adsorption from Solution

energetic distribution, one should then determine the adsorption enthalpy of the probe molecule. The sole adsorption isotherm usually does not allow, indeed, to estimate the role of surface heterogeneity and of the conformation changes as well as to discriminate between several mechanisms. There are two main ways to determine the adsorption enthalpy. One, called isosteric (because, for gas adsorption, it requires comparing two states with same amount adsorbed, i.e., same volume adsorbed), is the calculation of the differential adsorption enthalpy by using a set of two (or, better, three) adsorption isotherms at different temperatures. In dilute solution, the calculation of the isosteric enthalpy from adsorption isotherms at different temperatures is done by applying the following equation: . _

dadsh -

_

RT

2

(a In Xi) aT

(12.22) (T

nj

where the differentiation is performed while keeping constant all surface excess amounts. This condition makes it very difficult to apply this equation rigorously for liquid adsorption where, for instance, the surface charge varies with temperature. In the case of mixtures or concentrated solutions, activity coefficients have to be used. The second way to determine adsorption enthalpy is the direct measurement by microcalorimetry. Several papers are devoted to the analysis of the various ways to define liquid adsorption enthalpies and to measure them [51-55]. Experimentally, two types of calorimetric procedures can be distinguished on a thermodynamic basis: either the experiment is carried out in an open system or in a closed system. In the case of an open system, the main method consists in using a flowthrough setup. The sample is first equilibrated with the solvent, then with solutions of increasing concentration and, to end with, the desorption can be studied with a flow of pure solvent. Such an experiment mainly requires an equipment of chromatographic type, hence its name of "liquid frontal chromatography." The solid is placed in a column. Pumps are needed to inject solvent and solutions. It is possible to either prepare solutions in advance [56, 57] or to directly prepare various compositions by monitoring the flow rates of two pumps at constant total flow rate [51]. Downstream the column, a concentration detector (refractometer, UV, or IR spectrometer) allows recording the composition of the liquid as a function of time. Integration of the concentration profile vs time gives the reduced surface excess amount of the solute during one adsorption step. The limitations of this method are (i) that the sample grain size must fulfill some requirements (i.e., coarse enough to limit the pressure drop), and (ii) that the accuracy of the integration procedure depends on the long-term stability of the concentration recording. The main advantage is that all chemical potentials can be imposed throughout the experiment. This is important in pH-dependent experiments. Another interesting aspect is that such an experiment can be carried out in a microcalorimeter [56] giving

294

Chapter 12 Porous Texture and Surface Characterization from Liquid-Solid Interactions

both access to the surface excess amount and to the corresponding adsorption enthalpy. In the case of a closed system, the most common procedure is the immersion method [58]. It consists in immersing the solid in a liquid ofknown composition. After stirring and equilibration, the solid is separated from the liquid (centrifugation, filtration, or dialysis) and the final concentration is determined (UV, IR, refractometry or, still, Geiger counter in case radioactive tracers are used). Then the surface excess amount is calculated by using one of the equations derived in the preceding section. A direct analysis of the solid is also possible [59]. The immersion method is rewarding since it is simple (it does not need much equipment) though providing a good accuracy. It is also suited to follow the kinetics of adsorption. Another method using a closed system was devised by Nunn and Everett [60] with a flow-through equipment and a null procedure: the same solution is continuously circulated through the sample until equilibrium is attained, whereas a more concentrated solution is also injected to continuously restore the initial concentration. Since the concentration is continuously recorded, an independent kinetic experiment is not needed. For calorimetry, two different ways can be considered for closed systems experiments: • Immersion calorimetry of the dry solid in a solution (but this is not the safest way from a calorimetric viewpoint). • Direct determination of adsorption enthalpies (or more precisely displacement enthalpies as indicated earlier) by titration microcalorimetry, which is the main form of calorimetry used in adsorption from solution. For any method, care must be taken to define the reference state of the solute, which can be either the solution at equilibrium with the surface or the solution at infinite dilution state [4, 52]. An adsorption isotherm determined independently is needed to relate the calorimetric data with the surface excess amount. The most useful and convenient representation of calorimetric data shows the adsorption enthalpy as a function of surface concentration or coverage (or pore filling). Either integral or differential adsorption enthalpies can be determined. The integral enthalpy corresponds to the adsorption from zero coverage up to a given coverage. The differential enthalpy corresponds to the transfer of one mole of adsorbate from the bulk solution to the surface at a given coverage. In each case, the reference state can be either the equilibrium solution or the infinite dilution. The latter is suited when the properties of the solution are change much with concentration. This is the case with surfactant molecules, for instance. Strictly speaking, the above calorimetric experiments (either in closed or in open systems) provide "pseudodifferential" enthalpies of adsorption (rather than differential), because the actual experiments consist in discrete steps of surface concentration.

12.3

Characterization of Carbons by Adsorption from Solution

12.3.2

295

Applications

12.3.2.1

Surface area determination

Adsorption isotherms from solution have been used to determine the surface area of adsorbents for many years. Nevertheless, contrary to gas adsorption where nonspecific probes like argon or nitrogen can be used whatever the adsorbent, methods using adsorption from solution are generally specific for a class of material. For example, iodine or methylene blue are used for quick and convenient tests of adsorption capacity in the charcoal industry. A number of fundamental studies show how iodine [47, 61-63], p-nitrophenol [64, 65] salicylic acid [66], surfactants [67], or dyes [68] can be used for such applications. Nevertheless, most of these molecules present an affinity for the surface, which is highly dependent on the experimental conditions. For example, dyes and surfactants are very often electrically charged molecules and, because the adsorbing surface is also charged, the resulting adsorption isotherm depends on pH. A safe result cannot therefore be obtained from one experiment only. Also, the derivation of a surface area from a surface excess amount is based on the assumption that the average area per molecule is the same from one sample to the other. Because of these limitations we cannot specify a safe universal method to determine the surface area. Now, a particular feature ofadsorption from solution is the variety ofmolecules which can be used. Playing on their polarity or charge, it is then possible to define applications where the interest is not to determine the total surface area of the sample but, rather, to define the percentage of the surface, which can be considered as polar or nonpolar, hydrophilic or hydrophobic, acid or basic, etc. Groszek [69] extensively applied this approach, over 30 years, to the study of carbons Both calorimetry and adsorption isotherms may be used in such analysis. The influence of the surface charge may be very important on the adsorption from aqueous solution. In a recent review, Moreno-Castilla [70] gives examples of correlation ofthe adsorption data from solution (both isotherms and enthalpies of adsorption) and of the immersion energies with the amount of surface groups determined by an acid-base titration. These surface groups are generally directly related with the surface oxygen content of the carbon. 12.3.2.2

Pore size analysis

A way to proceed is to use probe molecules ofvarious sizes and to derive an accessible surface area from the amount adsorbed at the plateau of the adsorption isotherms [66]. Measurements with iodine showed that a method like the as plot, although originally devised for gas adsorption, could be extended to adsorption from solution. A set of adsorption isotherms, like those of Fig. 12.6, on various charcoals and on a nonporous reference sample was used to evaluate the method. The reference adsorption isotherm was normalized by dividing the amount adsorbed by the amount adsorbed at the plateau thus allowing a reference curve to be plotted as as vs equilibrium concentration. The amounts adsorbed on

296

Chapter 12 Porous Texture and Surface Characterization from Liquid-Solid Interactions

5

Microporous charcoal 4

4.5 C)

4

.........

(5

E

S "'0 CD

.0

0en

"'0 ctS

C :::J

0

E

3.5

Microporous charcoal 1

3 2.5 2 1.5

«

Nonporous carbon

0.5

0.00002

0.00004 0.00006 0.00008 0.0001 0.00012 Equilibrium concentration (mol/kg)

0.00014

0.00016

Figure 12.6 Adsorption isotherms of iodine on two microporous charcoals. (Adapted from [63].)

the charcoals were then plotted as a function of the as values. Plots similar to those for gas adsorption were obtained and allowed pore volumes and external surface areas to be calculated. The validity of the method was demonstrated by observing that when iodine completes the micropore filling its adsorption enthalpy becomes equal to that measured for the nonporous reference (Fig. 12.7). 80 70 (5

E

60

.........

~ ~ a.

50

co

E 40 CD

c: o

a

30

~

20

oen

10 O+------r----~-----.--------r--------.-----r-----.,

o

0.1

0.2

0.3

0.4 Coverage

0.5

0.6

0.7

Figure 12.7 Differential enthalpy of adsorption of iodine on two carbons (calorimetry). (Adapted from [63].)

References

297

For larger pores, say in the mesoporous range, much larger molecules are needed to characterize the pore size and the literature is scarce in this field. Polymers can be used (e.g., dextran) to evaluate the pore size of membranes. One then assesses a molar mass cutoff rather than a real pore size. The solute exclusion technique was also proposed to assess a pore size distribution [71]. It is well suited for wet porous materials [72].

REFERENCES 1. Rouquerol, J., Avnir, D., Fairbridge, C.W., et al. (1994). Recommendations for the characterization of porous solids. Pure Appl. Chern., 66(8), 1739-58. 2. Zettlemoyer, A.C., Chessick, J.J., and Hollabaugh, C.M. (1958). J. Phys. Chern., 62, 489-90. 3. Harkins, W.D. and Boyd, G.E. (1942). The binding energy between a crystalline solid and a liquid: the energy of adhesion and emersion. Energy of emersion of crystalline powders. II. J. Am. Chern. Soc., 64, 1195-204. 4. Rouquerol, F., Rouquerol, J., and Sing, K.S.W. (1999). Adsorption by Powders and Porous Solids: Principles, Methodology and Applications. Academic Press. 5. Sorensen, G.T. and Rouquerol, J. (eds) (2003). Sample Controlled Thermal Analysis: Origin, Goals, Multiple Forms, Applications and Future. Kluwer Academic Publishers. 6. Everett, D.H., Langdon, A.G., and Maher, P. (1984). Developments in immersion calorimetry- Design and testing of an improved sel-breaking technique. J. Chern. Thermodynamics, 16, 981-92. 7. Partyka, S., Rouquerol, F., and Rouquerol, J. (1979). Calorimetric determination of surface areas: Possibilities of a modified Harkins and Jura procedure. J. Colloid Interface Sci., 68(1), 21-31. 8. Gomez, F., Denoyel, R., and Rouquerol, J. (2000). Determining the contact angle of a nonwetting liquid in pores by liquid intrusion calorimetry. Langmuir, 16, 4374-9. 9. Denoyel, R. and Rouquerol, F. (2002). Adsorption from the liquid phase. Handbook of Porous Solids. Wiley-VCH, Chapter 2.6. 10. Douillard,J.M. and Zajac,]. (2006). Contact Angle Determination from Heat of 1mmersion and Heat of Wetting. Encyclopedia of Surface and Colloid Science. Marcel Dekker. 11. Chessick, J.J. and Zettlemoyer, A.C. (1959). Immersional heats and the nature of solid surfaces. Adv. Catal., 11, 263-99. 12. Zettlemoyer, A.C. (1965). Immersional wetting of solid surfaces. Ind. Eng. Chern., 57, 27-36. 13. Harkins, W.D. and Jura, G. (1944). Surfaces of solids. XII. An absolute method for the determination of the area of a finely divided crystalline solid. J. Am. Chern. Soc., 66, 1362-6. 14. Everett, D .H. (1972). Manual ofsymbols and terminology for physicochemical quantities and units. Appendix 2, Part 1. Pure Appl. Chern., 31(4), 579-638. 15. Lyklema, J. (1995). Fundamentals of Interface and Colloid Science. I Fundamentals. II. SolidLiquid Interfaces. London: Academic Press. 16. Israelachvili, J.N. (1992). Intermolecular and Surface Forces. Academic Press. 17. Medout-Madere, V. (2000). A simple experimental way of measuring the Hamaker constant All of divided solids by immersion calorimetry in apolar liquids. J. Colloid Interface Sci., 228, 434-7.

298

Chapter 12 Porous Texture and Surface Characterization from Liquid-Solid Interactions

18. Zettlemoyer, A.C., Chessick, J.J., and Hollabaugh, C.M. (1958). Estimation of the surface polarity ofsolids from heat of wetting measurements.]. Phys. Chem., 62, 489-90. 19. Morimoto, T. and Suda, Y. (1985). Heat of immersion of zinc oxide in organic liquids. 1. Effect of surface hydroxyls on the electrostatic field strength. Langmuir, 1, 239-43. 20. Young, G.J., Chessick, J.J., Healey, F.H., and Zettlemoyer, A.C. (1954). Thermodynamics of the adsorption ofwater on Graphon from heats ofimmersion and adsorption data.]. Phys. Chem., 58, 313-15. 21. Healey, F.H., Yu, Y.F., and Chessick, J.J. (1955). The detection of hydrophilic heterogeneities on a carbon surface.]. Phys. Chem., 59, 399-402. 22. Lopez-Ramon, M.V., Stoeckli, F., Moreno-Castilla, C., and Carrasco-Marin, F. (1999). On the characterization of acidic and basic surface sites on carbons by various techniques. Carbon, 37, 1215-21. 23. Robert, L. and Brusset, H. (1965). Heat of immersion of carbon products. Fuel, 44, 309-16. 24. Rodriguez-Reinoso, F. and Molina-Sabio, M. (1998). Textural and chemical characterization of microporous carbons. Adv. Colloid Inteiface Sci., 76-77, 271-94. 25. Lopez-Ramon, M.V., Stoeckli, F., Moreno-Castilla, C., and Carrasco-Marin, F. (2000). Specific and non-specific interactions of water molecules with carbon surfaces from immersion calorimetry. Carbon, 38, 825-9. 26. Stoeckli, F., Moreno-Castilla, C., Carrasco-Marin, F., and Lopez-Ramon, M.V. (2001). Distribution ofsurface oxygen complexes on activated carbons from immersion calorimetry, titration and temperature-programmed desorption techniques, Carbon, 39(14), 2235-7. 27. Szymaski, G.S., Biniak, S., and Rychlicki, G. (2002). Carbon surface polarity from immersion calorimetry. Fuel Process. Technol., 79(3), 217-23. 28. Bradley, R.H., Daley, R., and Le Gof£ F. (2002). Polar and dispersion interactions at carbon surfaces: further development of the XPS-based model. Carbon, 40(8), 1173-9. 29. Gonzalez-Martin, M.L., Gonzalez-Garcia, C.M., Gonzalez, J.F., et al. (2002). Thermodynamic characterization of a regenerated activated carbon surface. Appl. Suif. Sci., 191, 166-70. 30. Briant, J. and Cuiec, L. (1972). Comptes-Rendus du 4eme Colloque ARTEP, RueilMalmaison, 7-9 ]uin 1971. Paris: Ed. Technip. 31. Douillard, J.M., Zoungrana, T., and Partyka, S. (1995). Surface Gibbs free energy of minerals: some values.]. Petrol. Sci. Eng., 14,51-7. 32. Medout-Marere, V., Partyka, S., Dutartre, R., et al. (2003). Surface heterogeneity of passively oxidized silicon carbide particles: vapor adsorption isotherms.]. Colloid Inteiface Sci., 262, 309-20. 33. Spagnolo, D.A., Maham, Y., and Chuang, K.T. (1996). Calculation of contact angle for hydrophobic powders using heat of immersion data.]. Phys. Chem., 100, 6626-30. 34. Neumann, A.W. (1974). Contact angles and their temperature dependence: thermodynamic status, measurement, interpretation and application. Adv. Colloid Inteiface Sci., 4, 105-91. 35. Everett, D.H. and Powl, J.C. (1976). Adsorption in slit-like and cylindrical micropores in Henrys law region - Model for microporosity of carbons.]. Chem. Soc. Faraday Trans. I, 72, 619-36. 36. Denoyel, R., Fernandez-Colinas, J., Grillet, Y., and Rouquerol, J. (1993). Assessment of the surface area and microporosity of activated charcoals from immersion calorimetry and nitrogen adsorption data. Langmuir, 9, 515-18. 37. Olivier, J.P. (2000). Comparison of the experimental isosteric heat of adsorption on mesoporous silica with density functional theory calculations. Stud. Suif. Sci. Catal., 128. 81-7.

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38. Denoyel, R., Beurroies, I., and Vincent, D. (2000). Microcalorimetric methods for studying vapour adsorption and wetting of powders. J. Thermal Anal. Calorimetry, 70, 483-92. 39. Neugebauer, N.N. (1999). PhD Dissertation, Leipzig University, Germany. 40. Rodriguez-Reinoso, F., Molina Sabio, M., and Gonzalez, M.T. (1997). Effect of oxygen surface groups on the immersion enthalpy of activated carbons in liquids of different polarity. Langmuir, 13, 2354-8. 41. Silvestre-Albero, J., Gomez de Salazar, C., Sepulveda-Escribano, A., and RodriguezReinoso, F. (2001). Characterization of microporous solids by immersion calorimetry. Colloids Suif. A: Physicochem. Eng. Aspects, 187-188, 151-65. 42. Rouquerol, J., Llewellyn, P., Navarette, R., et al. (2002). Assessing microporosity by immersion microcalorimetry into liquid nitrogen or liquid argon. Stud. Sutj. Sci. Catal., 144, 171-6. 43. Cagnon, B., Py, X., Guillot, A., and Stoeckli, F. (2003). The effect of the carbonization/activation procedure on the microporous texture of the subsequent chars and active carbons. Microporous Mesoporous Mater., 57, 273-82. 44. Stoeckli, F., Slasli, A., Hugi-Cleary, D., and Guillot, A. (2002). The characterization of microporosity in carbons with molecular sieve effects. Microporous Mesoporous Mater., 51(3), 197-202. 45. Defay, R. and Prigogine, 1. (1951). Tension Supeificielle et Adsorption. Liege-Paris: DesoerDunod. 46. Schay G. (1970). In Proceedings of the International Symposium on Suiface Area Determination (D.H. Everett and R.H. Otterwill, eds). London: Butterworth, p. 273. 47. Kipling, J.J. (1965). Adsorption from Solution of Non-electrolytes. London: Academic Press. 48. Giles, C.H. and Smith, D. (1974). A general treatment and classification of the solute adsorption isotherm. 1. Theoretical]. Colloid Inteiface Sci., 47, 755-65. 49. Cases, J .M. (1979). Tensio-active adsorption at the solid-liquid interface - Thermodynamics and influence of adsorbant heterogeneity. Bull. Mineralogie, 102, 684-707. 50. Cases, J.M. and Villieras, F. (1992). Thermodynamic model of ionic and non-ionic surfactants adsorption-abstraction on heterogeneous surfaces. Langmuir, 8, 1251-64. 51. Johnson, 1., Denoyel, R., Everett, D .H., and Rouquerol, J. (1990). Adsorption at the liquid/graphite interface: Comparison of enthalpy data obtained from three different methods. Colloids Suif-, 49, 133-48. 52. Denoyel, R., Rouquerol, F., and Rouquerol, J. (1990). Thermodynamics of adsorption from solution: Experimental and formal assessment of the enthalpies of displacement. ]. Colloid Inteiface Sci., 136, 375-84. 53. Kiraly, Z. and Dekany, 1. (1989). Thermodynamics of multilayer adsorption of aqueous butanol solution onto printex and graphitized printex carbon-blacks.]. Chem. Soc. Faraday Trans. I, 85, 3373-83. 54. Kiraly, Z., Dekany, 1., and Nagy, L.G. (1993). Thermodynamic formulation of adsorption phenomena at the solid/solution interface: A practical approach. Colloids Sutj. A, 71,287-92. 55. Woodbury, G.W. and Noll, L.A. (1987). Heats of adsorption from flow calorimetry: Relationships between heats measured by different methods. Colloids Sutj., 28, 233-45. 56. Denoyel, R., Rouquerol, F., and Rouquerol, J. (1983). Interest and requirements of liquid-flow microcalorimetry in the study of adsorption from solution in the scope of tertiary oil recovery. In Adsorption from Solution (C. Rochester and A.L. Smith, eds.). Academic Press, pp. 225-34. 57. Kiraly, Z. and Findenegg, G.H. (1998). Calorimetric evidence of the formation of halfcylindrical aggregates of a cationic surfactant at the graphite/water interface.]. Phys. Chem. B., 102,1203-11.

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58. Everett, D .H. (1986). Reporting data on adsorption from solution at the solidisolution interface. Pure Appl. Chem., 58(7), 967-84. 59. Nunn, C. Schlechter, R.S and Wade, W.H. (1981). A direct method for measuring adsorption from solution onto solids. J. Colloid Interface Sci., 80, 598-605. 60. Nunn, C. and Everett, D.H. (1983). A note on the determination of adsorption from solution. J. Chem. Soc. Faraday Trans 1., 79, 2953-4. 61. Puri, B.R. and Bansal, R.C. (1965). Iodine adsorption method for measuring surface area of carbon blacks. Carbon, 3, 227-30. 62. Molina-Sabio, M., Salinas-Martinez de Lecea, C., et al. (1985). A comparison of different tests to evaluate the apparent surface area of activated carbons. Carbon, 23, 91-6. 63. Fernandez-Colinas, J., Denoyel, R., and Rouquerol, J. (1989). Adsorption of iodine from aqueous solutions onto activated carbons: correlations with nitrogen adsorption at 77 K. Adsorp. Sci. Technol., 6, 18-26. 64. Giles, C.H. and Nakhwa, S.N. (1962). Adsorption XVI The measurement of specific surface areas of finely divided solids by solution adsorption. J. Appl. Chem., 12, 266-73. 65. Lopez-Gonzalez, J., de, D., Valenzuela-Calahorro, C., et al. (1988). Adsorption of p-nitrophenol by active carbons prepared from olive wood. An. Quim., 84B, 47-51. 66. Femandez-Colinas, J., Denoyel, R., and Rouquerol, J. (1991). Characterization of activated charcoals by adsorption from solution. Stud. Surf. Sci. Catal., 62, 399-408. 67. Somasundaran, P. and Fuerstenau, D.W. (1966). Mechanisms of alkyl sulfonate adsorption at the alumina-water interface. J. Phys. Chem., 70, 90-6. 68. Giles, C.H., D'Silva, A.P., and Stridevi, A. (1969). In Proceedings of the International Symposium on Surface Area Determination (D.H. Everett and R.H. Ottewill eds). London: Butterworths, pp. 317-23. 69. Groszek, AJ. (1998). Flow adsorption microcalorimetry. Thermochim. Acta, 313, 133-43. 70. Moreno-Castilla, C. (2004). Adsorption of organic molecules from aqueous solutions on carbon materials. Carbon, 42, 83-94. 71. Lin, J.K., Ladish, M.R., Patterson, J.A., and Noller, C.H. (1987). Determining poresize distribution in wet cellulose by measuring solute exclusion using a differential refractometer. Biotechnol. Bioeng., 29, 976-81. 72. Denoyel, R. (2004). Adsorption of organic molecules in nanoporous adsorbents from aqueous solution. In Nanoporous Materials: Science and Engineering. (G.Q. Lu and S. Zhao, eds.). World Scientific, Ch. 23, pp. 727-55.

SURFACE CHEMICAL CHARACTERIZATION OF

CARBONS FROM ADSORPTION STUDIES Hans-Peter Boehm Department

of Chemistry and Biochemistry,

University

of Munich,

Germany

Contents 13.1 Introduction 13.2 Hydrophilic Carbon Surfaces 13.3 Surface Oxides of Carbon 13.4 Amphoteric Character of Carbons 13.5 Electrokinetic Phenomena 13.6 Effects on the Adsorption of Inorganic ions References

301 302 30 4 30 8 31 8 321

32 3

13.1 INTRODUCTION

The adsorption behavior of carbons is affected to a considerable extent by the chemical state of their surfaces, which is also of great practical importance in many other applications of carbon materials such as for catalysts and catalyst supports, and carbon-polymer composites. In the surface of carbon materials, the regular network of covalent C-C bonds is broken, and reactive sites result as a consequence. Usually "free valences," also called "dangling bonds," are saturated with foreign elements, in first line hydrogen and oxygen. In the case of carbon structures derived from the graphite lattice, the surface is inhomogeneous and is constituted to variable fractions of basal faces, i.e., honeycomb-like graphene layers, and of the edges of the graphene layers. While the basal faces are quite inert, the edge sites are reactive and can chemisorb other elements such as hydrogen, oxygen, nitrogen species, and halogens. In contrast, the surface of Adsorption by Carbons ISBN: 978-0-08-044464-2

© 2008 Elsevier Ltd.

All rights reserved.

301

302

Chapter 13 Surface Chemical Characterization of Carbons from Adsorption Studies

diamond is much more homogeneous and has a comparatively simpler chemical behavior. One would expect that many free radical sites (dangling bonds) exist on an atomically clean surface, but the number of free radicals determined by electron spin resonance (ESR) measurements on carbons is much smaller than corresponds to the estimated number of edge sites, and a part of them may also be located at vacancy sites within the graphene layers [1-3]. One reason might be that atomically clean surfaces of solids are frequently reconstructed, leading to new electronic states that can accommodate electron pairs. Also the localization of 11" electrons at free radical edge sites with formation of carbene-like structures (in-plane sigma pairs) has been suggested (see p. 229 in Ref [1] and Fig. 3 in Ref [4]). Measurement ofadsorption phenomena by chemical means require adsorbents that have a relatively high surface area, preferably in excess of 20-50 m 2 Ig, to provide sufficient sensitivity. Such carbons are, e.g., activated carbons, carbon blacks, graphite wear dust, and carbon nanotubes. Physical measurements, such as by X-ray photoelectron spectroscopy (XPS) , Auger electron spectroscopy (AES) , electron energy loss spectroscopy (EELS), Fourier transform infrared (FTIR), and special Raman spectroscopies, can be done with materials of much lower surface area.

13.2 HYDROPHILIC (ARBON SURFACES The basal faces and chemically"clean" edge faces, as well as those saturated with chemisorbed hydrogen, are hydrophobic, whereas surfaces with oxygencontaining surface groups are hydrophilic. Clean carbon surfaces with a surface roughness in the 40-50 nm range are "superhydrophobic" (Lotus effect), i.e., they have a contact angle with water of > 150 [5]. The hydrophilicity of a carbon surface determines its adsorption behavior toward water vapor. Hydrophobic surfaces show type III adsorption isotherms (type V in the case of porous carbons) [6]. Very little water is adsorbed at low relative pressures plpo because adsorption occurs only by dispersion forces, no hydrogen bonds can be formed. Water behaves similar to a gas of low molecular mass, such as neon, with a correspondingly low boiling point. At room temperature it would be supercritical. Only when some water molecules are adsorbed, the following ones can form hydrogen bonds, and larger water clusters are formed on the surface. At higher relative pressures, the nature of the adsorbed water will gradually change to that of normal liquid, hydrogen-bonded water, and the adsorption isotherms rise steeply at plpo values above 0.5. In the case of microporous carbons, adsorption is promoted by the higher adsorption potential in narrow pores, and the adsorption isotherms begin to rise steeply at much lower plpo values (type V isotherms). Consequently, one might expect that a superposition of type II and type III isotherms might occur if there existed only 0

13.2

303

Hydrophilic Carbon Surfaces

Adsorbed water (mg/g) 4.0

3.0

2.0

1.0

0.5

1.0

p/Po Water vapor adsorption isotherms on diamond powder (20m2 /g). (1) Treated with H 2 at 800°C (measured at 17.8 °C); (2) outgassed in vacuo at 900°C (18.3 °C); (3) oxidized with 02 at 420°C (19.8 °C). (Reprinted from Re£ [8] with permission from Elsevier.)

Figure

13.1

a small concentration of hydrophilic adsorption sites (chemisorbed oxygen) on an otherwise hydrophobic nonporous carbon. Figure 13.1 shows water vapor adsorption isotherms on a clean, a hydrogenated and an oxidized diamond surface. Clearly, water adsorption is promoted by surface oxygen complexes whilst the hydrogenated surface is the most hydrophobic one. If there is a superposition of type II and type III isotherms, it should be possible to estimate the concentration of hydrophilic sites by application of the Brunauer-Emmett-Teller (BET) adsorption equation [7] at relatively low plpo values. The BET equation is based on the assumption that the heat of adsorption is significantly higher in the first adsorbed layer than in the following adlayers where it is practically equal to the heat of liquefaction [7]. In our case, the first adlayer corresponds to the adsorption of one water molecule on each hydrophilic adsorption site. The heat of adsorption is significantly higher than in the following adsorption. Indeed, an excellent correlation of hydrophilic sites determined by application of the BET equation with active hydrogen (of hydroxyl groups) determined by independent methods was observed on the surface of diamond powder [8] and also on oxidized SiC [9], as summarized in Table 13.1 this method is not applicable, however, when there are higher concentrations of hydrophilic adsorption sites.

Chapter 13 Surface Chemical Characterization of Carbons from Adsorption Studies

304

Table 13.1 Hydrophilic adsorption centers on the surface of diamond, SiC, and pyrogenic silica (Aerosil) (Data from Refs [8, 9].)

Diamond, outgassed at 900°C (20 m 2 / g) Diamond, H 2 at 800°C (20 m 2 / g) Diamond, oxidized with O 2 at 420°C (20m2 /g) SiC, oxidized with air at 20°C (9.5m 2 /g) Si0 2 (Aerosil) a

b C

19

n.d.

n.d.

7

n.d.

n.d.

62

66

53

54

2160

2210

From weight increase on isotope exchange with D 2 0 (-OH to -OD). By reaction with CH 3 MgI (volumetric determination of evolved CH 4 ). By titration with NaOH of weakly acidic surface groups.

13.3

SURFACE OXIDES OF (ARBON

The most intensively studied surface complexes of carbons are those with oxygen. Such surface oxides can be produced by treatment with gaseous oxidants such as dioxygen (or air), ozone, oxygen plasma, or NO x ' Dioxygen molecules react only with carbon atoms at the edges the graphene layers or at defects, e.g., vacancies, within the planes [10-12]. The surface layers are, however, attacked by free radicals, atomic oxygen, and compounds that easily produce atomic oxygen by decomposition such as ozone. For instance, large, millimeter-sized flakes of well-crystallized graphite were converted to an evil-smelling sludge on prolonged exposition to UV-irradiated CC1 4 [13] Cl, and CC1 3 radicals are formed by photolysis.

13.3.1 Generation of Surface Oxides Reaction temperatures of 250-400 °C are usually taken for oxidation with dioxygen or air. Significant quantities of surface oxides of mostly acidic character are produced in a few hours. The required temperatures are the lower, the smaller the particle size of the carbon is. Clean surfaces of turbostratic carbons of high surface area such as activated carbons and carbon blacks will also be oxidized at room temperature. When the carbons are freed from surface complexes by heating to 900-1000°C in vacuo or under an inert gas, they will adsorb some

13.3 Surface Oxides of Carbon

305

oxygen on exposure to air at room temperature. The reaction is quite fast in the beginning, but slows down gradually [14] (see Section 13.4.2). Much more oxygen is bound on the surface in a slow reaction with moist air. This phenomenon, called "aging," was first described by Puri [15]. The presence of water vapor accelerates the reaction significantly [16-18]. The aging process takes several months at room temperature to become easily measurable. It can be followed easily within a few weeks when the reaction occurs at mildly raised temperatures [19,20]. as shown in Fig. 13.2. An activated carbon (Norit) and a furnace black (Corax 3) were oxidized in air of 85% relative humidity at 60°C or under ambient air of varying humidity at 110°C. Sodium hydroxide uptake was used as a measure of aging since acidic groups are formed in the reaction (see below). The figure shows clearly, that in the case of the activated carbon the surface oxidation occurred faster and to a higher extent at the lower temperature at higher relative humidity than at the higher temperature at a much lower relative humidity [19]. Aging is drastically increased when catalytically active metals, e.g., palladium, are deposited on the surface (Fig. 13.2). This aging process causes changes in the properties of carbon materials. The surface becomes more and more hydrophilic, and the adsorption capacity of activated carbons for noxious gases or methyl iodide is greatly reduced [16, 20]. With porous carbons, the surface oxidation begins at the outer surface of the particles, but progresses very slowly into their interior due to very slow diffusion of oxygen in narrow pores [21]. In consequence, the exterior and interior surfaces of activated carbons can differ significantly in their adsorption properties. Aging can

(a)

(b)

NaOH uptake

NaOH uptake

(Jlmol/g)

(Jlmol/g)

400

250

.

--~.=-------

300 150

.............

././

200 100

ro

50

20

40

60 days

- - Time

_-......_._ ...

_

-.

......... ....

<":'::·:7.:::~ 8".~.:.:~:::.:::8". 7.:.::~::::.:.::~~:".::§ o

20

40

60 days

~

Figure 13.2 Ageing of the surface of an activated carbon, Norit (a) and a furnace black, Corax 3 (b). Acidic groups that can be titrated with NaOH are formed in the reaction. Open square symbols: heating at 110°C in a drying oven; open circular symbols: heating at 60°C in air of 850/0 relative humidity. Filled symbols: the same carbons loaded with 200 J.L mol/g of Pd. (Reprinted from Ref. [37] with permission from Elsevier.)

306

Chapter 13 Surface Chemical Characterization of Carbons from Adsorption Studies

be inhibited to a large extent by treatment of the carbons with hydrogen at high temperatures when the reactive sites are saturated by hydrogen atoms [22, 23]. An other, often used way to oxidize the surface of carbons is by treatment with oxidising aqueous solutions, e.g., of hydrogen peroxide, ammonium peroxodisulfate, or sodium hypochlorite. Nitric acid is very frequently used because its oxidizing effect can be easily controlled by the concentration, the reaction temperature, and reaction time. One disadvantage of nitric acid is, however, that the pore structure of the carbon is considerably changed. The micropores become wider and the micropore volume is reduced [24], and also some nitrogen is bound on the surface [24, 25]. Oxidation with (NH4)2S20S has little effect on the pore structure and more relatively strongly acidic groups are produced than in the reaction with HN0 3 [26]. It is often overlooked that many metal ions have oxidising properties, too, e.g., coordination compounds of precious metals such as [PtCI 6 ]4-, Ag+, or Fe 3+ ions. They will oxidize the surface of carbon supports in the preparation of catalysts. The reducing power of the carbon surface decreases with increasing surface oxidation, and the extent of surface oxidation will depend on the oxidation potential of the oxidizing species. It has been reported that [Pt(NH 3 )4]2+ at pH 8.5 is not reduced by carbon [27]. Finely dispersed metal will be deposited on the carbon surface in the case of Ag+, [Ag(NH 3 )2]+ or complexes of the platinum metals [28-31]. Electrochemical oxidation of carbon surfaces is also a possibility. It is very convenient when carbon fibers are to be oxidized in a continuous process [32-35], but it can also be applied to activated carbons [36].

13.3.2 Functional Carbon Groups Oxygen is chemically bound to the carbon surface in the course of oxidation. It is to be expected that most of it is bound by covalent bonds in the form offunctional groups that are known from organic chemistry. The most important ones are shown in Fig. 13.3. Carboxyl groups can also occur as derivatives such as carboxylic anhydrides, lactones or lactols. Further, there are hydroxyl groups of phenolic character, carbonyl groups, often combined to quinone-type structures, and bridging, ether-like atoms at the edges ofthe graphene layers. Other, less likely groups are peroxides and carbonic di-esters of adjacent hydroxyl groups. Identification of such groups has been achieved by a combination of various methods, e.g., neutralization adsorption ofbases of different strengths, strong acids, infrared spectroscopy, temperature-programmed decomposition, and desorption combined with an analysis ofthe resulting gases (temperature-programmed desorption (TPD)), and XPS. For references to these methods, see Boehm [37, 38]. In TPD, peaks are observed for H 20, CO 2, and CO. It is usually assumed that CO 2 comes from carboxyl groups and their derivatives, and CO derives from carbonyl and ether oxygen. However, the results are not unambiguous since carboxylic anhydrides or lactones will thermally decompose to CO 2 plus CO [38]. The XPS method makes use of the fact that the electron density near

30 7

13.3 Surface Oxides of Carbon

o~ / 0 \ g0

0

O~

x;¢HX»X» xxx WW (a)

~

(b)

OH

~C-O OH

(c)

(d)

(g)

(h)

0

(e)

(f)

Figure 13.3 Possible functional groups on carbon surfaces: (a) carboxyl groups, (b) carboxylic anhydrides, (c) lactones, (d) lactols, (e) phenolic hydroxyl groups, (f) carbonyl groups, (g) o-quinone-like structures, and (h) ether-type (or pyran- or xanthene-like) oxygen atoms. (Reprinted from Ref. [37] with permission from Elsevier.)

the center of carbon atoms is reduced when the atoms are bonded to more electronegative atoms such as oxygen. In consequence, the binding energy (b.e.) of the core level 1s electrons is increased, and satellite signals appear at the high-binding-energy side of the main Cis peak. The shift in binding energy is different for carbon atoms having one, two or three covalent bonds to oxygen atoms (ethers and hydroxyls, carbonyls and ether bridges to two oxygen atoms, carboxyl groups and their derivatives, respectively). The peaks can be well resolved in modern instruments with an appropriate deconvolution program, see Fig. 13.4. The 01s spectra show also different peaks, but the sensitivity to differences in the bonding is relatively smaller due to the high electronegativity of oxygen.

IV

I

294

292

290

288

286

284

282

280

Binding energy (eV)

Figure 13.4 Cls photoelectron spectrum (XPS) of oxidized carbon fibers. Peak I: phenols or ethers; peak II: carbonyl groups; peak III: carboxyl groups; peak IV: plasmon peak. (Reprinted from Refs [32] and [38] with permission from Elsevier.)

308

Chapter 13 Surface Chemical Characterization of Carbons from Adsorption Studies

13.4

AMPHOTERIC CHARACTER OF CARBONS

The various groups differ in their acidity and basicity, and the carbon surface acquires acidic and/or basic properties, depending on the nature of the surface functionality. It is known for a long time that a given carbon can have either acidic or basic surface character, depending on its pretreatment [39, 40]. In the following, the acidic and basic surface oxides will be discussed in detail.

13.4.1 Adsorption of Bases Several of the oxygen-containing groups in Fig. 13.3 exhibit Br0nsted acidity, namely carboxyl and phenolic hydroxyl groups. Carboxylic anhydrides and lactones are easily hydrolyzed to carboxylic anions, -COO-, plus hydroxyl groups in the case of lactones. Lactols are in equilibrium with ketocarbonic acids a shown in the reaction scheme for 2-benzoylbenzoic acid (Reaction (13.1)): O~

"C-O

o

O~O

OH

o

(13.1)

The equilibrium favors the lactol side for the pure compound, but in slightly alkaline solutions the open, ionized form prevails [41]. Neighboring carboxyl and carbonyl groups on the zigzag edge of a graphene layer can react in an analogous way: O~

"C-O

(13.2) A voluminous literature exists on the acidic surface groups and their characterization. Therefore, this aspect of carbon surface chemistry can be here treated relatively briefly. The acidity of these groups opens a convenient way for their determination by titration with aqueous or alcoholic bases. The total of the Br0nsted acids, including phenols, reacts with aqueous sodium hydroxide solutions by neutralization adsorption, while carboxylic acids are neutralized already by the weak base sodium hydrogen carbonate carboxylic anhydrides (lactones). Lactones and lactols are opened to the carboxylate form by the stronger base

13.4 Amphoteric Character of Carbons

sodium carbonate. This method, sometimes called "Boehm titration," has found widespread application because of its simplicity. Weighed quantities of the carbons (usually 100-1000 mg) are agitated with an excess of dilute base solutions (0.1 M or, better, 0.05 M solutions are suitable), and the excess of the base is determined by back-titration as has been described earlier in detail [37, 42]. The ratio of carbon sample size to volume of base solution should be chosen so that at least 10% of the base is consumed, in order to have a sufficiently large concentration difference before and after neutralization. In the case of NaOH, a suitable aliquot is directly neutralized with 0.05N HCl. With NaHC0 3 and Na2 C0 3 , a known excess of 0.05N HCI is added and the liberated CO 2 is driven out by heating to just below the boiling temperature. Subsequently, the HCI is back-titrated with 0.05N NaOH. In the case of Na2 C0 3 , it should be kept in mind that the carbonate ions are converted to HCO~, and that a 0.05 molar (not normal!) solution must be used. An indicator of methyl red plus methylene blue or potentiometric indication is suitable. The time for equilibration can be quite long in the case of microporous carbons due to slow diffusion in narrow pores. Equilibration times of 24-48 h may be necessary [43]. The time can be shortened by equilibration at 70-100°C [44,45]. However, evaporation of water from the base solution must be prevented, and oxygen must be excluded since ageing is also accelerated, especially in aqueous media [46]. With a still stronger base, 0.1 M sodium ethoxide in ethanol, still higher adsorption values are obtained. It was shown [37, 42] that a quantity of ethoxyl groups is bound to the surface that is equal to the difference between NaOEt consumption and NaOH uptake (see Table 13.2). The conclusion is that sodium

Table 13.2 Reaction of reactive carbonyl groups with sodium ethoxide to produce the salt of a hemiacetal (Data from Ref. [37].)

Sugar char, heat treatment at 1100°C Sugar char, heat treatment at 950°C Oxidized with 02 at 400°C Activated carbon (Eponit), heat treatment at 1100°C, oxidized with (NH4)2S20S Carbon black (CK3), oxidized with O 2 at 400°C

480

460

670

680

630

640

210

180

31 0

Chapter 13 Surface Chemical Characterization of Carbons from Adsorption Studies

ethoxide reacts with reactive carbonyl groups on the surface to form the sodium salt of a hemiacetal: 0- Na+

~O

OEt

(13.3) Obviously, the acidity of carboxyl and hydroxyl groups on a carbon surface varies over a certain range, depending on the position and distance of neighboring electronegative groups and the local electronic structure. However, these acidity ranges are relatively small compared to the differences for various groups. This was demonstrated by Schwarz and associates [43, 47] by careful quasicontinuous titration of the acid functions with alkali. The titrations, in steps of 1 1-11 additions, had to be carried out extremely slowly, over several days, to allow for establishment of equilibrium, and CO 2 has to be carefully excluded from the reaction medium. The method is limited to a "window" of pH (or pKa ) values between 3.5 and 10.5 as a consequence of the buffering effect of water at very low and very high pH values. The result of the titrations was that four distinct peaks show up in the acidity distribution (Fig. 13.5) and that they agree quite well with the pH range for the bases used in the Boehm titration [25, 47]. However, with other oxidized carbons sometimes four and sometimes five peaks appeared in the acidity distribution curves [25, 48] (Fig. 13.6). The existence of distinct groups differing in acidity was also shown by conductometric titration of oxidized carbons with 0.05 M sodium methylate in methanol. Distinct breaks appear in the conductivity curve that agrees

2.5 2

1.5

£

B "to-.

0.5

0

-0.5

3

4

5

6

7

8

9

10

11

pK Figure 13.5 Distribution of acidity constants of acidic surface groups on an activated carbon oxidized with nitric acid. (Reprinted from Refs [38] and [43] with permission from Elsevier.)

311

13.4 Amphoteric Character of Carbons

0.7 0.6

-----8208 --"8208-0

0.5 C)

-...

.......... BPL

E 0.4

......... BPL-O

(5

S

~

0.3

S '+...

0.2 0.1 0

------BAX ----BAX-O ••••••••• PCB

0.8

:§ (5

E

---PCB-O

0.6

S

~ 0.4 S '+...

0.2

oa-_...........

...-..;I~ ..........-......:.............,~......--~-.-""""'--~ ...........

3

4

5

6

8

9

10

11

Figure 13.6 pKa distributions for several activated carbons in original form and oxidized with H 2 0 2 (suffix: 0). S208: from coconut shells; BPL: from bituminous coal; BAX: woodbased; PCB: from coconut shells. (Reprinted with permission from Re£ [48]. Copyright 2002 American Chemical Society.)

reasonably well with the titration values with NaHC0 3 and Na2 C0 3 [35]. Rivin [49] found very good agreement of NaHC0 3 titration values with the adsorption of diphenylguanidine from solution in benzene. The various functional groups were also identified by independent, chemical methods used in organic chemistry [38, 42]. Infrared spectroscopy has also been used for the identification of surface groups. In the beginning, the method suffered from the strong absorption of carbon materials, and poor spectra were obtained. Zawadzki used thin films of cellulose carbonized at 600°C to get acceptable transmission spectra [50], but it is debatable whether such chars are really representative for carbons. It was not possible to heat the cellulose chars

312

Chapter 13 Surface Chemical Characterization of Carbons from Adsorption Studies

to higher temperature because then the absorption becomes too strong. Infrared spectra of good quality can be obtained with modern FTIR spectrometers, especially by use of the "diffuse reflectance method (DRIFTS)." It is generally assumed that a peak at 1710-1717 cm- 1 is due to carboxyl groups. Cyclic anhydrides produce absorptions at 1840 and 1770cm- 1 [51]. The evidence for cyclic lactones is not as clear, different authors assign different peaks to such groups, and the interpretation of the spectra at lower wave numbers is also not unambiguous. Attempts have also been undertaken to distinguish between the functional groups by their decomposition products in thermal desorption spectroscopy. The problems with interpreting such spectra have been already mentioned above. Carbons with carboxyl and phenolic hydroxyl groups react with solutions of metal salts like weakly acidic cation exchangers. The metal ions are adsorbed, depending on the pH of the solution.

13.4.2 Adsorption of Acids Much less clear is the nature ofbasic sites on the surface ofcarbons. It is well known for a long time that carbons can adsorb acids. Hydrochloric acid is usually taken for the determination of acid-binding sites, and a preferred concentration is 0.05N [37, 38], analogous to the titration of acidic functions with NaOH. In particular, such carbons show basic behavior, which have been outgassed at high temperatures, e.g., 800-1100°C, and cooled to ambient temperature in a high vacuum or under an inert gas. Thus, many freshly produced carbon materials, such as activated carbons or carbon blacks, show basic reaction. When the carbons freed from surface oxides by high-temperature outgassing are exposed to oxygen (air) at room temperatures, some oxygen is chemisorbed [14]. At the same time, limited quantities of CO and CO 2 are evolved. This was also observed in experiments performed at 70-100°C [52, 53]. Obviously, the reaction ceases after some time when reactive carbon atoms are removed, which remained after the preceding decomposition reaction. It must be clarified that the true surface temperature during the chemisorption reaction is higher than the nominal reaction temperature because of the high exothermicity of the gasification reactions. On submersion of such carbons in dilute hydrochloric acid in a closed system, nearly the same quantity again of oxygen is taken up and hydrochloric acid is adsorbed at the same time, as shown in Fig. 13.7 [14]. Some hydrogen peroxide is formed, too, in the reaction, but its concentration peaks after a short time and falls to zero because carbons are good catalysts for H 2 0 2 decomposition. This second oxygen uptake occurs also in pure water; obviously it is a sufficiently strong Br0nsted acid. No acid is adsorbed in deaerated water under nitrogen [14,54]. Clearly, the formation ofbasic surface sites is associated with chemisorption of oxygen.

13.4 Amphoteric Character of Carbons

fleq.l9 HCI flmol/9 0 atoms

11--------It----It--

HCI

0_

o

300 ~

----)C

o

0/_/

__

02

.-----_

( 00

200

o/~

Ii t ll

1 100

5

10

15

20

Time (h)

Figure 13.7 Chemisorption of oxygen and HCI on immersion in dilute hydrocWoric acid of a heat-treated activated carbon from carbonized sugar char. Heat treatment at 950°C followed by "dry exposure" to 02 at room temperature. (Reprinted from Re£ [14] with permission from Elsevier.)

The adsorption isotherm for hydrochloric acid has an unusual shape (Fig. 13.8). At lower concentrations it resembles typical adsorption isotherms with a saturation uptake, but after flattening it rises again at concentrations exceeding O.1-0.2N [55-57]. The impression is that two adsorption isotherms are superimposed, one on more strongly basic sites, and one on very weak bases. The nature of the acid does not influence the uptake of HCl, HCI0 4 , H 2 S0 4 , and H 3 P0 4 at concentrations SO.lN (SO.l M for H 3 P0 4 ) [55]. Differences were observed, however, at considerably higher concentrations. In the case of organic acids, adsorption is larger and involves also van der Waals interactions to a significant extent between the graphene planes and the organic substituents of the acids. The dispersion interactions are particularly large in the case of carboxylic or sulfonic acids with "soft," easily polarized 7T electrons, e.g., of aromatic ring systems, in the hydrophobic part of the molecules. The two consecutive chemisorption reactions (before and after immersion in the acid) led to the conclusion that two oxygen atoms are involved in a basic surface site. This assumption was confirmed by Papirer et al. [58], who analyzed the gases of thermal decomposition ofbasic carbons. The hypothesis was evolved

Chapter 13 Surface Chemical Characterization of Carbons from Adsorption Studies

Adsorption (flmol/9)

,/'/' .

500 400

/

/

600

/-

---------~---~--x .~----..---_

/- ".---+

300

m

73°

,/"

200

+ 0__

•

100

0.1

0.2

0.3

0.4 C Hel

(mol/I)

Figure 13.8 Adsorption isotherms of HCI on a carbonized and activated sugar char, outgassed in vacuo at 1000°C. (Reprinted from Ref. [55] with permission from Elsevier.)

that pyrone-like structures are responsible for the basic reaction [14]. ),-Pyrone is a base that forms an oxonium ion on addition of a proton (Fig. 13.9). It is not necessary that both oxygen atoms belong to the same six-membered ring system. They could as well be located on different rings of polycyclic ring systems, provided that the 1T electron resonance system is not disturbed as exemplified in Fig. 13.10. This model was supported by some chemical reactions [59].

a

aH

1/

YY

~......./~'-/'

+ H+ + CI-

h

~~

).....~ a

Affi~ a

(I)

(II)

CI-

Figure 13.9 Basic character of pyrones. The wavy line indicates that the carbonyl group and the ether-type oxygen can be situated on different rings of polycyclic compounds (see Fig. 13.10). ')I-pyrone is the most simple compound with one ring. (Reprinted from Re£ [37] with permission from Elsevier.)

315

13.4 Amphoteric Character of Carbons

o II

Figure 13.10 Models for pyrone-type structures on polycyclic aromatic systems. (Reprinted from Ref. [37] with permission from Elsevier.)

Much earlier, Garten and Weiss [57, 60] attributed the basicity of carbons to the formation of chromene-type structures:

(13.4) Such structures are, in principle, quite similar to pyrone-type groups but less plausible to exist on the edges of graphene layers. They contain also only one oxygen atom per basic site. It was held against the pyrone model that ')I-pyrone is an extremely weak base [61]. However, it was shown later by theoretical calculations that the basicity of pyrone-type structures increases drastically when the ether-type oxygen atom and the carbonyl group are distributed over polycyclic aromatic systems similar to Fig. 13.10 due to the gain in resonance energy [62-64]. Some structures are even stronger bases than pyridine (the pKa of the pyridinium ion is 5.25). An other early theory for the nature of carbon basicity was put forward by Burshtein and Frumkin [65] and later modified by Matskevich [66]. In this "electrochemical" model the carbon surface acquires a positive charge by oxidation and oxygen is reduced to water (the vertical lines symbolize the surface): (13.5) (13.6)

316

Chapter 13 Surface Chemical Characterization of Carbons from Adsorption Studies

0.5

0.4 C)

.........

(5

E

0.3

-S ~ 0.2 0-

tt" 0.1

pH

Figure 13.11 Distribution of proton affinities for an activated carbon. (Reprinted from Ref. [61] with permission from Elsevier.)

Alternatively to Eqn (13.6), one oxygen molecule can be reduced by two electrons to hydrogen peroxide. In aqueous media, the anions of the acid, X-, are adsorbed as counter ions in the electric double layer near the carbon surface. Titration of a basic carbon surface with dilute HCI analogous to the quasicontinuous titration of acidic surface functions has been performed by Contescu et al. [61]. An activated carbon from coconut shells was used. The resulting basicity distribution curves (Fig. 13.11) show a large peak at pH 8-9 and a broad, asymmetric maximum in the pH range of 4-7 that obviously consists of two major components. A further medium-sized peak of strongly basic sites at pH> 9.5 is to its larger part outside of the "experimental window." Earlier, Zawadzki [50] had concluded from titration curves that two sites of different base strength exist with pKa values of the comjugate acids of 7.4 and < 3. Contescu et al. [61] assigned the peak at a pKa of rv8.6 to proton consumption in the reduction of quinone-type surface groups and the broad peak at pKa < 7 to a reaction of chromene-related structures. Both reactions involve electron transfer (oxidation and reduction of the surface), and rapid changes of the redox potential were measured in the suspension on immersion of the carbon and subsequent titration with acid [61]. The authors thought that pyrones are too weak bases to fall into the "experimental window." This is also the case for the 'IT basicity of the basal planes. Weak basicity is exhibited by 'IT electrons in C = C double bonds and aromatic systems. Evidence for the protonation of basal plane sites on carbons was presented by Leon y Leon et al. [56]. In Fig. 13.5 ofRe£ [61] a ratio of2.55 of adsorbed HCI (in mol) per mol of chemisorbed 0 atoms was given for a carbon black with a low oxygen content. The oxygen content before immersion was taken as a basis. This is much higher than the ratio of 1 expected for pyrone-type structures. However, from the data in Table 2 of this reference, a HCI/O ratio of 1.28 can be calculated, which is much closer to 1.

13.4 Amphoteric Character of Carbons

317

To solve the problem, Darmstadt and Roy [67] determined the surface oxygen content of several furnace blacks by use of XPS and put it into relation to their HCl uptake. They found that in all cases the surface concentration of basic sites was larger than that of surface oxygen atoms determined by XPS. The ratio of HCl/O atoms varied between 1.13 and 11.3 for the individual carbon black samples. In addition, an inverse relationship between the number of basic sites pernm 2 and the line width (full-width at half-maximum (FWHM)) of the main Cis signal indicated that the more acid molecules are adsorbed per unit area of carbon surface the fewer defects there are in the graphene layers of the surface. Such defects are vacancies, pentagons and heptagons, and, of course, layer boundaries at their edges. Defects in a graphene sheet tend to localize electrons and disturb the resonance system, and the 1T basicity is decreased. In consequence, acid adsorption on 1T sites should playa smaller role in strongly disordered carbons such as activated carbons. In agreement with this presumption, sizeable quantities of hydrochloric acid were adsorbed on high-purity graphites of small particle size [37]. The surfaces of the particles of such natural graphites consist to a large extent (c. 90%) of basal faces. With a series of synthetic graphites, the surface concentration of acid-adsorbing sites increased with decreasing surface area (Table 13.3). However, with a furnace black, the concentration of basic sites pernm2 changed only insignificantly after graphitization at rv3000°C [37]. Obviously, the cause of the surface basicity of carbons is still not satisfactorily understood. Most likely, basicity of oxygen-containing surface functions such as pyrones exists in addition to the 1T basicity of basal faces [37, 67]. Addition of isopropanol, benzene, toluene, or phenol to the hydrochloric acid solution had a deleterious effect on HCI adsorption [55]. The saturation HCI uptake at low concentrations was reduced in the presence of toluene, and

Table 13.3 Adsorption of o.oSN hydrochloric acid on graphite and carbon blacks (Reprinted from Ref. [37] with permission from Elsevier.)

Graphites Kroptrniihl AF (natural graphite) Lonza KS 75 (synthetic graphite) Lonza KS 15 Lonza KS 75/KM Carbon blacks (Degussa) CK3 Corax 3, outgassed at 300°C Corax 3, heat treatment at 900° C Corax 3, heat treatment at 3000°C

13 7.5 14 42

25 34 34 28

1.16 2.73 1.46 0.40

77 84 87 63

40 36 64 27

0.31 0.26 0.44 0.26

Chapter 13 Surface Chemical Characterization of Carbons from Adsorption Studies

318

there was no increase at higher concentrations [57]. Rivin [49] used washing with dry dioxane to remove physically adsorbed HCI while electrostatically held CI- ions remained on the surface. The adsorbed HCI can be washed out with water, in the case of nonporous carbon blacks in a reasonable time (500 ml of water was sufficient for a few hundred milligrams of carbon black), but with microporous carbons the elution is extremely slow [55]. Removal of adsorbed CI- by washing with hot water (in a Soxhlet extractor) may take weeks. Outgassing in a high vacuum at 100-120°C is much more effective. Regenerated carbon adsorbed nearly the original quantity (80-90 %) of hydrochloric acid in a second experiment in the case of a nonporous carbon black. With activated carbon, however, only 40% of the original uptake was found, but this was very likely due to the fact that not all of the adsorbed acid had been washed out [55]. No oxygen was taken up in the second acid adsorption. A carbon surface can carry basic and acidic surface groups at the same time. The concentration of basic surface sites decreases with increasing surface oxidation and creation of acidic surface groups [68]. The cause of the decrease can be the withdrawing effect of electronegative surface groups on the 'IT electron resonance system ofthe graphene layers [69]. But also pyrone-type combinations may be destroyed by oxidation ofether oxygen or carbonyl groups to carboxyl groups. A nitrogen content of the carbons increases the number of basic surface sites. This was observed after treatment of an activated carbon with ammonia at 900°C [70, 71]. Ammonia decomposes at such temperatures to radicals such as NH 2, NH, and H, which attack the carbon surface, leading to partial gasification. HCN, (CN)2' and CH 4 have been detected in the gas atmosphere [72, 73]. In the carbon surface, pyridine- or acridine-type and pyrrol-type edge sites are created, which have basic properties. An other way to produce such nitrogen-containing carbons is to carbonize organic precursor materials in the presence of nitrogencontaining compounds [74]. Such carbons showed a higher acid uptake than analogous carbons prepared without nitrogen addition. Amine groups on the surface are very likely not stable at high temperatures, in analogy to hydroxyl groups. The anions of adsorbed mineral acids are loosely bound at the surface and form a diffuse cloud of counter ions around the surface of the carbon particles. When the second oxygen chemisorption occurs on immersion in pure water, the bound counter ions are OH- ions. Obviously, the counter ions can be exchanged for other negatively charged ions, the carbons have anion exchange properties.

13-5

ELECTROKINETIC PHENOMENA

As with other colloids, the counter ions of negatively or positively charged carbon surfaces will disperse into a diffuse layer in aqueous dispersions. The ion density falls off gradually with distance, and the potential (negative or positive)

13.5 Electrokinetic Phenomena

319

approaches asymptotically zero. The extension of the double layer depends on the charge of the counter ions and the ion strength of the supporting electrolyte (for details, see textbooks of colloid chemistry). In order to determine whether a carbon surface has a prevailing acidic or basic character, it suffices to disperse it in water and measure the pH of the suspension, since the glass electrode will get in contact with the diffuse ion cloud. The measured values are often used for the characterization of carbons as their "pH". However, this is not correct since pH is defined as the negative decadic logarithm of the H+ activity in a homogenous solution. Carbons, analogous to ion exchange resins, do not have a pH. But, of course, the pH values measured in the suspension are an indication of surface acidity or basicity. When very pure water is used and the suspensions are allowed to settle, the pH of the supernatant will move toward neutral, as has been described for a basic carbon black [55]. In the presence of a neutral salt (NaCI), some ion exchange occurs, and the aqueous phase will become permanently basic [55]. When an electric field is applied to a carbon suspension, the particles will be attracted to the oppositely charged electrode. The resultant movement of the particles is called electrophoresis. However, not the total surface charge on the particles is effective. Several counter ions, especially multiply charged ions and ions with a "soft" electron shell may be specifically adsorbed on the surface (Stern layer). Further, due to friction the water molecules in immediate contact with the surface will not move during electrophoresis, or move only slowly, with respect to the particle surface. A velocity gradient is established between the water adhering to the particle surface and the free electrolyte. For practical reasons, the gradient is replaced by a stepwise velocity distribution in the theoretical treatment of electrophoresis, and a hypothetical shear plane at some distance from the particle surface is assumed. The electrolyte is treated as if it were fixed to the surface inside, and would have full velocity beyond the shear plane. The electric potential of the particles at this hypothetical shear plane is the potential effective for the electrophoretic phenomena, and it is called the electrokinetic potential or zeta potential (~-potential). It is dependent on the pH of the supporting electrolyte, becoming positive at low pH values and negative at high pH values. The ~ -potential passes through zero at a pH value that is characteristic for a given carbon. This is called the isoelectric point. The ~ -potentials can be calculated from the electrokinetic mobilities of the particles (velocity/ electric field strength). The electrokinetic mobilities are independent of the particle size, at least in first approximation. Electrokinetic mobilities can be measured by direct observation of the particle movement by use of a microscope or of the boundary between suspension and clear electrolyte separated from the suspension by centrifugation (moving boundary method). When electrolyte is forced through a fixed bed, e.g., of carbon fibers, a potential builds up between the ends of the bed. This streaming potential can also be used for the measurement of ~ -potentials. Details of these methods are described in textbooks of colloid chemistry.

Chapter 13 Surface Chemical Characterization of Carbons from Adsorption Studies

32 0

As described, the electrokinetic potential is not representative of the true surface potential (and surface charge) since some counter ions are held in the "fixed" electrolyte layer near the surface, and some other ions may be adsorbed in the Stern layer. The true surface potential passes through zero, too, when positive and negative charges on the surface are equal at a certain pH. This pH value is called the point of zero charge (PZC). The most convenient way to determine the PZC is by means of the so-called mass titration [75,76]. The pH of an electrolyte is changed in the direction toward the PZC when the solid is added. The pH approaches the PZC asymptotically with increasing ratio of mass of the solid to volume of the electrolyte (Fig. 13.12). The PZC can also be estimated by plotting the final pH vs. the initial pH of the solutions (pH drift method) [69].The values of PZC determined by these methods agree within experimental error with those obtained by surface titration methods.

Oxidized with 0.4 M HN03

Original activated carbon

12

10

8 I

I

0.

0.

• pHo = 3.0 • pHo = 5.6 • pHo = 11.0

2 0

1

4 6 8 Solid fraction (wtOlo)

2

6

• pHo = 3.0 • pHo = 5.6 .pH o = 11.0

4

10

2

0

2

8 4 6 Solid fraction (wt°lo)

10

Oxidized with 2 M HN03

10

8

• pHo = 3.0 • pHo = 5.6 A pHo = 11.0

I

0.

6

4

2L...--......L...--""'----......L...-~-----

o

2

4

6

8

10

Solid fraction (wt%)

Figure 13.12 Mass titration curves for the determination of the zero point of charge of carbons after different severity of oxidation. (Reprinted from Ref. [76] with permission from Elsevier.)

13.6 Effects on the Adsorption of Inorganic ions

321

With smooth, nonporous surfaces the zero-point of charge and the isoelectric point usually do not differ much from each other. However, when porous particles, e.g., of activated carbons, are measured, the surface of the grains or particles may be acidic in character due to ageing while the internal surface is still basic. As mentioned before, aging in narrow pores is very slow due to diffusion restrictions. The electrokineticallY measured IEP is determined by the ~-potential of the particle surface while the PZC is determined by the much larger interior surface of the particles [21].

13.6

EFFECTS ON THE ADSORPTION OF INORGANIC IONS

Neutralization adsorption of bases with univalent cations such as Na+ is used for the determination of acidic surface functions. Puri [77] reported that with Ba(OH)2 the quantity of adsorbed Ba 2+ equivalents corresponded to the NaOH uptake. However, use of Ba(OH)2 has two disadvantages. If the carbons contain adsorbed CO 2, BaC0 3 will be precipitated. Furthermore, equivalent neutralization adsorption occurs only when the acidic surface sites are in relatively close vicinity as is the case with commercial ion exchange resins (Reaction (13.7)). If they are more isolated, equimolar neutralization adsorption will occur as shown in Reaction (13.8).

t-~eOOH

eOOH + Ba(OH)2

(13.7)

Equivalent ion exchange

t

eooH eOOH

+2 Ba(OHh

~

t

eoo-

Ba2+ OH-

eoo-

Ba2+ OH-

(13.8)

Equimolar ion exchange Equimolar reaction is favored because of the smaller separation of opposite charges and minimizing of electrostatic energy. Such equimolar exchange reactions have been observed with kaolinite [78], silica [79], and titania [80]. In the adsorption of Cd2+ on activated carbon two H+ ions were released for each 2 adsorbed Cd + ion at small concentrations, but the molecular ratio decreased to 1.7 at higher concentrations and Cd 2+ uptakes [24]. The possibility of equimolar reactions should always be kept in mind in adsorption studies of bivalent ions. Cation charges higher than +2 are not very common in neutral or basic solutions due to the tendency for hydrolysis of hydrated metal ions. Whilst significant hydrolysis occurs at pH > 7, trivalent ions tend to hydrolyze already

322

Chapter 13 Surface Chemical Characterization of Carbons from Adsorption Studies

at pH values in the acidic range. However, in acidic solutions H 30+ ions will compete with other cations, and weakly acidic groups will not be dissociated. For instance, hydrated aluminum ions will form hydroxo-pentaquo complexes: (13.9) Further hydrolysis leads to binuclear and oligonuclear complex ions. The situation is similar with [Fe(HzO)6]3+. Only [Cr(HzO)6]3+ is kinetically stable at neutral pH. In the so-called basic aluminum chloride solutions at pH 4-8, the cation [Al 13 0 4(OH)Z4(H zO)lZ]7+ is formed [81]. It has a spherical Keggin-like structure with a central tetrahedrally coordinated Al 3+ ion, analogous to the structure of the phosphomolybdate anion [PMo 1Z 0 40 ]3- . Larger complex ions, in particular polynuclear ones, can close the entrances to narrow micropores and reduce the surface area available for adsorption. On the other hand, the adsorption of hydrated cations, and especially of larger, polynuclear cations, will be promoted by formation of hydrogen bonds to oxygen or hydroxyl surface functions close to the negatively charged surface site. In consequence, no simple relationship for binding by a specific surface group can be established. Carbonyl or hydroxyl groups on the carbon surface can also replace water molecules of the hydration shell of the cations, giving rise to bidentate adsorption sites. The matter becomes still more complicated with heavy-metal cations that have a "soft", easily polarizable electron shell that can also interact with the 1T electron systems of the graphene layers. Quite a large number of publications have appeared dealing with the adsorption of hydrated or otherwise coordinated metal cations for the purification of contaminated waste waters. However, the experimental conditions can not be compared with those described in the preceding sections since usually very dilute solutions are used (often in the range of 10- 5 - 10- 4 M) to simulate realistic conditions (see also Chapter 25 and Refs [4, 82]). Although no direct correlation with the number of specific surface groups can be found, in general the adsorption of metal cations increases with the concentration of acidic surface functions [24]. Infrared spectroscopic experiments showed that free carboxyl groups absorbing at 1717 cm-1 are converted to the ionized carboxylate form (1576cm- 1) on adsorption ofCd z+ ions [24]. The adsorption capacity for transition metal ions can be further increased by introducing nitrogen surface groups, e.g., by treatment with ammonia at high temperatures [83]. Increased adsorption, compared to the activated carbons in oxidized form, was observed with Cd 2 +, Ni z+, and Cu z+ ions. The authors suggest that pyridine-type nitrogen on the edge of the carbon layers is responsible. In particular pairs of nitrogen atoms in a situation analogous to that in 1,10-phenanthroline would allow very stable bidentate coordination. As mentioned in Section 13.3.1, precious metal complex ions can be reduced by the carbon to the metal [28-31]. An interesting phenomenon was observed with [Au(CN)z]- solutions that playa role in the leaching of gold ores. Clearly, such ions are bound by the basic sites of the surface. XPS studies of the adsorbed

References

gold species showed relatively sharp Au 4f peaks. The Au 4f7 / 2 binding energy of 91.5 eV, however, was in between that of elementary gold (90.8 eV) and that ofK[Au(CN)2J (93.8eV), see Ref. [84] or Section 6.8.1.4 in Ref. [82]. One can conclude that the gold is not reduced to the elementary state, but to a gold cluster compound [Aun(CN)m]X- in which gold has formally a fractional oxidation number smaller than 1.

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Chapter 13 Surface Chemical Characterization of Carbons from Adsorption Studies

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35. Kozlowski, C. and Sherwood, P.M.A. (1987). X-ray photoelectron spectroscopic studies of carbon fiber surfaces. VIII. - A comparison of type I and type II fibers and their interaction with thin resin films. Carbon, 25, 751-60. 36. Barton, S.S. and Evans, M.J.B., Halliop, E. and MacDonald, J.A.F. (1997). Anodic oxidation of porous carbon. Langmuir, 13, 1332-6. 37. Boehm, H.-P. (1994). Some aspects of the surface chemistry of carbon blacks and other carbons. Carbon, 32, 759-69. 38. Boehm, H.-P. (2002). Surface oxides on carbon and their analysis: a critical assessment. Carbon, 40, 145-9. 39. Kruyt, H.R. and de Kadt, G.S. (1929). The electric charge of colloidal carbon (in German). Kolloid-Z., 47, 44. 40. Kolthof"L I.M. (1932). Properties of active charcoal reactivated in oxygen at 400°C. J. Am. Chern. Soc., 54, 4473-80. 41. Newman, M.S. and Muth, C.W. (1951). Normal and pseudo esters of2-benzoylbenzoic acid types. III. J. Am. Chern. Soc., 73, 4627-9. 42. Boehm, H.-P., Diehl, E., Heck, W., and Sappok, R. (1964). Surface oxides of carbon. Angew. Chern.) Int. Ed. Engl., 3, 669-78. 43. Bandosz, T.J.,Jagiello,J., Contescu, C., and Schwarz,J.A. (1993). Characterization of the surfaces of activated carbons in terms of their acidity constant distributions. Ca~on, 31,1193-202. 44. Puri, B.R. and Bansal, R.C. (1964). Studies in surface chemistry of carbon blacks. Part II. Surface acidity in relation to chemisorbed oxygen. C'arbon, 1, 457-64. 45. Puri, B.R. (1970). Surface complexes on carbons. In Chemistry and Physics of Carbon, Vol. 6 (P.L. Walker, Jr, ed.). Marcel Dekker, pp. 191-282. 46. Boehm, H.-P., Mair, G., and Stohr, T. (1985). Oxidative degradation of carbons in alkaline media. Extended Abstracts) 17th Biennial Conference on Carbon) Lexington) KY. The American Carbon Society, pp. 381-2. 47. Contescu, A., Contescu, C., Putyera, K., and Schwarz, J.A. (1997). Surface acidity of carbons characterized by their continuous pK distribution and Boehm titration. Carbon, 35, 83-94. 48. Bashkova, S., Bagreev, A., and Bandosz, T.J. (2002). Effect of surface characteristics on adsorption of methyl mercaptan on activated carbons. Ind. Eng. Chern.) Res., 41,4346-5. 49. Rivin, D. (1962). Hydride transfer reactions of carbon black. In Proceedings 5th Biennial Conference on Carbon) Pennsylvania State University) University Park) PA, Vol. 2. Pergamon Press, pp. 199-209. 50. Zawadski, J. (1989). Infrared spectroscopy in surface chemistry of carbons. In Chemistry and Physics of Carbon, Vol. 21 (P.A. Thrower, ed.). Marcel Dekker, pp. 147-380. 51. Meldrum, B.J. and Rochester, C.H. (1990). In situ infrared study of the surface oxidation of activated carbons in oxygen and carbon dioxide. J. Chern. SOc.) Faraday Trans., 86, 861-5. 52. Ismail, I.M.K. and Walker, P.L., Jr (1989). Detection of low temperature carbon gasification using DSC and TGA. Carbon, 27, 549-59. 53. Zhang, Z.L., Kyotani, T., and Tomita, A. (1989). Dynamic behavior of sutIace oxygen complexes during oxygen chemisorption and subsequent temperatureprogrammed desorption of calcium-loaded coal chars. Energy Fuels, 3, 566-71.

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54. Burstein, R. and Frumkin, A. (1929). On the behaviour of outgassed activated carbon towards electrolytes (in German). Z. Physik. Chemie (Leipzig) A, 141,21920. 55. Boehm, H.-P. and Voll, M. (1970). Basic surface oxides on carbon - I. Adsorption of acids (in German). Carbon, 8, 227-40. 56. Leon y Leon, C.A., Solar, ].M., Calemma, V., and Radovic, L.R. (1992). Evidence for the protonation of basal plane sites on carbon. Carbon, 30, 797-811. 57. Garten, V.A. and Weiss, D.E. (1957). A new interpretation of the acidic and basic structures in carbon. II. The chromenel carbonium ion couple in carbon. Austral. J. Chem., 10, 309-28. 58. Papirer, E., Li, S., and Donnet, ].-B. (1987). Contribution to the study of basic groups on carbon. Carbon, 25, 243-7. 59. Voll, M. and Boehm, H.-P. (1971). Basic surface oxides on carbon - IV. Chemical reactions for the identification of surface groups (in German). Carbon, 9, 481-8. 60. Garten, V.A. and Weiss, D.E. (1957). Ion and electron exchange properties of activated carbon in relation to its behaviour as a catalyst and adsorbent. Rev. Pure Appl. Chem., 7, 69-122. 61. Contescu, A., Vass, M., Contescu, C., et al. (1998). Acid buffering capacity of basic carbons revealed by their continuous pK distribution. Carbon, 36, 247-58. 62. Suarez, D., Menendez, ].A., Fuente, E., and Montes-Moran, M.A. (1999). Contribution of pyrone-type structures to carbon basicity: an ab initio study. Langmuir, 15, 3897-904. 63. Suarez, D., Menendez,].A., Fuente, E., and Montes-Moran, M.A. (2000). Pyronelike structures as novel oxygen-based organic superbases. Angew. Chem., Int. Ed. Engl., 39, 1320-23. 64. Fuente, E., Menendez, ].A., Suarez, D., and Montes-Moran, M.A. (2003). Basic surface oxides on carbon materials: a global view. Langmuir, 19, 3505-11. 65. Burshtein, R. and Frumkin, A. (1941). Hydrogen peroxide formation in the adsorption of acids by activated charcoal (in Russian). Dokl. Akad. Nauk SSSR, Seriya A, 32,327-9. 66. Matskevich, E.S., Strazhesko, D.N., and Goba, V.E. (1974). Oxidation-reduction properties of carbon in electrolytic solutions. Adsorbtsiya Adsorbenty, 2, 36-9. 67. Darmstadt, H. and Roy, C. (2003). Surface spectroscopic study of basic sites on carbon blacks. Carbon, 41, 2662-5. 68. Puri, B.R., Singh, D.S., Nath, ]., and Sharma, L.R. (1958). Chemisorption of oxygen on activated charcoal and sorption of acids and bases. Ind. Eng. Chem., 50, 1071-4. 69. Lopez-Ramon, M.V., Stoeckli, F., Moreno-Castilla, C., and Carrasco-Marin, F. (1999). On the charactreization of acidic and basic surface sites on carbons by various techniques. Carbon, 37, 1215-21. 70. Biniak, S., Pakula, M., Szymanski, G., and Swiatkowski, A. (1999). Effect of activated carbon surface oxygen groups on adsorption of copper(II) ions from aqueous solutions. Langmuir, 15, 6117-22. 71. Mangun, C.L., Benak, K.R., Economy,]., and Foster, K.L. (2001). Surface chemistry, pore sizes and adsorption properties of activated carbon fibers and precursors treated with ammonia. Carbon, 39, 1809-20. 72. Boehm, H.-P., Mair, G., Stohr, T., et al. (1984). Carbon as a catalyst in oxidation reactions and hydrogen halide elimination reactions. Fuel, 63, 1061-3.

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73. Stohr, B., Boehm, H.-P., and Schlogl, R. (1991). Enhgancement of the catalytic activity of activated carbons in oxidation reactions by thermal treatment with ammonia of hydrogen cyanide and observation of a superoxide species as a possible intermediate. Carbon, 29, 707-20. 74. Mang, D., Boehm, H.-P., Stanczyk, K., and Marsh, H. (1992). Inhibiting effect of incorporated nitrogen on the oxidation of microcrystalline carbons. Carbon, 30, 391-8. 75. Noh, J.S. and Schwarz, J.A. (1990). Estimation of surface ionization constants for amphoteric solids. J. Colloid Interface Sci., 139, 139-48. 76. Noh, J.S. and Schwarz, J.A. (1990). Effect of HN0 3 treatment on the surface acidity of activated carbons. Carbon, 28, 675-82. 77. Puri, B.R. (1966). Chemisorbed oxygern evolved as carbon dioxide and its influence on surface reactivity of carbons. Carbon, 4, 391-400. 78. Weiss, A. (1959). Cation exchange properties of clay minerals III. Cation exchange in kaolinite (in German). Z. AnoIg. Allg. Chern., 299, 92-120. 79. Boehm, H.-P. and Schneider, M. (1959). The hydroxyl groups on the surface of the amorphous silicon dioxide "Aerosil" and their reactions (in German). Z. Anorg. Allg. Chern., 301, 326-35. 80. Herrmann, M. and Boehm, H.-P. (1969). On the chemistry ofthe titanium dioxide surface - II. Acidic hydroxyl groups on the surface (in German). Z. Anorg. Allg. Chern., 368, 73-86. 81. Baers, R.F. and Mesmer, R.E. (1976). The Hydrolysis of Cations. J. Wiley & Sons, p. 112. 82. Bansal, R. C., Donnet, J.-B., and Stoeckli, F. (1988). Active Carbons. Marcel Dekker, Chapter 6. 83. Jia, Y.F., Xiao, B. and Thomas, K.M. (2002). Adsorption of metal ions on nitrogen surface functional groups in activated carbons. Langrnuir, 18, 470-8. 84. McDougall, G.J., Hancock, R.D., Nicol, M.J., et al. (1980). The mechanism of adsorption of gold cyanide on activated carbon. J. South African Inst. Mining Metall., 80,344-56.

ADSORPTION ON FULLERENES Fabian Suarez-Garcfa, Amelia Martfnez-Alonso, and Juan M.D. Tasc6n Instituto Nacional del Carbon, CSIC, Oviedo, Spain

Contents 14.1 Introduction 14.2 Adsorption for Porosity Characterization 14.3 Adsorption in the Study of Surface Energetics: Nonreactive Permanent Gases 14.4 Adsorption of Organic Gases and Vapors 14.5 Oxygen Adsorption 14.6 Adsorption Studies using IR Spectroscopy 14.7 Hydrogen Adsorption: Gas Storage 14.8 Adsorption from Solution: Environmental Applications 14.9 Adsorption from Solution: Analytical Applications 14.10 Adsorption from Solution: Colloidal and Biological Systems 14.11 Conclusions Acknowledgments References

32 9 330 33 2 338 34 1 343 346 35 1 353 357 359 359 359

14.1 INTRODUCTION

The first report of the existence offullerenes in 1985 [1], and the subsquent discovery in 1990 of a method to produce them in macroscopic amounts [2], paved the way to a new era of carbon science that involves curved surfaces on the nanoscopic scale. As is well known, the aggregation of fullerene molecules at moderate temperatures and pressures leads to molecular solids termed fullerites. The C 60 (buckminsterfullerene) and C 70 fullerenes and the corresponding fullerites are the easiest to produce, and for this reason they have been the subject of most experimental works. Certain aspects of the solid-state science of fullerenes (e.g., crystal structures, phase transitions, formation of exo- and Adsorption by Carbons ISBN: 978-0-08-044464-2

© 2008 Elsevier Ltd. All rights reserved.

329

330

Chapter 14 Adsorption on Fullerenes

endohedral compounds) relevant to surface studies have been nicely summarized by Bandosz et al. [3] More detailed information can be found in the (already classical) book by Dresselhaus et al. [4]. Adsorption studies on fullerenes have been carried out with a variety of objectives. Thus, in addition to characterizing porosity by means of physisorption, extensive work with either inert gases, organic vapors or even reactive gases as adsorbates has been focused on the characterization of the surface energetics of this type of carbonaceous material. In the case of oxygen, the objective has changed from an initial interest in explaining the high oxidative reactivity of fullerenes to the more recent concern with the effect of oxygen on properties such as electrical conductivity. Although the amount of work devoted to fullerenes has been scarce compared with the interest shown in carbon nanotubes, fullerenes have been studied as hydrogen adsorbents in connection with the storage of hydrogen as a source of energy. In the field of adsorption from aqueous solutions, the applications of fullerenes as analytical tools clearly prevail over other topics such as environmental or biological applications. This disparity in objectives makes the corresponding groups of papers very different from each other. Therefore, in this chapter, we have classified adsorption works on fullerenes according to mixed criteria based on the nature of the adsorbate, the objectives pursued and the methodology followed. This explains the disparity that may exist between the sections that constitute the chapter. The complementary research field where fullerenes constitute the adsorbate rather than the adsorbent has produced interesting results for C 60 adsorption on such materials as zeolite Y [5], activated carbons [6] carbon nanohorns [7], or even clusters of C 60 itself [8] However, this topic is not reviewed here since this book is concerned with solid carbons used exclusively as adsorbents. For similar reasons, we have excluded from this study fullerene-like noncarbon structures such as WS 2 , MoS 2 , NbS 2 , TiS 2 , or BN despite their interest as adsorbents [9] (a review on hydrogen storage on these inorganic nanotubes has been published by Chen and Wu [10]). However, adsorption works on fullerene soot (also termed fullerene black, a solid formed by the condensation of carbon species from the gas phase from which fullerenes are usually extracted) are discussed in view of their possible relevance to fullerenes. Also included in this chapter are simulations of adsorption on schwarzites, due to the close connection between this (still hypothetical) structure and that of the fullerenes.

14.2 ADSORPTION FOR POROSITY CHARACTERIZATION

Soon after the discovery of methods for the mass production of fullerenes, the pyrolysis and gasification behavior of these novel carbons attracted considerable interest due to unexpected findings regarding traditional carbons [11, 12]. In this context, Ismail and Rodgers [11] reported some of the first results on adsorption on fullerene solids. Batches of C 60 of different origin were studied.

14.2

Adsorption for Porosity Characterization

331

Kr, N z, and Oz isotherms at 77 K yielded a low surface area, but CO z adsorption at 298 K indicated that the C 60 crystals studied contained micropores. The solids in each batch studied exhibited different characteristics depending on sample preparation, purification, and age. Kaneko et al. [13] detected microporosity when adsorbing N z on C 60 powder, and interpreted this as being due to the presence of point defects, which had probably been generated by desolvation (i.e., the removal of excess solvent used to extract/purify the fullerene) during heating. Later on, the same team investigated the control of the concentration of defects in C 60 crystals by recrystallization and annealing [14]. N z adsorption isotherms showed the presence of both mesopores (average width of 5 nm) and micropores (average width of 0.8 nm), of which the former disappeared by annealing to rv393 K, whereas the micropores remained even when heating up to 673 K. The authors associated the mesopores with the aggregation of point defects and stacking faults, whereas the micropores were attributed to molecular defects and octahedral vacancy sites. Rathousky et al. [15] found evidence for low-pressure hysteresis in cyclopentane adsorption on a C 60 /C 70 mixture. Later on, they characterized pure C 60 powder by krypton and cyclopentane adsorption [16, 17]. Krypton, which was selected as adsorbent due to the very low surface area of the material, gave rise to a sigmoidal isotherm [16]. Cyclopentane was found to penetrate into the bulk of the C 60 crystals, its presence being detected in the octahedral interstices between the fullerene molecules [17]. Schlagl and coworkers used N 2 adsorption to study the porous texture of several types of fullerene black [18]. The surface areas varied over a rather wide range (11-557 m 2 / g). The fullerene blacks studied contained small amounts of soluble fullerenes. Consequently, the relevance of these results to fullerenes is not much significant. More recently, Beck et al. [19, 20] used N z adsorption to characterize the porosity of fullerene blacks modified by the Diels-Alder reaction. They found that the surface area of micropores increased considerably

after this reaction. Here too, the results bear little relevance to fullerenes since the fullerene blacks studied had been preextracted with toluene to remove the smallest traces of soluble fullerenes. Cascarini de Torre and coworkers [21] measured adsorption isotherms ofN2 , 02' and Ar at 77 K and CO 2 at 298 K on shungite from Zazhoginskoye (Karelia, Russia), a natural carbonaceous material from which fullerenes can be extracted. This rock is made up of a homogeneous distribution of crystalline silicate particles in a noncrystalline carbon matrix. The adsorption results indicated that the material has a low surface area ( rv 25 m z/ g) and an average pore radius of rv 1.7 nm. The gas-solid potential distribution suggested a rather homogeneous surface, with maxima at similar adsorption potentials for N z and Ar. Nagano et al. [22] measured the CO z uptake in C 60 in a study of the effects of supercritical fluid treatment, the aim of which was to remove solvent molecules from C 60 . Carbon dioxide was found to interact strongly with C 60 , and to have a remarkable effect on the orientational phase transition of C 60 crystals at 250 K. The kinetic features of the process suggested that CO 2 absorbs inside the C 60

332

Chapter 14 Adsorption on Fullerenes

solid lattice rather than adsorbing physically on micropores. Later on, Gusev et al. [23] studied nitrogen and argon adsorption on the fullerene C 60 (99.5% purity) and a mixture of (76% C 6o /22% C 70 ), and found no trace of microporosity in their samples. Likewise, Martinez-Alonso et al. found no case of hysteresis or micropore filling in adsorption isotherms of N 2 [24] or Ar (77 K) [25], and the CO 2 (273 K) isotherm they measured was linear [25]. They attributed this lack of microporosity to the high purity and crystallinity degree of the C 60 used. In the above works it was customary to compare novel findings for fullerenes with the behavior ofwell-known carbonaceous solids such as graphite [11], Saran char [11], various types of carbon black [16, 23, 24], orpolycrystalline diamond [16, 24]. Strong similarities were found between fullerene and "graphitized" carbon black for adsorption at low coverages of either Kr [16] and N 2 / Ar [23]. A close similarity was also found between the heterogeneity degrees calculated from the experimental isotherms for C 60 and polycrystalline diamond [24].

14.3

ADSORPTION IN THE STUDY OF SURFACE

ENERGETICS: NONREACTIVE PERMANENT GASES

Some of the papers discussed previously were aimed at characterizing surface energetics rather than porosity, and included theoretical calculations and/or simulations. Thus, Gusev et al. [23] analyzed their experimental data for N 2 and Ar argon adsorption on C 60 using a virial expansion in the Henry's law region and found that, in the low-pressure limit where the fluid-fluid interactions are negligible, the N 2 interaction with the fullerene surface is macroscopically similar to the interaction with "graphitized" carbon black. However, on most of the monolayer the N 2 and Ar affinity for the fullerenes was weaker than for "graphitized" carbon black. Martinez-Alonso et al. [24, 25] combined grand canonical Monte Carlo (GCMC) simulations and experimental isotherms in their studies of adsorption of simple gases (N 2 and Ar at 77 K, and CO 2 at 273 K) on high-purity C 60 . In the simulations, they employed a perfect crystalline structure (face-centered cubic, fcc) of C 60 molecules with lattice parameters and a density that matched the experimental values. The agreement between the simulated and experimental isotherms for all the gases studied was excellent. The adsorption energy distribution functions were calculated from the experimental isotherms, and 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, the experimental distribution reflecting 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 matched those of other authors well (see below), even though very different adsorbates and methods of study were used. Ar and CO 2 adsorb in a solid-like phase in the voids of the fullerene solid. The contribution of the "internal" space to the

14.3 Adsorption in the Study of Surface Energetics: Nonreactive Permanent Gases

333

total area was estimated to be 30%. Values for the cross-sectional areas of the gases employed were also given. In a subsequent paper, Tascon and Bottani [26] carried out 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 nitrogen adsorption, could be ascribed to the difference in surface areas and degree of heterogeneity between the two solids. More recently, the same authors [27] studied ethylene adsorption on C 60 using GCMC simulations. The results validated the simulation model employed and confirmed the assignment of adsorption sites previously reported for other gases. A map of the simulation cell obtained with methane as probe molecule (very similar to that obtained previously with nitrogen) [24] is shown in Fig. 14.1. The C 60 solid exhibits three preferential sites for adsorption: one is located between four fullerene molecules, the second is located in the channels formed between two fullerene molecules, and the third is on the top of the C 60 molecules. The analysis of the adsorption energy distributions with the aid of the gas-gas interaction potential suggested that ethylene is adsorbed in a liquid-like state into the voids of the solid, and that the adsorbed molecules prefer aT-shaped stacking, in agreement with the calculations and experiments reported by other authors [28]. N ext we will discuss a series of theoretical studies from Sandler and coworkers on fullerenes and schwarzites. Following a chronological sequence, we will start with adsorption on schwarzite, a hypothetical structure related to that of the

Figure 14.1 Topographic map ofthe C 60 simulation cell obtained with an ethylene molecule. The X and Yaxes are in arbitrary units and the Z-axis is in angstroms. (Reprinted from Ref. [27] with permission from Elsevier.)

Chapter 14 Adsorption on Fullerenes

334

fullerenes but encompassing convex curvature (either alone, or combined with concave curvature). The interest of these authors in schwarzite was motivated by the possibility of using this and other nanoporous carbons to separate gases of similar dimensions (carbon molecular sieves). Jiang and Sandler chose for their calculations the so-called buckygym C 168 schwarzite [29], and assumed it to be rigid. This model structure has convex and concave surfaces as a result of combining Sp2 and Sp3 hybridizations of carbon atoms, and contains two types of pores with average diameters of 0.7 and 0.9 nm. The pores in the same layer are isolated from each other, but they are connected with those in the neighboring layers by channel intersections. Jiang and Sandler simulated the adsorption of O 2 and N 2 by the GCMC method [30], whereas to simulate the adsorption of an equimolecular 02-N2 mixture they used both this and the Gibbs ensemble Monte Carlo (GEMC) method [31]. Regarding the pure gases, the adsorption isotherms, Henry's constants and isosteric heats of adsorption were calculated for each gas at different temperatures. The calculations showed the dependence of the isosteric heat of adsorption on temperature to be small. For the equimolecular 02-N2 mixture, the GCMC and GEMC methods yielded consistent results. Predictions for the mixture adsorption using the ideal adsorption solution theory (lAST) based solely on the adsorption of pure gases agreed well with the simulation results. The authors of the works just mentioned [30, 31] warned that the accuracy of the Lennard-Jones interaction potentials is critical for accurately computing the properties from molecular simulation, and that inaccurate potentials would lead to large errors. More specifically, they pointed out that the use of parameters such as the Steele potential, which is based on graphite, could lead to errors when calculating the Lennard-Jones interaction potentials, since the effect of surface curvature would not be taken into account. Accordingly, Jiang et al. [32] carried out further calculations for 2, N 2' and a mixture of these two gases in the proportion found in air using two types of potentials for the additive atomatom interaction of each gas with carbon schwarzite. In addition to the Steele potential, they used an ab initio potential obtained from first-principles quantum chemical computations. Their results showed that only the ab initio potential could predict the large adsorption separation the authors expected for 02 and N 2 on C 168 schwarzite. With both potentials, the adsorbed molecules were found to preferentially align along the channel intersection of the schwarzite structure. The predictions for mixture adsorption using the lAST again agreed with the simulations. More recently, Jiang and Sandler carried out similar studies for the adsorption of CO 2, N 2, and their mixture [33] on the same C 168 schwarzite model adsorbent. As an illustration of their results, Fig. 14.2 shows the calculated (competitive) adsorption isotherms, as well as the selectivities of CO 2 over N 2 as a function of pressure for a CO 2-N2 (0.21:0.79) mixture (the composition of this mixture corresponds to the flue gas emitted from the complete combustion of carbon with air). As the isotherms show, the use of the ab initio potential results in a larger difference between the amounts of adsorbed CO 2 and N 2

°

335

14.3 Adsorption in the Study of Surface Energetics: Nonreactive Permanent Gases

8

:§ (5

E

1000

6

C\l

z

B

S

(ti Z v

()

4

N2 C02

en

ab initio Q • Steele 0 •

2

100 C168 (Steele)

oo.-iiiiiGII=tllIE:I:::Q::r:::c::r.dIt:::z:::lit.'c~==~=a;d)

1

10

100

P(kPa)

1000

10000

10

.4-' -0- -

....

-O--Siiicalite

Io..o-I...........~_ _............~-""-..........

1

10

100

....-..-'--l.................".,

1000

10000

P(kPa)

Figure 14.2 Left, adsorption isotherms of the CO 2 -N 2 mixture (bulk composloon CO 2 /N 2 = 0.21:0.79) in the C 168 schwarzite as a function of the total bulk pressure. Right, selectivity of CO 2 over N 2 as a function of the total bulk pressure (bulk composition CO 2 /N 2 = 0.21:0.79) in the C 168 schwarzite (with the Steele and ab initio potentials), silicalite, Na-ZSM-5 (Si/AI = 23), and Na-ZSM-5 (Si/Al = 11). (Reprinted with permission from Ref. [33]. Copyright 2005 American Chemical Society.)

compared with the results obtained using the Steele potential. The selectivities are also higher when calculated with the ab initio potential (values between 100 and 300) than with the Steele one (overall value r-v20). As zeolite membranes have an excellent selectivity to separate CO 2 and N 2 by competitive adsorption [34], the authors also simulated the CO 2 /N 2 competitive adsorption on three types of zeolites, and included the results in Fig. 14.2. These simulations suggest that the SC02 /N2 selectivity for the C 168 schwarzite, predicted by means of either the ab initio or the Steele potential, is greater than that of silicalite, but lower than those of the Na-ZSM-5 zeolites (the increase in selectivity with decreasing Si/AI ratio in the latter zeolite is attributed to an increase in nonframework Na+). The authors therefore concluded that nanoporous carbon adsorbents such as the C 168 schwarzite may be useful for the separation of flue gases. Following their work with schwarzites, Sandler and coworkers carried out theoretical studies on N 2 adsorption at 77 K on C 60 [35] and C 70 [36] using the ab initio-based potential. In the case of C 60 ' Jiang et al. [35] considered the adsorptions on the surface of and within a C 60 crystal separately, these locations yielding type II and type I isotherms, respectively. On the C 60 surface, with increasing pressure, the N 2 molecules were found to sequentially occupy three favorable sites: octahedral ones (between four C 60 ), tetrahedral ones (between two C 60 ) and the top of a C 60 molecule. Therefore, the nature of the sites and the energy sequence agree with results from other teams [24, 27] (see also Sections 14.4 and 14.6). Finally, multiple layers are formed and wetting occurs as the bulk N 2 saturation pressure is reached. Within the C 60 crystal, however, the use of the ab initio potential led to a significantly greater adsorption than the well-known Steele potential. N 2 molecules were observed to intercalate only the octahedral sites, the isosteric heat of adsorption being almost constant.

Chapter 14 Adsorption on Fullerenes

336

Ideal hcp: cIa =1.63

Rhombohedral

fcc

y

Deformed hcp: cIa =1.84

z

~x

Monoclinic

Figure 14.3 Orientational ordering of C 70 in various crystal phases. The semitransparent plane represents the plane along which N 2 was adsorbed in the simulations. (Reprinted with permission from Ref. [36]. Copyright 2005 American Chemical Society.)

In a subsequent study on N 2 adsorption on C 70 ' Arora et al. [36] carried out quantum mechanical calculations to predict N 2 adsorption on five different known structures for C 70 . In this case it has been found that, besides the surface curvature of the C 70 molecule, an additional difference with graphite may arise from changes in the electronic configuration due to the presence of five-membered rings. The surface area, monolayer capacity, and isosteric heat of adsorption were calculated for various C 70 crystal phases [37] that are shown in Fig. 14.3: fcc, deformed hexagonal-closed-packed (hcp I), ideal hexagonalclosed-packed (hcp II), monoclinic (mono), and rhombohedral (rh). Figure 14.4 shows the isosteric heats of adsorption (q~) for N 2 in all of these structures, calculated using both the fluctuation theory and numerical differentiation over a range of loading. The results from both methods are consistent for all crystal types over the entire range of loading. There is a considerable difference in the q~ at the infinite dilution limit as shown in Fig. 14.4. The fcc crystal has the highest value of q~ as a result of its stronger affinity for nitrogen. It can also be seen that the shear-induced phase transformation has a greater effect on the heat of adsorption (substantial drop in q~ between the rh and the hcp II phases) than the orientational ordering transformation (equivalent q~ values for the hcp and mono phases). The isosteric heats of adsorption obtained also indicated that the C 70 fcc crystal surface has a similar affinity for nitrogen to the C 60 fcc crystal surface, both being considerably higher than that of the planar graphite sheets.

14.3 Adsorption in the Study of Surface Energetics: Nonreactive Permanent Gases

337

24 22 20 (5

E -... J

C (;)

0-

•

• fcc iii. hcp I "I' hcp II • mono

•

• rh

18 16 14 12 10 8 0.01

0.1

1

10

(Jlmol/m 2)

Figure 14.4 Isosteric heat of adsorption of N 2 on various C 70 crystal structures at 77 K as a function of loading. The points marked with symbols were obtained from the fluctuation theory, and the solid curves were obtained from numerical differentiation of the configurational internal energy. Reference codes for crystal structures: see text. (Reprinted with permission from Ref. [36]. Copyright 2005 American Chemical Society.)

The adsorption of noble gases on fullerenes was studied by Breton et al. [38] with the objective of defining the conditions that lead to the endohedral or exohedral adsorption of an atom, and also to determine the criteria for the confinement of an atom in a cage. A simple model of interaction potential based on a continuum description of the C 60 molecule was used to describe the encaging properties of alkali metal ions or rare gas atoms. Later on, these authors [39] studied the equilibrium structure of the noble gas-C 6o exohedral complexes (dimer and trimer) on the basis of empirical potentials. They found that the complexes display radial bonds that have magnitudes similar to those between noble gases and aromatic species, and that these complexes behave like floppy supermolecules due to the small corrugation of the fullerene surface. Comparisons were made with equivalent complexes of graphite or benzene instead of C 60 . More recently, Gburski and coworkers used the molecular dynamics method to study systems consisting of a C 60 molecule surrounded by a monolayer or multilayer Ar film [40], as well as exohedral complexes of Ar and Ne that form an ultrathin monolayer film physisorbed on a fullerene surface [41]. Interestingly, since the Ar-fullerene attraction is much stronger than the Ar-Ar attraction, the Ar atoms form a kind of "atmosphere" that surrounds the surface of the C 60 "ball" in the C 60 Ar n conglomerate, which is composed of a fullerene molecule coated with a few dozen argon atoms. Figure 14.5 shows a snapshot of the dynamic, spherically shaped monoatomic layer formed by argons spreading out more or less evenly over the C 60 surface. Szybisz and Urrutia [42] used a physisorption potential to describe the adsorption of 4He inside and outside a single C 60 molecule. They concluded that

Chapter 14 Adsorption on Fullerenes

Figure 14.5 Snapshot of the instantaneous configuration of the Ar atmosphere surrounding C 60 at 48K. Reprinted with permission from Re£ [40]. © 2003, The American Physical Society.

only one 4He atom may be introduced in this fullerene, and that its binding energy is very strong. These authors studied the energetics of the adsorption and determined the structure of the films within the framework of nonlocal density functionals. The evolution toward bulk liquid and surface thickness at the free interface was discussed. In a step forward in the investigation of adsorption of helium isotopes on curved substrates, the same team [43] showed that 3He impurities in sufficiently large 4He systems adsorbed onto substrates with curved geometries form surface bound states. They also found that a single 3He impurity diluted into adsorbed structures such as 4He on the external surface of C 60 behaves as on films on planar substrates and as on 4He pore clusters.

14.4

ADSORPTION OF ORGANIC GASES AND VAPORS

Most work on the interaction of organic vapors with fullerenes has been carried out using inverse gas chromatography (IGC) [44-47]. This is an extension of traditional gas chromatography in which the material to be investigated is packed into a gas chromatographic column, and volatile probe molecules of interest are injected into it. The application of IGC to the study of the surface energetics of different types of carbons has been reviewed by Bottani and Tascon [48]. Abraham et al. [44] determined the gas-solid partition coefficients

14.4 Adsorption of Organic Gases and Vapors

339

for 22 gases and vapors on a C 60 /C 70 mixture using IGC at near zero surface coverage. The probe molecules studied included aliphatic (alkanes, alkyl halides, ethers, esters, ketones, alcohols) and aromatic compounds with different substituents. The results were analyzed using a solvation equation that linearly relates a given property (in this case, the partition constant) ofa series ofsolutes in a fixed phase with different solvation parameters that characterize the solubility properties of the probe vapors (dipolarity-polarizability, 'IT interaction, hydrogen bond formation ability, and dispersion interactions). It was concluded that fullerenes are weakly polarizable and have some hydrogen bond basicity, in agreement with their behavior as "giant closed-cage alkenes" rather than as polyaromatic molecules. The same methodology was used later to study the adsorption of a larger series of organic compounds on fullerene, fullerene-coated surface acoustic wave sensors, graphite, and low-polarity polymers [45]. It was shown that the linear solvation equation calculated for the fullerenes by IGC can be used to determine the relative vapor sensitivities of the fullerene-coated surface acoustic wave sensors. In addition, this equation is useful for comparing the sensitivity of different materials. In all the cases studied in this work, sorption was caused primarily by dispersive interactions. The assembled fullerene layer behaved in a similar way to nonpolar sorbents (graphite and low-polarity polymers) in terms of adsorption selectivity, but yielded less sensitive vapor sensors than linear organic polymers. Davydov et al. [46] used IGC to determine several adsorption thermodynamic properties (equilibrium constants and adsorption heats) for the adsorption of organic compounds on C 60 crystals, and compared them with those obtained for "graphitized" carbon black. The adsorption potential of the surface of fullerene crystals was much lower than that of a carbon black surface. The dispersive interaction of organic molecules with C 60 is much weaker than with carbon black. The adsorption equilibrium constant for alkanes and aromatic compounds is therefore lower in the case of fullerenes. Aliphatic and aromatic alcohols as well as electron-donor compounds such as ketones, nitriles and amines were adsorbed more efficiently on the surface of fullerene crystals. This was taken as proof that fullerene molecules have electron-donor and electron-acceptor properties, which is in agreement with the results of Abraham et al. [44] Papirer et al. [47] showed also by means of IGC that the dispersive component of the surface energy is lower for C 60 than for graphite or carbon black. As an illustration, Fig. 14.6 compares the adsorption energy distribution curves for n-heptane on C 60 , two synthetic carbon blacks (A and B, differing only in the batches), a natural graphite (A) and a synthetic graphite (B). The carbon blacks and graphites show some similarity, with maxima at 18-19 k]lmol (assigned to graphene layers) and 33-34 k]/mol (assigned to adsorption sites located on prismatic planes). For the fullerene, the maximum on the lower-energy side (c. 20 k]lmol) was assigned to graphene-like structures and the second one to oxygenated surface sites; indeed, the occurrence of oxidation was detected by X-ray photoelectron spectroscopy (XPS). No assignment was made to the third peak (29 k]lmol). Therefore, the interpretation of Papirer et al. is not the same as that proposed by other authors [24, 27, 35] (see also

Chapter 14 Adsorption on Fullerenes

34°

0.25

0.20

0.15 0.10

0.05

o 10

16

22

28

34

40

Energy (kJ/mol)

Figure 14.6 Comparison of n-heptane adsorption energy distribution curves determined on C 60 and other carbon materials. (Reprinted from Ref. [47] with permission from Elsevier.)

Section 14.6) for similar three-peak distributions. Specific interactions with cyanomethane, pyridine, chloroform, nitromethane, and i-butanol (polar compounds) exhibited high values for the fullerene, which qualitatively reveals the electron-donor character of C 60 , in agreement with the results of Abraham and coworkers [44]. Chao and Shih [49] used a piezoelectric crystal detection system to study the adsorption of various organic molecules on C 60 . The selectivity of C 60 for polar organic compounds followed the sequence: carboxylic acids>aldehydes> amines> alcohols> ketones. The reversibility of the piezoelectric crystal oscillation frequency during desorption allowed the authors to establish the type of interaction that is produced between organic molecules and fullerene. The behavior of polar molecules must be classified as physical adsorption, except for amines and dithiols, which were chemisorbed. Regarding nonpolar organic molecules, alkynes exhibited a much stronger adsorption on the fullerene than alkenes or alkanes. Chemisorption was also observed to occur in the case of alkynes and 1,3-dienes. The authors concluded that the fullerene-coated piezoelectric quartz crystal can be effectively applied as a detector for various different organic compounds.

14.5 Oxygen Adsorption

34 1

More recently, Hayashi et al. [50] found that toluene can be retained by adsorption on C 6o Pd n , a polymer-like material, at room temperature and at low toluene concentrations. Toluene seems to absorb through its 1T-electrons on partially positive Pd atoms of C 60 Pd n • Theoretical studies have suggested that 1T-electrons of C 60 and toluene overlap through the d-electron orbitals of a Pd atom (thus, not only physical adsorption takes place). This may open a route to fullerene-based materials as adsorbents for harmful volatile organic compounds (VOCs). Other recent studies on organic vapor adsorption on C 60 are connected with either applications in chromatography [51], or as a reference for comparison with carbon nanotubes [52]. Mixteco-Sanchez and Guirado-Lopez [53] carried out semiempirical (MNDO) and ab initio (density functional theory) calculations for the structural and electronic properties ofthiol [SCH3 and S(CH3)2CH3] molecules adsorbed on C 60 and various types of carbon nanotubes. The results showed that, in the low-coverage regime, the adsorbed thiols prefer to aggregate as a cluster on one side of the C 60 cage, something which, according to the authors, could be of fundamental importance for the synthesis of C 6o -Langmuir monolayers in specific environments. With increasing coverage, increasing repulsion desestabilizes the molecular bundle and a transition to a more unform distribution is achieved. The authors also observed considerable distortions of the spherical carbon structure upon thiol adsorption, which clearly demonstrate the considerable strain to which fullerene materials may be subjected. Turning our attention now to studies on the by-products of producing fullerenes as adsorbents for VOCs, a so-called fullerene-type deposit was investigated as an adsorbent in connection with its possible use in organic compound gas chromatographic separation [54]. At the same time, a fullerene-extracted soot was studied as an adsorbent for collecting VOCs in ambient air [55]. In more recent works, the adsorption of organic vapors such as benzene and ethanol on fullerene blacks [56, 57] has been compared with that of permanent gases (Ar, N 2 , CO 2 ).

14.5

OXYGEN ADSORPTION

In 1992, Rao and coworkers [58] reported pioneering experimental work by XPS on oxygen and nitrogen adsorption on C 60 films. The interactions of both gases with the fullerene were strong, and a sharp feature around 400.6 eV in the case ofN2 at 80 K was attributed to a strongly chemisorbed molecular species. In the case of oxygen, reactive interaction with the formation of oxygenated C 60 was found to occur without any special irradiation treatment. The same authors [59] also found strong interactions of fullerenes with transition metals such as Cr, Ni, and Cu deposited on the C 60 films. Schlagl and coworkers were also among the first to investigate C 60 interaction with oxygen [60], although in connection with degradative chemical reactions

Chapter 14 Adsorption on Fullerenes

34 2

o

;

~ Intercalation

Peroxides?

Insoluble polymer

Opened cages

Reactive intermediates

Figure 14-7 Reaction pathway for the thermally induced oxidation of C 60 with molecular oxygen. (Reprinted from Ref. [61] with kind permission of Springer Science and Business Media.)

(alluded to above [11, 12]) rather thanjust adsorption. Later on, they summarized the results ofoxidation experiments on solid C 60 and related them to intercalation and de-intercalation experiments with 02' CO, and CO 2 [61]. The intercalated species were characterized by temperature-programmed desorption (TPD) and infrared (IR) spectroscopy. Figure 14.7 shows a scheme proposed by these authors for the reaction pathway for C 60 with oxygen. It has been found that the intercalation/de-intercalation process of molecular oxygen in C 60 formed clathrates in the interstitial voids of the C 60 lattice. Therefore, once exposed to the oxygen, C 60 samples cannot be retrieved without changes to their original form. The C 60 material either contains intercalated oxygen or is to some extent oxidized or polymerized due to the heat treatment necessary for removing the oxygen. In the light of these results, the authors acknowledged that C 60 could not be regarded as an appropriate host lattice for the intercalation of oxygen [60]. More recently, Wu et al. [62] studied oxygen adsorption on the surface of Rb 6 C 60 films in connection with the superconducting properties of this and other alkali fullerides, as their electrical conductivity disappears after they are exposed to air. XPS and ultraviolet photoelectron spectroscopy showed that oxygen first adsorbs rapidly to form a peroxide on the top surface. After most of the Rb atoms intercalated in the C 60 film have moved to the surface, a linear oxygen uptake occurs together with the formation of carbonate and superoxide species. Also in connection with electrical conductivity, Tanaka et al. [63] carried out a study on the semiconducting properties of C 6o /zeolite Y and K-C 6o lzeolite Y systems and their dependence on a gas atmosphere. Oxygen

14.6 Adsorption Studies using IR Spectroscopy

343

adsorption experiments under UV irradiation have resulted in both rapid and slow current decays with time, indicating that the photogenerated carriers are mainly electrons, with a small contribution from holes. The slow current decay has been interpreted as the diffusion of oxygen into zeolite pores. The authors also pointed out that ethylene sensing on C 6o /zeolite is possible in the dark and follows the behavior of a Langmuir-type isotherm, which is attributable to the compression of ethylene molecules into zeolite pores. Matsumoto et al. [64] investigated gas occlusion in C 60 crystals by spectroellipsometry. They found that some oxygen remains in the voids (associated with polycrystals) in chemisorbed form. This is in contrast with the behavior of C 60 crystals in the presence of He, Ar, H 2 , or N 2 , where the spectra changed reversibly with pressure, in accordance with a physisorption model whereby gas molecules enter the voids and are occluded as a quasiliquid. Niklowitz et al. [65] studied the interaction of oxygen molecules with a fullerene surface using electron energy loss spectroscopy and TPD. On the basis of the vibrational excitation behavior, the authors concluded that molecular oxygen was physisorbed on C 60 under the conditions studied (20 K). In other words, the adsorbed molecules were only weakly perturbed by the C 60 substrate.

14.6

ADSORPTION STUDIES USING

IR

SPECTROSCOPY

In this section, we will review a series of papers [66-72] on the adsorption of several gases with different reactivities (carbon and nitrogen oxides, light hydrocarbons, alcohols) on C 60 fullerene. The works discussed here were produced by a single team (Folman and coworkers) and have in common the experimental approach used, viz. the study of the species adsorbed on C 60 films by IR spectroscopy. Some other papers dealing with the adsorption of some of these gases (C0 2 , light hydrocarbons) on C 60 have been discussed elsewhere in this chapter as they bear a closer relation (in experimental methodology or objectives) to the topics treated in those sections. As early as 1992, Fastow et al. [66] reported the IR results for CO and NO adsorption on C 60 . The spectra recorded at 77 K for CO adsorbed on C 60 films, which have led to further analyses being carried out, are reproduced in Fig. 14.8. Two partially overlapping absorption bands, positioned at 2135 ± 1 and 2128 ± 1 cm- 1 , can be observed. The appearance of two bands suggests that CO adsorbs on two different sites on the C 60 surface. The large spectral shifts regarding gas-phase frequency (2153 em -1) indicate that the interaction is relatively strong. A similar conclusion was drawn from NO adsorption, which also showed a multiplicity on the two absorption bands, an indication that NO is adsorbed on its dimer form in two different sites. Shortly after this work, IR spectra for CO 2 and N 2 0 adsorption on C 60 , graphite and diamond films were also studied [67]. In this case, only one adsorption site was

344

Chapter 14 Adsorption on Fullerenes

2200

2150 2100 Frequency per (cm)

2050

Figure 14.8 IR spectra of CO adsorbed on C 60 • The different absorption bands correspond to different coverages. (Reprinted with permission from Re£ [66]. Copyright 1992 American Chemical Society.)

detected on the three allotropes. Large spectral shifts and long desorption times were recorded for both the CO 2 and N 2 0 adsorbed on C 60 in comparison with the graphite and diamond studied. All these findings, combined with the available literature for CO and NO adsorption, indicated a strong interaction of CO, CO 2 , N 2 0, and NO with C 60 compared to the two other carbon allotropes. In another study, Heidberg et al. [68] investigated CO and CO 2 adsorption under ultrahigh vacuum conditions on C 60 thin films deposited on KBr(100). The IR spectra were recorded at different polarizations. The results obtained with both adsorption systems again point to the existence of two different adsorption sites on the C 60 film. The spectra showed different absorption intensities depending on the type of polarization. This was interpreted by the authors as being due to the anisotropy of the C 60 film. From the studies discussed hitherto [66, 68], it has been assumed that the two CO adsorption sites at 77 K on the C 60 surface could be on top ofa C 60 molecule, and in voids between these molecules. To obtain further information on the

14.6 Adsorption Studies using IR Spectroscopy

345

nature of these sites, calculations of adsorption potentials and spectral shifts were made by Fastow et al. [69] and Folman et al. [72] using the Buckingham-Corner (six-exponential) and the Lennard-Jones potentials. A number of adsorption sites were chosen, including the void space between four, three, and two neighboring C 60 molecules on their respective surface planes, and the center of the hexagon and pentagon on the surface of a single C 60 molecule. The potentials calculated clearly indicated that the adsorption sites in the voids between the C 60 molecules are energetically preferred to sites on top of the C 60 molecules (for the latter sites, higher potentials and lower spectral shifts were obtained). In turn, the calculated spectral shifts for the sites between four (-15 cm -1) and two (-8 cm -1) C 60 molecules were very similar to the experimentally measured values, suggesting that indeed those are the preferred sites. The results of the work of other teams [24, 25, 27, 35] later on were found to agree with this interpretation on the nature of the adsorption sites on the C 60 surface, despite the significant differences in probe molecules and measurement techniques used. The nature of the adsorption sites for CO on C 60 gave rise to yet another work, in which Lubezky et al. [71] used LiFjC 60 and NaCljC 60 mixed films as adsorbent in an attempt to obtain spectra of CO adsorbed on individual C 60 molecules which might be present in the films as a result of their simultaneous deposition from two separate sublimation sources. The results obtained with the LiF j C 60 films fulfilled their expectations: apart from two bands ascribable to CO adsorption on LiF, a third band at 2130 cm -1 could be ascribed to CO adsorption on C 60 . This clearly showed that CO adsorbs on top of individual C 60 molecules dispersed in the LiF matrix. With NaCljC 6o , however, no IR bands for CO adsorbed on C 60 were found. Isosteric heat calculations revealed that the isosteric heat of CO on NaCI (18.8 kJ/mol) is considerably higher than that on single C 60 molecules (11.7 kJ/mol). Therefore, preferential adsorption is thought to take place on NaCI, which would explain the absence of bands for CO adsorbed on C 60 . Finally, the same team [70] also studied the IR spectra of light hydrocarbons, methanol and their deuteriated counterparts adsorbed on C 60 films at different temperatures. In the case of methane, deuteriated methane, ethylene, and acetyene, shifts in the frequencies of the adsorbed molecules compared to the gas phase were found. The shifts were larger for C 2 H 4 and C 2 H 2 than for CH 4 , which was attributed to the occurrence of a higher dispersion interaction and possibly 1T-1T interactions for the former gases. Adsorbed methanol gave an O-H stretching vibration band at a frequency (3320cm- 1 ) similar to that of liquid methanol, suggesting that CH 3 0H adsorbs in the form of clusters. In addition, a strong band at 1028 cm- 1 (attributed to the c=o stretching vibration) persisted in part and was shifted to 1024 cm -1 at higher temperatures and on evacuation. This suggested that a small fraction of methanol was either chemisorbed, or physisorbed on high-energy sites. Similar results were obtained when deuteriated methanol was adsorbed on C 60 .

Chapter 14 Adsorption on Fullerenes

346

14.7

HYDROGEN ADSORPTION: GAS STORAGE

Interest in hydrogen as a fuel has increased very sharply in recent years due mainly to advances in technologies for hydrogen production and utilization. However, it is also necessary to develop efficient systems for storing it before the mass-scale use of hydrogen as a fuel can be achieved. The strategy elaborated by the US Department of Energy (DOE) requires that a weight efficiency of 6.5 wt% and a volumetric density of 62 kgH 2 /m 3 at room temperature be reached before hydrogen can be used as a potential source of energy. Numerous studies have been published in recent years on the use of different carbon materials as adsorbents for hydrogen storage. These include activated carbons as well as novel carbon forms such as carbon nanofibers, multi-wall carbon nanotubes (MWNTs), single-wall carbon nanotubes (SWNTs), and also fullerenes. Much work on the reversible adsorption of hydrogen was stimulated by results published by Dillon et al. [73] In this work, TPD was used to measure the amount of hydrogen desorbed from soots containing around 0.1-0.2 wt% open SWNTs (as estimated by transmission electron microscopy). The amount of hydrogen desorbed at a peak at c. 300 K corresponds to a gravimetric storage density per SWNT of 5-10 wt%. According to the authors, the rest of the carbon material (> 99 wt%) is not thought to take part in hydrogen adsorption. Since then, a number of papers [73-77] and reviews [78, 79] have been published on the use of new carbons for hydrogen storage. Among the problems referred to were the wide dispersion of results and the lack of reproducibility. The discrepancies identified may be due to the use of low purity materials (especially in the case of nanotubes) or experimental errors, especially when hydrogen is used at high pressures [76] and, in the case of theoretical studies, unrealistic models. In principle, fullerenes could meet some of the requirements established by the DOE. Thus, C 60 is theoretically able to store 7.7wt% H 2 assuming the bonding of one hydrogen atom per one carbon atom (chemisorption), which would lead to the formation of C 6o H 60 [79]. In a recent survey of possible states for hydrogen in the hydrofullerene, Schur et al. [80] identified at least two states: lattice and fullerenated hydrogen (exo and endo, respectively). Lattice hydrogen is present in the form of solid solution and is distributed in the interstitial sites of the lattice of fullerenes (fullerite). Depending on the type of cubic lattice of the fullerite (fcc, or body-centered cubic (bcc)) the maximum hydrogen content in the lattice per fullerene molecule is two atoms (C 6o H 2 ) for the fcc and six atoms (C 6o H 6 ) for the bcc (see Fig. 14.9). According to the authors, these structures are stable below 293 K. The other possible state for hydrogen, the fullerenated state, contains hydrogen atoms that are chemically bound with the carbon atoms forming the fullerene cage. Figure 14.10 shows a unit cell of hydrofullerite with an fcc structure, where both the lattice and fullerenated hydrogen can be seen. Fullerenes exohydrogenated to different degrees have also been experimentally prepared, the

14.7 Hydrogen Adsorption: Gas Storage

(a)

347 (b)

Figure 14.9 Unit cells of fullerite with fcc (a) and bcc (b) structures with lattice hydrogen only. (Shaded circle) Sites ofcrystalline lattices, in which fullerenes molecules are distributed; (.) octahedral interstitial sites; (0) tetrahedral interstitial sites, in which atoms of lattice hydrogen are located. (Reprinted from Ref. [80] with permission from Elsevier.)

Figure 14.10 Unit cell of hydrofullerite with an fcc structure, containing both lattice and fullerenated hydrogen. (Shaded circle) Sites of crystalline lattice, in which hydrofullerenes are distributed; (.) octahedral interstitial sites; (0) tetrahedral interstitial sites, in which atoms of lattice hydrogen are located. (Reprinted from Re£ [80] with permission from Elsevier.)

most stable being C 6o H 6 , C 6o H 18 , and C 6o H 36 • Figure 14.11 shows a molecule of exohydrogenated C 6o H 60 ' The process of hydride formation in the fullerites consists of two steps: saturation of the fullerite lattice with mobile hydrogen and the hydrogenation of fullerene molecules by excess mobile hydrogen. There are various methods for

348

Chapter 14 Adsorption on Fullerenes

Figure 14.11 Exohydrogenated molecule of fullerene. (.) Carbon atoms forming the molecule cage; (0) atoms of fullerenated exohydrogen. (Reprinted from Ref. [80] with permission from Elsevier.)

the synthesis ofhydrofullerenes, such as reaction with gaseous hydrogen (direct, or metal-catalyzed), Birch reduction, hydrogen transfer reactions, and others. From a practical point of view, gas-solid processes would seem to be the most appropriate options. C 60 hydrogenation through Birch reduction (Li, liquid NH 3 , tert-BuGH) was reported by Haufler et al. [81], who identified (using mass spectrometry, 1 H nuclear magnetic resonance and IR spectroscopy) C 6o H 36 and C 6o H 18 as reaction products, although it was not posible to determine whether the latter was the result of Birch reduction or C 6o H 36 pyrolysis. The authors studied the dehydrogenation by treating a solution of hydrofullerene in toluene with dichloro dicyano quinone under reflux. Thin-layer chromatographic and mass spectrometric analyses showed that the dehydrogenated material was exclusively C 60 , and led the authors to conclude that the reaction of fullerenes could be totally reversible with no alteration to the molecular skeleton occurring during the Birch reduction. Direct, noncatalyzed hydrogenation of fullerenes at high pressures has been reported by different authors. The methodology followed and the degree of hydrogenation achieved vary widely. Kolesnikov et al. [82] studied samples of fullerite hydrogenated at 3 GPa, and found that the resulting material consisted of C 6o H 32 molecules with molecular hydrogen dissolved on interstitial sites. No results on the dehydrogenation were reported. Ye et al. [83] studied the adsorption and desorption of hydrogen at 12 MPa and 77 K on different fullerite samples (with an approximate composition of75% C 60 and 22% C 70 ) as well as

14.7 Hydrogen Adsorption: Gas Storage

349

on pure C 60 and C 70 . Pure (>99.9%) C 60 adsorbed 0.83 wt% Hz and desorbed 0.70 wt%. One of the fullerite samples exhibited a maximal hydrogen adsorption of 4.4wt% and a desorption of up to 4.38wt% Hz. Jin et al. [84] attempted to determine whether treating C 60 with hydrogen at a high pressure (65 MPa) and temperature (573 K) would suffice to provoke the opening of the fullerene cage and the entry of hydrogen molecules. Mass spectroscopic analyses revealed the formation of C60HZ-18, corresponding to hydrogens bound exohedrally to the fullerene cage. Apparently, therefore, no access of hydrogen to the inner part of the cage takes place under these conditions. Meletov et al. [85] carried out fullerene hydrogenation at 3 GPa, between 650 and 700 K for different durations of time. The main product obtained (95%) was C 6o H 36 , the remaining 5% being fullerenes hydrogenated to smaller extents. No data on desorption were provided since this work was aimed at studying the formation of different isomers of C 6o H 36 by Raman spectroscopy. Kurmaev et al. [86] also carried out the hydrogenation at 3 GPa, between 620 and 770 K, and for different durations of time. The product obtained was C6oH37.S-46.S (as determined by elemental analysis). Again, no desorption results were presented as the main objective of this work was to study hydrofullerene isomers by X-ray fluorescence. Tarasov et al. [87] tried to hydrogenate (deuterate) fullerites (85% C 60 + 15% C 70 + 2% of higher fullerenes) at moderate pressures (1-2.5 MPa) by mixing the fullerite with intermetallic compounds (LaNi s ' LaNi4.6sMno.3s, and CeC0 3) or metals (V and Pd). Hydrogenation does not occur at room temperature, it being necessary to work in the range of 573-673 K. In addition, several hydrogenation cycles are necessary to obtain the maximum hydrogen (deuterium) content. Thus, C6oDz4-Z6 was obtained after seven cycles at 2.5 MPa and 673 K. These authors studied the decomposition of the hydrogenated materials by means of differential thermal analysis and thermogravimetry. A first peak at 350-600 K was attributed to hydrogen desorption from the metal hydrides. A second peak at 800 K probably corresponds to fullerite dehydrogenation. At higher temperatures, the fullerene structure decomposes giving rise to metal carbides, except in the case of Pd where no peaks are observed above 800 K. In contrast to these results, Brosha et al. [88] showed that dehydrogenation occurs alongside the decomposition of the fullerenes. These authors carried out the hydrogenation of C 60 (direct hydrogenation) and C 6o Ru 3 (catalyzed hydrogenation) at 0.3 MPa and 673 K, giving rise to C6oH18.7 and C6oRu3Hz4' respectively. The dehydrogenation was monitored by means of thermogravimetry, which showed that the samples are stable up to 703 K. Above 727 K, mass loss occurs due to dehydrogenation, accompanied by the destruction of fullerenes (these authors observed the evolution of methane besides that of Hz). The X-ray diffraction patterns of the dehydrogenated samples did not correspond to C 60 , but to an amorphous carbon material. Another method for preparing hydrogenated fullerenes is that of transfer hydrogenation [89-93]. This consists of transferring hydrogen from 9,10-dihydroanthracene to C 60 at 623 K, to yield mainly C 6o H 36 , but sometimes

350

Chapter 14 Adsorption on Fullerenes

accompanied by C 6o H 18 • Most works in this regard have focused on the determination and characterization of the isomers of C 6o H 36 that are formed. However, in a work by Dorozhko et al. [91], the temperature evolution of C 6o H 36 and C 6o H 18 was studied. It was concluded that the isothermal treatment of C 6o H 36 at 660 K leads to C 6o H 18 as an intermediate product. As the temperature increases to 700 K, dehydrogenation takes place and an increase in the mass spectrometry peak corresponding to C 60 is observed. Nevertheless, differences were observed between the IR spectra of the hydrogenated samples and the original C 60 , which led the authors to conclude that no pristine C 60 was recovered under the conditions of their experiment. An additional possibility is that of endohydrogenated fullerenes. The formation of these compounds implies that hydrogen must cross the rings in the fullerene cage. Figure 14.12 illustrates this possibility, with hydrogen molecules located inside the cage [94]. Endohedral hydrogen adsorption has been approached theoretically [94-97], and would seem to offer little chance for practical application as the desorption could only be produced by the rupture of the fullerene cage [80]. However, Narita and Oku [95] point out that the energy required for the discharge ofH 2 from fullerene materials is similar to that of H 2 storage. These authors simulated H 2 storage in C 60 by means of molecular

Figure

14.12 Endohedral structures with various amounts of hydrogen molecules (from 9 to 24) inside the C 60 cage. (Reprinted from Ref. [94] with permission from Elsevier.)

14.8 Adsorption from Solution: Environmental Applications

35 1

dynamics calculations, and concluded that the H 2 molecules are in a stable state inside the C 60 cage at 298 K and 0.1 MPa. They also confirmed that a pressure of over 5 MPa is required to store H 2 molecules in a C 60 cage, and that H 2 molecules can enter through the hexagonal rings in the fullerenes. Barajas-Barraza and Guirado-L6pez [96] analyzed the hydrogen storage behavior in spheroidal C 60 and C 82 , as well as in cylindrical finite-length (5, 5) armchair C and BN fullerenes, by means of semiempirical (MNDO) as well as ab initio density functional theory calculations at T = 0 K. They observed that, whereas chemisorption of hydrogen individual atoms can be produced on the external surface of fullerenes, the hydrogen atoms cannot be bound to any internal surfaces. Therefore, hydrogen can only exist in molecular form inside the fullerenes. The maximum amount of hydrogen that can be stored inside a C 60 molecule is 23 molecules. This maximum storage capacity is in good agreement with the result reported by Tiirker and Erkoc; [94] (24 hydrogen molecules). The latter study was carried out by means of the AMl self-consistent field molecular orbital method at the restricted Hartree-Fock level. These authors pointed out that all the systems nH 2 @C 60 (n: 9, 12, 15, 19, 21, 24) studied are stable but highly endothermic. In a recent work, Oksengorn [98] presented an experimental procedure for preparing endohydrogenated fullerenes, whereby a beam of light with A = 532 nm (from an Nd-Y AG laser) is used to excite C 60 in the presence of hydrogen at a pressure of 0.1 GPa. The fraction of C 60 that was hydrogenated contained 18% endohydrogenated fullerene, an amount higher than those produced in previous attempts to produce endohydrogenated fullerene. Before concluding this section, we would like to mention a theoretical work by Turnbull and Boninsegni [99] on p-hydrogen adsorption on the outer surface of a single fullerene. Monte Carlo simulations showed that a single solid monolayer is thermodynamically stable, and is commensurate with the corrugated surface of the fullerene. As the chemical potential was increased, a discontinuous change to an inconmensurate, compressible layer was observed. No evidence for quantum exchanges between the p-H 2 molecules was observed.

14.8

ADSORPTION FROM SOLUTION: ENVIRONMENTAL ApPLICATIONS

Studies of fullerenes as adsorbents from an aqueous solution in relation with the removal of pollutants are relatively scarce. Thus, Berezkin et al. [100, 101] investigated the adsorptive activity of fullerenes for organic pollutants in water and compared them with activated carbon and soots with and without fullerenes. They studied the purification of natural river water and waste from a pharmaceutical plant. The latter liquid contained various aliphatic, cyclic and aromatic compounds, the overwhelming majority of organic impurities being chlorinated compounds. The adsorption behavior ofsoot was found to be similar

Chapter 14 Adsorption on Fullerenes

35 2

to that of activated carbon, but fullerenes were more efficient than these two sorbents. The authors concluded that adsorption on fullerenes proceeds mainly by physical adsorption through dispersive interaction forces (it is worth recalling at this point that Abraham and coworkers [45] proposed that VOC adsorption on fullerenes also takes place through dispersive interactions). Berezkin et al. [101] also found a correlation between the adsorption properties of fullerenes and specific features of their solubility, and attributed the existence of this correlation to the action of the same intermolecular forces when interacting with the same molecules of adsorptives or solvents. Cheng et al. studied the interactions between C 60 and two common environmental contaminants, naphthalene [102, 103] and 1,2-dichlorobanzene [103]. Both adsorption and desorption were studied using C 60 either deposited as a thin film, or dispersed in water. Enhanced dispersion of C 60 in water (which was attained by causing the disaggregation of C 60 particles) was found to increase the extent of organic pollutant adsorption by several orders of magnitude. As Fig. 14.13 shows, a strong adsorption/desorption hysteresis effect could be

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Figure 14.13 Adsorption-desorption isotherms of naphthalene on C 60 (plots a and b correspond to two different samples of "C 60 small aggregates"). Solid diamonds, adsorption data; empty diamonds, desorption data; solid line, Freundlich isotherms (fitted with the adsorption data). (Reprinted with permission from Ref. [102]. Copyright 2004 American Chemical Society.)

14.9 Adsorption from Solution: Analytical Applications

353

observed (the authors ascertained the accuracy of equilibrium). The authors explained this occurrence of hysteresis using a "two-compartment" model, whereby adsorption takes place first on the external surface that is in contact with water (this adsorption being reversible), irreversible adsorption occurring on the internal surface inside the aggregates of C 60 molecules.

14.9

ADSORPTION FROM SOLUTION: ANALYTICAL

ApPLICATIONS

In their review of the impact of fullerenes in analytical sciences, Valcarcel and coworkers [104] identified two main connections between fullerenes and analytical chemistry. The first relationship views fullerenes as analytes. This would involve quantifying them in various types of samples, such as biological tissues (in relation to the possible toxicity of C 60 ) or geological materials (shungite, fulgurite). The second relationship attributes to fullerenes the function of analytical tools, namely as chromatographic stationary phases, as electrochemical and optical sensors, or as sorbent materials in continuous flow systems. These three alternatives are sketched in Fig. 14.14. Interestingly, adsorption interactions playa key role in all of these analytical systems. Here we will briefly outline the relationship between adsorption on fullerenes and these analytical applications, taking advantage of the framework provided by the review ofBaena et al. [104]. Let us first consider adsorption in relation with fullerene applications in liquid chromatography (LC) and high-performance liquid chromatography (HPLC). Saito et al. [105] first used a chemically bonded C 6o -silica as a stationary phase for LC, and found it to have a selectivity different from that of more traditional

~:" . '" ,."' . ~

Chemical sensor

GC LC

Figure 14.14 The three main possibilities for direct use of fullerenes in analytical processes. MP, mobile phase; I, injector; D, detector; GC and LC, gas and liquid chromatographs. (Reprinted from Ref. [104] with permission from Elsevier.)

Chapter 14 Adsorption on Fullerenes

354

(a)

(b)

a .....----- 43.4A - - - - -...

Figure 14.15 Molecular modelling scheme for interaction between PAHs and C 60 bonded silica phases by space filling model. (a) triphenylene and o-terpenyl on the C-high type C 60 phase. (b) o-terpenyl on the C-Iow type C 60 phase. (Adapted from Ref. [106] - reproduced by permission of the Royal Society of Chemistry.)

octadecylsilyl silica (ODS) phases. A good correlation existed between the retention data for polyacyclic aromatic hydrocarbons (PAHs) with this C 60 bonded phase, and with C 60 itself as a stationary phase. In another work, the same team [106] synthesized various chemically bonded C 6o-silica phases, and investigated systematically the retention behavior of PAHs. They found that the chemically bonded C 6o -silica phases showed a higher selectivity for aromatic compounds and planar molecules that resulted in a unique molecular recognition capability for PAHs. The C 60 bonded phases with high surface coverage (termed C-high type) had a selectivity different from that of phases with low surface coverage (termed C-low type) for the separation ofisomeric PAHs. To explain these findings, the authors proposed a molecular model, which is reproduced in Fig. 14.15. The cavities between the closely bonded ligands of the C-high type C 60 phases are smaller. Nonplanar molecules such as o-terphenyl may be expected to have more difficulty in penetrating these cavities than planar molecules such as triphenylene. This would lead to a decreased 1T-1T interaction of the surface with C 60 for the nonplanar molecules. In this case, the planar molecules would be retained longer than the nonplanar molecules. In contrast, the C-low type C 60 phases contain larger cavities between less densely bonded ligands (Fig. 14.15). This kind of cavity can readily receive both nonplanar and planar molecules. Therefore C-low type C 60 phases cannot be expected to discriminate between PAH isomers in terms of planarity and will produce smaller retentions for PAHs than the C-high type. The same type of selectivity was found by Stalling et al. [107] in the HPLC separation ofpolychlorinated biphenyls (PCBs) using a C 6o / 7o -polystyrene divinylbenzene bonded phase. This material acted as an electron donor-acceptor adsorbent which provided enhanced enrichment of coplanar PCB constituents,

14.9 Adsorption from Solution: Analytical Applications

355

including chlorinated dibenzofurans and dibenzo-p-dioxins. Bianco et al. [108] developed another HPLC stationary phase based on a fullerene derivative covalently linked to silica gel microparticles. Exceptionally high size selectivities were obtained for cyclic oligomeric compounds such as calixarenes and cyclodextrins. In this new phase, solute dimensions dictated the retention behavior of macrocyclic compounds, while shape and functionality modulated the relative retentions of a series of protected peptides. In the field of gas chromatography (GC), Golovnya et al. [109] first developed a fullerene-based stationary phase (consisting of a C 60 coating on a capillary glass column) that was used for the retention ofhigh-boiling organic compounds, such as aromatic and aliphatic hydrocarbons, amines, alcohols, and esters. Later on, fullerene-containing polysiloxanes were developed for use as stationary phases in GC [110-112]. These phases were highly suitable for the separation of high boiling point compounds like PAHs and phthalic esters. PAHs were eluted in the sequence of their increasing dispersion force, and the methyl esters of the unsaturated acids were eluted after the corresponding esters of saturated acids due to '1T-'1T interaction of fullerene with the double bond of the methyl ester of the unsaturated acid. Therefore, as in the case ofLC, the adsorption mechanism is attributed to strong '1T-'1T interactions and donor-acceptor interactions of fullerene with analytes. This close similarity in mechanisms involved in LC and GC prompted us to include here some discussion on the latter technique despite the fact that, in GC, adsorption takes place from the gas phase rather than the liquid phase. Fullerenes as sensors is the second field of analytical applications considered in Baena et al.'s review [104]. Some studies relative to the use of fullerenes as sensors for organic vapors have already been reviewed in Section 14.4 [44, 45, 49]. Following their inclusion of a fullerene-coated piezoelectric (PZ) quartz crystal membrane to study the adsorption of various organic molecules from the gas phase [49], Shih et al. [113] developed several applications of this type of sensor to organic and inorganic species in solutions. Thus, it was found that a C 6o -cryptand22-coated piezoelectric crystal sensor could be used as an LC detector not only for organic molecules but also for metal ions in solutions. In the field of organics, the C 6o -cryptand22-coated LC-PZ system compared well in performance with a commercial UV-VIS detector. Moreover, cryptands are well-known for their remarkable complexing ability for both cations and anions and, accordingly, the C 6o -cryptand22-coated LC-PZ detector has been shown [113] to act as a switch-type multifunctional detector that can be used either as a cationic detector at pH 2: 7 or as an anionic detector at pH ~ 6. Other applications of fullerenes as sensors [114-116] bear little or no connection with adsorption phenomena. The third field of analytical application of fullerenes identified by Baena et al. [104] is as phases for cleaning and preconcentrating analytes. Practically all of the work carried out in this field with fullerenes was carried out by one laboratory. As early as 1994, Gallego et al. [117] first reported on the analytical potential of C 60 fullerenes as sorbent materials for the preconcentration

356

Chapter 14 Adsorption on Fullerenes

of metal traces through the formation of neutral chelates. The model system they used was to determine Pb traces in waters by using ammonium pyrrolidine dithiocarbamate as a ligand. The chelate is formed in a continuous flow system, adsorbed on a C 60 fullerene microcolumn, and subsequently eluted for transfer to an analyzer (e.g., an atomic absorption spectrometer). The authors determined the adsorption isotherms of Pb at low concentrations, and found that C 60 had a greater adsorption capacity than ODS and activated carbon, which were tested as sorbents under equivalent conditions. The value of the Freundlich K constant was maximum for C 60 , indicating that the van der Waals interactions between the ligand (chelate) and the fullerene are stronger than with the other two sorbents. Therefore, of the three sorbent materials studied, C 60 was considered the most effective for the preconcentration of traces oflead thanks to its higher adsorption capacity. More importantly [104], C 60 exhibited the highest selectivity. Subsequently, the same team using C 60 and/or C 70 as sorbents for preconcentratation in continuous systems were able to determine Cd [118], Cu [119], Cd, Pb, and Ni [120], and also Co [121]. Fullerenes were found to exhibit better properties in metal preconcentration than more conventional sorbents such as ODS, activated carbon, and resins. C 60 fullerene was also tested as a sorbent for organic and organometallic compounds from aqueous solution [122]. For this purpose, C 6o -packed minicolums were inserted in continuous flow systems and gas chromatographic or flame atomic spectrometry was used for detection, depending on the nature of the compounds assayed. The fullerene was found to adsorb many types of organic substances (for example, N-methylcarbamates, phenols, PAHs, or amines), with efficiencies depending on the nature of the compound concerned. Nevertheless, conventional sorbents such as XAD-2 (a nonionic polystyrene divinylbenzene resin) or polyurethane foam were more efficient than C 60 for this purpose. As an illustration, the chromatographic areas for four phenolic compounds (phenol, 3,4-dimethylphenol, 2-tert~butylphenol and 4-chlorophenol) obtained with a variable pH are shown in Fig. 14.16, in which these results are also compared with those provided by XAD-2 as sorbent and ethyl acetate as eluent. The optimal pH range was wider with C 60 (1-9.5) than with XAD-2 (1-6.5). However, the signal obtained with C 60 was smaller, which was attributed [122] to its lower sorption capacity for these compounds. The adsorption efficiency of C 60 was observed to decrease with the increasing polarity of the organic compounds, which is consistent with the adsorption mechanism assigned to fullerenes via 1T-electron interactions. In addition, when using solutes that contain polar groups, dispersion prevails over retention. Organometallic compounds such as metalocenes and organoleads were quantitatively adsorbed on C 60 via the formation of neutral complexes or chelates, and the adsorption constant was dramatically increased by the use of classical reagents such as pyrrolidinedithiocarbamate or diethyldithiocarbamate. It was therefore concluded [122] that the fullerenes possess a high analytical potential for preconcentrating organometallic compounds, which is superior to that of conventional sorbents such as RP-C18, silica gel and activated carbon.

14.10

Adsorption from Solution: Colloidal and Biological Systems

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Figure 14.16 Influence of the sample pH on the adsorption of phenols on XAD-2 (dashed line) and C 60 (solid line). 1 = 2-tert-butylphenol; 2 = 3,4-dimethylphenol; 3 = 4-chlorophenol; 4 = phenol. Sample = 10 ml of aqueous solution containing 100 ng/ml of each phenolic compound. (Adapted from Re£ [122] with permission from Elsevier.)

Dithiocarbamate fungicides containing different metal ions such as Zn 2 +, Mn 2 + and Fe3+ were resolved using a C 60 column that performed better than the conventional RP-C18 sorbent [123]. However, the method did not allow the speciation of dithiocarbamates that contain no metal. Finally, C 6o -fullerene was reported to be an effective sorbent material for preconcentrating mercury compounds, and to be preferable to RP-C 18 on account of its large specific surface area and volume, which endow it with an increased physical sorption capacity [124]. Also recently, Pereira et al. [125] developed a new alternative for Cd and Pb determinations at low concentrations, using the preconcentration of a C 60 /C 70 mixture coupled to thermospray flame furnace atomic absorption spectrometry.

14.10 ADSORPTION FROM SOLUTION: COLLOIDAL AND BIOLOGICAL SYSTEMS In a review on the relationship of fullerenes with biological sciences, fullerenes and their derivatives were reported by Jensen et al. [126] to influence biological processes "in vivo." However, the mechanism was not yet fully understood as interactions of fullerenes at the biomolecular level had not been sufficiently studied. This was due, in turn, to the low solubility of fullerenes in water, a drawback which has led to some work on the production of stable water solutions of fullerenes. Indeed, the low solubility in water of fullerenes and the

358

Chapter 14 Adsorption on Fullerenes

limited accessibility of their inner spaces have significantly dampened the study of fullerene interactions with molecular species, and therefore alternatives such as water-soluble "nanographites" [127, 128] have been developed as a substitute for fullerenes in research being carried out in the interdisciplinary field between intermolecular and interfacial interactions. Several methods for producing stable aqueous dispersions of C 60 and C 70 without the addition of any stabilizer have been reported [129-131]. These methods are based on the exchange of molecules of an organic solvent, which covers the fullerenes, with water molecules. The resulting aqueous solutions of fullerenes, termed fullerene-water systems (FWSs), have the properties of colloidal systems. This type of dispersion has a high stability, no essential changes taking place during several months of storage at normal conditions [132-134]. The molecular system of C 60 in water (C 6o FWS) contains individual hydrated fullerenes and their fractal clusters in a hydrated state. The stabilization mechanism of such dispersions is not clear at the moment. Nevertheless, a negative charge of colloidal particles detected in different works [130, 131, 135, 136] seems to play a significant role in this stabilization. High resolution transmission electron microscopy and small-angle neutron scattering have revealed the polycrystalline nature of the clusters. Using a different approach, aqueous solutions of fullerenes were obtained by means of a chemical method based on oxidation of the C(;o anion in watermixable organic solvents [137]. The authors checked to see whether the sol was made up of hydrated C 60 . The colloidal particles were about 10 nm in diameter, and they were noncrystalline and quite homogeneous. Mchedlov-Petrossyan et al. [138] studied the interaction of cationic dyes such as indopolycarbocyanine and methylene blue with the C 6o FWSs, and demonstrated the occurrence of a strong interaction between the cationic dyes and the dispersed phase of the C 60 hydrosol, which resulted in adsorption at the surface of the colloid particles and finally in the coagulation of the sol [131, 134] Such adsorption processes are accompanied by the neutralization and hydrophobization of the C 60 /water interface and play a decisive role in coagulation phenomena. The same team [139] also studied the interaction of human serum albumin with hydrated fullerenes using electron spin resonance and differential scanning microcalorimetry. Their results suggested that the thermal stability of the protein, the surface tension of this protein-water matrix and the dynamics of water molecules in the vicinity of the protein surface are affected by hydrated fullerenes in water-salt solutions. The authors attributed these effects to similarities between protein and fullerene hydrations which cause long-range protein-protein, fullerene-fullerene, and protein-fullerene interaction forces and probably entropic depletion. They also suggested that the hydrated C 6o -induced stabilization of protein clusters can lead to the formation of polarized multilayers of water similar to those discovered in living cells, and that this can modify the biological activity of proteins and support the osmotic homeostasis of biological liquids.

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359

14.11 CONCLUSIONS There is reasonable agreement among authors regarding the nature of the adsorption sites for gases and vapors on solid C 60 . At least three sites on the surface of C 60 have been identified, the energy decreasing in the following sequence: void space between four neighboring C 60 molecules > void space between two neighboring C 60 molecules > on top of a C 60 molecule. This is supported by studies with different adsorbates (N2 , Ar, CO 2 , CO, alkanes, alkenes) and techniques (isotherms, IGC, IR spectra, GCMC simulations). Concerning the possible use offullerenes for hydrogen storage, there is enough evidence to suggest that hydrofullerenes could be prepared to different degrees of hydrogenation. The easiest material to prepare would be C 6o H 36 , which has a gravimetric storage density of 4.5 wt% (close to DOE's requirements). However, there is a serious discrepancy concerning their dehydrogenation since some works suggest that the original fullerene could be recovered, whereas others indicate that dehydrogenation would be accompanied by irreversible fullerene decomposition. The efficiency and selectivity of fullerenes as adsorbents from aqueous solutions has resulted in a number of analytical applications of C 60 and C 70 as chromatography stationary phases, as chemical sensors and, especially, as sorbents for the preconcentration of analytes. In the latter case, the adsorption properties of fullerenes are more useful for inorganic and organometallic compounds than for organic compounds. On the other hand, the fullerenes exhibit a selectivity for aromatic compounds and planar molecules that makes them very attractive as stationary phases for liquid chromatography.

ACKNOWLEDGMENTS Financial support from the Spanish CSIC is gratefully acknowledged.

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Chapter 14 Adsorption on Fullerenes

by electrothermal atomic absorption spectrometry. J. Anal. Atom. Spectrosc., 14, 711-6. Ballesteros, E., Gallego, M., and Valcarcel, M. (2000). Analytical potential of fullerene as adsorbent for organic and organometallic compounds from aqueous solutions. J. Chromatogr. A, 869, 101-10. Baena, J.R., Gallego, M., and Valcarcel, M. (2000). Group speciation of metal dithiocarbamates by sorption on C 60 fullerene. Analyst, 125, 1495-9. Munoz, J., Gallego, M., and Valcarcel, M. (2004). Solid-phase extraction-gas chromatography-mass spectrometry using a fullerene sorbent for the determination of inorganic mercury(II), methylmercury(I) and ethylmercury(I) in surface waters at sub-ng/m1levels. J. Chromatogr. A, 1055, 185-90. Pereira, M.G., Pereira Filho, E.R., Berodt, H., and Arruda, M.A.Z. (2004). Determination of cadmium and lead at low levels by using preconcentration at fullerene coupled to thermospray flame furnace atomoc absorption spectrometry. Spectrochim. Acta B, 59, 515-21. Jensen, A.W., Wilson, S.R., and Schuster, D.1. (1996). Biological applications of fullerenes. Biootg. Med. Chem., 4, 767-79. Kamegawa, K., Nishikubo, K., Kodama, M., et al. (2003). Dissolutionaggregation behaviour of water-soluble nanographites and their adsorptive characteristics for 2-naphtol in aqueous solutions. J. Colloid Interface Sci., 268, 58-62. Kamegawa, K., Nishikubo, K., Kodama, M., et al. (2005). Aqueous-phase adsorption of aromatic compounds on water-soluble nanographite. Colloids Surf., 254, 31-5. Andrievsky, G.V., Kosevich, M.V., Vovk, O.M., et al. (1995). On the production of an aqueous colloidal solution of fullerenes. J. Chem. Soc., Chem. Commun., 12, 1281-2. Deguchi, S., Alargova, R.G., and Tsujii, K. (2001). Stable dispersions of fullerenes, C 60 and C 70 , in water. Preparation and characterization. Langmuir, 17, 6013-7. Mcheldov-Petrossyan, N.O., Klochkov, V.K., and Andrievsky, G.V. (1997). Colloidal dispersions of fullerene C 60 in water: some properties and regularities of coagulation by electrolytes. J. Chem. Soc., Faraday Trans., 93, 4343-6. Prilutski, Yu.l., Durov, S.S., Yashchuk, V.N., et al. (1999). Theoretical predictions and experimental studies of self-organized C 60 nanoparticles in water solution and on the support. Bur. Phys.J. D, 9, 341-3. Andrievsky, G.V., Klochkov, V.K., Karyakina, E.L., and Mcheldov-Petrossyan, N.O. (1999). Studies of aqueous colloidal solutions of fullerene C 60 by electron microscopy. Chem. Phys. Lett., 300, 392-6. Mchedlov-Petrossyan, N.O., Klochkov, V.K., Andrievsky, G.V., et al. (1999). Interaction between cationic dyes and colloidal particles in a C 60 hydrosol. Mendeleev Commun., 2, 63-4. Andrievsky, G. V., Klochkov, V. K., Bordyuh, A., and Dovbeshko, G. I. (2002). Comparative analysis of two aqueous-colloidal solutions of C 60 fullerene with help ofFTIR reflectance and UV-Vis spectroscopy. Chem. Phys. Lett., 364, 8-17. Avdeev, M.V., Khokhryakov, A.A., Tropin, T.V., et al. (2004). Structural features of molecular-colloidal solutions of C 60 fullerenes in water by small-angle neutron scattering. Langmuir, 20, 4363-8.

References

137. Wei, X., Wu, M., Qi, L., and Xu, Z. (1997). Selective solution-phase generation of C 60 n- (n = 1, 2) and formation of an aqueous colloidal solution of C60. ]. Chern. Soc., Perkin Trans. 2, 1389-93. 138. Mcheldov-Petrossyan, N.G., Klochkov, V.K., Andrievsky, G.V., and Ishchenko, A.A. (2001). Interaction between colloidal particles of C 60 hydrosol and cationic dyes. Chern. Phys. Lett., 341, 237-44. 139. Rozhkov, S.P., Goryunov, A.S., Sukhanova, G.A., et al. (2003). Protein interaction with hydrated C 60 fullerene in aqueous solutions. Biochem. Biophys. Res. Commun., 303, 562-6.

HYDROGEN ADSORPTION IN SINGLE-WALLED CARBON NANOTUBES J. Karl Johnson 1,2 and Milton W. Cole 3 1 Department of Chemical & Petroleum Engineering, University of Pittsburgh, Pittsburgh, PA, USA 2National Energy Technology Laboratory, US Department of Energy, Pittsburgh, PA, USA 3Department of Physics, Pennsylvania State University, University Park, PA, USA

Contents 15.1 Introduction 15.2 Experiment, Simulation, and Theory of Hydrogen Storage 15.3 Quantum Sieving 15.4 Phase Transition Phenomena 15.5 Summary and Conclusions Acknowledgments References

36 9 370 385

39 1 393 393 394

15.1 INTRODUCTION This chapter is concerned with the properties of hydrogen molecules adsorbed within bundles of carbon nanotubes. A body of background information relevant to this problem is discussed in Chapter 9, which is concerned primarily with gases other than hydrogen in nanotubes. What is so unusual about hydrogen that justifies a separate discussion? The answer is the same as the reason why this particular gas has probably received more attention than all other gases combined. It is because many researchers have been investigating the possibility Adsorption by Carbons ISBN: 978-0-08-044464-2

© 2008 Elsevier Ltd. All rights reserved.

369

370

Chapter 15 Hydrogen Adsorption in Single-Walled Carbon Nanotubes

of storing significant quantities of hydrogen in nanotubes. This search was stimulated in large part by an experiment reported in Nature claiming to observe 5-10 wt% of hydrogen stored on single-walled carbon nanotubes (SWNTs) at room temperature and low pressure [1]. Such a high storage capacity, if confirmed, might well provide the basis for a vehicular fuel cell hydrogen storage technology. About the same time another experimental paper appeared, widely reported in the popular media, claiming to find more than 50 wt% hydrogen in carbon nanofibers [2, 3]. These "fantastic" results have never been confirmed by independent groups [4]. However, these reports were sufficient to start a flurry of experimental, theoretical, and simulation work on hydrogen adsorption on carbon nanotubes. This article describes three research topics in the subsequent sections. Section 15.2 describes experimental and theoretical research pertinent to the exploration of hydrogen storage capacity, mostly at room temperature. Section 15.3 discusses the problem of quantum sieving, which is the separation oflight isotopes, e.g., hydrogen from deuterium, by adsorption within nanotube bundles. Section 15.4 summarizes a variety of open questions concerning phase transition phenomena that have been proposed to occur for hydrogen within nanotube bundles.

15.2 ExPERIMENT, SIMULATION, AND THEORY OF HYDROGEN STORAGE

In this section we first briefly review the main experimental findings for hydrogen adsorption on SWNTs and then review in detail the simulation and theory findings. We focus mainly on the modeling of hydrogen adsorption in SWNTs because the experiments are so far hampered by a lack of pure and well-characterized nanotube samples. In many ways, experimental work is more of a materials issue, since the presence of catalyst particles, amorphous and graphitic carbon impurities, and chemical and geometrical defects on the nanotube samples make it difficult to unambiguously compare different experiments and interpret the observations. Experimental work on hydrogen adsorption in carbon nanotubes has yielded a wide range of sometimes conflicting results and several reviews have appeared [5-11]. Dillon and coworkers [1] were the first to report very high adsorption at room temperature, claiming to observe 5-10wt%. Chen et al. [12] observed apparent hydrogen adsorption of up to 20 wt% on alkali-doped SWNTs. These results were later shown to be due to water impurities reacting with the alkali metals [13, 14]. Liu and coworkers have measured reversible hydrogen adsorption of about 3-4 wt% on SWNTs at room temperature and pressures of about 10 Mpa [15, 16]. In contrast, there have been a number of publications from different groups finding much more modest hydrogen uptake by SWNTs at room temperature and pressures less than 30 Mpa

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Experiment, Simulation, and Theory of Hydrogen Storage

371

[17- 28]. There are other experiments showing high levels of hydrogen adsorption on SWNTs at cryogenic temperatures, typically around 77 K [4, 29-31], but these conditions are not particularly relevant to vehicular fuel cells. One of the challenges of experimental measurements is that the uptake of hydrogen has been shown to be sensitive to the pretreatment of the SWNT samples [7, 25, 29, 32-34]. This challenge may also be an opportunity, as we will discuss later in this chapter. The simulations and theory of hydrogen adsorption on carbon nanotubes can be placed into three broad categories: (1) Modeling of physisorption using classical potentials. (2) Ab initio modeling of physisorption energies and geometries of molecular hydrogen on nanotubes. (3) Ab initio modeling of chemisorption of molecular and atomic hydrogen on nanotubes. We discuss each of these areas below. 15.2.1 Modeling of Physisorption with Classical Potentials

Statistical mechanical modeling with classical potentials has been used successfully to model physisorption of many different gases on microporous sorbents such as activated carbons and zeolites [35-43]. It is fairly common to observe quantitative agreement between experimentally measured quantities, such as isotherms, isosteric heats of adsorption, layering transitions, and monolayer ordering, and these same quantities computed from molecular simulations. The statistical mechanical calculations are essentially exact, to within statistical accuracy. However, there are two critical problems with these simulations. The first is that the potential models for both fluid-solid and fluid-fluid interactions are not known to good accuracy. The second is that the molecular level structure of the sorbent is not always 'known. Errors in the potential models or the sorbent geometry can lead to quantitative and even qualitative disagreement with experiments. These two problems are relevant issues with regard to modeling of hydrogen adsorption in carbon nanotubes. It is commonly assumed that the potential for H 2-nanotube interactions can be taken as the H 2 -graphene interactions with the graphene sheet wrapped into the appropriate nanotube. This is an untested hypothesis, since an unambiguous answer would require very high-level ab initio calculations, such as at the coupled cluster level of theory. These calculations are unfeasible with current algorithms and computer resources. We note that the van der Waals part of the Hz/Nanotube interaction requires knowledge of the anisotropic dielectric function of the tubes, as was done for Hz/graphite; see Vidali et al. [44] The analogous dielectric response problem for the nanotubes has not been solved, even in principle. A precise description of the SWNT sorbent is also problematic. In theory, nanotubes should form perfectly ordered hexagonal bundles, giving a structure as well-defined as zeolites. In practice, nanotubes contain significant quantities of metal catalyst particles, amorphous carbon impurities, and geometric and chemical defects in the nanotubes themselves. Thus, the accurate modeling of gas adsorption on SWNTs is a challenge at all levels. Nevertheless, statistical

Chapter 15 Hydrogen Adsorption in Single-Walled Carbon Nanotubes

37 2

modeling can yield important information about hypothetical limits of hydrogen storage and optimum geometric arrangements of nanotubes. There have been a number of simulations and theoretical calculations carried out that assess the hydrogen storage capacity of SWNTs [25, 45-63]. The first molecular simulations of hydrogen adsorption in carbon nanotubes were carried out by Darkrim and Levesque [45]. They simulated a square array of nanotubes, although nanotubes are known to form hexagonal arrays. The temperature and pressure studied corresponded to 293 K and 10 MPa. They varied the lattice spacing and nanotube diameter. They found optimal uptake in the case of a nanotube with a diameter of 11.75 A and a tube-tube distance (van der Waals gap) of 7 A. This is similar to optimum conditions found for hexagonal arrays from simulations by other groups. For example, Wang and Johnson [49] performed simulations at 298 K and 50 atm with arrays consisting of either (9, 9), or (12, \2), or (18, 18) nanotubes and found an optimum with a (9, 9) (diameter of 12.2A) array with a van der Waals gap of 6A. We note that the optimum was defined in terms of the excess adsorption, (15.1) where fads is the total amount adsorbed (assuming only pore volume in the sorbent), Pbulk is the bulk gas density, and Vfree is the free volume, or the volume of the system minus the volume occupied by the solid sorbent. In a molecular simulation the total amount adsorbed is computed directly. Computing the excess adsorption is ambiguous because there can be different definitions of the free volume, with particularly large consequences in a nanoscale geometry [64]. Rzepka et al. [47] compared adsorption in graphene slit pores with adsorption inside a nanotube, where the slit pore width was the same as the diameter of the nanotube. They found that in general the slit pore geometry was better for hydrogen uptake than the nanotube at most temperatures and pressures studied. The amount of hydrogen stored at room temperature was found to be small, on the order of 1 wt% at 10 MPa. These same general conclusions were later confirmed by more elaborate calculations of Wang and Johnson, who performed path integral simulations with accurate classical potentials to account for quantum effects in the translational motion ofH 2 • Quantum effects are fairly small for adsorption in pores that are more than two molecular diameters wide at temperatures greater than 77 K. For example, the volumetric adsorption at 77 K in a slit pore 10 A wide from the classical Rzepka and coworkers is only a few percent larger than the path integral values from Wang and Johnson at the same conditions. Levesque et al. [60] state that quantum effects reduce adsorption by 4% at 293 K and 20% at 77 K. Many different groups have concluded that slit pores are overall a better geometry for hydrogen storage, but that pure graphene structures, whether nanotubes or slit pores, were incapable of storing more than about 1 wt% at room temperature and 10 MPa. This is far short of the Department of Energy (DOE) hydrogen storage gravimetric target of around 6 wt% (which takes into account the weight of the tank and associated hardware) [65]. I".J

I".J

15.2

Experiment, Simulation, and Theory of Hydrogen Storage

373

1.8

o .~ 1.6 ~

"u «S

~1.4

()

Q)

::c

rn

1.2

::> 1.0

20

40 60 Storage pressure (atm)

80

100

Figure 15.1 The usable capacity ratio for hydrogen adsorbed in idealized slit pores and idealized nanotube arrays. The discharge pressure is 0.1013 MPa and the temperature is 298 K. The open circles, open diamonds, and open squares are data for slit pores with widths of6.15, 9.23, and 20.51 A, respectively. The filled triangles and filled circles are data for arrays of (18, 18) and (9, 9) SWNTs, respectively. (Reprinted with permission from Ref. [48] Copyright 1999 by the American Institute of Physics.)

One useful measure of the effectiveness of a sorbent for gas storage is the so-called usable capacity ratio (VCR). This is defined as the mass of the available fuel in a sorbent-Ioaded storage tank divided by the mass of available fuel in a compressed gas tank of the same size. Thus, the VCR is a measure of the effectiveness of adsorption compared with compressed gas storage at the same conditions. If the UCR value is less than unity then compressed gas is more effective than adsorption. If the UCR value is greater than unity then the sorbent system gives more deliverable hydrogen than compression. Figure 15.1 is a plot of the VCRs for idealized slit pores and idealized arrays of nanotubes. We note that the (9, 9) nanotube array is always less effective than simple gas compression, whereas the larger diameter nanotubes have VCRs that are above unity, although they are always <2. The idealized graphene slit pores have much better UCRs than the nanotube arrays. This is due to the packing of the nanotubes. It was shown that if the van der Waals gap is increased, then the VCRs for the (9, 9) array increase above unity [49]. Simonyan et al. [51] investigated the effect of charging nanotubes, individually and in arrays, on the amount of hydrogen stored. Nanotubes could become charged through intercalation of metals, such as Li or K. Simonyan and coworkers assumed that alkali metal intercalation results in approximately 0.1 electron per carbon atom charge transfer to the nanotube. They performed adsorption calculations using a model of hydrogen that included the charge-quadrupole and charge-induced dipole interactions. Results from their calculations are shown

Chapter 15 Hydrogen Adsorption in Single-Walled Carbon Nanotubes

374

VDW gap is 11.2A

VDW gap is 3.2 A

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80

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40

60

80

100

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Figure 15.2 Total adsorption isotherms for (9, 9) nanotube arrays with two different lattice spacings and different charges on each carbon atom. (Reprinted with permission from Re£ [51] Copyright 1999 by the American Institute of Physics.)

in Fig. 15.2. The total adsorption is increased by charging the nanotubes, either positively or negatively, due to the enhancement of the H 2 -nanotube interaction potential. The amount ofincrease is quite substantial at the highest pressures (100 atm) , but still too low to make the charged nanotube system reach the DOE storage targets. The largest amount adsorbed is for an array in which the van der Waals gap has been artificially increased to 11.2 A. Even so, the total weight of hydrogen stored is only on the order of 2% at room temperature and 100 atm. It may be that in real systems the H 2 -charged nanotube interaction would be much larger than that estimated by Simonyan et al. However, we have no reason to expect that the classical potential is substantially in error. Several groups have reported calculations of hydrogen storage at cryogenic temperatures [47-49, 51-54, 56, 62]. The general consensus from simulations is that optimized nanotube arrays and bundles can store large amounts of hydrogen at 77 K, reaching and even exceeding the DOE storage targets. This prediction has been partly confirmed by at least two different experiments [29, 30, 66]. However, adsorption in perfect arrays of nanotubes with the experimentally observed van der Waals gap of about 3.2 A cannot store enough hydrogen at cryogenic temperatures and reasonable pressures to meet the DOE targets. This is due to the fact that the external surface of the nanotubes is not accessible for gas adsorption. Therefore, the experiments that report high storage of hydrogen around 77 K [29, 30, 66] must have either small bundles or, as assumed by Ye et al. [66] the bundles must swell to accommodate substantial H 2 adsorption on the external surface of the nanotubes. Both Williams and Eklund [52] and Simonyan and Johnson [56] note that the simulations of hydrogen adsorption on nanotube bundles at 77 K do not qualitatively match the experiments of Ye and coworkers. At low pressures the simulations overestimate the amount adsorbed compared with experiments, even for the smallest lattice spacing. At high pressures the simulations underestimate the amount adsorbed, unless the van der Waals gap is almost quadrupled (increasing from 3.2 to 12.2A). Figure 15.3

15.2

Experiment, Simulation, and Theory of Hydrogen Storage

375 12

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Figure 15.3 The best fit of the simulation data to the experimental data from Re£ [66] The optimum van der Waals gap (VDW) for the tubes in the bundle is plotted on the right-hand axis. (Reprinted with permission from Re£ [56], copyright Elsevier.)

illustrates this situation. At pressures below about 80 bar the simulation data show a Langmuir type isotherm (concave downward) while the experimental data are concave upward. The smallest van der Waals gap gives adsorption much higher than observed in experiment at pressures less than 50 bar. At about 80 bar the experimental and simulation data match. If the gap between nanotubes was not increased then the experimental data would be much larger than the predictions from simulations. Instead, we adjust the gap continuously, in order to mimic the swelling of a bundle by the high-density hydrogen. The experimental data can be matched for pressures greater than 80 bar using this procedure. The simulated low pressure branch of the isotherm could be matched with experimental data by stipulating that most of the nanotubes are closed to adsorption. However, the increase in adsorption with pressure would require that the nanotubes be opened to adsorption with increasing pressure. Otherwise, unrealistically large van der Waals gaps would be required to match the experiments. Thermodynamic density functional theory (TDFT) has been used by a few groups to study hydrogen adsorption on nanotubes [50, 61-63]. Thermodynamic density functional theory should not be confused with ab initio density functional theory, discussed later. The former method uses classical potentials for fluidfluid and solid-fluid interactions and minimizes the grand potential as a function of the inhomogeneous adsorbed gas density. The latter formalism assumes that the properties of atoms, molecules, and solids can be computed in terms of the electron density. The main advantage of TDFT over molecular simulations is that the TDFT calculations are much faster. Larger sorbent systems and more state points can be explored. The results from TDFT and molecular simulations do not exactly match, but they do give qualitative agreement. The results from the TDFT calculations of Gordon and Saeger confirm the general conclusions from molecular simulations; namely that nanotubes are not able to store large enough quantities of hydrogen to be useful for vehicular fuel cell applications [50]. This is also the case with the calculations of Zhang et al. [62] for room

Chapter 15 Hydrogen Adsorption in Single-Walled Carbon Nanotubes

temperature adsorption. The work of Gu and coworkers [61] is unique, in that they develop an approximate way to use TDFT for quantum systems. This is much less computationally demanding than performing path integral calculations, but the method does not work at all conditions. The general conclusion from modeling hydrogen adsorption on carbon nanotubes using classical potentials is that standard physisorption potentials cannot account for the high uptake of hydrogen observed in some experiments at room temperature. We note that the models used include a wide range of different H 2 -H 2 and H 2 -nanotube interaction potentials. The results are independent of whether the hydrogen model is spherical or anisotropic or whether it contains a quadrupole term and whether the carbons in the nanotubes are treated as rigid or flexible. The effect of the packing geometry of the nanotubes in a bundle on hydrogen uptake in open nanotubes has been studied by Smith and coworkers [25]. The interstitial sites at packing defects, due to the SWNTs in a bundle being having a variety of different diameters, were found to be very important for matching experimental data for gas adsorption on closed bundles [67]. However, interstitial adsorption is not an important factor for H 2 isotherms on opened nanotubes. A sample of the type of bundles used in the simulations performed by Smith et al. is shown in Fig. 15.4. The interstitial channels (ICs) provide highly attractive sites for H 2 adsorption, but the amount is small

Figure 15.4 Sample nanotube bundle used in the molecular simulations ofhydrogen adsorption by Smith et al. [25] This bundle contains 45 nanotubes of various diameters. (Reprinted with permission from Re£ [25] Copyright 2003 by the American Chemical Society.)

15.2

Experiment, Simulation, and Theory of Hydrogen Storage

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Figure 15-5 Adsorption isotherms computed from simulations for several different disordered nanotube bundles and experimental data for hydrogen adsorption on raw nanotubes. (Reprinted with permission from Re£ [25] Copyright 2003 by the American Chemical Society.)

compared with adsorption inside the SWNTs. The simulation isotherms for H 2 adsorption at 298 K in a variety of different model bundles were compared with experimental isotherms by Smith and coworkers [25]. Results for three different model bundles are compared with an experimental isotherm at 298 K up to a pressure of about 48 bar in Fig. 15.5. The SWNT sample used in the experiment was purified and heated to 973 K in flowing He. The agreement between simulations and experiments is remarkable, but perhaps fortuitous. The simulated SWNT bundles contained between 50 and 100 individual nanotubes of various diameters, ranging from 10.8 to 16.2 A in diameter. All of the nanotubes were open in the simulations. It is unknown how many of the nanotubes in the experimental samples were open for H 2 adsorption. We now return to the observation made earlier in this chapter, namely that the SWNT pretreatment protocol can make a substantial difference in the amount of H 2 uptake. This point is illustrated by comparing experimental H 2 uptake before and after activation of a SWNT sample by CO 2 oxidation [25]. The storage capacity has been shown to increase from about 0.3 wt% to over 1 wt% at room temperature and 48 bar. Compare the experimental data plotted in Fig. 15.5 with those plotted in Fig. 15.6, for the same sample after CO 2 oxidation (circles in both figures). The increase in capacity after activation cannot be explained simply in terms of opening of the nanotubes. We consider the possibility that the adsorption potential is substantially in error for the pristine H 2-SWNT interaction. Then, the CO 2 activation processing step may just be opening more of the nanotubes for adsorption. If this were the case, then we should be able to

Chapter 15 Hydrogen Adsorption in Single-Walled Carbon Nanotubes

378

1.2

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Figure 15.6 Adsorption isotherms computed for nanotube bundles with different gaps and modified solid-fluid potentials. (Reprinted with permission from Re£ [25] Copyright 2003 by the American Chemical Society.)

empirically adjust the H 2 -nanotube potential used in the simulation, until we achieve good agreement with the experimental isotherm. Figure 15.6 indicates that this is not possible. If one just increases the potential, keeping the nanotube bundle geometry fixed, then the adsorption isotherm has a qualitatively different shape from that observed in the experiments. The computed isotherm (not shown) is concave downward, while the experimental isotherm is quite linear with pressure. Smith et al. therefore tried a combination of increasing the solidfluid potential, ~f' and increasing the van der Waals gap between the tubes in the bundle. The data in Fig. 15.6 are from simulations where the gap has been increased from 3.2 to 6.4 and 12 A, while increasing V:f by factors of 1.3, 1.5, and 1.5, respectively. It can be seen that none of the simulations is able to match the experiments quantitatively. This indicates that the pretreatment procedure is modifying the nanotubes in a way that cannot readily be accounted for by simple changes in the physisorption potential and geometric configuration of the nanotubes. Cracknell reached similar conclusions, namely that dispersion forces cannot account for the H 2 uptake reported in experiments and that substantial adsorption outside the nanotube (i.e., expansion of the bundle) is required to match experimental data [57]. The experimental data ofPradhan et al. [29,30] for adsorption of H 2 at cryogenic temperatures is also intriguing. They show that an aggressive pretreatment protocol dramatically changes the shape of the isotherm and the total amount of H 2 stored. Dillon and coworkers [7, 32-34] also noted that aggressive pretreatment (cutting) of the nanotubes through highpower sonication increases the hydrogen uptake at ambient conditions. The cutting procedure has been shown to introduce a TiAlV alloy into the nanotubes,

15.2

Experiment, Simulation, and Theory of Hydrogen Storage

379

through degradation of the sonication tip. The hydrogen adsorbed in these experiments comes out in two high-temperature peaks, measured by temperature desorption spectroscopy (TDS). Hirscher et al. attribute the increase in H 2 uptake in the SWNT samples entirely to the formation of a Ti hydride phase, as shown by TDS and X-ray analysis [10, 11, 18-20]. Dillon and coworkers dispute this finding, showing that a fraction of their experiments result in higher H 2 uptake than can be explained by the presence of the Ti alloy alone [34]. Three out of about 25 of their experiments exhibit H 2 content of 6 wt% or above. There appears to be a great deal of difficulty in achieving reproducible SWNT samples that store significantly more hydrogen than the Ti alloy. We note that the hydrogen adsorbed in the experiments by Smith et al. [25] and Pradhan et al. [29, 30] cannot be due to metal hydrides, because the adsorption is completely reversible with pressure at room temperature and below. Assuming that the experimental data from these studies are valid means that there are additional adsorption sites being produced through various pretreatment methods and that it the physical phenomena responsible for H 2 adsorption on these sites is not understood. Clearly, this is a problem that requires further work. Identification of the adsorption sites and mechanisms could lead to a method to dramatically enhance the storage capacity of nanotubes or other carbonaceous sorbents. 15.2.2 Ab Initio Modeling of Physisorption

It is clear from the preceding section that the weakness of using classical potentials to model the H 2 adsorption process is the uncertainty over the solidfluid interaction. Both experiments and theory indicate that the curvature of nanotubes, specifically at local defect sites, increases the chemical reactivity, and perhaps the physisorption potential as well [29, 68-74]. An accurate and precise calculation of the interaction energy between H 2 and nanotubes from accurate first principles is obviously needed in order to definitively establish the magnitude and character of the solid-fluid potential energy surface. With the correct potential in hand, accurate adsorption calculations could then be performed through statistical mechanical simulations. A number of different ab initio calculations have been performed to characterize the hydogen-nanotube and hydrogen-graphene binding energy[73 , 75-81]. We specifically note the controversy currently in the literature over publications in this area by Cheng et al. [72, 82], Li et al. [83], and Li and Yip [84]. Part of the controversy surrounding calculation of ab initio energies for H 2 nanotube systems stems from the inherent difficulty in computing weak interactions, especially those due to long-range electron correlation (van der Waals or dispersion interactions), from ab initio methods. Highly accurate methods, such as coupled cluster with single, double and (perturbation) triple excitations [CCSD(T)] are capable, when coupled with very large correlation consistent basis sets, ofcomputing accurate van der Waals interactions. However, CCSD(T) cannot be applied to compute H 2-nanotube interactions because of the large number of atoms involved [85]. The MP2 method (second-order M0ller-Plesset

Chapter 15 Hydrogen Adsorption in Single-Walled Carbon Nanotubes

perturbation theory) is often used as a surrogate for higher accuracy methods, but MP2 is known to fail for some very important weakly bound systems. Even so, MP2 is also too computationally expensive to apply to the Hz-nanotube system [85]. The most accurate ab initio method that can be applied to compute Hz-nanotube interactions is density functional theory (DFT). This formalism does not actually compute the true wave functions of a system, but rather computes the functions that give rise to the electronic density. DFT is approximate in that the exact functionals for the electron exchange and correlation energies are unknown. This is not so much of a problem for chemically bound systems. However, for weakly bound systems DFT is known to give the wrong longrange interaction energy, either within the local density approximation (LDA) or the generalized gradient approximation (GGA) [86-90]. LDA-DFT is known to predict binding energies that are typically too large (overbinding). GGA-DFT can be as accurate as MP2 for strongly interacting systems, but typically underestimates the binding energies for weakly bound systems. It appears that for specific cases LDA-DFT is able to reproduce binding energies and geometries for weakly bound systems that are in fairly good agreement with experiments. [80, 91-93] This is most likely due to a fortuitous cancellation of errors. Most of the calculations for the binding energies of Hz on nanotubes and on graphene clusters have relied on LDA-DFT. There is general agreement among these different studies; the binding energy for Hz-nanotubes and Hz-graphene is always less than about 175 meV. For example, Zhao and coworkers computed the binding energy for Hz interacting with different nanotubes and for different adsorption sites within a nanotube array. The computed energies ranged from 49 to 174 meV, with the most favorable site being the interstitial site. The striking exception to these calculations is the work of Cheng et al. [72] who have taken a fundamentally different approach to computing interaction energies. The other calculations are all static, that is, the geometry of the system is relaxed to its (zero temperature) ground state to obtain the binding energy. Cheng et al. performed LDA-DFT molecular dynamics at different temperatures, ranging from 77 to 600 K. At these elevated temperatures the nanotube (they used a single nanotube in a periodic box to mimic an array of nanotubes) is quite flexible, giving a distribution of C-C-C bond angles along the nanotube axis different from the ideal (zero temperature) value of 180 The calculated bond angle deformations are shown in Fig. 15.7. The angles are observed to change depending on the temperature and the presence of a Hz molecule inside (endohedral) or outside (exohedral) of the nanotube. Cheng et al. calculated average energies (computed over 5 ps) ranging from 167 to 473 meV. They concluded that these remarkably large binding energies were due to the bond distortions and the resulting partial charge transfer from Hz to the distorted carbon atoms. Li et al. attempted to verify the results ofCheng and coworkers by carrying out similar LDA-DFT calculations, but on a slightly different system [83]. Li et al. generated distorted nanotube structures using an empirical many-body potential developed by Brenner [94]. This potential is known to reproduce the elastic and vibrational properties·ofSWNTs with reasonable accuracy [95]. They then 0

•

Experiment, Simulation, and Theory of Hydrogen Storage

15.2

Nanotube axis

0.3

r--r-"lr-T"""1"""T""'T"""T""'T""'T"'"T"""T"""T'""'T"'""T'"""""'-"T'""T""""'"

I""'"'"T"'""....-r-I""""'-'''''"T'''''T""'T'''"T"""T''''''T'""'T"'"''T'".......--r-"T'""T""'''''''

0.12

T=77K Without H2

0.25

0.14

T=300K Without H2

0.1

0.2

0.04

0.08

0.03

0.06

0.02

T=600K Without H2

0.15 0.1

0.04

0.05

o 0.16

0.01

0.02

0L....L..-.L.......&.....l................................L-J.-'--L.....L.-I-........................................

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0.08

0.14

T = 77K

0.07

0.12

Exohedral H2

0.06

r--T""'1r-T"""1---r""T"""T""'T""'T"'"T"""T"""T'""'"T""'T'"""""'-"T'""T""""'"

0.08 0.07

T=300K Exohedral H2

0.06

0.1

0.05

0.05

0.08

0.04

0.04

0.06

0.03

0.03

0.04

0.02

0.02

0.02

0.01

o

0

0.14 0.12 0.1

0.07

r--T""'1r"'""T"""1"""T""'T""'T"'"T"""T"""T'"-.--r.......--r-"T'""T""..,.--r-.,....,

0.05

T=300K Endohedral H2

Ou...L...;J=:.......I.-.1..................L-J.-'--L........................................................ 0.05 0.04

0.08

0.04

0.03

0.06

0.03

0.02

0.04

0.02

0.02

0.01

r--T""'1r"'""T"""1"""T""'T"""T""'T.....,.....,..-.--r.......--r-.,.....,.-..,.--r-.,....,

T=600K Endohedral H2

0.01

o 160

T=600K Exohedral H2

0.01 ......I......L...L-J.-'--L........................................................

L..L-.II.-.L.-I.............

0.06

T=77K Endohedral H2

I""'"'"T"'""....-r-I,.....,..-,"""T""'T"""T"'""T""""T'"'"'"T'""'T"'""T'".......--r-..,.--r-~

165

170

175

180

0 160

OL....L..-.L.......&.....l............................................-'--L.....L.-I-....L.-I-............... 160 165 170 175 180 ..&......I

165

170

175

180

Figure 15.7 Longitudinal SWNT deformations at 77, 300, and 600 K as indicated by the distribution of C-C-C angles for the higWighted carbon atoms illustrated on a section of the SWNT wall. Each graph represents a distribution of C-C-C angle populations over 5000 steps of the 5.0 ps molecular dynamics (MD) simulation. The longitudinal C-C-C angle of a perfectly circular and straight "armchair" SWNT is 180 (Reprinted with permission from Ref. [72] Copyright 2001 by the American Chemical Society.) 0

•

used the same LDA-DFT methods used by Cheng and coworkers to compute static binding energies on distorted nanotube structures. The nanotube structure chosen for the calculations is shown in Fig. 15.8, along with the positions of the H 2 molecules considered for the binding energy calculations. However, the

Chapter 15 Hydrogen Adsorption in Single-Walled Carbon Nanotubes

(a)

(b)

(c)

(d)

(e)

(f)

Figure 15.8 Various partially stahle configurations (outcome of relaxing H 2 ) with the corresponding adsorption energies: (a) L1E= 54 meV, (h) L1E= 114meV, (c) L1E= 80 meV, (d) L1E= 56 meV, (e) L1E= 67 meV, and (f) L1E= 110meV. (Reprinted with permission from Refs [25, 83] Copyright 2003 hy the American Institute of Physics.)

bond angle distribution generated with the Brenner potential was not identical to that generated by the method of Cheng et al. Li and coworkers also used a smaller diameter nanotube, (7, 7) rather than the (8, 8) nanotube used by Cheng et aI., and a different unit cell. It seems reasonable to assume that these

15.2

Experiment, Simulation, and Theory of Hydrogen Storage

differences would not have a dramatic effect on the calculated binding energies. However, Li and coworkers [83] found a maximum binding energy ofl14meV, which is much less than the energies computed from dynamic calculations [72]. Cheng and coworkers [82] have commented on the work of Li and Yip [84], who have responded to the comment. The validity of the calculations appears to be an open question at this point, since the calculations of Li and coworkers can not conclusively rule out the validity of the earlier calculations. Nor is it the case that the calculations of Li et al. are fundamentally wrong. Assuming that both sets of calculations are correct would require that the very high binding energies be very sensitive to the precise bond angle distortions and perhaps to the size of the nanotube and the details of the periodic boundary conditions used in the calculations. This is a rather disconcerting prospect. If the effect is real then the ergodic hypothesis states that the high binding energies must be observable through static single point energy calculations with the correct H 2-nanotube geometries as well as through finite temperature molecular dynamics. Careful work is needed to resolve the issues spelled out in the papers of Cheng et al. [72, 82], Li et al. [83], and Li and Yip [84]. We note that Okamoto and Miyamoto [73] reported MP2 binding energies on curved graphene structures of up to 308 meV. This is for a single H2 molecule on the inside of a highly curved C SO H 10 graphene structure. This large binding energy is probably due to two factors. One is the spurious charges induced on the cluster due to curvature that would be absent in real nanotubes because of symmetry. Another is the effect of basis set superposition error in their calculations, which they apparently did not account for through standard counterpoise corrections [96]. Two groups have independently addressed the issue of how alkali metal doping of nanotubes affects the H 2-nanotube interaction [77, 78]. Both observe an enhancement of the binding. Dubot and Cenedese [77] predict that the H 2 stretching mode will shift upon adsorption and that this shift should be observable experimentally. Froudakis [78] predicts a binding energy of about 150 meV that decreases as the number of H 2 molecules per metal atom is increased. A series of calculations on hydrogen adsorption in SWNTs have been carried out by Lee and coworkers [97-102], using both a semiempirical tight binding formalism and DFT. They report remarkably high hydrogen storage capacities for endohedral adsorption. The limits they predict, however, have nothing to do with realistic adsorption conditions. They essentially predict the bursting strength of nanotubes as more and more H 2 molecules are forced into the nanotube interior. Unfortunately, these calculations may give the mistaken impression that the adsorption they report is somehow energetically favorable. This is not the case, as the repulsive energies are extremely high. They also report a curious "pathway" for hydrogen adsorption by chemisorption of atomic hydrogen on the external surface of a nanotube, followed by a high-energy "flip" of the H atom (breaking the C-C bond) into the nanotube interior. This is an implausible mechanism for anything close to room temperature processes.

Chapter 15 Hydrogen Adsorption in Single-Walled Carbon Nanotubes

In summary, using DFT to compute the physisorption interactions ofH 2 with SWNTs is not entirely satisfactory. What is needed to resolve the issues of the precise nature of the H 2-nanotube interaction potential is the development of new methods. Specifically, multilevel calculations in periodic systems would be useful, so that the majority of the nanotube could be treated with DFT while the H 2-nanotube binding could be treated locally with CCSD(T). Alternatively, methods for rigorously including van der Waals interactions into periodic DFT need to be developed and tested. Computing dispersion energies from D FT is currently an active area of research [89, 90,103-108].

15.2.3 Ab Initio Modeling of Chemisorption The chemical adsorption of hydrogen on carbon nanotubes and on graphene structures has been studied by a number of different groups using ab initio and semi-empirical methods [71, 109-123]. Froudakis [124] has reviewed the ab initio calculations, focusing mainly on chemisorption. As with the previous section, most of the calculations utilize the DFT formalism because it is applicable to periodic as well as cluster systems and is highly efficient compared with molecular orbital methods, such as MP2 and CCSD(T). The chemical binding energies, energy barriers, electronic structures, and geometries of hydrogen bound to SWNTs have been calculated. The general conclusions are that dissociation and chemical binding of a single H 2 molecule to a nanotube is energetically unfavorable. Chemisorption of atomic hydrogen can be energetically favorable, depending on the nanotube and number of atoms being adsorbed. Binding of hydrogen to the inside of the nanotube is generally unfavorable, unless an alternating pattern is produced, so that the lattice strain energy is reduced. Binding on the external surface of nanotubes is enhanced for very narrow nanotubes, which have a high degree of curvature. By way of example, the electronic charge densities for H 2 in a preadsorbed state and a chemisorbed state on a (5, 5) SWNT are shown in Fig. 15.9, as

(a)

(b)

Figure 15.9 (a) Contour plots of charge densities of H 2 physisorbed at a distance of 1.85 A above the C-C bond of a (5,5) SWNTs. (b) H 2 associatively adsorbed on a (5, 5) nanotube. The C-H bond length is 1.06 A. The contour spacing is 0.05 a. u. The black and gray circles represent the C and H atoms, respectively. (Reprinted with permission from Re£ [118] Copyright 2002 by the American Physical Society.)

15.3 Quantum Sieving

0.5

:>

o

~ -0.5 Q) ()

c

~

-1

:.c e> Q)

-1.5

~

~

c

-2

Q)

(ij

-2.5

;2 -3 -3.5

+-..,.___r___r____r_---r____.~,.___r__..,.___r___r____r____r____.~~_r____1

o

1

2

3

4

5

6

7

8

9 10 11 12 13 14 15 16 17

Number of chemisorbed hydrogens

Figure 15.10 The change in total energy on chemisorption ofhydrogen on the (8, 8) SWNT as computed by LDA-DFT. (Reprinted with permission from Ref. [119] Copyright 2003 by the American Physical Society.)

computed from GGA-DFT by Lee and coworkers [118] for a (5, 5) nanotube. Note how the charge density changes as the H 2 molecule dissociates and binds to the nanotube. The weakening of the C-C bond can be seen by a reduction in charge density at the C-C bond center. These calculations indicate that there is a substantial energy barrier for dissociative adsorption of H 2 of approximately 3 eVe In contrast, H atoms can chemisorb with a relatively small energy barrier of about 0.3 eV [118]. Stojkovic et al. [119] have shown that shown that successive adjacent chemisorption of H atoms can lead to a decrease in the energy penalty for chemisorption of hydrogen onto an (8, 8) nanotube. Atomic hydrogen adsorption is initially energetically unfavorable on the (8, 8) nanotube, in contrast to the (5, 5) nanotube [118], which has more Sp3 character due to the high curvature. However, if additional H atoms are chemisorbed in a specific pattern then the strain penalty is lowered, leading to exothermic binding. This is shown in Fig. 15.10 for up to 16 H atoms on an (8, 8) nanotube. The pattern involves hydrogens on alternate C atoms pointing into and out of the nanotube [119].

15.3

QUANTUM SIEVING

Molecular sieving is typically defined as separation of molecules based on a combination of size, shape, and specific solid-fluid interactions. Beenakker et al. [125] first proposed the idea that microporous sorbents with cylindrical pore diameters very close to the diameter of a molecule will act as quantum

Chapter 15 Hydrogen Adsorption in Single-Walled Carbon Nanotubes

386

molecular sieves. Radial degrees of freedom will be so restricted in a quantum sieving material that light molecules, with a large zero-point energy, will be excluded from the pores in favor of heavier molecules. The idea that adsorption will exhibit an isotope effect has been known for many years [126, 127], but Wang et al. were the first to carry out rigorous molecular simulations with realistic potential models on systems that exhibit quantum sieving. Their work showed that carbon nanotubes of the correct diameter could be very effective quantum sieving sorbents [128]. They showed that very narrow carbon nanotubes could be used to separate isotopes of hydrogen very efficiently, with zero pressure selectivities on the order of 105 , where the selectivity is defined as

x·lx. 5 .. =_'_J 1J

I

(15.2)

Yi Yj

where x and Y refer to the mole fractions in the adsorbed and bulk phases, respectively. For a mixture adsorbed in a cylindrical pore the selectivity at zero pressure (no sorbate-sorbate interactions) can be written in terms of the transverse energy levels of each component, (15.3)

E;

where is the transverse energy level for molecule i in energy state k [129]. This is a very simple expression that can be easily evaluated for hydrogen isotopes in carbon nanotubes by assuming a smooth H 2-nanotube potential and a spherically symmetric H 2 molecule. The energy levels can then be computed by expanding the wave function of the adsorbed molecule in terms of a harmonic oscillator basis set. More rigorous computer simulations can be carried out to check the predictions of Eqn (15.3) by using the path integral formalism of Feynman as used by Wang and Johnson [48]. Predictions from Eqn (15.3) along with exact path integral simulation results are plotted in Fig. 15.11 for T 2/H2 mixtures at 20 K. The simple theory is remarkably accurate for the cases where the calculation converges. The data indicate that the selectivity drops dramatically with increasing nanotube diameters, so that quantum sieving is only effective for very narrow nanotubes. However, the ICs of perfectly packed (10, 10) nanotubes happen to be the correct size for producing very high selectivities. The theory and simulation results for interstitial sites are shown as the asterisk and square in Fig. 15.11 , respectively. The path integral simulations can be extended to higher pressures, including the effect of adsorbate-adsorbate interactions. The selectivity as a function of pressure can be computed by performing a grand canonical Monte Carlo simulation of a mixture. The selectivity for the D 2 /H 2 mixture, with a bulk composition of 99.95% H 2 , is shown in Fig. 15.12. The gases are assumed to adsorb only in the ICs of a perfect (10, 10) SWNT bundle and the temperature

15.3 Quantum Sieving

(3,6) (10,10) interstice

~

(2,8)

1

10

-

-

-

-

-6 - U - Cf - - - - - -

(6,6)'i 10° 5

(10,10) 10

(18,18)

15

20

25

Tube diameter (A)

Figure 15.11 Zero pressure selectivity at 20 K for T 2 - H 2 mixtures as a function of tube diameter. The diamonds are computed from an approximate theory, given by Eqn (15.3). The circles are computed from path integral simulations. A few specific tubes are labeled on the graph with their (n, m) indices. So in the (10, 10) interstice is shown as an asterisk (theory) and an open square (simulations). (Reprinted with permission from Ref. [129] Copyright 2001 by the American Physical Society.) 1400

~----r----~------,------,r------,

1200

os~

uCD CD

en

I

I

1000

C\I

I

~ 0

C\I

800

600 13 10-

I

I

II 10-11

10-9

10-7

10-5

10-3

Pressure (torr)

Figure 15.12 Selectivity in the (10, 10) interstice at 20 K for a D 2 - H 2 mixture with bulk composition of 99.95 mol% H 2 • The solid line is computed from the ideal adsorbed solution theory. The points are from path integral simulations. (Reprinted with permission from Re£ [130] Copyright 2002 by the American Institute of Physics.)

is 20 K. Note that the selectivity increases with increasing pressure. The solid line plotted in Fig. 15.12 denotes the prediction from ideal adsorbed solution theory and the symbols are path integral simulations [130]. The previous calculations have considered hydrogen molecules as spheres. Hathorn, Sumpter, and Noid calculated the rotational eigenvalues of hydrogen

388

Chapter 15 Hydrogen Adsorption in Single-Walled Carbon Nanotubes

isotopes to compute the rotational contribution to quantum sieving [131]. They found that the rotational selectivities are much smaller than the translational selectivities. Similarly, Trasca and coworkers investigated both isotope and spin selectivity for preferential adsorption of D 2 over H 2 in a bundle of carbon nanotubes [132]. They found reasonably high spin selectivities in ICs at temperatures lower than 100 K; selectivities in groove sites and on graphite were found to be considerably lower. The translational selectivities computed by Trasca et al. for H 2 /D 2 in ICs are substantially larger than the calculations of Challa et al. [130] This may qe due to the different potential models and harmonic oscillator approximation used by Trasca and coworkers. Gordillo, Boronat, and Casulleras have used diffusion Monte Carlo to compute isotope effects for hydrogen adsorbed in narrow carbon nanotubes [133]. They observed quantum effects in energetic and structural properties of the isotopes. They computed the ground state energies of hydrogen isotopes in a SWNT with a radius of 3.42 A using the smoothed hydrogen-nanotube potential of Stan and Cole [46]. The zero-pressure selectivity computed from their reported ground state energies for T 2 and H 2 is 22.8 at 20-K. This selectivity is much lower than the value of 419 predicted by Challa et al. for T 2/H2 in the (5, 5) nanotube at 20 K [129]. The radius of the nanotube used by Challa et al. was 3.39 A, slightly smaller than that used by Gordillo et al. The difference in diameter will account for part but not all of the difference between the two selectivities; note that a nanotube with a radius of 3.59 A is predicted to have a selectivity of 32 for T 2 /H 2 at 20 K according to the calculations of Challa et al. [129]. Lu and coworkers have computed rotational and translational degrees of freedom for hydrogen isotopes confined in different carbon nanotubes [134]. They solved a Hamiltonian for the system with four degrees of freedom. The reduced density plots resulting from their calculations are shown in Fig. 15.13. Note that the smallest nanotubes, (3, 6) and (8, 0), the H 2 molecule is confined in the center of the nanotube. For the largest nanotubes, (6, 6) and (10, 10), the confinement is annular, as the molecule is trapped next to the wall of the nanotube. Confinement in the (2, 8) nanotube is in the crossover region, where the potential just starts to exhibit a double well potential. The selectivity calculations of Lu et al. are in quantitative disagreement with the theory and path integral calculations of Challa et al. [128-130] Lu and coworkers observe a zero pressure selectivity for T 2 /H 2 in the (3, 6) nanotube on the order of 100, compared with a value of about 105 as calculated by Challa et al. [129] The difference between these two results is attributed to the specific solid-fluid potential used [134]. This is a conjecture that should be tested. If the quantum sieving phenomenon is very sensitive to the specific solid-fluid potential used in the calculations then the predictions are of limited utility until the potential is known to higher accuracy. We note that the calculations of Trasca et al. [132] give even higher selectivities than those reported by Challa et al., in contrast to the results from Lu et al. and Gordillo et al. The potential models

15.3 Quantum Sieving

0.8

0.8

0.6

0.6

0.4

0.4 0.2

0.2

<' -;:

<' -;:

0

0

-0.2

-0.2

-0.4

-0.4

-0.6

-0.6

(3,6) -0.8 -1 '--............. ""'--......--. .............---.1 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

-0.8

(8,0)

-1 '---""-......-....-------......-....-----' -1 -0.8-0.6-0.4-0.2 0 0.2 0.4 0.6 0.8 1

X(A)

X(A)

1.5 - - - - - - - - - - - - - - - - .

2 -------------

1.5

0.5

0.5

-0.5

-0.5

-1 -1

-1.5

-1.5 L . -1.5

" " ' - - _ - " " - _ - ' - - _......_

-1

-0.5

0

......

1.5

0.5

-2 I . . . - - - ' - - - -........- - - -........----~----I -2 -1.5 -1 -0.5 0 0.5 1.5 2 X(A)

X(A)

5 4

3 2

1

<' ~

0 -1

-2 -3

-4 -5

-5 -4 -3 -2 -1

0

1

2

345

X(A)

Figure 15.13 Reduced density plots of the ground state of H 2 confined inside the (3, 6), (8, 0), (2, 8), (6, 6), and (10, 10) nanotubes. (Reprinted with permission from Re£ [134] Copyright 2003 by the American Chemical Society.)

and methods used by these four groups are all different, so it appears that the selectivities do exhibit a good deal of model dependence; it is not clear which predictions are most accurate. In principle, the path integral calculations are exact at finite temperatures. However, the accuracy of the potential models

39°

Chapter 15 Hydrogen Adsorption in Single-Walled Carbon Nanotubes

and exact geometries of the nanotube bundles are unknown. In short, all the simulation results confirm the quantum sieving phenomenon, but there are qualitative differences as to what nanotube diameters are required to achieve very high selectivities at a given temperature. Indirect experimental evidence for quantum sieving of H 2 /D 2 on carbon nanotubes has been noted by Pradhan et al. [29] and also by Wilson et al. [31] Pradhan noted that the adsorption isotherm of D 2 on a purified SWNT sample was significantly larger than for H 2 on a molar basis at 77 K. Wilson et al. measured significantly higher isosteric heats of adsorption for D 2 than for H 2 on closed SWNT bundles at 77 K. It is not definitively clear in either of these experiments where on the nanotube bundle the hydrogen is actually adsorbing. The experiments of Pradhan et al. were on opened nanotubes, so that the adsorption is presumably inside the tubes. Wilson et al. used closed nanotubes, so that the adsorption must be in either the ICs, the groove sites, or on the external surface of the bundle. The near zero coverage limit for the isosteric heats measured by Wilson et al. are about 1100 K for D 2 and 900 K for H 2 [31]. If we take the difference in isosteric heats as a good approximation to the negative of the difference between the transverse energies of the two isotopes, then we can apply a simplified version of Eqn (15.3) to compute an expected selectivity. We assume that only the ground state is occupied, which certainly not very exact at the experimental temperature of 85 K. The selectivity calculated by this method is 5.3. This can be compared with the value computed by Challa et al. at 77K for HT/H 2 in the (10, 10) interstice of r-v3 [129]. Note that within the approximations of the theory HT behaves the same as D 2 • Using a different model, Trasca et al. predict a value of r-vSOO for D 2 /H 2 in an IC and r-v4 in a groove site at 85 K [132]. Thus, we cannot tell from these calculations if the adsorption measured by Wilson et al. is in the groove site or the ICs. This last point brings us to a side issue. The ability to distinguish where gases are adsorbing on closed SWNT bundles, on groove sites or in interstitial sites, is a challenging problem at present. All of the theoretical predictions indicate that H 2 and He should be readily adsorbed inside the interstitial channels of perfect nanotube bundles, while most larger molecules will be excluded from the interstices. This depends on the diameters of the nanotubes making up the bundles and the actual lattice constant of the tube array, but H 2 should adsorb in the ICs for the most common nanotube sizes, (9, 9) and (10, 10) diameters, and for the experimentally observed van der Waals gap of3.2A [137]. Experiments, however, have not been able to identify IC adsorption ofH 2 or even He [136137]. There are some experiments where Ie adsorption is assumed to be present [22,138-140] However, there is no definitive evidence of interstitial adsorption. Taking the case of the isosteric heats computed above, the calculations ofTrasca et al. estimate the difference in binding energies for D 2 and H 2 adsorbed in the IC to be 374 K, while for the groove site the difference in binding energies is predicted to be 137 K. These calculations employed a rather unconventional potential developed by Kostov [141]. If we compare these calculations with

15.4 Phase Transition Phenomena

39 1

the isosteric heat data of Wilson et al. then we would conclude that groove site adsorption is indicated. However, recent calculations by Calbi [143] using a conventional potential model for H 2 -nanotube interactions and accounting for quantum zero-point energies gives energy differences of 165, 140, and 55 K for D 2 /H 2 in rigid ICs, dilated ICs, and groove sites, respectively. The dilated ICs were computed using the observation that H 2 adsroption in ICs can lead to slight dilation of the nanotube lattice spacing in a perfect lattice. [142, 143] The calculations of Calbi clearly indicate that the Wilson data are consistent with IC adsorption, not groove site adsorption. Hence, whether or not H 2 can adsorb in the ICs of perfect SWNT bundles is an open question; it will likely remain an unanswered question until perfect arrays of pure aligned nanotubes are produced.

15-4

PHASE TRANSITION PHENOMENA

A wide variety of phase transition phenomena have been described in Chapter 9. For completeness, we briefly summarize those predictions and refer the interested reader to either the original literature or the other chapter. The first phase transition of hydrogen that was explored is the so-called "axial phase transition," occurring within the interior ofa nanotube [144]. This phenomenon is analogous to capillary condensation, differing in three important respects. One is that the nanotube provides a nearly ideal environment, a realization of many theoretical models, employing cylindrical pores. A second difference is that the small size of the tubes means that macroscopic equations, such as Kelvin's equation, are not reliable methods for estimating the condensation pressure as a function of tube radius. For the same reason, small size, the phenomenon of hysteresis, ubiquitous in capillary condensation, is not expected to occur (since the various hypothetical mechanisms ascribed to the condensation are not applicable to very small radius situations). These features make the phenomenon particularly interesting topics of future study; experimentally, this will require opening the tubes, which is not always done. Studies of similar structural transitions for hydrogen within the nanotubes have been carried out by Xia et al. [145], Ying et al. [146], and Ma et al. [147] These results exhibit a wide variety of linear, cylindrical, and helical phases, the existence of which is strongly dependent on the tube radius and the molecular density. Obviously, the transitions between these novel phases are of considerable interest, but space considerations prevent us from discussing the results in detail. Scattering experiments would provide ideal probes of these phases but their interpretation will be difficult unless the tubes are aligned. Chapter 6 described a set oftransitions within the groove phase on the external surface of the bundle. While not extensively studied thus far, similar behavior

39 2

Chapter 15 Hydrogen Adsorption in Single-Walled Carbon Nanotubes

is expected to occur for hydrogen. Thus, one expects the film to evolve from groove phase to monolayer and higher coverage film. Several transitions have been proposed to occur within ICs. One of them is condensation into an anisotropic liquid phase, due to interactions between molecules in different channels [148]. This has been claimed to occur at remarkably high temperature when the phenomenon of dilation of the lattice of tubes is taken into account [142, 143]. That is a collective phenomenon, analogous to the phonon-mediated superconductivity, but with a higher energy scale associated with the enhanced binding within the channel. The most exotic transition predicted to occur is Bose-Einstein condensation (BEC) of parahydrogen, a consequence of the presence of heterogeneity within the distribution of tube radii [149, 150]. We present a heuristic argument for this phenomenon, omitting most details, and refer the reader to the original papers [149, 150]. Consider a molecule moving within a single IC; its energy spectrum is given by the following relation: (15.4) Here Et(R) is the transverse energy and p is the momentum parallel to the IC; R is a shorthand notation for the three radii of the adjacent tubes. In this model, we consider only threefold coordinated ICs, which we believe have the lowest possible energy, assuming them to be present within the sample. The density of states for the molecules within this IC satisfies

h(E,R) = I:D[E-E(R,p)] =L- (m)1/2 [E-E t (R)]-1/20[E-E t (R)] 7Th 2 p (15.5) where 0(x) is the Heaviside unit step function. A general relation between density of states and dimensionality D is a dependence of the form N(E) rv (E -.Emin)X, where x = (Dj2) -1 This inverse square root dependence on energy above threshold is thus characteristic of a one-dimensional (1D) problem. Considering an inhomogeneous distribution of ICs, the density of transverse energy states is given by integrating over the distribution n( R) of R values

g(E)

=

JdRn(R)0 [E - Et(R)]

(15.6)

The total density of states is found by summing over all states of the ICs present in the sample: (15.7)

Acknowledgments

393

In the monodisperse case, this relation would yield the lD spectrum mentioned above. In the polydisperse case, however, the regime of ultralow energy exhibits quite different behavior. If there exist tubes having transverse energy in the vicinity of the energy minimum, E min , by integrating over the vicinity of this minimum R min one finds a transverse density of states g( E) proportional to (E - Emin ) 1/2 this case, the integral (15.7) yields a final equation N(E) proportional to (E - Emin ). This dependence corresponds to that expected for a 4D Bose gas. Such a 4D gas is expected to exhibit BEC.

15.5

SUMMARY AND CONCLUSIONS

Scientists usually like to conclude descriptions of research activities with enthusiastic summaries of progress, with definitive conclusions, supplemented by an enumeration of a few remaining areas that still need to be "mopped up." Unfortunately, this chapter must end on a less satisfactory note. Many of the most important questions have not yet been answered. We have identified two principal sources of this situation. One is a very serious materials problem, meaning that most of the many groups exploring this problem are using somewhat different nanotube samples from the other groups. The other difficulty is a problem with theory. Our community has not yet converged on a reliable determination of either the adsorption potential or the importance of the nanotubes' dynamics. To some extent, this is a consequence of the challenge of computing physisorption potentials and the uncertain role of chemisorption interactions; these are difficult to compute accurately for nonperiodic systems involving many atoms. In the present circumstance, the preceding "bad news" is complemented by the following "good news": progress is being made in many directions - experimental, conceptual, and simulationa!' The phenomena being explored are so diverse that both fundamental and applied efforts to explore them remain frontier topics in both science and englneenng.

ACKNOWLEDGMENTS

We gratefully acknowledge Mercedes Calbi, Hansong Cheng, Anne Dillon, Silvina Gatica, Evelyn Goldfield, Michael Heben, Susana Hernandez, Michael Hirscher, Ju Li, AIdo Migone, and Oscar Vilches for helpful discussions. We acknowledge NSF for support of this work (grants 0208520,0303915, 0085480).

Chapter 15 Hydrogen Adsorption in Single-Walled Carbon Nanotubes

394

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40 0

Chapter 15 Hydrogen Adsorption in Single-Walled Carbon Nanotubes

123. Zaporotskova, I.V., Lebedev, N.G. and Chemozatonskii, L.A. (2004). Single and regular hydrogenation and oxidation of carbon nanotubes: MNDO calculations. Int.]. Quant. Chern., 96, 149-54. 124. Froudakis, G.E. (2002). Hydrogen interaction with carbon nanotubes: a review of ab initio studies.]. Phys. Condens. Mater., 14, R453-R465. 125. Beenakker, J.J.M., Bonnan, V.D. and Krylov, S.Y. (1995). Molecular-transport in subnanometer pores - zero-point energy, reduced dimensionality and quantum sieving. Chern. Phys. Lett., 232, 379-82. 126. Katorski, A. and White, D. (1964). Theory of adsorption of the isotopic hydrogen molecules at low temperatures.]. Chern. Phys., 40, 3183-94. 127. Moiseyev, N. (1975). Isotope effect on physical adsorption on a nonhomogeneous surface.]. Chern. Soc., Faraday Trans. I, 71, 1830-7. 128. Wang, Q.Y., Challa, S.R., Sholl D.S., and. Johnson, J.K. (1999). Quantum sieving in carbon nanotubes and zeolites. Phys. Rev. Lett., 82, 956-9. 129. Challa, S.R., Sholl, D.S., and Johnson, J.K. (2001). Light isotope separation in carbon nanotubes through quantum molecular sieving. Phys. Rev. B, 63,245419. 130. Challa, S.R., Sholl, D.S., and Johnson, J.K. (2002). Adsorption and separation of hydrogen isotopes in carbon nanotubes: Multicomponent grand canonical Monte Carlo simulations.]. Chern. Phys., 116,814-24. 131. Hathorn, B.C., Sumpter, B.G., and Noid, D.W. (2001). Contribution ofrestricted rotors to quantum sieving of hydrogen isotopes. Phys. Rev. A, 64, 022903. 132. Trasca, R.A., Kostov, M.K., and Cole, M.W. (2003). Isotopic and spin selectivity ofH 2 adsorbed in bundles of carbon nanotubes. Phys. Rev. B, 67, 035410. 133. Gordillo, M.C., Boronat, J., and Casulleras J. (2002). Isotopic effects of hydrogen adsorption in carbon nanotubes. Phys. Rev. B, 65, 014503. 134. Lu, T., Goldfield, E.M., and Gray, S.K. (2003). Quantum states of molecular hydrogen and its isotopes in single-walled carbon nanotubes. J. Phys. Chern. B, 107, 12989-95. 135. Stan, G., Bojan, M.J., Curtarolo, S., et al. (2000). Uptake of gases in bundles of carbon nanotubes. Phys. Rev. B, 62, 2173-80. 136. Talapatra, S., Zambano, A.Z., Weber, S.E., and Migone, A.D. (2000). Gases do not adsorb on the interstitial channels of closed-ended single-walled carbon nanotube bundles. Phys. Rev. Lett., 85, 138-41. 137. Wilson, T. and Vilches, O.E. (2003). Helium adsorbed on carbon nanotube bundles: one-dimensional and/or two-dimensional solids? Low Ternp. Phys., 29, 975-9. 138. Teizer, W., Hallock, R.B., Dujardin, E., and Ebbesen, T.W. (1999). He-4 desorption from single wall carbon nanotube bundles: a one-dimensional adsorbate. Phys. Rev. Lett., 82, 5305-8. 139. Teizer, W., Hallock, R.B., Dujardin, E., and Ebbesen, T.W. (2000). Erratum: He-4 desorption from single wall carbon nanotube bundles: a one-dimensional adsorbate. Phys. Rev. Lett., 84, 1844-5. 140. Fujiwara, A., Ishii, K., Suematsu, H., et al. (2001). Gas adsorption in the inside and outside of single-walled carbon nanotubes. Chern. Phys. Lett., 336, 205-11. 141. Kostov, M.K., Cheng, H., Hennan, R.M., et al. (2002). Hindered rotation of H 2 adsorbed interstitially in nanotube bundles.]. Chern. Phys., 116, 1720-4. 142. Calbi, M.M., Toigo, F., and Cole, M.W. (2001). Dilation-induced phases of gases absorbed within a bundle of carbon nanotubes. Phys. Rev. Lett., 86, 5062-5.

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143. Calbi, M.M., Toigo, F., and Cole, M.W. (2002). Dilation and intercalation of gases within carbon nanostructures. J. Low Temp. Phys., 126, 179-86. 144. Gatica, S.M., Stan, G., Calbi, M.M., et al. (2000). Axial phase of quantum fluids in nanotubes.]. Low Temp. Phys., 120,337-59. 145. Xia, Y.Y., Zhao, M.W., Ma, Y.C., et al. (2003). Condensation and phase transition of hydrogen molecules confined in single-walled carbon nanotubes. Phys. Rev. B, 67,115117. 146. Ying, MJ., Xia, Y.Y., Liu, X.D., et al. (2004). Quasi-one-dimensional liquid hydrogen confined in single-walled carbon nanotubes. Appl. Phys. A, 78, 771-5. 147. Ma, Y.C., Xia, Y.Y., Zhao, M.W., and Ying, MJ. (2002). Structures of hydrogen molecules in single-walled carbon nanotubes. Chem. Phys. Lett., 357, 97-102. 148. Gatica, S.M., Calbi, M.M., and Cole M.W. (2003). Universal anisotropic condensation transition of gases in nanotube bundles.]. Low Temp. Phys., 133, 399-406. 149. Ancilotto, F., Calbi, M.M., Gatica, S.M., and Cole, M.W. (2004). Bose-Einstein condensation of helium and hydrogen inside bundles of carbon nanotubes. Phys. Rev. B, 70, 165422. 150. Marcone, B., Orlandini, E., Toigo, F., and Ancilotto, F. (2006). Condensation of helium in interstitial sites of carbon nanotubes bundles, Phys. Rev. B, 74, 085415.

ADSORPTION ON ORDERED POROUS CARBONS Hans Darmstadt 1,* and Ryong Ryoo 2 Departement de genie chimique, Universite Laval Quebec, QC, Canada National Creative Research Initiative Center for Functional Nanomaterials and Department of Chemistry (School of Molecular Science BK21), Korea Advanced Institute of Science and Technology, Daejeon, Korea * Present address: Rio Tinto Alcan, Arvida Research and Development Centre, jonquiere, QC, Canada 1

2

Contents 18.1 Ordered Porous Carbons 18.2 Characterization of Ordered Porous Carbon by Gas Adsorption 18.3 Conclusions Acknowledgments References

455 458 474 474

475

18.1 ORDERED POROUS CARBONS 18.1.1

Synthesis of Ordered Porous Carbons

Ordered mesoporous carbons (aMes) are new carbon materials that were developed over the last ten years. Their mesopores have a defined width with a very narrow pore size distribution. This sets them aside from "older" nanoporous carbons, such as activated carbons or activated carbon fibers. The last two classes of carbons are produced from various carbon-containing materials by carbonization followed by partial oxidation (activation). To a certain degree, the pore structure of these materials can be controlled by the carbonization and activation conditions. However, it is not possible to produce purely mesoporous activated carbons or activated carbon fibers. Furthermore, these materials generally exhibit a broad pore size distribution [1, 2]. Adsorption by Carbons ISBN: 978-0-08-044464-2

© 2008 Elsevier Ltd.

All rights reserved.

455

Chapter 18 Adsorption on Ordered Porous Carbons

456

For some important applications, such as adsorption and catalytic transformation of voluminous hydrocarbon molecules, and for the synthesis of nanostructured inorganic compounds by nanocasting, carbons with uniform mesopores are highly desirable. Thus, OMCs with their regular and controllable pore structure offer significant advantages in these applications. Their synthesis is performed with the aid of a matrix. Two general strategies were developed. The OMC synthesis can be performed in the pore system of a mesoporous matrix (exotemplating) or in the voids in between nanoparticles of a nonporous, regular-sized matrix (endotemplating) [3]. In both cases, a regular pore system is formed upon removal of the matrix. Colloidal silica is an appropriate matrix for the endotemplating route [4]. The pore system of the resulting OMC corresponds to the voids in between the spherical silica particles. Suitable matrices for the exotemplating route are microporous zeolites [5]-[7] or mesoporous silicas [8]. The obtained OMCs have a very regular pore structure. As an example, transmission electron microscopy (TEM) images of an OMC, known as CMK-3, are presented in Fig. 18.1 [9]. The images show a regular hexagonal array of straight carbon rods, corresponding to the cylindrical mesopores of the SBA-15 silica matrix. Depending on the synthesis procedure, OMCs with mesopore widths between approximately 2 and some 10 nm can be obtained. A typical exotemplating synthesis procedure consists of an acid catalyzed polymerization of a carbon precursor (e.g., sucrose [10] or furfuryl alcohol [11]) adsorbed in the pore system of the matrix followed by carbonization of the polymerization product at elevated temperatures. In the next synthesis step, the OMC is liberated by removal of the matrix. In the case of zeolite or silica matrices, this can be achieved by treatment with hydrofluoric acid or sodium hydroxide. Finally, the OMC may be modified in a postsynthesis heat-treatment (a)

(b)

Figure 18.1 Transmission electron microscopy (TEM) images of CMK-3: (a) projection along the direction and (b) parallel to carbon rods. (Reprinted with permission from Ref. [9].)

18.1

Ordered Porous Carbons

457

procedure [12, 13]. Other synthesis procedures are based on pitch. In this case, no polymerization step is required. For carbonization, the pitch-loaded matrix is directly heated in an inert atmosphere [14, 15]. Obviously, the structure of the produced carbon material is controlled by the pore structure of the matrix or the "template." Mesoporous silicas are attractive templates as they are available in a large variety of structures; the thickness of their pore walls can be tailored [16]; they exhibit a high structural order and methods for their cost-effective synthesis have been developed [17,18]. In some cases, the OMC is a replica of the matrix pore system. This was proven by synthesis of a mesoporous silica in the pore system of an OMC. The structure of the silica initially used for the synthesis of the OMC and of the silica synthesized in the pore system of the OMC was identical, proving that no structural changes occurred during the entire synthesis route [19]. In other cases, changes of the structure have been observed. For example, the pore system of the mesoporous silica MCM-48 consists of two interwoven but unconnected three-dimensional pore systems [20]. It is evident that upon removal of the MCM-48 matrix the structure of the OMC, known as CMK-l, changes [11]. The OMC structure also depends on the polymerization step. As mentioned above, the polymerization of the precursor adsorbed in the pore system of the matrix is catalyzed by acids. Different synthesis procedures were developed. For example, an acid solution can be added to the reaction mixture. In this case, the polymerization will take place throughout the entire pore system of the matrix. The resulting OMC can be described as a three-dimensional network of interconnected carbon rods. An example is CMK-3, already presented in Fig. 18.1. In this OMC, parallel-arranged carbon rods with a diameter of approximately S nm are connected by narrower carbon rods. The narrow carbon rods were formed in micropores that connect the mesopores of the SBA-1S silica matrix [21]. In an alternative synthesis procedure, a matrix with acid sites on the pore walls (e.g., an aluminosilicate) can be used. In this case, the polymerization of the precursor takes place on the mesopore walls and a carbon film is formed there, whereas the much narrower micropores are entirely filled with the polymerization product. Thus, after pyrolysis and removal of the matrix, the OMC consists of interconnected nanopipes, as opposed to interconnected carbon rods. An example is CMK-S. This OMC is synthesized in an acid form of the matrix used for the synthesis of CMK-3. Thus, CMK-S consists of interconnected carbon nanopipes, arranged in the same fashion as the carbon rods of CMK-3 (Fig. 18.2) [22]. However, the pore system of these two OMCs differs. The pore system of CMK-3 consists of the voids in between the carbon rods, whereas in addition to these pores CMK-S also has pores inside the nanopipes.

18.1.2

Applications of Ordered Porous Carbons

OMCs have very high mesopore volumes of up to 2 cm3 / g [23]; as already mentioned the mesopore widths can be controlled, and OMCs without micropores can be synthesized [13]. Several potential applications could take advantage

Chapter 18 Adsorption on Ordered Porous Carbons

458

Figure 18.2 Transmission electron microscopy (TEM) images ofCMK-S taken (a) along the channel direction and (b) perpendicular to it. (Reprinted with permission from Re£ [22].)

of these exceptional properties. These include, for example, the adsorption and separation of bulky molecules such as proteins and vitamins [24]; the use of OMCs in electrochemical double-layer capacitors, especially when the electrolyte solution contains bulky molecules that can enter into mesopores but not into micropores [25]; the use as template for the synthesis of nanostructured inorganic compounds that are not accessible by other synthesis routes [26]; and as catalyst support [27]. For all these applications, the OMC pore structure is of critical importance. Its determination by gas adsorption will be discussed in the next section.

18.2 CHARACTERIZATION OF ORDERED POROUS CARBON BY GAS ADSORPTION

In this section, the characterization of OMCs by nitrogen adsorption at 77 K will be reviewed. On modern automated gas adsorption instruments, different data treatment methods for adsorption data of carbon materials are available. However, many of these methods were developed for activated carbons, assuming that the pores have a slit-like shape and that their walls consist of the basal planes of perfect graphene layers. Unfortunately, this is a rather poor description of the geometry and surface chemistry of the OMC pores. Thus, application of these "standard" data treatment methods may lead to misleading results for OMCs. In this text, particularities of gas adsorption on OMCs will be discussed in detail. Special attention will be paid to the adsorption potential distribution (APD). As outlined below, from the APD, information on many OMC properties such as the specific surface area, the presence ofmicropores, and the graphitic character of the internal surface can be obtained. An important advantage of this method is that no assumptions about the pore geometry have to be made.

18.2

Characterization of Ordered Porous Carbon by Gas Adsorption

18.2.1

459

General Features of the Nitrogen Adsorption Isotherms

First, some general features ofthe adsorption isotherms will be discussed. As mentioned above, OMCs are predominately mesoporous and exhibit a narrow mesopore size distribution. In the OMC isotherms, the mesopores cause a steep increase in adsorption at relative pressures (PI Po) between 0.4 and 0.8 and a hysteresis loop between the adsorption and desorption branch of the isotherm (Fig. 18.3). With increasing mesopore width, the hysteresis loop is shifted to higher PIPo. The small increase in adsorption for PIPo above 0.95, where multilayer formation takes place, indicates a small external surface of the OMC particles. From the amount of nitrogen adsorbed just before the increase of adsorption due to multilayer formation, one can estimate the combined volume of micro- and mesopores [28]. 18.2.1.1

Low-pressure nitrogen adsorption isotherm

Adsorption below a PI Po of approximately 0.05 is due to adsorption in micropores and to adsorption on mesopore walls. It is not easy to quantify these two contributions because in OMCs the micropore volume might be small as compared to their mesopore volume. However, some preliminary information on the presence of micropores can be obtained from the low-pressure portion of the adsorption isotherm. This will be illustrated by the discussion of some isotherms of nonmicroporous reference compounds. On a perfect graphene layer, adsorption at very low pressures (PIPo < 10- 4 ) is small. An example is the

1000

750

Ci

;, E

.£

en

'U

500

';::::..(fj

250

o

• CMK-3 (700°C) o CMK-3 (11 OO°C) A CMK-3 (1600°C) B--....L...-.....L..---J......--L---L..--...L---'---'----L---J

0.0

0.5

1.0

P/Po [-]

Figure 18.3 Nitrogen adsorption isotherms of ordered mesoporous carbons (OMes) synthesized at different temperatures. (Reprinted with permission from Re£ [13].)

460

Chapter 18 Adsorption on Ordered Porous Carbons

1.5

r-----------~i),oor_,

Graphitized CB

1.0

Microporous "\-. CB

0.0 ~~~L.L.I.LIIlII-...L..L.L.I.LIIlII-...L.."""""""'-"""""""""""'-""""1..L.LLWI 10-6 10-4

P/Po [-]

Figure 18.4 Low-pressure nitrogen adsorption isotherms ofvarious nonmicroporous carbon blacks (CB) with different graphitic order and of microporous CB. (Adsorption data taken from Refs [[39], [40], and [50]] for the graphitized, the thermal CB, and the furnace, respectively.)

low-pressure adsorption isotherm of graphitized carbon black (CB), a standard for a graphitic surface with very few defects, shown with a logarithmic PI Po scale in Fig. 18.4. If the graphene layers contain defects, adsorption at very low pressures is somewhat enhanced, because adsorption on some defect sites (e.g., steps of pits) is stronger as compared to a defect-free surface [29]. Examples are the isotherms of furnace and thermal CB (Fig. 18.4). The low-pressure adsorption isotherms of microporous carbons differ considerably from the previous examples. In micropores, assumed to be slit-like in carbons, adsorbed molecules interact with two surfaces, as opposed to just one on an open surface. Thus, on microporous carbons significant adsorption already occurs at low pressures and is much larger as compared to an open surface. This is also the case in comparison to an open surface that contains defects. For example, at a PI Po of 10- 6 on the microporous CB, approximately 10% of the monolayer is already formed (Fig. 18.4), whereas on the nonmicroporous thermal and furnace carbon black, less than 2 % are formed (All data are presented in Fig. 18.3). By comparing isotherms of the reference compounds and of OMCs, one can obtain qualitative information on the presence of micropores in the OMCs. The low-pressure isotherms ofOMCs synthesized at 1300°C and lower temperatures show substantial adsorption at very low PI Po. As on the microporous CB, at a PIPo of 10-6 , approximately 10% of the monolayer is formed (Fig. 18.5), clearly indicating the presence of micropores. The situation is different for the OMC sample synthesized at 1600 C. Here, adsorption at low PI Po is very small

18.2

Characterization of Ordered Porous Carbon by Gas Adsorption

1.5 r--;:=======::::::::;---------.rtr---,

eMK-3 700 0 e 900 0 e o 11000 .. 13000 e 0 /:i. 1600 e

• ()

e

:2: 1.0 CD

~

(5

c

o

~

.........

en

"0

~(fj

0.5

0.0 -6 10

Figure 18.5 Low-pressure nitrogen adsorption isotherms of various ordered mesoporous carbons (OMes) synthesized at different temperatures. (Reprinted with permission from Re£ [13].)

and the general shape of the isotherm resembles to a certain degree the one of the graphitized CB (Fig. 18.4). It can be concluded that the OMC sample synthesized at 1600°C does not contain micropores and that its surface has a relatively high graphitic order. 18.2.2

Determination of the Pore Size Distribution

As mentioned above, preliminary information on the mesopore widths can be obtained from the position of the hysteresis loop. With increasing mesopore width, its position is shifted to larger PIPo. The three OMC samples, of which isotherms are presented in Fig. 18.3, were synthesized at temperatures ranging from 700 to 1600°C. With increasing synthesis temperature, the hysteresis was shifted to a larger PI Po, indicating a widening of the mesopores. This was explained by a heat-induced contraction of the carbon rods, enlarging the voids in between them [13]. For a qualitative determination of the mesopore size distribution, mathematical models have to be used. Of these, the Barrett, Joyner, Halenda (BJH) method [30] is widely used for OMCs [14, 31, 32] and other carbon materials. However, for OMCs this model has some important shortcomings. As already mentioned above, the OMC mesopores might be as narrow as 2 nm. For such mesopores, the BJH method seriously underestimates the pore width [33]. Thus, improved data treatment methods have been proposed [33, 34]. As an example, the mesopore size distributions for an OMC of the CMK-l type calculated with

Chapter 18 Adsorption on Ordered Porous Carbons

the BJH and a modified BJH method [34], respectively, are shown in Fig. 18.6. A pore width (maximum in the pore size distribution) of 2.5 nm is obtained with the traditional BJH method, whereas the modified method yields - more realistically - 3.3 nm. However, it should be considered that in the case of this OMC, the mesopores are the voids in between the carbon rods. Thus, the shape of the mesopores is irregular and is poorly described by the traditional and modified BJH models, which assume a cylindrical pore shape. To the best knowledge of the authors, no model for the calculation of the mesopore size distribution was developed for solids like CMK-3, where the pore system corresponds to the voids in between cylinders. Another model applied for the calculation of the OMC pore size distribution is the density functional theory (DFT). This model assumes that the micro- and mesopores are slit-shaped and that the pore walls consist of defect-free basal planes of graphene sheets [35]. Both assumptions might be justified to a certain degree for micropores in activated carbons. However, they are certainly not valid for mesopores in OMCs. As mentioned above, the OMC mesopores correspond to the voids in between the carbon rods. Thus, their shape is not slit-like. Furthermore, the graphitic character strongly depends on the OMC synthesis temperature. For OMC synthesized at low temperature (i.e., < 1300°C), the graphene layer contain numerous defects (see below). Finally, in some pitchbased OMC, the graphene layers are orientated perpendicular to the OMC

Modified BJH method

2

345

6

Pore width, w [nm]

Figure 18.6 Mesopore size distribution of an ordered mesoporous carbon (OMC) (sample CMK-1F(A) of Ref. [13]) calculated with the Barrett, Joyner, Halenda (BJH) [30] and a modified BJH method [34], respectively, using desorption data.

18.2

Characterization of Ordered Porous Carbon by Gas Adsorption

surface. Thus, for these samples, the surface consists of the edges of the graphene layers [15]. Consequently, for OMCs, the DFT model may give misleading results. Other potential pitfalls in the determination of the pore size distribution of predominately mesoporous materials were reviewed elsewhere [36]. It can be summarized that regardless of the data treatment method used, there will always be some error in the calculation of the mesopore size distribution of OMCs. In general, the obtained mesopore widths increase in the order BJH < DFT < modified BJH method. The mesopore widths calculated with the modified BJH method and with the DFT method, respectively, are approximately 0.4 nm [11] and 0.8 nm wider than those obtained with the "traditional" BJH method (Fig. 18.6). In the opinion of the authors, at the present time, the improved BJH methods [33, 34] yield the most reasonable results for OMCs.

18.2.3 Adsorption Potential Distribution It was mentioned above that from the APD, valuable information on various OMC properties can be obtained. Before this is outlined in detail, the calculation of the APD is briefly reviewed. The adsorption potential (A) is defined as the negative change of the Gibbs free energy of adsorption:

A

= -~G = -RT In (PIPo)

(18.1)

where R is the gas constant, T the absolute temperature, and PI Po the relative pressure [37]. The APD is defined by the following equation: APD = -d VI(Vmonolayer' dA)

(18.2)

where d V and dA are the differences in volume of adsorbed gaseous nitrogen [cm3 STP/g] and in the adsorption potential, respectively, between two neighboring points of the adsorption isotherm, and Vmonolayer is the monolayer volume. Thus, the APD can be regarded as the negative derivative of the adsorption isotherm. First, the APD of nonmicroporous carbon materials is discussed. Graphene layers are the basic building units of many carbon materials such as CB, activated carbons, and OMCs. On surfaces consisting of well-ordered graphene layers, all adsorption sites have the same energy. Thus, formation of the first monolayer takes place in a very narrow pressure range. For noble gases, such as krypton, the corresponding adsorption isotherms indeed show distinct steps for the formation of the first three to four monolayers [38]. The situation is different when nitrogen is used as adsorbate. The nitrogen molecule has a quadrupole moment. Therefore, in the nitrogen adsorption isotherm of graphite, the monolayer steps are less pronounced. However, in the corresponding APD the formation of the first monolayer is indicated by a well-defined peak. The position and intensity of the monolayer formation peak depend on the graphitic order of the surface. As an example, the nitrogen adsorption isotherms

Chapter 18 Adsorption on Ordered Porous Carbons

Graphitized CB

2

468 Adsorption potential, A [kJ/mol]

Figure 18.7 Adsorption potential distribution (APD) of various carbon blacks (eB); the curves were vertically shifted for better presentation.

and the corresponding APDs of three CB with different degrees of surface order are presented in Fig. 18.7. The isotherm of the graphitized CB shows a prominent increase of adsorption at a PIPo of approximately 10- 4 (Fig. 18.4). A second, smaller step at a PI Po of approximately 10- 2 is due to a two-dimensional disordered fluid/two-dimensional ordered solid phase transition [39]. These two steps correspond to two peaks in the APD at adsorption potentials of approximately 3.5 and 5 kJ/mol, respectively (Fig. 18.7). The furnace CB has a less ordered surface than the graphitized CB. In its isotherm, the formation of the monolayer is indicated by a fuzzy step, whereas in the corresponding APD, a monolayer formation peak is still clearly visible at an adsorption potential of approximately 5 kJ/mol. The surface of thermal CB consists of pyrolytic carbon deposits with a low graphitic order. This is also confirmed by its feature-less adsorption isotherm. However, the APD of the thermal black still shows a shoulder at an adsorption potential of approximately 4 kJ/mol. These examples illustrate that the monolayer formation peak can be used to obtain information of the graphitic order of carbon surfaces. For graphitized CB, a good correlation between the bulk order of various graphitized CB (as determined by X-ray diffraction (XRD)) and the position of the monolayer formation peak in the APD was observed. With decreasing graphitic order of the surface, the smonolayer formation peak is shifted to lower adsorption potentials [39]. The APD of thermal CB also correlates well with surface spectroscopy data [40].

18.2

Characterization of Ordered Porous Carbon by Gas Adsorption

18.2.3.1 Determination of the graphitic character of the OMC surface In addition to the pore size distribution and surface area, surface chemistry is one of the most important properties of carbon materials. The surface chemistry can be studied by spectroscopy methods such as X-ray photoelectron spectroscopy (XPS) and secondary ion mass spectroscopy (SIMS). However, these techniques can only be applied to the external surface. In the case of micro- and mesoporous carbons (e.g., activated carbons and OMCs), the external surface represents only a small portion of the surface. The largest portion of the surface is located in the pores. How information on the graphitic character of the surface of OMC can be obtained from low-pressure nitrogen adsorption data is discussed in this chapter. It was discussed above that for nonporous carbon materials the position of the monolayer formation peak depends on the graphitic order of the surface. In principle, this can also be used to study the graphitic order of the surface of porous carbons. The APD of OMCs synthesized at 900°C and above showed a monolayer formation peak. As these peaks are relatively wide, the APD data were fitted to a Gauss-Lorentzian function (Fig. 18.8). With increasing synthesis temperature, the monolayer formation peak became more pronounced

a

CMK-3

a • ()

700°C 900°C

o 1100°C •

1300°C

a

1600°C

o e Gl

• • • • ••••••••

o...l

...O...~ aa a

•••

•••

! a

2

4

6

8

Adsorption potential, A [kJ/mol]

Figure 18.8 Adsorption potential distribution (APD) of ordered mesoporous carbon (OMC). (Reprinted with permission from Re£ [13].)

466

Chapter 18 Adsorption on Ordered Porous Carbons

and its maximum was shifted to higher adsorption potentials (see Table 18.1), indicating that the graphitic order of the surface increased. This finding is reasonable, because generally with increasing temperature the graphitic order of carbons increases. In order to verify the APD results a comparison with surface spectroscopic results can be made. This is possible because for OMCs one can reasonably assume that the chemistry of the carbon rods at the external surface of the OMC particle (probed by the spectroscopic methods) and the surface chemistry of the carbon rods in the bulk of the OMC particle are similar. The carbon rods are produced by polymerization and subsequent carbonization of a precursor adsorbed in the pore system of a matrix. As long as the concentration of the precursor and of the acid catalyst is uniform throughout the entire pore system of the matrix, the polymerization and carbonization reactions proceed everywhere in a similar fashion, leading to a homogenous material. This is in agreement with the TEM images of OMCs (Figs 18.1 and 18.2). The situation is different for other carbon materials such as activated carbons. During activation of the precursor, partial oxidation of the carbon proceeds from the external surface of the carbon particle to the interior. Thus, the portion of the activated carbon particle close to the external surface is more severely activated than the interior and chemistry of the external and internal surface is most likely to be different. Before surface spectroscopy and gas adsorption data of OMCs are compared, the surface spectroscopic analysis of the carbon materials is reviewed very briefly.

18.2.3.2 Analysis of the OMC surface by XPS XPS is a very attractive tool for the surface characterization of carbon materials, such as carbon fibers [41], CB [42], and OMCs [12]. The fundamentals of this technique were already presented in Chapter 17. Here, XPS will be discussed only with respect to the characterization of the graphitic order of the surface of carbon materials. The most intense signals in the XPS carbon spectra of OMC are the so-called graphite peak and the 1T -+ 1T* peak (Fig. 18.9). Several parameters of these peaks depend on the graphitic order of the carbon material. With increasing graphitic order, the width (full width at half maximum (FWHM)) of the graphite peak decreases [43] and it becomes more asymmetrical [44]. Furthermore, the relative area of the 7T -+ 7T* peak increases [45]. As an example, the XPS carbon spectra of a series of CMK-l OMC samples, synthesized at different temperatures, are discussed. The differences between the spectra are relatively small, but significant. In the enlarged spectra it is easy to notice that with increasing synthesis temperature the area of the 7T -+ 7T* peak increases (Fig. 18.9). The changes of the width and asymmetry of the graphite peak are not very easy to see in the figures, but can be quantified by numerical treatment of the spectra. With increasing OMC synthesis temperature, the width of the graphite peak decreases (Table 18.1) and it becomes more asymmetrical, indicating, in agreement with the APD results, that the graphitic order increased.

18.2

Characterization of Ordered Porous Carbon by Gas Adsorption

CMK-1 (1100°C) Sample 2

280

285

290

295

285

290

295

300

Binding energy [eV]

Figure 18.9a (a) Carbon 1s spectra, CMK-1 samples synthesized at different temperatures; normalized to the same height. (Reprinted with permission from Ref. [12].)

1100°C Sample 2

280

285

290

295

285

290

295

300

Binding energy [eV]

Figure 18.9b (b) X-ray photoelectron spectroscopy (XPS) carbon 1s spectra, CMK-1 samples synthesized at different temperatures; enlarged to 10 % of maximum height. (Reprinted with permission from Re£ [12].)

Of the three XPS parameters discussed, the width of the graphite peak was found to be the most suitable parameter for the graphitic order of the OMC surface [12]. The correlation between the width ofthe XPS peak and the position of the monolayer formation peak is presented in Fig. 18.10. This figure also includes a data point for a nonporous graphitized CB. The correlation between

468 Table

Chapter 18 Adsorption on Ordered Porous Carbons

18.1

Parameter for the graphitic order of the OMC surface

Graphitized carbon blackb OMC CMK-3 (700°C) CMK-3 (900°C) CMK-3 (1100°C) CMK-3 (1300°C) CMK-3

a

b c

5.4

0.82

4.3 4.3 4.5 5.0

1.22 1.18 1.11 1.04 0.92

Full width at half maximum (FWHM). Carbopak Y. No monolayer formation peak detected.

1.2 .......---------------. •

a •

0 CMK-1

•

CMK-3

~

Graphitized Carbon black

0.8 L...--L.--L-..L..-J~--1.-..1--II-...L..-.L-....L.-.l----l...~ 4.0 4.5 5.0 5.5 APD, Position of the monolayer formation peak [kJ/mol]

Figure 18.10 Correlation between the graphitic order of the external surface (as determined by X-ray photoelectron spectroscopy (XPS» and the surface ofthe mesopores (as determined by nitrogen adsorption).

XPS and APD data is very good, confirming that the APD is indeed a suitable method for the determination of the graphitic order of an internal surface. This information is very important because the graphitic order can strongly influence the interaction between the carbon surface and adsorbents. It might also be crucial for the anchoring of active sites such as metal clusters in OMes [46]. To the best knowledge of the authors, the APD method presented here is the only technique that can directly characterize the internal surface of carbon materials. Techniques such as XRD and Raman spectroscopy might be used

18.2

Characterization of Ordered Porous Carbon by Gas Adsorption

to obtain information on the OMC bulk order. However, results of these techniques may not apply to the pore surface. For example, as already mentioned, in some pitch-derived OMCs the graphene layers are arranged perpendicular to the surface of the carbon rods [15]. Thus, even if these layers contain few defects, the pore surface consists of the edges of these layers and is most probably very heterogeneous.

18.2.3.3 Applicability of APD to determine the graphitic character

of carbon materials In addition to the OMCs synthesized in mesoporous silica templates, the APD can also be used to determine the graphitic order of other meso- and macroporous carbon materials that have no significant volume of micropores. These materials include colloidal-imprinted carbons [4] and xerogel-derived carbons [16]. The application of the APD method to microporous activated carbons is more delicate because the formation of the first nitrogen monolayer and filling of some micropores occurs in the same pressure range. On a perfect graphene layer, the first nitrogen monolayer is formed at PI Po between approximately 5 x 10- 5 and 5 x 10- 4 (see the isotherm of the graphitized CB in Fig.18.4). According to theoretical calculations, in this pressure range micropores with widths between 0.9 and 1.1 nm are filled as well [47]. Thus, for a carbon sample of unknown pore structure, adsorption at this pressure cannot be unambiguously assigned to either monolayer formation or micropore filling. However, in some activated carbons (e.g., strongly oxidized samples) most micropores are so wide that the first nitrogen monolayer is formed on the micropore walls before the micropores are filled. In the corresponding APDs, two distinct peaks for monolayer formation and micropore filling are observed [48]. For such samples, the position of the monolayer formation peak should be a measure for the graphitic order of the micropore surface.

18.2.4 Verification of the Presence of Micropores by the a-plot

Method As discussed above, the models presently available for the analysis ofporous carbons may yield misleading results for the pore size distribution of OMCs. This also applies to other materials. For example, for purely n1esoporous zeolites, some models wrongly indicate the presence of micropores [36]. Thus, it is preferable to verify the presence of micropores by "model-less" methods, such as a-plots. In a-plots, the amount of nitrogen adsorbed on the sample ofinterest (~dsJ is compared for all data points to the amount adsorbed on a nonporous standard (as, Fig. 18.11). The quantity as is the amount of nitrogen adsorbed on the standard relative to the amount adsorbed at PI Po = 0.4. From the so-called high-resolution a-plots, which use low-pressure adsorption data, qualitative information on the micropore size can be obtained.

470

Chapter 18 Adsorption on Ordered Porous Carbons

FS

Wide Micropores, Mesopores

o

2

Figure 18.11 High-resolution a-plots of carbons with pores of different widths (full line adsorption on porous sample, dotted line adsorption on nonporous reference). (Adapted with permission from Ref. [47]).

The high-resolution a-plots can be classified into three types [47]. First, a-plots of carbons with very narrow micropores will be discussed. In micropores, the interaction between the surface and the adsorbate is enhanced because of the overlapping of the potential of the opposite pore walls. Thus, as compared to an open surface, formation of the first monolayer occurs at a lower pressure. The corresponding high-resolution a-plot shows at as below 0.5 a so-called filling swing as an upward deviation (middle graph in Figure 18.11). If the micropores are not wider than the double diameter ofan adsorbate molecule, after formation of the monolayer the micropore is already filled. Thus, at higher pressures, adsorption takes place only at the small external surface. In the corresponding a-plot, only a very small slope will be observed for higher as (upper graph in Fig. 18.11). The situation is different for carbons with wider micropores. In this case, after formation of the monolayer, adsorption in the micropores will continue until they are filled. As compared to an open surface, filling of the space between the adsorbate covered pore walls is accelerated and indicated by a so-called cooperative swing at as above 0.5. Thus, the corresponding a-plot will show a filling and a cooperative swing (middle graph in Fig. 18.11). Finally, if the pore width increases further, the distance between the pore walls is so large that the formation of the monolayer is not influenced by the opposite pore wall. Thus, the formation of the first nitrogen monolayer layer in these pores and on an open surface occurs at the same pressure. The corresponding a-plots

18.2

Characterization of Ordered Porous Carbon by Gas Adsorption

47 1

do not show any filling swing. However, there will still be a cooperative swing because at a certain point the nitrogen layers on the pore surfaces will be close enough so that accelerated pore filling occurs (lower graph in Fig. 18.11). In the case of cylindrical mesopores, it is more appropriate to label this feature as capillary condensation [47]. Monte Carlo simulations were performed for carbons with slit-like pores with walls consisting of the basal planes of perfect graphene layers [47]. According to these calculations, the a-plots of carbons with pore widths smaller than 1.1 nm will show a filling swing, whereas cooperative swings are found for pores wider than 0.9 nm. For carbons with different pore geometries and/or other surface chemistry (such as OMCs), the filling and cooperative swings may occur at somewhat different pressures. However, the general features of the a-plots will be similar. It is therefore possible to obtain qualitative information on the micropore widths of OMCs from their a-plots. The a-plots of CMK-3 OMCs synthesized at different temperatures showed pronounced capillary condensation swings at as above 1 (Fig. 18.12), indicating the filling of the mesopores. However, there were important differences for lower as' For the OMC synthesized at 1600°C, no filling swing was found. Instead, up to the capillary condensation swing, the a-plot showed a straight

CS FS

/

/",

V,,'

CMK-3

700°C

cs

en

~ FS

I

1100°C

CS

o

2

Figure 18.12 High-resolution a-plots of ordered mesoporous carbons (aMCs) synthesized at different temperatures (full line: adsorption on aMCs, dotted line: adsorption on nonporous reference; broken line: the difference between the dotted and the broken line indicates the relative increase of adsorption due to micropores). Reference compounds: Thermal carbon black for CMK-3 700°C and Furnace carbon black for the other aMCs.

47 2

Chapter 18 Adsorption on Ordered Porous Carbons

line passing through the orIgIn, indicating that this sample did not contain any micropores. For the OMC samples synthesized at 1100°C and 700°C, clear filling swings were found, indicating the presence of micropores narrower than approximately 1 nm. The corresponding a-plots can be regarded as a combination of the a-plots of carbons with narrow micropores (upper graph in Fig. 18.11) and of carbons with wide micropores or mesopores (lower graph in Fig. 18.11). It is possible to estimate the volume of the micropores from the a-plots. Between the filling and the capillary condensation swings, the a-plots showed a straight line (broken lines in Fig. 18.12). In this pressure region, the micropores are already filled and adsorption takes place only in the OMC mesopores and on the external surface. A line with the same slope passing through the origin corresponds to an OMC with the same mesopore volume and external surface area but without micropores (dotted lines in Fig. 18.12). Thus, from the distance between these two lines, one can estimate the micropore volume. In the present case, the OMC micropore volume clearly decreased with increasing synthesis temperature. It is also possible to obtain some information on the micropore width from the position of the filling swing. For the OMC sample synthesized at 700°C, the filling swing extended to higher as (corresponding to higher pressures) as compared to the sample synthesized at 1100°C, indicating that the micropore width decreased with increasing synthesis temperature. For the series of OMC samples presented here, it was concluded that the micropores correspond to defects in the carbon rods. With increasing temperature, the carbon rods contracted, thereby decreasing width and volume of the micropores until they disappeared completely [13]. When using comparison methods, such as a-plots, it is important that the nonmicroporous reference compound and the sample of interest have a similar surface chemistry [49]. As outlined in the previous section, information on the surface chemistry can be obtained from the APD. A similar APD indicates a comparable graphitic character of the pore surface. For the samples discussed here, the APDs of the nonporous CB (Fig. 18.7) and of the OMCs (Fig. 18.8) were compared. For the OMC synthesized at 700°C, the thermal black was selected as reference compound, whereas for the other OMC samples the furnace black was chosen. The adsorption data of this furnace CB are available in the literature [50].

18.2.5 Determination of the Specific Surface Area The specific surface area of solid materials is usually determined by applying the Brunauer-Emmett-Teller (BET) equation to nitrogen adsorption data between relative pressures (PIPo) of approximately 0.05 and 0.3 [51]. However, there are many shortcomings of the BET model. For example, it does not consider adsorption in pores. It is well known that the BET method seriously overestimates the specific surface area for many porous materials. For carbons, the theoretically highest possible specific surface area is approximately 2630 m 2 / g

18.2

Characterization of Ordered Porous Carbon by Gas Adsorption

473

[47], assuming a "free-floating," perfect graphene layer with both basal planes accessible to the adsorbate. However, for some activated carbons BET surface areas as high as 3000 m 2 / g were reported [52]. The surface areas of the predominately mesoporous OMCs are certainly much smaller than the theoretically highest possible surface area for carbons mentioned above. Nonetheless, BET surface areas higher than 2000 m 2 /g were found for OMCs [23]. Thus, methods that are more appropriate should be used for the calculation of the specific surface area of OMCs. In the opinion of the authors, the DFT method is also not suitable for the reasons discussed in the previous section (i.e., assumption of slit-like pores and pore walls consisting of perfect graphene layers). Values for the specific surface area of OMC and other porous carbons can be obtained from the APD. As mentioned above, in this data treatment method, no assumptions about the pore geometry are made. Thus, a possible source for error is eliminated. However, the APD of the carbon sample should show a monolayer formation peak. Thus, the surface of the carbon material has to have a certain graphitic order. This is, for example, the case for graphitized and furnace CB. For these samples, the completion of the monolayer formation is clearly indicated by a minimum in the APD at the high adsorption potential end of the monolayer formation peak, located at adsorption potentials of2.3 and 2.8 kJ/mol, respectively (Fig. 18.7). The amount of nitrogen adsorbed corresponds to the monolayer, from which the specific surface area can be calculated. The surface areas calculated by the APD and the BET method differ by 7 % and 15 %, respectively (Table 18.2). For activated carbons, the difference between the surface areas obtained by APD and the DFT method is usually less than 10% [39]. For some samples, the APD method cannot be applied to calculate the specific surface area. Thermal CB, for example, has a lower graphitic order than the other CB discussed above. In the APD of thermal black, monolayer formation is only indicated by a shoulder (Fig. 18.7). Thus, the end of the monolayer formation cannot be determined with the required precision, making a meaningful determination of the surface area impossible. It can be summarized that as long as the carbon samples have a sufficient graphitic order, from the APD a reasonable estimate for the specific surface area can be obtained. Its application to OMCs is illustrated by an example. The APDs of CMK-3 OMC samples synthesized at temperatures of 900°C and above show a monolayer formation peak (Fig. 18.8). The minimum at the high adsorption potential side of the monolayer formation peak is located at an adsorption potential of 3 kJ/mol, corresponding to a PI Po of approximately 0.01. The surface areas calculated from the corresponding amount of adsorbed nitrogen are considerably smaller than the corresponding BET surface areas (Table 18.2). The table also includes a value for the surface area of the OMC sample synthesized at 700°C. In this case, no monolayer formation peak was observed. Thus, it was assumed that the formation of the monolayer was completed at the same pressure as the other OMC. However, in this case, the obtained value is only rough estimate.

474

Chapter 18 Adsorption on Ordered Porous Carbons

Table

18.2 Specific surface areas of carbon materials, calculated from nitrogen adsorption data

Graphitized carbon blacka Furnace carbon black OMC CMK-3 (700°C) CMK-3 (900°C) CMK-3 (1100°C) CMK-3 (1300°C) CMK-3

a b

18.3

6.1 40.2 1721 1322 1218 1200 837

6.5 34.1 (1320)b 1040 1040 1018 727

Carbopak F. Approximation, see text for details.

CONCLUSIONS

OMCs are new carbon materials with very high mesopore volumes (up to 2 cm3 / g) and controllable pore geometry. Because of these special properties, OMC will find applications in fields such as in the adsorption and catalytic conversion of voluminous hydrocarbon molecules, as nanoreactors for the synthesis of inorganic nanostructured materials, and in electrical devices. Many important OMC properties can be determined by nitrogen adsorption. The OMC pore structure differs from activated carbons for which most of the data treatment methods were developed. Thus, noncritical application of these data treatment methods to OMCs might lead to misleading results. Up to now, no data method adapted to the pore geometry ofOMCs has been developed. Thus, it is suggested that several methods be used and their results compared with the qualitative predictions that can be made from the shape of the isotherm. Useful information on OMC properties can be obtained from the APD. This includes the characterization of the graphitic character of the mesopore surface, which cannot be done with any other analytical method.

ACKNOWLEDGMENTS

H. Darmstadt is grateful to Prof C. Roy for liberating him from other responsibilities while writing this text, to Dr W. Lukens for providing the program used for the calculation of the pore size distribution with the modified BJH model, to Dr W.R. Beetz for supplying the graphitized CB, and

References

475

finally to Dr A. Adnot for recording the XPS spectra. R. R yoo gratefully acknowledges that his research on OMCs was supported in part by the Korean Ministry of Science and Technology through the Creative Research Initiative Program and by the School of Molecular Science through the Brain Korea 21 Project.

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Chapter 18 Adsorption on Ordered Porous Carbons

16. Lee, K.T. and Oh, S.M. (2002). Novel synthesis of porous carbons with tunable pore size by surfactant-templated sol-gel process and carbonisation. Chem. Commun., 22, 2722-3. 17. Ryoo, R., Joo, S.H., and Kim, J.M. (1999). Energetically favored fonnation of MCM-48 from cationic-neutral surfactant mixtures.]. Phys. Chem. B, 103, 7435-40. 18. Kruk, M., Jaroniec, M., Ryoo, R., and Joo, S.H. (2000). Characterization of M CM-48 silicas with tailored pore sizes synthesized via a highly efficient procedure. Chem. Mater., 12, 1414-21. 19. Kang, M., Vi, S.H., Lee, H.I., et al. (2002). Reversible replication between ordered mesoporous silica and mesoporous carbon. Chem. Commun., 17, 1944-5. 20. Thommes, M., Kohn, R., and Froba, M. (2000). Systematic sorption studies on surface and pore size characteristics of different MCM-48 silica materials. Stud. Surf. Sci. Catal. Characterisation Porous Solids V, 128, 259-68. 21. Choi, M., Heo, W., Kleitz, F., and Ryoo, R. (2003). Facile synthesis of high quality mesoporous SBA-15 with enhanced control of the porous network connectivity and wall thickness. Chem. Commun., 1340-1. 22. Kruk, M.,Jaroniec, M., Kim, T.-W., and Ryoo, R. (2003). Synthesis and characterization of hexagonally ordered carbon nanopipes. Chem. Mater., 15, 2815-23. 23. Dannstadt, H., Roy, C., Kaliaguine, S., et al. (2003). Surface and pore structures of CMK-5 ordered mesoporous carbons by adsorption and surface spectroscopy. Chem. Mater., 15, 3300-7. 24. Vinu, A., Streb, C., Murugesan, V., and Hartmann, M. (2003). Adsorption of cytochrome c on new mesoporous carbon molecular sieves.]. Phys. Chem. B, 107, 8297-9. 25. Zhou, H.S., Zhu, S.M., Hibino, M., and Honma, I. (2003). Electrochemical capacitance of self-ordered mesoporous carbon.]. Power Sourc., 122, 219-23. 26. Kim].Y., Yoon, S.B., and Yu,].S. (2003). Template synthesis ofa new mesostructured silica from highly ordered mesoporous carbon molecular sieves. Chem. Mater., 15, 1932-4. 27. Yu, J.S., Kang, S., Yoon, S.B., and Chai G. (2002). Fabrication of ordered unifonn porous carbon networks and their application to a catalyst supporter,]. Am. Chem. Soc., 124, 9382-3. 28. Rodriguez-Reinoso, F., Molina-Sabio, M., and Gonzalez, M.T. (1995). The use of steam and CO 2 as activating agents in the preparation of activated carbons. Carbon, 33, 15-23. 29. Turner, A.R. and Quirke, N. (1998). A grand canonical Monte Carlo study of adsorption on graphitic surfaces with defects. Carbon, 36, 1439-46. 30. Barrett, E.P., Joyner, L.G., and Halenda, P.P. (1951). The detennination of pore volume and area distributions in porous substances. I. Computations from nitrogen isothenns.]. Am. Chem. Soc., 73, 373-80. 31. Lu, A.H., Schmidt, W., Splietho£I: B., and Schuth, F. (2003). Synthesis of ordered mesoporous carbon with bimodal pore system and high pore volume. Advan. Mater., 15, 1602-6. 32. Shi, Z.-G., Feng, Y.-Q., Xu, L., et al. (2003) Synthesis of a carbon monolith with trimodal pores. Carbon, 41, 2677-9. 33. Kruk, M., Jaroniec, M., and Sayari, A. (1997). Application of large pore MCM-41 molecular sieves to improve pore size analysis using nitrogen adsorption measurements. Langmuir, 13, 6267-73.

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ELECTROCHEMICAL BEHAVIOR OF CARBON MATERIALS Agustfn E. Bolzan and Alejandro

J. Arvia

Instituto de Investigaciones Fisicoqufmicas Te6ricas y Aplicadas (lNIFTA), UNLP-CIC-CONICET, La Plata, Argentina

Contents 19.1 A Brief Summary of Electrochemical Concepts 19.2 Thermodynamic Data for Carbon Electrodes 19.3 Relevant Characteristics of Carbon Electrode Materials 19.4 Chemically Modified Electrodes and Supramolecular Configurations 19.5 Electrochemical Kinetics on Carbon Electrodes in Aqueous Solutions 19.6 Organic Electrochemistry at Carbon Electrodes 19.7 Reactions on Biological Active Electrodes 19.8 Corrosion Processes 19.9 Carbon Electrodes in Molten Salts 19.10 Carbon Electrode Manufacturing Techniques Acknowledgments References

19.1 19.1.1

A BRIEF

479 484 485 492 494 501 502 503 504 506 507 507

SUMMARY OF ELECTROCHEMICAL CONCEPTS

The Electrochemical Interface

Electrochemical reactions involve the transfer of electric charge across an interface consisting of an electrode (metal or semiconductor) in contact with an ionic conductor (electrolyte solution, molten salt, or solid electrolyte). The electrode material-ionic conductor interface exhibits a high electric capacitance. For instance, its value for a spherical gold surface in 1 M NaCl0 4 aqueous solution is on the order of 10- 6 F, in contrast with the capacitance of the same Adsorption by Carbons ISBN: 978-0-08-044464-2

© 2008 Elsevier Ltd. All rights reserved.

479

480

Chapter 19 Electrochemical Behavior of Carbon Materials

spherical surface gold-vacuum interface that amounts only to about 10- 13 F. This large difference is due to a spatial charge localized at the immediate vicinity of the metal in the electrochemical interface. The electrochemical interface is considered as ideally polarizable when the application of any potential difference between both the phases produces no charge transfer across it. In this case, when an electrical potential is applied, a transient current (capacitive current) related to the electric charges on both sides of the interface can be measured. The reverse situation is the ideally nonpolarizable electrochemical interface. In this case, for any applied electric potential the charge transfer across the interface involves a transient capacitive current and a faradaic current that is exclusively related to an electrochemical reaction. Real electrochemical interfaces are intermediate between the two limiting polarization situations. The region of the electrochemical interface comprising an electrolyte layer of a certain thickness in contact with the electrode surface in which the charge distribution differs from that in the bulk of the ionic conductor is known as the electrical double layer region. In this region, long- and short-range electrostatic forces determine both the structure of the electrochemical interface and in part the kinetics of faradaic processes. At the electrical double layer, the electric charge accumulated on the metal is equal to that in the ionic conducting phase. The sign of this charge is either positive or negative depending on the polarity of the applied electric potential. The thermodynamics of the electrochemical interface is based on the Gibbs adsorption equation. For a plane electrode in contact with an ionic conductor, under equilibrium conditions, the Gibbs equation is [1]

dy = -lTd T - redjLe -

L ridjLi - L IjdjLj - L rkdjLk - L rhdjLh k

(19.1)

h

where y is the surface tension, lT is the excess of entropy, T is the absolute temperature, x is the surface excess of component x, x = e, electron, x = i, ionic conducting species; x = j, x = k, and x = h cations, anions, and neutral species, respectively; {Lx is the electrochemical potential of x

r

(19.2)

/-Lx' Zx' and

(19.3)

where ax is the activity of component x, and /-Lo its chemical potential when ax = 1.

19.1

A Brief Summary of Electrochemical Concepts

Considering that f h == 0 and f e == qM' at constant temperature (T), pressure (P), and solution composition, it results in

y a) ( a4>

==-qM

(19.4)

P, T,/L

Relationship (19.4), known as Lippmann equation, permits the evaluation of the excess of charge at the electrode surface from the electrocapillary curve y == y(4)). For interfaces relatively simple such as the mercury/1 M aqueous KCl interface, Eqn (19.4) results in a parabola with a maximum at ay/a4> == 0, i.e., for null charge at the electrode surface. This condition corresponds to the potential of zero charge (Epzc ) for the electrode in the electrolyte solution. The second derivative of Eqn (19.4) represents the capacitance C

2y ) a ( a4>2

p. T.IL

(aqM) = - a4> p. T.IL = - C

(19.5)

When y == y( 4» is a perfect parabolic function, it results that d y / d4> is proportional to 4>, and the electrochemical interface is characterized by a constant value of C. For real systems, /a4> changes with 4>, and therefore a differential capacitance (Cd) has to be defined

aqM

qM

d Cd = ( dE

)

(19.6)

p. T.IL

where E is the electric potential difference across the capacitance. Values of r i and y can be obtained by integration of the electrocapillary curve provided that the value of E pzc is known. 19.1.2

Adsorption at Electrodes

In the absence of chemical or electrochemical processes, the adsorption of molecules, ions or both at the electrode surface becomes possible. This fact involves electrode-solvent, electrode-ionic species, and solvent-ionic species as the most relevant interactions and the possible contribution oflateral interactions. These interactions play an important role in the behavior of C vs E curves. The adsorption of either ions or neutral molecules on the electrode surface depends on i.e., on the applied electric potential. Correspondingly, the electric field at the electrochemical interface is an additional free-energy contribution that either favors or restricts the adsorption of species on the electrode from the ionic conducting phase. A variety of adsorption isotherms has been proposed to account for the behavior of different electrochemical systems. Among them are the Langmuir, Frumkin, and Temkin isotherms [2]. Frumkin and Temkin isotherms, at variance with the Langmuir one, include effects such as adsorbate-adsorbate or adsorbate-surface interactions.

qM'

482

Chapter 19 Electrochemical Behavior of Carbon Materials

Langmuir Q) C)

Q) C)

~

~

Q)

>

0

()

Q)

> 0

Temkin

()

Q) ()

Q) ()

«S

«S

't:

't:

CJ)

CJ)

'0

'0

::::J

::::J

Q) Q)

Q)

~

0,

C) Q)

Q)

0

0

log pressure

Potential difference

Figure 19.1 Comparison of chemical and electrochemical isotherms. The arrow indicates the shift of the curves as the lateral interactions term increases.

A comparison of the dependence of OJ, the degree of surface coverage by species i, on either P (chemical adsorption) or E (electrochemical adsorption) is shown in Fig. 19.1. At the electrochemical interface, adsorption of either charged or neutral molecules and charge transfer processes may occur simultaneously. Electroadsorption and electrodesorption processes play a key role in electrocatalytic reactions [2].

19.1.3 Relevant Kinetic Parameters The rate of an electrochemical reaction involving reactant i, expressed as dNj / dt, where N j is the number of moles of i electrolyzed at time t, is proportional to the faradaic current (I) flowing across the cell. However, as the electrode process is a heterogeneous reaction, its rate is usually expressed as moles s cm2 1 dNj

j

A dt

zjF

(19.7)

where A is the electrode area and j is the current density, i.e., j = II A. A basic problem in electrochemical kinetics is to determine the current (I) as a function of the applied potential (E), particularly under steady-state conditions. The departure of the electrode potential from the equilibrium value (Erev = N ernst potential) is the electrode polarization that is measured by the overpotential (1])

1] = E - Erev

(19.8)

19.1

A Brief Summary of Electrochemical Concepts

The overall current efficiency for the nth process is given by the ratio between the fraction of the number of coulombs (Qn) involved in the nth process and the total charge (Qr) passed across the cell (19.9) For a single electrochemical process p = 1. Generally, the rate of the electrode process is influenced by the mass transport of reactants to and products from the electrode surface, the proper electron transfer process, and the chemical reactions preceding or following the electron transfer. Accordingly, the value of YJ may involve a concentration (mass transport), activation (electron transfer), and ohmic (ohmic resistance) polarization contribution. Let us consider a simple redox reaction involving species 0 and R in the solution

(19.10)

kf and kb being the rate constants for the forward (£ cathodic) and backward (b, anodic) reactions. The net current flowing through the electrochemical interface is the algebraic sum of the currents If and I b of the partial reactions (19.11) Co (O,t) and CR (O,t) being the concentration of 0 and R on the electrode surface at time t. The rate constants depend on the overpotential

kf

= k°exp [aZF - R T (E = E 0)]

kb=k°exp [(l-a)ZF( RT E=E 0)]

(19.12)

(19.13)

kO being the standard rate constant, a the transfer coefficient assisting the reaction in the forward direction, and EO the standard potential of the redox reaction. The value of kO is related to the exchange current density (jo) of the reaction at the reversible potential. Equations (19.12) and (19.13) are usually expressed as Tafel relationships. For the cathodic reaction, the Tafel equation is

YJ=a+blnj

(19.14)

with a = RTjjoa and b = -RTjaF. A similar Tafel equation can be written for the anodic reaction with a = RTjjo(l- a) and b = RTj(l- a)F.

Chapter 19 Electrochemical Behavior of Carbon Materials

Most electrochemical processes can be described by complex reaction mechanisms with a rate-determining step (rds). Besides, a stoichiometric number of the rds is defined as the number of times the rds has to occur for every complete act of the overall reaction. From the temperature dependence of Eqs (19.12) and (19.13), the activation energy of the cathodic and anodic reactions at different values of 1] can be obtained.

19.2 THERMODYNAMIC DATA FOR CARBON ELECTRODES

Standard aqueous electrode potentials for reactions involving carbon have been calculated from the free energy of formation of carbon-containing compounds at different pH and temperature[3-6]. These data, displayed as potentialpH equilibrium diagrams, determine the domains of relative predominance of carbon as such or under a dissolved carbon-containing species such as methanol, aldehyde, acetic acid, carbonate, bicarbonate, or gaseous species such as methane, carbon dioxide, and carbon monoxide. As an example, a scheme of a typical E/pH equilibrium diagram for graphite/water at 25°C is shown in Fig. 19.2. Lines (a) and (b) represent Nernst equation for the reduction (a) and oxidation (b) of water, respectively, under hydrogen and oxygen 1 atm pressure. Lines 1 and 2 delimit the regions for the equilibria between H 2 C0 3 , HC0 3 - , and C0 3 2 - in aqueous solution free from

-............

". ..----.b ~ CO2 ................................

~

H2C0 3

~

HCO;

(ij

E Q) (5 a. 0

".

~-·-··,-· ...C

CO~-

3

........................

CH 30H CH 4

-1 -2

0

2

4

6

8

10

12

14

16

pH

Figure 19.2 Potential-pH equilibrium diagram for the system C(graphite)-water at 25°C and for log(concentration) or log(partial pressure) equal to zero. (Reproduced from Ref. [3] with permission from Elsevier).

19.3 Relevant Characteristics of Carbon Electrode Materials

oxidizing agents. The domain above lines 3, 4, and 5 corresponds to solutions containing 1 M of dissolved carbon in the form of H 2 C0 3 + HC0 3 - + C0 32(corrosion region). The domain below these lines refers to solutions saturated with solid carbon in equilibrium (immunity or stability region). Above line (b) CO 2 is the stable form of carbon. For log c = logPcH4 = logPcoz = 0, carbon in the form of graphite is thermodynamically stable only over a limited domain. Thermodynamic data have also been calculated for carbon-oxygen reactions in fused salts [7, 8]. The oxidation of solid carbon principally yields carbon dioxide at low temperature and carbon monoxide at high temperature. In this case, at constant temperature, the CO/C0 2 concentration ratio at solid carbon depends on pressure. The carbon-oxygen electrode is used as reference to investigate cryolite-alumina melts at c. 1000°C [9] and molten slags at higher temperatures. Thermodynamic data for other systems involving carbon and carboncontaining compounds are given in the original publications [3, 6, 10].

19.3

RELEVANT CHARACTERISTICS OF CARBON ELECTRODE

MATERIALS

19.3.1 Types of Carbons Used in Electrochemistry Carbon has been widely used since the times of Humphrey Davy (17781829), who used charcoal electrodes in some of his experimental work [11]. Carbon electrodes are extensively employed in a large number of electrochemical processes [12, 13], including electrochemical energy storage and energy conversion devices, halogen production, electrometallurgical processes in melts and aqueous solutions, water preparation and water decontamination systems, preparation of organic compounds by chemically modified electrodes, as well as inorganic electrosynthesis to generate peroxide, ozone, fluoride, chloro-alkali, and metals from fused salts [14, 15]. Carbon and graphite are often used as supports for electrocatalysts, but they also have an electrocatalytic function in electrode reactions such as oxygen reduction in alkaline electrolytes, chlorine alkali industry, and SOCl2 reduction in lithium-thionyl chloride batteries. Carbon electrodes are also employed in electroanalytical applications due to the very low residual current over a wide range ofpotentials that makes it possible to study electrochemical reactions even at the level of trace concentration. Among the different types of such electrodes, wax-impregnated graphite rods, carbon powder bound with an inert viscous liquid (carbon paste), glassy carbon, pyrolytic graphite and carbon fibers, and, more recently, nanotubes and fullerenes can be mentioned. Carbon fibers have radial, random, or anion distributions that lead to a different distribution of step and step-step interactions.

486

Chapter 19 Electrochemical Behavior of Carbon Materials

19.3.2 Structural Aspects Carbon in the form of graphite behaves as a good metal. In the form of diamond it constitutes a wide-gap super hard semiconductor; with the intercalation of appropriate guest species it turns into a superconductor [16]; as a flexible polymer it reacts with hydrogen and other species. Carbon-based electrode materials show the entire range of dimensionalities (D) from fullerenes (OD quantum dots), to carbon nanotubes (lD quantum wires), to graphite (2D layered anisotropic material), and to diamond (3D wide gap semiconductor). Graphite represents the ground state for a system containing a large number of carbon atoms. Each small graphite sheet has a large energy per carbon atom at edge sites. In contrast, a small number of carbon atoms form closed shell configurations as in fullerenes and carbon nanotubes [1 7, 18]. The tunneling conductance between neighbor carbon nanotubes can be uniquely specified in terms of their individual chiral vectors and the pentagon and heptagon that must be introduced in the junction region. The conductance between two metallic nanotubes is found to be ballistic with some reflection effects occurring in the junction region. A metal semiconductor nanotube junction shows tunneling across the junction [19]. Results from scanning tunneling microscopy (STM) measurements indicate that one metallic nanotube 8.7 nm in diameter exhibits an ohmic behavior, whereas semiconducting tubules 4.0 and 1.7 nm in diameter show plateaus at zero current passing through null voltage. The slope of the current vs voltage plot provides a measure of the density of states. The current peak heights in these plots depend on the square root of the energy gap-dependent singularities in the lD density of states. Semiconducting tubules show a linear dependence of their energy gap on the reciprocal tubule diameter [20]. The electronic and phonon dispersion relationships for pristine graphite have constituted the basis of models for other less well-ordered forms of graphite such as disordered graphite, graphite intercalation compounds, and ion-implanted graphite [16, 21]. The electrical resistance of carbon increases with oxygen chemisorption at the surface. Powdered carbon reactions with oxygen at SOO-700°C result in a 4% oxygen content and in a 100-fold increase in the electrical resistance [22].

19.3.3 Surface Free Radical States Electron paramagnetic resonance (EPR) is of considerable value for identifying paramagnetic surface groups and clarifying their role in electrochemical reactions. The variety of EPR characteristics of carbon and graphite reflects the diversity of structural and electronic properties of these materials that depend on crystalline size and perfection, impurities, preferred orientation, electrical resistivity, physical adsorption of gases, preparation procedure, and measuring techniques [23]. The surface of carbons is characterized by their capability for oxygen chemisorption at low temperatures. Well-defined crystalline graphite exhibit well-ordered stacks of carbon layers that are fairly unreactive toward

19.3 Relevant Characteristics of Carbon Electrode Materials

oxygen chemisorption, in contrast to more disordered structures such as carbon blacks yielding carbon-oxygen surface complexes. Free radical states have an important role in the surface chemistry of carbons. They are formed as a result of thermal splitting of the C-H bonds to produce carbon rings. Unpaired electrons stabilize by occupying a molecular orbital in the 7T-bond system. The ratio between the electron density in the 7T-bond system and conduction electrons depends on temperature and on the treatment of the material. Polyconjugated carbon structures that provide 7T-electrons usually involve three kinds of free (7-radicals: single radicals, side radicals, and (7-radicals without participation in the conjugated system. The electron capture by the broken (7-bonds is more favorable than that by the 7T-bond as the corresponding energy difference is about 403]/mol. This fact leads to a variety of primary oxygencontaining surface states yielding the appearance of carbonylic, carboxylic, hydroxylic, and quinone groups at the edges of carbon layers. Hydrogencontaining groups are also formed, as demonstrated by surface analysis. These surface states affect the chemical and electrochemical properties ofcarbon surface [24]. The amount of carboxylic and phenolic groups can be determined from the amount ofnitrogen produced by their reaction with diazomethanes (19.15)

(19.16) The distinction between these groups can be made by reaction of the carboxylic group with HCI [25] R-COOCH 3 + HCL --* R-COCI + CH3 0H

(19.17)

Quinone groups can be quantitatively determined from the amount of hydroquinones that is produced by reaction with NaBH 4 [25]. Lactones exhibit IR bands at 1760 cm- 1 because of the CO group of a lactone, and at 1600 cm- 1 because of the CO group hydrogen bonded to a phenolic OH. The band at 1600 cm -1 disappears upon formation of the sodium salt. The surface of carbons can be modified from hydrophobic to hydrophilic by means of oxidation processes. Consequently, carbons can exhibit selective adsorption properties depending on their oxygen content. For instance, commercial carbon blacks with a significant oxygen content selectively adsorb methanol from a methanol/benzene mixture, whereas one with much lower oxygen content exhibits selectivity for benzene.

19-3-4 Double-layer Properties The capacitance-potential curves of the basal plane of highly ordered pyrolytic graphite (HOPG) (Fig. 19.3) show an anomalous low capacitance

488

Chapter 19 Electrochemical Behavior of Carbon Materials

4.0 .----.....----....-----......-.....

N 3.0 E

~

.6 (,)

2.0

0.5

o

-0.5

E(V)

Figure 19.3 Capacitance-potential curves for HOPG in NaF solutions of pH of about 6 at 25°C; a.c. measurements at 20 Hz. (Reproduced from Re£ [26] with permission from Elsevier.)

value that is in the range 1.9-3.0 J.LF/cm2 , depending on the electrolyte solutions concentration [26]. It exhibits a negligible frequency dependence, both in acid and in base, and is nonsensitive to the presence of iodide in the solution. These facts indicate that the surface is free of functional groups to interact with the ions. The low capacitance value for the basal plane is related to a space charge caused by the semimetal characteristics of HOPG. The capacitance-potential curve of graphite is essentially parabolic rather than hyperbolic, probably because of imperfections on the exposed basal plane giving rise to sites with degenerated surface electronic states. Thus, the capacitance calculated from slow scan voltammetry is about 29 J.LF/cm2 at -0.2 V (vs normal hydrogen electrode (NHE)), a value considerably higher than that obtained from alternating current impedance measurements. This suggests that the much larger capacitance represents a portion of the surface with a micro-orientation that exposes other than the basal plane, or it might correspond to the possible existence of microfissures or microvoids. Exposed edge orientations have a much higher capacitance of about 60 J.LF/ cm2 that adds a large resistive component in series arising from the electrolyte resistance. Similar conclusions have been derived from glassy carbon [27]. Conversely, the voltammogram of HOPG in 0.5 M aqueous H 2 S0 4 and 1 M aqueous NaOH at 25°C is relatively featureless

19.3 Relevant Characteristics of Carbon Electrode Materials

at least in the range 0-0.75 V (vs NHE), in agreement with the features of the capacitance/potential curves [28]. The potential distribution across the carbon-electrolyte solution interface in general will be changed by the surface functional groups. Correspondingly, the oxygen-containing groups may influence the potential of zero charge and the potential at the outer Helmholtz plane (OHP) of the electrical double layer [1]. Thus, even for the redox species that are not specifically adsorbed, their concentration at the OHP would be changed and this would also affect the kinetics of the reaction. Potentials of zero charge of various types of carbons in aqueous solutions are in the range 0.0-0.32 V (vs NHE) [6] Black carbons form a homogeneous material series with graphitized black as the reference. For this series the chemical response ranges from Lewis baselike to Brnsted acid-like, while the work function varies appreciably through a minimum across a seven order of magnitude variation in the aqueous solution pH. The decreasing portion shows the lessening influence of the Lewis basic-like carbon basal plane electronic structure as acidic localized oxide functionalities are added to the carbon surface. The subsequent increase in the work function for pH < 6 is attributed to the accumulation of an outwardly pointing surface dipole layer with electric dipoles of2.6 D associated with the stronger (carboxyl) acidic functionalities. The work function measurement has been made using the Kelvin-Zisman reciprocal capacitor technique that consists of determining the contact potential difference between the carbon black and a gold reference surface. Values of the work function are in the range 0.19-0.30eV [29]. Capacitance measurements of carbon electrodes have also been made in molten halides, particularly chlorides [30-32], molten nitrates [33, 34], and in cryolite-alumina melts (graphite and glassy carbons). In cryolite-alumina melts, the double-layer capacitance of the basal plane of graphite, in the range 0.7-1.0 V (vs aluminum reference electrode) is about 20 f.1F/ cm2 at 0.9 V, i.e., in a potential range where no appreciable flow of current has been observed. Data indicate that the capacitance is influenced by adsorbed species from the melt, possibly yielding intercalation compounds, and uncertainty in the true area of the electrode [34].

19-3-5 Roughness Factor Carbon surfaces, except the HOPG basal plane, have some degree of roughness. The roughness factor (a) can be defined as (19.18) On the assumption that the surface roughness is on a distance scale which is large compared to the analyte molecules, Am is the microscopic area that is relevant for adsorption or kinetic measurements. A g is the geometric area determined either visually or by chronoamperometry on a scale where J15:i is much greater than any surface roughness. D; is the diffusion coefficient of the reactant

49°

Chapter 19 Electrochemical Behavior of Carbon Materials

i in the ionic conductor and t the electrolysis time. The value of (J" > 1 refers to the entire microscopic area disregarding the amount or distribution ofedge planes. For the edge plane area (A edge )

(19.19)

Ie represents the fraction of edge planes on the surface, and depends strongly on the nature and preparation of the carbon surface. The roughness of carbons is sensitive to the applied potential routine, as seen by sequential nanoscopic images of HOPG surfaces in aqueous solutions subjected to potential cycling of different duration [35] (Fig. 19.4). A stabilized carbon electrode topography merges after a prolonged potential cycling. These topographic changes can be described as time effects that depend on the type of carbon and ionic conductor, and the characteristics of the current or potential perturbation routines [20].

19-3-6 Fractality The problem of transfer across a fractal surface has been considered in the electrochemical behavior of rough and porous carbon electrodes [36]. The fractal dimension can be determined from nitrogen gas adsorption data, from transmission electron microscopy (TEM), and nanoscopy image analysis. Fractal electrodes exhibit a constant phase element (CPE) behavior in electrochemical impedance spectroscopy (EIS) [37]. The relationship between the CPE behavior of rough, irregular electrodes and fractality depends on the scale of irregularities, i.e., whether it is on the micrometer or centimeter scale. In real situations, however, both microscopic and macroscopic geometric effects probably occur simultaneously. For imprinted mesoporous carbons, the overall fractal dimension, determined from gas adsorption data, indicate that these materials are composed of two groups of pores. The surface fractal dimension of the carbonization-induced pores surface and that of the silica-imprinted pores surface has been obtained from TEM image analysis [38].

19-3-7 Intercalation of Ions in Graphite Intercalation constitutes an important case of inclusion phenomena in which the host lattice is characterized by a lamellar structure [39]. Graphite yields both anion and cation intercalation compounds and charge transfer processes are the driving forces for their formation. Due to the action of an oxidizing agent electrons are drawn from the graphite lattice and anions beside neutral species are intercalated. These processes can be driven in a direct reversible electrochemical way, as has been demonstrated for carbon in concentrated sulfuric acid [39]. For a graphite electrode in concentrated acid solution, the formation of intercalation compounds occurs when the threshold potential for the intercalation

19.3 Relevant Characteristics of Carbon Electrode Materials

49 1

Figure 19.4 Constant-current scanning tunneling microscopy images (600 x 600 nm2 ) of HOPG after anodic oxidation in 0.1 M H 2 S0 2 at 0.05 V vs Ag/Ag+ electrode. (a) HOPG surface before electro-oxidation (blank); (b) HOPG surface after 20 potential cycles; (c) HOPG surface after further electro-oxidation cycles. (Reprinted with permission from Ref. [35]. © 1988 American Chemical Society.)

Chapter 19 Electrochemical Behavior of Carbon Materials

49 2

process is exceeded (intercalation overpotential). The first step of this process is the oxidation of graphite to form a macroradical cation (19.20) the electron being removed from the highest filled level of graphite. This process resembles the anodic oxidation oforganic hydrocarbons such as perylene yielding a radical cation. In both cases, the anion acts as the counterion required to balance the positive charge. The second step is the transfer of anions across the electrochemical interface (19.21) and correspondingly, the graphite lattice has to be expanded. For weakly solvated cations of low melting points, this process is highly reversible, as has been concluded from voltammetry and impedance measurements [39]. For carbon in concentrated sulfuric acid, the overall reaction can be represented as follows: (19.22) From reaction (19.22) intercalation compounds (i) with x = 24 have been obtained. Alkaline metals, particularly rubidium, potassium, and cesium, intercalate graphite layers yielding compounds of the form CsMe when a layer of alkaline metal atoms is formed between each pair of carbon planes [6].

19.4

CHEMICALLY MODIFIED ELECTRODES AND

SUPRAMOLECULAR CONFIGURATIONS

The electrochemical and electrocatalytic properties of carbon electrodes can be modified changing their surface composition by anchoring foreign compounds. This can be accomplished by adsorption, by chemical reaction with a surface group, by specific chemical binding, and by adsorption immobilization on a sublayer of a polymer material [40]. Chemically modified electrodes constitute a part of supramolecular chemistry. Typical examples of the adsorption procedure are the irreversible attachement of metal-N4 complexes on HOPG and the adsorption of aromatic molecules for anchoring complex species. Ion-N4 complexes are adsorbed in a planar orientation on the HOPG surface and cobalt and iron tetrasulfate phtalocyanines are arranged sideways relative to the surface [41].

19.4 Chemically Modified Electrodes and Supramolecular Configurations

493

Complexes like [Ru(NH 3 )sL]2+ with a large aromatic ligand such as 4aminomethylpyridine or N-(4-picolinic)benzamide; [(RubipY)2L]2+·2(PF 6 -); 1,5 diihydroxyanthraquinone, can be adsorbed on glassy carbon by evaporation from a nonaqueous solution [42]. For chemical attachment, the carbon surface is first activated by oxidation at 160°C in air or by oxygen plasma. Then, activated COOH carbon groups react with thionyl chloride yielding -COCl groups at the carbon surface. Subsequently, the active group (R) is attached via a reaction with amines leading to -CONHR. Thus, different functional groups (R) can be attached. Covalent attachment of active molecules to graphite surfaces can be made via OH groups using cyanuric chloride, 2,4-dinitrophenylhydrazine or chlorosilanes as intermediate reagents [43]. The adsorption of polymers, poly(vinyl pyridine) or poly(acrylonitrile) either to coordinate metal atoms or to adsorb biopolymers has been used to prepare chemically modified electrodes for immobilization of enzymes either by physical or by chemical adsorption (carrier binding), cross-linking, and entrapping at lattice sites or in microcapsules [43]. A wide application of these types of electrodes has been made for electrochemical reactions ofbiological interest [44]. Chemically modified electrodes resulting from the attachment of quinones, phenantroline, dipyridyl complexes, and N 4 complexes, from the development of polymer-coated carbon materials, and from electrodes modified by enzymes have been specifically designed for the electrocatalytic reduction of molecular oxygen (OERR). Carbon materials with immobilized hydroquinone have also been utilized to accelerate the electrochemical oxidation of molecular hydrogen. Modified carbon and graphite electrodes have been found adequate for producing a mixture ofoptically active isomers and stereoselective addition reactions such as the chlorination of anisole at an a-cyclodextrine-modified graphite electrode [45]. The kinetics of the electrochemical reactions at arrangements of chemically modified electrodes has been interpreted by a charge and mass transfer electrochemical mechanism. Charge transfer can be, in general, described by an electron jump and a molecular diffusion step. At electrodes modified by complexes, the rate of electron tunneling (W(r)) can be described by the equation

W(r) = V' exp (-r/ A')

(19.23)

r being the distance covered by the electron, V'is a constant, and A' depends on the geometry of the potential energy barrier. Accordingly, the transfer efficiency should depend on the distance from the active center to the electrode plane. For r < rerit' W(r) should be greater than the rate of the reaction at the active center. For r > rerit' the reverse situation occurs. The influence of ron the rate of the OERR has been studied on laccasemodified carbon electrodes [46]. In this case, rwas varied by a monolayer of adsorbed lipid that had either planar (cholesterol) or vertical (lecithin) orientation on the electrode surface. In this case, a sharp decrease in the rate of OERR was found within a narrow range of r, which is determined by rerit ~ 2 nm.

494

Chapter 19 Electrochemical Behavior of Carbon Materials

The diffusion step becomes important for polymer-modified electrodes. Thus, the apparent diffusion coefficient depends on the concentration of redox groups because the acceleration of the electron exchange decreases with the ion distance. These conclusions were drawn from a series of polyvalent ions anchored electrochemically to poly(4-vinyl pyridine) on graphite [47]. Electronic conductivity is favored by electron transfer through the polymer delocalized band structure, via redox conductivity by site-site hopping. Redox conductivity occurs at electron energies centered around the formal equilibrium potential for the redox polymers.

19.5

ELECTROCHEMICAL KINETICS ON CARBON

ELECTRODES IN AQUEOUS SOLUTIONS

19.5.1 Direct Electrode Processes Although carbon electrodes are frequently used for electroanalytical studies of oxidizable compounds, many of them exhibit heterogeneous charge transfer rates that are very low at carbon electrodes, as concluded from their corresponding ill-defined voltammograms [48]. Thus, the surface properties of carbon electrodes can have remarkable effects on the voltammetric response of these direct electrode reactions. One typical example of this behavior is the voltammogram of the ferro/ferricyanide couple (test reaction) that at carbon electrodes is less reversible than at noble metal electrodes. The kinetics of the test reaction in 1 M aqueous KCI was used as the reference to compare its electrochemical behavior on different carbon electrodes [20]. This electrochemical reaction occurs via an outer sphere mechanism and its rate depends on the electrolyte composition and can be increased by appropriate treatment of carbon electrodes, for instance, by application of a high current potential routine to electrodes of carbon fibers. Similar results have been obtained with glassy carbon surfaces that had been pretreated at SOO°C under reduced pressure. An alternative activation method is based on careful electrode surface polishing [6]. The kinetics of the test redox reaction on the cleavage HOPG surface is almost under pure diffusion control, whereas on the edge surface, where ionspecific adsorption is favored, it is under combined kinetic and diffusion control. Accordingly, surface heterogeneity is a new variable in the kinetics of electron transfer processes at carbon surfaces, as the surface energy of sites at each domain (plane, edges, kinks, etc.) is different. Let us assume the existence of two surface domains (1 = basal and 2 = edge) for graphite with specific rate constants for the test reaction (k~ and k~) and consider that the 1-1 and 2-2 domain distances are R 11 and R 22 , respectively. The value of these distances relative to ffi may have a significant effect on the voltammetry that depends on whether R 11 , R 22 «ffi, R ll < ffi < R 22 , and R ll , R 22 »ffi. The value

19.5 Electrochemical Kinetics on Carbon Electrodes in Aqueous Solutions

495

°

of kg = 0.10 cmls is about 25 times greater than k 1 = 0.004 cmls, in agreement with the difference in reactivity between the basal plane of graphite and the edge sites. The remarkable anisotropy of kO coincides with that of C, E pzc and the work function (Section 19.3.4). Carbon composites have been developed as alternative materials for carbon paste electrodes because of the limited utility of the latter in most organic solvents. These composites include polyethylenelcarbon black [49], Kel-F/graphite [50], carbon black immobilized in cross-linked polyethylene [51], and epoxy/graphite [52]. A collection of kO for these materials is available [20]. Thus, for platinum kO = 0.24 cm/s, for pyrolytic graphites 0.002 < kO < 0.007 cm/s, and for graphite carbons 0.005 < kO < 0.14 cm/s. Simple redox solutes, ferrocene, N, N, N, N -tetramethyl-1 ,4-phenylenediamine, decamethylferrocene, bis(i-propylcyclopentadienyl) iron(II), [Ru(phen)3] (CI0 4)2' [Fe(bpY)3] (CI0 4)2' [Co(bpY)3] (CI0 4)2' and iodine have been studied at electrodes modified with polymeric fullerene films. Fullerene-modified electrodes were prepared by electropolymerization of C 60 initiated by traces of dioxygen or by simultaneous electroreduction of fullerene and Pd(II) acetate trimer. For the former films, the electrochemical activity decreases upon potential cycling. The electrochemical activity of the film is stabilized by the redox solute added to the electropolimerization stage due to the catalytic oxidation of the fullerene film by the oxidized form of the redox system. Similarly, positively charged species can also be incorporated into the structure of the film. The reversible behavior of redox solutes decreases with the increase in the thickness of the Pd/C 60 film. This film also incorporates ferricinium ion, N, N, N, N -tetramethyl-1 ,4-phenylenediamine cation, decamethylferricinium ion, and to a smaller degree [Co(bpY)3]n+ [53]. Microcrystals of fullerene-C 6o on glassy carbon mediate the oxidation of cysteine in the presence ofaqueous potassium-containing electrolytes. The potential for the oxidation of cysteine is lowered by approximately 100 illV and current is enhanced significantly as compared to bare glassy carbon electrodes. Additional mediation occurs when the potential range of C 60 1C 60 n- redox couples are covered. The electrochemical response is sensitive to pH, temperature, and C 60 dosage. Excellent analytical and/or recovery data are obtained with vitamin pill (alcovite), cassamino acid (hydrolyzed casein), and for a range of beverages [54].

19.5.2 Oxygen Electroreduction on Carbon Electrodes The reversible potential of the water decomposition reaction is 1.23 V at 25°C. The overpotential for OERR in aqueous alkaline solutions (19.24) is 0.3-0.4 V at 60-80°C, and in acid solutions 02 + 4H+ + 4e- -+ 40Hit is 0.4-0.5 V at c. 190°C

(19.25)

Chapter 19 Electrochemical Behavior of Carbon Materials

The oxygen electrode polarization is a measure of the degree of irreversibility of the electrochemical reaction. To find an effective electrocatalyst for reactions (19.24) and (19.25) is of a great interest because of their technical relevance in water electrolysis, fuel cells, metal corrosion in aqueous environments, biological processes, etc. The OERR is usually considered to proceed via two reaction pathways, namely, the peroxide and the direct four-electron pathways. The scheme of the peroxide pathway is H02(ad) + OH-

H2 0 + O2

~I ~

(19.26)

where (ad) stands for peroxide adsorbed species on carbon. The peroxide species are either electroreduced further to OHHOH + H02-

~ ~

3HO-

(19.27)

or catalytically decomposed to OH- and O 2 2H0 2

(19.28) 2H02" (ads)

The overall reaction is the four-electron electroreduction of molecular oxygen. The oxygen resulting from reaction (19.28) is recycled via reaction (19.26). The direct four-electron pathway involves no hydrogen peroxide formation in the solution. This fact, however, does not preclude the participation of an adsorbed peroxide intermediate in the course of the reaction. The distinction between both reaction pathways is usually investigated by the rotating ring-disc electrode technique [55]. From the rotation speed and potential dependence of the disc electrode to ring electrode current ratio, it is possible to determine the relative contribution of each reaction pathway to the overall reaction [56].

19.5 Electrochemical Kinetics on Carbon Electrodes in Aqueous Solutions

19.5.2.1

497

OERR kinetics in alkaline solutions

The kinetics of the OERR on carbon [27] and graphite [27] in alkaline solution has been explained in terms of the dominant contribution of the peroxide reaction pathway. On the other hand, the direct four-electron pathway predominates on graphite electrodes modified by adsorbed tetrasulfonated phtalocyanine [57] and attached face-to-face di-cobalt-porphyrin complexes [58]. In principle, when both pathways operate simultaneously on a given surface, the kinetics is referred to as involving a parallel mechanism [59]. In alkaline solutions porous carbon electrodes are effective catalysts for the OERR. In this case, the exchange current density of reaction (19.26) for both carbon and graphite in 1 M KOH + 10-3 M peroxide concentration [59] is in the range 10- 4 < Jo < 10-3 AIcm2 (true area). For porous carbon electrodes (10 4 -10 5 cm2 true area per cm2 superficial area) large values ofJo indicate a small activation polarization for the OERR. The predominant process occurs then via the peroxide pathway. In general, the presence of impurities determines the extent of the rate of desorption of adsorbed peroxide, although the catalytic peroxide elimination effect decreases during the electrode operation. For porous structured carbons this effect can be due to the buildup of a substantial amount of peroxide in the solution within pores. Furthermore, the high peroxide concentration contributes to increasing the O 2- radical ion and OH radical concentration within the pores via the following equilibrium: (19.29) the equilibrium constant of reaction (19.29) being K ~ 10-7 .5 at 25°C [60]. Radicals such as O 2 and OH, which are produced as intermediates in the homogeneous peroxide decomposition, may favor the attack of carbon via oxidation. This fact is accompanied by a change in hydrophobicity and porous clogging by gel formation, particularly because of sodium peroxide. Suppression of H0 2- concentration in porous carbon electrodes is usually accomplished by the dispersion in carbon of specific catalysts such as silver, Mn0 2, and Ni-Co spinels. For very active catalysts such as platinum supported on carbon, the direct four-electron and the peroxide-producing reaction occur in parallel, the first on the catalyst, and the latter on carbon surface domains. Accordingly, it is possible to diminish the peroxide activity to the equilibrium value of reaction (19.29). In this case, the electrode potential would approach the equilibrium value for the overall four-electron electroreduction reaction (19.24). The stationary cathodic current-potential polarization curve of the OERR on pyrolytic graphite exhibits the Tafel slope -0.120 V per decade- 1 at 25°C, and the stoichiometric number is 2 for the O 2 to OH 2- electroreduction reaction. For glassy carbon, the Tafel slope is -0.060 V per decade- 1 , and the corresponding stoichiometric number is 1, as expected for reaction (19.26) [28]. The OERR is first order in 02 and zero order in OH- for both carbons.

Chapter 19 Electrochemical Behavior of Carbon Materials

For graphite the following mechanism for the OERR has been proposed [27]: O 2 -+ 02(ads) O 2(ads) + e- -+ O~ 20~(ads) +HOH -+ O 2 +HO~ +OH-

(19.30a) (19.30b) (19.30c)

with step (19 .30b) being rate determining in the Tafel range of the polarization curve. Reaction (19.30c) is a complex process involving several steps. For glassy carbon, the mechanism of the OERR [28] starts with reaction (19.30a) followed by 02(ad)+e- -+ [02(ads)]-

(19.31a)

02(ads)- -+ {02(ads)}-

(19.31b)

{02(ads)}- +HOH-+ H0 2(ads)+OH-

(19.31c)

H0 2(ads) + e- -+ HO~(ads)

(19.31d)

HO~(ads) -+ HO~

(19.31e)

step (19.31c) being rate determining. [02(ads)] and {02(ads)} indicate different adsorbate structures. For Teflon-bonded gas-fed electrodes prepared from carbons that have little peroxide-decomposing activity, the OERR at the highest current densities appears to be limited by converging characteristics related to carbon itself, its electrocatalytic activity for oxygen reduction to peroxide and peroxide decomposition, the gas mass transport, and the electronic conductivity. To advance in the understanding of the OERR mechanism on carbon and graphite, more information at the molecular level of surface functional groups at these cathodes in air is still required. 19.5.2.2 OERR in acid solutions

In acid solution the OERR proceeds mainly via the formation of H 20 2 on porous carbon electrodes. This is also supported by experiments with 18 0 isotope that showed a lack of 0-0 bond break during the OERR. In acid media, the OERR appear to be independent of pH and the Tafel slope is close to -0.120 V per decade 1 , the transfer of a first electron to an adsorbed oxygen molecule being the rds. (19.32) The reaction is first order with respect to molecular oxygen. The efficiency of the OERR is increased considerably when mesometal and nanoparticles (Pd, Au) on carbon surfaces are used as electrocatalysts [61]. This electrocatalytic enhancement is related to the geometry of these metal islands

19.5 Electrochemical Kinetics on Carbon Electrodes in Aqueous Solutions

499

and it appears that the most active domains are located at edges of islands in contact with the HOPG surface [62]. This is consistent with the fact that gold nanoparticles electrochemically formed on graphite are preferentially deposited on the upper plane of step edges due to the nonuniform electron density that results from relaxation of the graphite lattice near steps [63].

19.5.3 Oxygen Reduction on Macrocyclic Transition Metal Complexes on Graphite and Carbon Surfaces In contrast to the interaction of O 2 with graphite and carbon surfaces, the electrodes modified by transition metal complexes provide the possibility of extending the type of interactions derived from inorganic chemistry to the electrochemical system. A typical example is the face-to-face anchorage of porphyrins as catalysts on carbon electrodes for the OERR [58, 60, 64]. For cobalt porphyrin on graphite, when the Co-Co distance is about 0.4 nm, which makes the formation of an 0-0 bridge between Co centers possible, the presence of the Co porphyrin catalyzes the four-electron reaction in acid solutions, whereas for smaller Co-Co distances, the peroxide pathway is catalyzed. These behaviors have been related to the cis and trans surface complex configurations that assist the four-electron reaction and the peroxide pathway, respectively. Similar electrocatalysis for the OERR has been found in alkaline solutions when the macrocycles are adsorbed on graphite [28]. The thin layer of transition metal macrocycles attached to carbon generally lack long-term stability in concentrated acid and alkaline solutions. This drawback can be overcome by thermal treatment at 450-900°C for cobalt tetramethoxy phenyl porphyrin (Co-TMPP) [65]. Under these conditions, the Co-TMPP is substantially degraded to cobaltous oxide. Pyrolyzed layers involve high-area carbonaceous materials with a significant surface nitrogen and the transition metals as small oxide and metallic particles dispersed on the high-area substrate. These layers catalyze peroxide elimination in alkaline solutions. The catalytic current for the OERR in aqueous solutions at glassy carbon electrodes modified by the physical adsorption of 1,2-dihydroxyanthraquinone is significantly increased under insonization because of the increase in mass transport [66].

19.5.4 Oxygen, Hydrogen, and Chlorine Electrode Reactions Hydrogen, oxygen, and chlorine overpotential measurements on the basal and edge planes of stress-annealed graphite are complicated by intercalation and oxidative attack of the surface. Both hydrogen and oxygen overpotential are quite high on most graphite and carbon surfaces, probably in part because of the existence of functional groups. The interaction of adsorbed groups, both directly or through electronic substrate effects, would produce broad voltammetric peaks that reflect in large Temkin terms in the adsorption isotherm. This fact makes the voltammogram interpretation difficult.

Chapter 19 Electrochemical Behavior of Carbon Materials

500

19.5.4.1 Hydrogen evolution on carbon and graphite Carbons exhibit a low electrocatalytic activity for the hydrogen electrode reaction (HER). Structural characteristics have significant electrocatalytic effects on the HER as Jo changes from 2 X 10-9 to 2.5 X 10- 8 A/cm- 2 on going from the basal plane to the side face of pyrolytic graphite. On glassy carbon, the HER overpotential decreases as the pretreatment temperature is increased. This thermal treatment leads to structural and chemical transformations from carbonization, precrystallization, and to graphitization. Kinetic parameters for the HER on different carbon and graphite electrodes show that depending on the type of electrode and acid solution Jo varies between 2 x 10- 7 and 2 x 10- 13 A/cm2 and the cathodic Tafel slope is usually close to -0.120 V per decade, although some unexpected higher values have also been recorded. The reaction order with respect to the hydrogen ion concentration is 1, but unexpected values of 0 and 2 have also been reported [6]. The rds is usually the initial discharge step and the surface coverage ofhydrogen atoms is low. Electrochemical reductions of fullerene films in the presence ofBrnsted acids yield hydrogenated fullerenes H n C 60 , where n depends on the acid, its concentration, and on the electrode potential. Hydrogenated fullerene films behave as semiconductors with increased photoefficiency [67].

19.5.4.2 Oxygen evolution on carbon and graphite The rate of the oxygen evolution reaction (OER) on pyrolytic graphite is higher than that for glassy carbon. For both the carbon electrodes, the temperature pretreatment has no influence on the current measured at constant potential. Carbon dioxide is the main reaction product for E < 1.1 V (vs reversible hydrogen electrode (RHE)) on pyrolytic graphite. For a pH between 1 and 9, the Tafel slope changes from 0.150 to 0.240 V per decade, depending on the solution composition and electrode preparation. The anodization of both glassy carbon and HOPG in aprotic solutions (DMSO, ACN) is characterized by a reversible one-electron O 2 to 02 - reaction. Kinetic data of the oxygen electrode on carbon materials have been compiled in Ref [68].

19.5.4.3 Chlorine electrode In aqueous solutions, the equilibrium potential for the reaction

(19.33) is 1.359 V vs NHE at 25°C [3]. This figure is approached for smooth pyrolytic graphite in aqueous NaCI (a = 1) under chlorine saturation (PC1 2 = 1) to attain 1.320 V [6]. Therefore, carbons are useful for applications in the chlorine evolution reaction as both, the carbon oxidation reaction and the OER exhibit larger overpotentials.

19.6 Organic Electrochemistry at Carbon Electrodes

501

The kinetics and mechanism of the chlorine evolution reaction in aqueous solutions have been studied on smooth, porous, and impregnated graphite [68, 69]. The Tafel slope depends also on the nature and history of carbons. For HOPG and glassy carbon, the anodic Tafel slope is about 0.060 and 0.120 V per decade at 25°C, respectively, whereas for a graphite electrode consisting of a section parallel to the c-axis, three regions in the polarization curve with anodic Tafel slopes from 0.060 to 0.160V per decade have been observed. For reaction (19.33), current flow for the porous electrodes is under ohmic regime. Specifically adsorbed anions hinder chlorine evolution, in contrast to cations such as Fe3+ that probably produce a change in the potential distribution at the electrical double layer. The residual gas evolution at graphite, after switching the anodic current 0[£ decays by desorption via self-discharge. graphite(Cl)ad + e- ~ ClCl- + graphite(Cl)ad ~ C12 + e-

(19.34) (19.35)

The rate of diffusion of atomic chlorine is determined by an equilibrium between diffusion ofadsorbed chlorine from graphite outward (Eqn. (19.34)) and the formation of molecular chlorine (Eqn. (19.35)). As the surface concentration of chlorine diminishes, it is replenished by diffusion, a process that gradually becomes rate determining. The kinetics of molecular chlorine evolution follows a first-order law with respect to chlorine, and zero order with respect to chloride ion concentration. The chlorine impregnation of carbon electrodes results in lamellar compounds such as CsCl [6]. The cathodic Tafel slope corresponding to reaction (19.33) in the reverse direction is close to -0.120 V per decade at 25°C. For both cathodic and anodic reactions, the interfacial capacity results in 30-35 f.1F cm2 . This figure is consistent with a low surface coverage by chlorine atoms. Kinetic parameters for the chlorine evolution reaction on carbon electrodes are assembled in Ref [6].

19.6

ORGANIC ELECTROCHEMISTRY AT CARBON

ELECTRODES

Carbon, graphite, vitreous carbon, carbon felt, carbon fibers and cloth, as well as reticulated carbons, are of common use either as anodes or cathodes for the electrochemical synthesis of organic compounds. A typical example is the Kolbe electrosynthesis in which a carboxylate salt is electrochemically discharged at vitreous carbon anodes, in both aqueous and nonaqueous media, yielding a hydrocarbon with high efficiency and carbon dioxide.

Chapter 19 Electrochemical Behavior of Carbon Materials

502

At ordinary graphite electrodes in aqueous solutions, the reaction products are those derived from the formation of carbonium ion intermediates, RCO~

~

R+C0 2 +e-

(19.36)

2R

~

R-R

(19.37)

~

R++e-

(19.38)

R

H2 O

R+ ~ ROH+H+

(19.39)

RCO-

R+

~2 RC0 2R

-H+

R + ~ olefin or rearranged species

(19.40) (19.41)

The difference in the yields of products appears to be a carbon surface area effect that acts as product-determining characteristics. For an extensive description of this matter, see Ref [15].

19.7

REACTIONS ON BIOLOGICAL ACTIVE ELECTRODES

Electrochemical reactions ofa large number ofbiological active compounds such as aminoacids, proteins, catecholamines, alkaloids, purines and their nucleosides, NAD, FAD, FMN, and nucleic acids have been investigated on HOPG, paste electrode, graphite, glassy carbon, carbon fibers, and fullerenes [68]. In this case, the ability of the anchored compound to remain stable by repetitive potential cycling between its different oxidation states is essential to successfully design a supramolecular electrode for this particular type of electrocatalytic reactions. One example of this type of electrodes is a gold electrode covered by a selfassembled monolayer of gluthation and covalently bound fullerene [70], that has been proposed for the consecutive electro-oxidation of nicotinamide adenine dinucleotide (NADH) to NAD+. A first high power density of about 100 J.1 W 1cm2 miniature biofuel cell uses supramolecular modified carbon fiber electrodes operating in aqueous solution at pH 5 and room temperature. The electrocatalytic film at the anode catalyses the electro-oxidation of glucose to gluconolactone, and at the cathode catalyses the electroreduction of oxygen to water. The supramolecular ensemble involves OS2+ IOs3+ centers and enzymes that are immobilized in the electron-conducting redox-polymer films. The film of the anode consists ofa cross-linked electrostatic adduct of glucose oxidase, and at 0.1 V (vs Agi AgCI) a redox potential electronconducting redox polymer, which electrically connects the glucose oxidase redox centres to one fibre. The film ofthe cathode consists oflaccase and a 0.55 V

19.8 Corrosion Processes

503

(vs Agi AgCI) electron-conducting redox polymer, electrically connecting the laccase redox centres to the second fiber [71]. A miniature biofuel cell operating at 37°C in a glucose-containing aerated physiological buffer consists of two electrocatalyst-coated carbon fibers. Glucose is electro-oxidized to gluconolactone on the anode fibers and dissolved oxygen is electroreduced to water on the cathode fiber. The power output of the cell operating at 0.52 V is 1.9 f.1 W, i.e., a power density of 4.3 f.1 W Imm2 [72]. These advances would increase the probability of achieving technical devices such as sensors, reactors, and energy storage and energy conversion devices, resulting from engineering and design approaches converging to the efficiency found in natural systems.

19.8

CORROSION PROCESSES

The degree of carbon corrosion .depends on the type of carbon, the electrode potential, the temperature, and the carbon pretreatments that affect its surface structure [73]. Corrosion reactions occur at distinct domains of the carbon surface with different rates. The main surface domains are the plane boundaries or defects, outer interplanar areas, and intercalation areas between the planes. The stronger the edge attack, the greater the amorphous domains of carbons. Intercalation between the planes becomes more important with HOPG provided that some edges are exposed to the environment. The corrosion process changes with pH [74]. Nonbasal dislocations play an important role in the oxidation of graphite carbons. In hot 96% phosphoric acid at 135-160°C different carbons exhibit similar corrosion behavior as a function of time [75, 76]. At constant potential, the corrosion current that was initially relatively large decreases rapidly with time. The principal corrosion reaction is (19.42) Different surface oxides are formed as intermediate oxidation products in reaction (19.42). Both the formation of surface oxides and the evolution of carbon dioxide decrease with time. But as the surface coverage by oxide increases, carbon dioxide formation prevails and proceeds via surface oxides at preferred sites. Corrosion rates of carbons appear to be independent of water content and carbon dioxide partial pressure. In acid electrolytes, the Tafel slope for the carbon corrosion reaction appears to be indicative of the degree of disorder on the carbon surface. The larger the Tafel slope, the greater the degree of disorder. The influence of heat treatment on the corrosion rate depends on the structure of the parent carbon, particularly on the lattice parameters. Thus, in hot phosphoric acid at cathodic potentials, as

Chapter 19 Electrochemical Behavior of Carbon Materials

504

used in the phosphoric acid fuel cell technology at 150-200°C, samples of heattreated Vulcan XC-72R after boron doping and heat treatment at 1000-2000°C show an enhanced resistance to corrosion. Changes in Brunauer, Emmit, Teller (BET) surface areas, lattice parameters, and electrochemical behavior converge to show that the addition of boron results in an additional graphitization to that achieved by the heat treatment itself Boron acts as an electron acceptor and can enter the graphite lattice by substituting carbon atoms at trigonal sites that would provide traps for metal clustering. The corrosion of carbon in alkaline solutions is of interest for alkaline batteries. For acetylene black electrodes at 0.45-0.60 V (vs Hg/HgO) in concentrated aqueous KOH, carbon dissolution to carbonate ion, gasification of carbon to carbon monoxide, and oxygen evolution are the main anodic processes, although the potential and temperature dependence of these processes is different. Correspondingly, for E < 0.50 V and T < 50°C, carbon dissolution is the primary process; for 0.50 < E < 0.60 V and T> 50°C, carbon dissolution and oxygen evolution occur at comparable rates; for E > 0.60 V and T > 60°C, oxygen evolution and carbon gasification are the dominant processes. The current efficiency of these processes also depends on whether a catalyst such as cobalt oxide has been added to the carbon electrode, although the major effect is produced on the OER.

19-9

(ARBON ELECTRODES IN MOLTEN SALTS

Carbon electrodes are crucial for a number ofimportant processes in molten salt electrometallurgy. A long list of commonly used metals, such as aluminum, sodium, potassium, calcium, and magnesium are produced by these processes [77, 78].

19.9.1 Cryolite-Al 2 0 3 Melts Carbon anodes are used in the electrolysis of cryolite-alumina mixture to produce aluminum. The overall reaction in the electrochemical cell is (19.43) in which the anode is partially oxidized to CO and CO 2 • The overall anodic reaction is (19.44) However, considering reaction (19.43), reaction (19.44) has been interpreted by a complex reaction pathway that includes the formation of a C(O) surface intermediate as primary process (19.45)

19.9 Carbon Electrodes in Molten Salts

505

followed by a secondary chemical process yielding carbon oxides

C(O) --+ carbon oxides

(19.46)

Another interpretation considers the formation of a nonstoichiometric surface oxide as primary process (19.47) that subsequently decomposes into CO and CO 2 (19.48) The complex mechanism of reaction (19.44) is probably controlled by diffusion and the rate of the heterogeneous chemical reactions. For various carbon electrodes in cryolite melts saturated with alumina at 1010°C, values of 0.0048 < jo < 0.24 AI cm2 have been reported [79]. The overpotential of the anodic reaction increases when the concentration of alumina in the melt decreases, and the wettability of the electrode by the melt decreases because of the accumulation of C(O), CO, and CO 2 species, leading to the dangerous anodic effect. Intercalation compounds such as (CF)n' (C 2 F)n' and C x F(AlF 3 )y are also formed. Compounds having a covalent bond are unique in their low surface energy. The noncovalent intercalation compound results in a conductor better than the original carbon. These findings provided new methods for water proofing the carbon surface and for new materials to be used as cathodes in lithium batteries.

19-9-2 Halides-containing Melts Fluorine is produced by electrolysis of molten salts on carbon anodes including KF-2HF at about 100°C, potassium bifluoride at about 250°C, and fluoride salts at about 1000°C. The decomposition potential ofmolten potassium bifluoride is 1.75 V at 250°C, a value close to that estimated thermodynamically [80]. The kinetics of the anodic process is characterized by a Tafel slope of 0.56 V per decade, jo = 1 X 10-4 A/cm2 [81], and by a complex reaction mechanism involving the formation of fluorine atoms on carbon. During the electrolysis, C-F surface compounds on the carbon anode are formed via side reactions. Intercalation compounds such as (CF)n contribute to the anodic effect in the electrochemical cell, which can be made less harmful by addition of LiF. The kinetics ofthe chlorine electrode in different chloride melts was studied in the range 190-430°C. Different controlled processes involving the participation of chlorine atoms on graphite have been proposed [82, 83]. The evolution and dissolution of chlorine at graphite electrodes was studied in molten lithium chloride. The anodic evolution involves a fast discharge of chloride ions followed by the combination of chlorine atoms that is the rds

50 6

Chapter 19 Electrochemical Behavior of Carbon Materials

of the process. The graphite surface is appreciably covered by chlorine species under Temkin adsorption conditions. The cathodic dissolution of cWorine is limited by diffusion of cWorine in the melt to the electrode surface under high current conditions, whereas at low currents the process of dissociation of chlorine on the surface is followed by the charge transfer process [83].

19.9.3 Oxygen-containing Melts Deposition of carbon from the electrolysis of molten carbonates (Li 2 C0 3 , Na2 C0 3 , and K2 C0 3 ) involves the gradual reduction of the degree of oxidation of carbonate to carbon. At temperatures below 700°C, the formation of carbon is thermodynamically favored compared to that of carbon monoxide [6]. Voltammetry data of graphite electrodes in molten NaN0 3 /KN0 3 at 240-350°C indicate an anodic reaction involving O 2 - ion and NO that proceeds via an oxide group on the graphite surface. The corrosion of graphite was related to the formation of a N0 3 intermediate [84, 85]. For graphite in NaN0 2 /KN0 2 melt at 236°C no appreciable corrosion was observed [86, 87]. The kinetics of the hydrogen electrode reaction on dense porous graphite electrodes in molten KHS0 4 from 245°C to 280°C [88-90] showed that the cathodic and anodic reactions are not strictly conjugated processes. The cathodic reaction was discussed in terms of conventional mechanisms, but the anodic reaction involves the simultaneous oxidation of hydrogen and graphite surface. The reaction exhibits a one-half power dependence on hydrogen pressure. The kinetics of the electro-oxidation of graphite in molten KHS0 4 to volatile compounds (carbon dioxide, carbon monoxide, and traces of sulfur dioxide) was studied in the range 180-320°C. The faradaic yield for carbon dioxide (4 F per mol of carbon dioxide) is about 90 %. The rds is the desorption of oxygen-containing intermediate species [91].

19.10 CARBON ELECTRODE MANUFACTURING TECHNIQUES

Industrial carbon materials are used for molds, structural forms, electrodes of all kinds to be used in current production, metal deposition, and chemicals manufacturing [92]. Their fabrication involves a number of specific operations and processes. For instance, carbon blacks are deposited, collected, and processed. Cokes must be crushed and calcined; binders (pitches) must be pulverized and classified. Green mixtures are formed, molded, extruded, baked, and some carbons are also graphitized to provide special properties.

References

507

Different electrode designs were developed. Porous conductive electrodes having at least two zones can be used either as reversed dual porosity electrode or as electrode assembly with conductive, noncompressible porous carbon matrices [92]. The gas-diffusion electrode constitutes a system in which a reactive gas is supplied under pressure to a porous electrode partition that separates gas and electrolyte phases from each other [93]. By adjusting the gas pressure and average pore diameter, the electrolyte fills only part of the pore chemical system. In recent years, the preparation and properties ofPt-Ru/C electrocatalysts for polymer electrolyte fuel cell applications have received considerable attention [94-97].

ACKNOWLEDGMENTS This work was financially supported by the Consejo Nacional de Investigaciones Cientificas y Tecnicas (CONICET), Agencia Nacional de Promoci6n Cientifica y Tecno16gica (PICT 98 06-03251) of Argentina, and the Comisi6n de Investigaciones Cientificas de la Provincia de Buenos Aires (CIC).

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References

5°9

34. Thonstadt, J. (1973). Double-layer capacity of graphite in cryolite-alurnnina melts and surface area changes by electrolyte consumption of graphite and baked carbon. J. Appl. Electrochem., 2, 315-19. 35. Gewirth, A.A. and Bard, AJ. (1988). In situ scanning tunneling microscopy of the anodic oxidation of highly oriented pyrolytic graphite surfaces.]. Phys. Chern., 92, 55663-6. 36. Bunde, A. and Havlin, S. (1996). Fractals and Disordered Systems. Springer. 37. Bard, AJ. and Faulkner, L.R. (1980). Electrochemical Methods. John Wiley & Sons. 38. Pyun, S.1. and Rhee, C.K. (2004) An investigation of fractal characteristics of mesoporous carbon electrodes with various pore structures. Electrochim. Acta, 49, 4171-80. 39. Ebert, L.B. (1982). Electrochemistry of intercalation compounds of graphite. Proceedings of the Workshop on the Electrochemistry of Carbons, Vol. 84-5. Pennington: The Electrochemical Society, p. 595. 40. Murray, F. (1999). Modified electrodes. Electroanalytical Chemistry, Vol. 13. Marcel Dekker. 41. Zagal,J. Sen, R.K., and Yeager, E. (1977). Oxygen reduction by Co(II) tetrasulfonatephthalocyanine irreversibly adsorbed on a stress-annealed pyrolytic graphite electrode surface.]. Electroanal. Chem., 83, 207-13. 42. Brown, A.P. and Anson, F.C. (1977). Molecular anchors for the attachment of metal complexes to graphite electrode surfaces. J. Electroanal. Chem., 83, 203-7. 43. Schreurs, J. and Barendrecht, E. (1984). Surface-modified electrodes. Reel. Trav. Chim. Pays-Bas, 103,205-19. 44. Dryhurst, G. (1977). Electrochemistry if Biological Molecules. Academic Press. 45. Matsue, T. FUjihira, M., and Osa, T. (1979). Selective chlorination with a cyclodextrin modified electrode.]. Electrochem. Soc., 126, 500-1. 46. Tarasevich, M.R., Yaropolov, A.I., Bogdanoskaya, V.A., and Varfolomeev S.D. (1979). Electrocatalysis of a cathodic oxygen reduction by laccase.]. Electroanal. Chern., 104, 393-403. 47. Yamaguchi, N.O., Nishiki, Y., Tokuda, K., and Matsuda, H. (1982). Apparent diffusion coefficients for electroactive anions in coatings of protonated poly(4-vinylpiridine) on graphite electrodes.]. Electroanal. Chem., 139,371-82. 48. Wightman, R.M., Kovach, P.M., Kuhr, W.G., and Stutts, KJ. (1982). Increasing electrochemical reversibility at carbon electrodes. Proceedings of the Workshop on the Electrochemistry of Carbons, Vol. 84-5. Pennington: The Electrochemical Society, p.510. 49. McLean, J.D. (1982). Carbon electrodes for liquid chromatography detection. Anal. Chem., 54, 1169-74. 50. Anderson, J.E. Hopkins, D. Shadrick, J.W., and Ren Y. (1989). Apparatus for the fabrication ofpoly(chlorotrifluoroethylene) composite electrodes. Anal. Chem., 61, 2330-2. 51. Park, J. and Shaw, B.R. (1989). Electrochemical performance of crosslinked poly(styrene)-co-poly(vinylpyridine) composite electrodes containing carbon blacks. Anal. Chern., 61, 848-52. 52. Falat, L. and Cheng, H.Y. (1983). Electrocatalysis of ascorbate and NADH at a surface modified graphite epoxy electrode.]. Electroanal. Chem., 157, 393-7. 53. de Bettencourt-Dias, A., Winkler, K., Fawcett, W.R., and Balch, A.L. (2003). The influence of electroactive solutes on the properties of electrochemically formed fullerene C 6o -based films.]. Electroanal. Chem., 549, 109-17.

51 0

Chapter 19 Electrochemical Behavior of Carbon Materials

54. Tan, W.T., Bond, A.M., Ngooi, S.W., et al. (2003). Electrochemical oxidation of L-cysteine mediated by a fullerene-C 6o -modified carbon electrode. Anal. Chim. Acta, 491, 181-91. 55. Levich, B.G. (1962). Physicochemical Hydrodynamics. Prentice-Hall. 56. Albery, W.J. and Hitchmann, M.1. (1971). Ring-Disc Electrodes. Clarendon Press. 57. Zagal, J., Bindra, P., and Yeager, E. (1980). A mechanistic study of oxygen reduction on water soluble phtalocyanine adsorbed on graphite electrodes.]. Electrochem. Soc., 127, 1506-17. 58. Collman, J.P., Denisevich, P., Konai, K., et al. (1980). Electrode catalysis of the four-electron reduction of oxygen to water by dicobalt face-to-face porphyrins. ]. Am. Chem. Soc., 102, 6027-36. 59. Damjanovic, A., Genshaw, M.A., and Bockris, J.O'M. (1967). The role of hydrogen peroxide in oxygen reduction at platinum in H 2 S0 4 solution.]. Electrochem. Soc., 114,466-72. 60. Lu, J.T., Tryk, D., and Yeager, E. (1982). Determination of the equilibrium constant for the superoxide dismutation. Extended Abstracts of the Electrochemical Society Meeting, Abstract 82-1. 61. Gimeno, Y., Hernandez Creus, A., Gonzalez, S., et al. (2001). Preparation of 100-160 nm sized branched Pd islands with enhanced electrocatalytic properties in HOPG. Chem. Mater., 13, 1857-64. 62. Gimeno, Y., Hernandez Creus, A., Carro, P., et al. (2002). Electrochemical formation of Pd islands on HOPG: kinetics, morphology and growth mechanism. ]. Phys. Chem. B, 106, 4232-44. 63. Boxley, Ch., J., White, H.S., Listex, T.E., and Pinhero, P.J. (2003). Electrochemical deposition and reoxidation of Au at HOPG. Stabilisation of Au nanoparticles on the upper plane of step edges.]. Phys. Chem. B, 107,451-8. 64. Liu, H.Y., Weaver, MJ., Wang, C.B., and Chang C.K. (1983). Dependence of electrocatalysis for oxygen reduction by adsorbed dicobalt cofacial porphyrins upon catalyst structure.]. Electroanal. Chem., 145, 439-47. 65. Iliev, I. (1981). Air cathodes for primary metal air batteries. Extended Abstracts of the Electrochemical Society National Meeting. 66. Salimi, A., Banks, C.E., and Compton, R.G. (2003). Ultrasonic effects on the electroreduction of oxygen at a glassy carbon anthraquinone-modified electrode. The Koutecky-Levich equation applied to insonated electrocatalytic reactions. Phys. Chem. Chem. Phys., 5, 3988-93. 67. Szucs, A., Budavari, V., Berkesi, 0., and Novak M. (2003). Electrochemical hydrogenation of C 60 fullerene films.]. Electroanal. Chem., 548, 131-7. 68. Tarasevich, M.R. and Khrushcheva, E.1. (1989). Electrocatalytic Properties if Carbon Materials, Modern Aspects if Electrochemistry, Vol. 19. Plenum Press, p. 2J5. 69. Janssen, L.J. and Hoogland, J.G. (1970). The electrolysis of an acidic NaCl solution with a graphite anode. III. Mechanism of chlorine evolution. Electrochun. Acta, 15, 941-51. 70. Fang, C. and Zhon, Y. (2001). The electrochemical characteristics of C 6o -glutathione modified Au electrode and the electrocatalytic oxidation of NADH, Electroanalysis, 13, 949-54. 71. Chen, T., Barton, S., Binyamin, G., et al. (2001). A miniature biofuel cell.]. Am. Chern. Soc., 123,8630-1. 72. Mano, N., Mao, F., and Heller, A. (2002). A miniature biofuel cell operating in a physiological buffer.]. Am. Chem. Soc., 124, 12962-5.

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73. Stonehart, P. and MacDonald,].P. (1982). Corrosion of carbons in acid electrolytes. Proceedings of the Workshop on the Electrochemistry of Carbons, Vol. 84-5. Pennington: The Electrochemical Society, p. 292. 74. Kokhenov, G. and Milova, N. (1969). Effect of pH on the anodic oxidation of graphite. Elektrokhimiya, 5, 93-6. 75. Kinoshita, K. and Bett,]. (1973). Electrochemical oxidation of carbon black in concentrated phosphoric acid at 135C. Carbon, 11, 237. 76. Kinoshita, K. and Bett, J.A.S. (1974). Corrosion problems in energy conversion and generation. The Electrochemical Society. 77. Koehler, W.A. (1951). Principles and Applications of Electrochemistry, Vol. II. John Wiley & Sons. 78. Galloni, P. (1973). Trattato di Ingenieria Eletrochimica. Tamburini. 79. Thonstadt, J. (1970). The electrode reaction on the C, CO 2 electrode in cryolitealumina melts. I. Steady state measurements. Electrochim. Acta, 15 1569-80. 80. Arvia, A.J. and de Cusminsky, J.B. (1967). EI Potencial del Electrodo de Fluor en el Bifluoruro de Potasio Fundido. An. Asoc. Quim. Arg., 55, 41-6. 81. Arvia, A.J. and de Cusminsky, J.B. (1962). Kinetics of the electrochemical formation of fluorine at carbon electrodes. Trans. Faraday Soc., 58, 1019-32. 82. Vandenbroele, H.J. and Arvia, A.J. (1967). Estudio Cinetico del Electrodo de Cloro en Medios I6nicos Fundidos. An. Asoc. Quim. Atg., 55, 21-40. 83. Triaca, W.E. Solomons, C., and Bockris, J.O.M. (1968). The mechanism of the electrolytic evolution and dissolution of chlorine on graphite. Electrochim. Acta, 13, 1949-64. 84. Arvia, A.J. and Triaca, W.E. (1965). Anodic reactions of molten nitrates on graphite. Electrochim. Acta, 10, 1188-9. 85. Arvia, A.J. and Triaca, W.E. (1966). Electrolysis of molten nitrates on graphite electrodes: kinetics of the anodic reaction. Electrochim. Acta, 11, 975-88. 86. Arvia, A.J. and Calandra, A.J. (1967). Kinetics of the discharge of nitrite ions in the electrolysis of molten nitrites on graphite electrodes. Electrochim. Acta, 12, 1441-55. 87. Sustersic, M.G. Triaca, W.E., and Arvia, A.J. (1974). Potentiodynamic behaviour of graphite and platinum electrodes in sodium nitrite-potassium nitrite melts. Electrochim. Acta, 19, 19-25. 88. Balskus, E.J., Podesta, J.J., and Arvia, A.J. (1970). Kinetics of electrochemical hydrogen evolution and dissolution on graphite in molten KHS0 4 . Electrochim. Acta, 15, 1557-8. 89. Balskus, E.J., Podesta, J.J., and Arvia, A.J. (1971). Hydrogen evolution and dissolution on graphite electrodes in the electrolysis of molten KHSO 4' I. Kinetics of the reactions on dense graphite. Electrochim. Acta, 16, 1663-70. 90. Balskus, EJ., Triaca, W.E., and Arvia, AJ. (1972). Hydrogen evolution and dissolution on graphite electrodes in molten potassium bisulphate. II. Kinetics and mechanism of the reactions on porous graphite. Electrochim. Acta, 17, 45-62. 91. Arvia, A.J., Triaca, W.E., and Videla, A.H. (1970). Kinetics and mechanism of the electrochemical oxidation of graphite in bisulphate melts. Electrochim. Acta, 15,9-24. 92. Kordesch, K., Jahangir, S., and Schautz, M. (1982). Carbon electrodes manufacturing techniques. Proceedings of the Workshop on the Electrochemistry of Carbons, Vol. 84-5. Pennington: The Electrochemical Society, p. 387. 93. Bockris, J.O'M. and Srinivasan, S. (1969). Fuel Cells: Their Electrochemistry. McGraw-Hill.

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94. Schneider, J., Wambach, C., Pennemann, B., and Wandelt, K. (1999). Scanning tunneling microscopy and scanning tunneling spectroscopy studies of powdery palladium/graphite model catalysts. Langmuir, 15, 5765-72. 95. Pozzio, A., Silva, R.F., De Francesco, M., et al. (2002). A novel route to prepare stable PtRu/C electrocatalysts for polymer electrolyte fuel cell. Electrochim. Acta, 48,255-62. 96. Steigerwalt, E.S., Deluga, G.A., Cliffel, D.E., and Lukehart, C.M. (2001). A Pt-Ru/graphitic carbon nanofiber nanocomposite exhibiting high relative performance as a direct-methanol fuel cell anode catalyst. J. Phys. Chem. B, 105, 8097-101. 97. Adora, S., Soldo-Olivier, Y., Faure, R., et al. (2001). Electrochemical preparation of platinum nanocrystallites on activated carbon studied by X-ray absorption spectroscopy. J. Phys. Chem. B, 105, 10489-95.

SELF-AsSEMBLED MONOLAYERS ON (0001) Fernando Teran Arce,* Jose L. Zubimendi, Maria E. Vela, Roberto C. Salvarezza, and Alejandro J. Arvia Instituto de Investigaciones Fisicoqufmicas Te6ricas y Ap/icadas. (lNIFTA), Universidad Nacional de La Plata-Consejo Nacional de Investigaciones Cientfficas y Tecnicas, La Plata, Argentina *Present address: Center for Nanomedicine, Department of Medicine, University of Chicago, Chicago, IL, USA

Contents Introduction Characteristic of the HOPG Substrate 20.3 Self-Assembled Submonolayers and Monolayers Acknowledgments References 20.1

51 3

20.2

51 4 521 52 7 52 7

20.1 INTRODUCTION Scanning nanoscopies have led to a new stage in the study of interfacial processes. Data derived from these techniques, especially scanning tunneling microscopy (STM) and atomic force microscopy (AFM), offer the possibility of studying the physical chemistry of surfaces on solid substrates at the atomic and molecular level [1-5]. Heterogeneous catalysis is an important field for the application of these techniques. Because of the use of these nanoscopies, advances have been made in the knowledge of the geometry and effective area of solid catalysts, the sintering process that decreases their performance and lifetime, the adsorbate film structure on crystallographically well-defined surfaces, and the influence of surface defects on the dynamic behavior of these films during adsorption, desorption, and chemical reaction stages. Adsorption by Carbons ISBN: 978-0-08-044464-2

© 2008 Elsevier Ltd. All rights reserved.

513

Chapter 20 Self-Assembled Monolayers on C(OOOl)

Nanometer-scale (nm) nanoscopies provide information on restricted molecular domains that comprise some hundreds of molecules. This information at the local level is not accessible by other surface analysis techniques because the latter provide average data on the whole sample. Studies at the local level reveal the complexity of physicochemical processes taking place at solid/fluid interfaces under different perturbation conditions. Local data are a solid basis for the theoretical interpretation of these processes by the use of Quantum Mechanics procedures. Nanoscopies supplemented with conventional techniques will allow the rational handling of the catalyst/reactive system based on its knowledge at the atomic/molecular level. The application of nanoscopies in surface chemistry offers the possibility for determining the nanostructure of solid surfaces, surface reconstruction phenomena, to identify the structure of ionic and molecular adlayers, to study the dynamics of these adlayers in their adsorption and desorption at the submonolayer and monolayer (ML) level. Likewise, they are important tools to follow reactions at solid surfaces in real time in different environments. The reader can get acquainted with the state of the art on these topics in Refs [5-12]. This chapter describes the application of tunneling and AFM to the study of inorganic and organic adsorbates on C(OOOl) at the submonolayer and ML level. The C(OOOl) surface can be taken as a model system for the study of adsorption processes because it is atomically smooth and exhibits a low chemical reactivity, allowing an easy handling in the atmosphere. The knowledge of adsorption on carbon is important in the field of electrocatalysis because carbon is widely used as a matrix for the dispersion of catalytically active metallic clusters.

20.2 CHARACTERISTIC OF THE 20.2.1

HOPG

SUBSTRATE

General Considerations

Highly oriented pyrolytic graphite (HOPG) is the most adequate type of carbon to investigate the adsorption of both molecules and atoms, and the formation of molecular and atom clusters on the C(OOOl), the basal plane of graphite [1-5],[9-12] The procedure for HOPG fabrication was developed by Union Carbide in USA. HOPG is prepared from the thermal decomposition of gaseous hydrocarbons on a surface heated at 1200-3800°C followed by highpressure compression of the surface under heating [13]. HOPG's first use was as an X-ray diffraction grating. Later, with the advent of nanoscopies it became of particular interest as a carbon material with flat terraces constituted by the basal plane that could be resolved at the atomic scale. Accordingly, HOPG was utilized as a calibration standard for STM, and as a substrate for adsorption studies. Besides, the ease with which HOPG can have a

20.2

Characteristic of the HOPG Substrate

pristine basal plane surface just by exfoliation with scotch tape and its chemical inertia make HOPG a very important substrate to be utilized in STM and AFM. HOPG consists of ordered layers (graphene sheets) of carbon atoms constituting a honeycomb lattice. The arrangement of graphene sheets is of the type A.B.A.B (Fig. 20.1 (a)), the nearest neighbor graphene sheets are shifted horizontally by one interatomic distance [14]. The separation distance of nearest neighbor graphene sheets is 0.355 nm, and the lattice constant in the vertical direction is 0.67 nm. Correspondingly, for alternatively located graphene sheets, three carbon atoms out of the six atoms forming each hexagon of the 2D lattice lie on the same vertical, whereas the remaining three carbon atoms lie on the vertical containing the center of hexagons (Fig. 20.1 (b)). For each graphene sheet the atomic lattice consists ofsix carbon atoms forming an open honeycomb type hexagon with 0.142 nm between nearest neighbor atoms. The Bravais lattice, however, corresponds to a hexagonal lattice centered with two carbon atoms for each unit cell, and 0.246 nm separation between neighbor Bravais point so that 0.246/0.142 = J3. The interaction between graphene layers is determined by van der Waals weak forces, making exfoliation of HOPG easy. Graphite is thermodynamically stable under usual conditions, but its structure is typically anisotropic as it is reflected, for instance, by the Young's modulus that is 10.3 x 10- 5 MPa along the basal plane and 0.3 x 10- 5 MPa in the direction perpendicular to the basal plane. A similar effect occurs with the capacitance of the HOPG/aqueous electrolyte interface, the potential of zero charge, and the work function values (see Chapter 21).

1,42A!

(a)

(b)

Figure 20.1 (a) Scheme of the 3D higWy oriented pyrolytic graphite (HOPG) atomic layer. Note the lateral displacement of atomic layers. (b) Little circles form the honeycomb lattice. Big circles correspond to the Bravais cell. The unit cell is drawn (shadow) at the upper right part of the figure. The corrugation between two carbon atoms located within the ellipse is the region sensed by the tip in the contact mode atomic force microscopy (AFM).

Chapter 20 Self-Assembled Monolayers on C(OOOl)

51 6

The four valence electrons of carbon are involved in three IT bonds and one 'IT bond with its neighbors in plane. The electrical conductivity of graphite is due to 'IT bonded electrons. In contrast to insulator diamond, the electrical resistance of graphite along the basal plane direction is 4.1 x 10- 5 n cm, a figure of the same order of magnitude as that of metals such as platinum and palladium. According to the band theory, graphite is considered as a semimetal, the overlapping of the conduction and valence bands is about 0.04 eVe The electronic structure of graphite accounts for its hydrophobicity [15]. 20.2.2

Nanoscopy Characterization of HOPG

20.2.2.1

The hexagonal lattice

AFM images (10 x 10 f-Lm 2 ) of a fresh HOPG surface (Fig. 20.2) show a number of features, namely, large monoatomic terraces about 100 nm wide and several micrometer long. Terraces are separated by steps of either one atom or a few atoms in height. Some triangular-shaped terraces with angles that are multiples of 30° are consistent with the hexagonal lattice (Fig. 20.3(a)). Besides, STM images also show some features that are artifacts from the exfoliation technique (Fig. 20. 3(b)). These artifacts have been classified as steps, strings, fibers [16] either single or agglomerated, small pieces of graphite, and very tiny particles. A detailed analysis of these additional features is required to avoid a wrong interpretation of the structure of adsorbate patterns on HOPG. When terraces are imaged at high resolution (Fig. 20.4(a)), i.e., below 10 x 10 nm2 , the STM image ofC(0001) depicts a hexagonal lattice with nearest neighbor distance d = 0.246 nm. The corrugation of this type of image depends

10.0

7.5

5.0

·2.5

o

o 2.5

5.0

7.5

10.0 Jlrn

Figure 20.2 Ex situ atomic force microscopy (AFM) image of the basal plane of highly oriented pyrolytic graphite (HOPG). Wide terraces separated by steps can be seen.

20.2

Characteristic of the HOPG Substrate

(a)

(b)

Figure 20.3 (a) Ex situ 3.8x3.8 f.1m 2 atomic force microscopy (AFM) image of highly oriented pyrolytic graphite (HOPG) that shows steps of different heights. (b) A 4.15 x 4.15 f.1m 2 AFM image of HOPG where strings produced by the exfoliation technique are shown.

(a)

(b)

Figure 20.4 (a) Ex situ 3 x 3 nm2 scanning tunneling microscopy (STM) image usually found in highly oriented pyrolytic graphite (HOPG). (b) Honeycomb structure observed by STM (1x1 nm2 ).

518

Chapter 20 Self-Assembled Monolayers on C(OOOl)

on the tunneling current (It) and the voltage (~) applied between the STM tip and the sample surface. Thus, corrugation of about 0.1 nm results for It ~ 1 nA and ~ ~ 0.05 V, whereas the corrugation decreases to 0.02 nm for ~ ~ 1 V. The change in voltage polarity has practically no effect on the HOPG image. Occasionally, the typical honeycomb structure of graphite can be observed by STM (Fig. 20.4(b)). As discussed below, the origin of this type of images is controversial. They have been considered as "high-resolution images" that are obtained when the STM tip is extremely sharp or as an "artifact" arising from a multiple tip [17]. The lattice shown in Fig. 20.1(b), which is usually imaged by STM or AFM, is formed by only three instead of six carbon atoms. The corresponding nearest neighbor carbon-carbon atom distance is that of the Bravais hexagonal lattice referred to above. The scheme depicted in Fig. 20.1 (a, b) accounts for the appearance of this image.

20.2.2.2

Additional features

Step corrugations of about 10-20 nm are easily observed with thin graphite samples that have been exfoliated several times. However, the Bravais lattice can be observed by small-size imaging (~10 x 10 nm2 ) , and at slightly higher magnifications (50 x 50 nm2 ) superstructures of different periodicity are occasionally observed. These superstructures of HOPG (Fig. 20.5.) make it difficult to recognize unambiguously the structure of molecular adsorbates.

Figure 20.5 Ex situ 46 x 46 nm2 atomic force microscopy (AFM) image of higWy oriented pyrolytic graphite (HOPG) showing a lattice that is not correspondent with the lattice shown in Fig. 20.1.

20.2

Characteristic of the HOPG Substrate

Strings are thin graphite stripes that are removed by exfoliation from steps and attached to another step [16]. The three threads shown in Fig. 20.3(b) that covered the entire image are 66 nm large and about 2.8 nm wide. Fibers are observed by STM as thin tubes about 2.5 nm in diameter and 20 nm long formed by agglomeration of threads. Atomic resolution at fibers can also be obtained, although with a poor definition. They are produced by step rupture by exfoliation. Island-like pieces, most of them at the border of holes, are also sometimes produced by exfoliation (Fig. 20.6). The islands depicted in this figure are about 0.3 nm high, a figure that is similar to the depth of holes. Different superlattices with x periodicity have been imaged. This periodicity has been related to rotation of graphite lattice [17]. These superlattices can be produced by either a multiple tip effect [17b] or electronic perturbations caused by adsorbed molecules [17c]. A hexagonal superlattice with a 4.4nm periodicity, rotated 30° with respect to the HOPG lattice, and 0.38 nm corrugation has also been reported [17a]. This superlattice was also attributed to rotation of the surface layer of graphite. As this type of superstructures is most frequently observed for thin layers of material, they have been associated with charge density waves [14, 18]. Occasionally, a sort of lattice of holes is also imaged. The structure of this lattice can be interpreted as an atomic honeycomb lattice in which each hole in the image would represent the hole of a hexagon in the honeycomb lattice. According to theoretical calculations, graphite STM images with atomic

-J3 -J3

2.00

1.00

o

o 1.00

2.00

flm Figure 20.6 Ex situ atomic force microscopy (AFM) image that shows island-like pieces produced on higWy oriented pyrolytic graphite (HOPG) by step rupture from the exfoliation procedure.

Chapter

52 0

20

Self-Assembled Monolayers on C(OOOl)

resolution should be dominated by independent Fourier components [19] of three carbon atoms usually imaged. The multiple tip effect would produce a relative change in the amplitude and phase of other components, this fact being reflected in the change of the maximum amplitude observed by STM. A poor instrument resolution might produce a comparable effect [20]. The same features from atomic resolution AFM images of graphite (Fig. 20.7(a, b)) can be distinguished. Two models have been proposed to explain the AFM images of graphite [21]. In one of these models the calculations are based on the scanning of the graphite surface with a single potassium atom. For applied forces of the order ofl nN, i.e., a value lower than about 50 nN used in the contact mode AFM, the corrugation between two carbon atoms located within the ellipse (Fig. 20.1(b)) would be indistinguishable by the AFM cantilever tip. But the situation would be reversed when the tip goes through two ellipses via the hexagon centers. Another possibility considers the asymmetry of carbon sites in the graphite lattice (Fig. 20.1 (a)). Thus, the carbon atom located in the upper graphene, which is directly above the carbon atom in the lower graphene, would suffer a weaker interaction with the tip than that facing the centers of the hexagon. This explanation would be similar to that admitted for the interpretation of the corresponding STM images. Therefore, it can be concluded that STM imaging on HOPG is influenced by structural defects, adsorbates and electronic effects [22]. The latter would prevail at step sites where an asymmetric distribution of electric charges would be more favorable.

o (a)

6.00nmO (b)

2.93nm

Figure 20_7 Ex situ atomic force microscopy (AFM) images of higWy oriented pyrolytic graphite (HOPG). The distance is 0.246 nm.

20.3

Self-Assembled Submonolayers and Monolayers

521

20.3 SELF-AsSEMBLED SUBMONOLAYERS AND MONOLAYERS

One important aspect of heterogeneous chemical reactions at solid surfaces is related to the presence of adsorbed species that play a key role in determining the rate and efficiency of these processes. Therefore, the knowledge of molecular arrangements on solid catalysts of reactants, reaction intermediates, or products is of outstanding importance in dealing with fundamental aspects of heterogeneous catalysis. Self-assembled molecular arrangements on HOPG can be spontaneously produced by different procedures that are based on the type of interactions between either bare HOPG regions or functional oxygen-containing groups existing at the HOPG surface (see Chapter 21). These arrangements, covering from the submonolayer to the multilayer level, are dominated by either physical or chemical adsorption. The adsorption of an atom on a molecule at a solid surface is attributed to a physisorption phenomenon principally because of van der Waals forces. In physisorption no appreciable reordering in the adsorbate electronic distribution occurs. This situation is generally found in the adsorption of noble gases on metal surfaces, in which adsorption energy values in the range 1-10 k] I mol are involved. These figures are of the same order of magnitude as that of the thermal energy (k7) ofmolecules at T = 298 K (approximately 2.5 k]lmol). Accordingly, to observe physisorbed systems by atomic resolution STM or AFM, experiments have to be performed at a very low temperature and above 1 atm pressure [23]. The formation of supramolecular layers (see Chapter 21) is another way of producing adequate architectural molecular designs on HOPG and carbons in general, although the structural analysis of these layers by nanoscopic techniques is still a complicated matter. A few typical examples of adsorbates on C(OOOl) are described in the following sections. 20.3.1 Alkane Adsorption on ((0001)

In principle, the adsorption of alkane molecules on C(OOOl) would appear unlikely because of the inert character of the substrate. In this case, however, besides van der Waals forces, other contributions come into play and can make energy adsorption reach values of up to 100 kJ/mol, which are comparable to those of chemisorption processes. This enables determining the structure of aliphatic hydrocarbons adsorbed on C(OOOl) by AFM or STM because the adsorbate withstands tip-sample interaction forces. The adsorption energy of alkanes on C(OOOl) decreases with temperature and increases with the chain length [24] due to an increase in the affinity of alkane carbon atoms with C(OOOl) atoms. This involves the adsorption of aliphatic molecules ordered with the chain axis lying parallel to the C(OOOl) plane. Under these conditions, the interaction of the adsorbed molecule increases because of

522

Chapter

20

Self-Assembled Monolayers on C(OOOl)

the geometric matching of the carbon lattice of the C(OOOl) plane with that of the zigzag aliphatic chain, each CH2 occupying the hexagon area in the graphite lattice. With this configuration the adsorption energies are 21.6 k]/mol for n-hexane and 105.6 kJ/mol for n-hexadecane.

20.3.2

Sulfur Atom Submonolayers on HOPG

Sulfur electroadsorbs on HOPG from SH- -containing neutral buffered aqueous solution (pH 8) at potentials (E) close to -0.8 V (versus NHE) , i.e., at values ofE more negative than the reversible potential (Er ) for the SH- = S + H+ + ereaction. The surface coverage by sulfur atoms, estimated from the electroadsorption/electrodesorption charge, is close to 1/2. Different structures of sulfur atom submonolayers on HOPG have been observed by STM [25a, b]. One of these structures corresponds to sulfur trimers with d = 0.24 nm and S atoms atop C atoms (Fig. 20.8(a)). Conversely, for E > E r , other submonolayer structures are formed, namely, a J3J3 R30° structure with d = 0.42 nm, a sulfur atom honeycomb lattice with d = 0.24 nm, rectangular arrays of sulfur atoms with d = 0.21 nm (Fig. 20.8(b)). The influence of the HOPG surface on sulfur atom electroadsorption is reflected in the values of d = 0.42 nm and d = 0.24 nm, whereas the S-S distance, d = 0.21 nm, which is observed for E > E r , is close to that found for polysulfide species [26]. A similar behavior has been observed for sulfur atom electroadsorption on Au(lll) surfaces [26]. Adsorption energy values for S atom adsorption on HOPG in the range 30-40 kJ/mol have been evaluated theoretically [25b].

20.3.3

Alkanethiol Adsorption on ((0001)

The contrast of organic molecules adsorbed on C(OOOl) in STM images depends on the functional group at the molecule head [27]. Contrast is generally enhanced for functional groups than for aliphatic chains. For functional groups it decreases in the order SH> I>Br> NH 2. This sequence offers the possibility to discriminate the functional group from the rest of the molecule by STM. It should be noted that for OH and chloride groups, contrast is comparable to that of the remaining aliphatic chain, which turns their distinction by STM practically impossible. The structures of the CH3(CH2)22SH adlayers on C(OOOl) [28] are similar to those of the alkanes. They consist of molecular domains lying parallel to each other forming a 90° angle with respect to the chain direction. A kind of disorder is also observed in the vicinity of neighbor SH groups. Ex situ AFM images of a 1-dodecanethiol ML on C(OOOl) (Fig. 20.9(a)) exhibit an array of parallel-oriented bright rows [29]. At a higher resolution (Fig. 20.9(b)) pale bands between rows, corresponding to aliphatic chains, and bright circles along each row, attributed to S heads, can be seen. Similar images

20.3

Self-Assembled Submonolayers and Monolayers

523

(b)

Figure 20.8 Ex situ atomic resolution scanning tunneling microscopy (STM) images of sulfur atoms adsorbed on higWy oriented pyrolytic graphite (HOPG): (a) 3 x3 nm 2 ; (b) 6.32x6.32 nm2 •

are obtained by STM (Fig. 20.10) although, in this case, pale bands cannot be seen. Bands 1.2 nm in length become somewhat shorter than that of the extended chain molecule. The interband separation, which would be related to the intermolecular separation, is 0.65 nm. The angle between a row of S heads and the chain direction is 120 The S heads along a row are generally placed behind the chain of the neighbor row. 0

•

Chapter 20 Self-Assembled Monolayers on C(0001)

52 4

o

16.1 nmO

8.00 nm

(b)

(a)

Figure 20.9 Atomic force microscopy (AFM) images of l-dodecanethiol monolayer adsorbed on C(OOOl). (a) Bright spots are attributable to sulfur heads. Image (a) exhibits an array of parallel-oriented bright rows. At a higher resolution (b) pale bands between rows corresponding to aliphatic chains and bright circles along each row attributed to sulfur heads can be seen.

o (a)

40.2nm 0

20.1 nm

(b)

Figure 20.10 Scanning tunneling microscopy (STM) images of l-dodecanethiol monolayer adsorbed on C(OOOl). (a) and (b) Sulfur heads exhibit an array of parallel-oriented bright rows, At a higher resolution only the higWy oriented pyrolytic graphite (HOPG) lattice can be observed (not shown).

20.3

Self-Assembled Submonolayers and Monolayers

o (a)

7.29nm

16.1 nmO (b)

Figure

20.11 Molecular resolution atomic force microscopy (AFM) images of a l-butanethiol monolayer on higWy oriented pyrolytic graphite (HOPG). Distance between bright lines are compatible with the length of adsorbed molecules.

Ex situ AFM images of 1-butanethiol on C(OOOl) (Fig. 20.11) exhibit a structure similar to that described above. In the lower left part of the image depicted in Fig. 20.11 some bright spots along the rows, probably related to S heads, and a few pale bands, associated with aliphatic chains, can also be observed. The intermolecular separation distance between two bright spots is 0.45 nm. The 0.55-nm-Iong band is consistent with the aliphatic chain length (Fig. 20.11). As observed for 1-dodecanethiol, the angle between the chains and the direction of a bright row of S heads is 115 Alkanethiols with short- and medium-length aliphatic chains adsorbed on C(OOOl) display heads with the molecular axis lying parallel to the basal plane of the substrate. This conclusion that was drawn from the analysis of AFM images is consistent with the interrow separation ofS heads deduced from STM images, and agrees with previous results for alkanethiol with 22 carbon atoms [27, 28]. However, aliphatic chains of intermediate length seem to be extended on the substrate surface only a fraction of their length. As in the case of Au(lll), for alkanethiols adsorbed on C (000 1) the longer the adsorbate aliphatic chains the more ordered they are [30]. The fact that in some regions in the images (Figs 20.9 and 20.10) the length of 1-dodecanethiol does not match exactly that of the molecule fully extended on the surface is attributed to the occurrence of a mixed cis-trans configuration (gauche conformation). The scheme of this configuration (Fig. 20.12) includes C atoms located at the same sites as those of the C(OOOl) lattice, and the change in configuration is shown by an ellipse (see Fig. 20.12). The S atom separation between two aliphatic chains in a row is 1.25 nm, a figure that agrees with that determined from the images. The S atom separation between two molecules 0

•

526

Chapter

20

Self-Assembled Monolayers on C(OOOl)

120

a

~

W

Figure 20.12 Scheme ofthe l-dodecanethiol structure adsorbed on highly oriented pyrolytic graphite (HOPG). The axis of the hydrocarbon chain is oriented parallel to the surface, although partially extended.

located at neighbor rows is 0.75 nm, and the angle formed between the molecule axis and the direction of S heads is 120 These figures agree reasonably well with measured values. The adsorption energy of alkanethiols on C(OOOl) can be estimated considering the energy of lateral interactions between the aliphatic chains, which is of the order of 4 kJ/mol for CH 2 , and the intermolecular interaction energy in liquid alkanes, which for hexadecane is 57 kJ/mol. The energy difference for the interaction between the chains of the hexadecanethiol ML on Au(lll) and in liquid alkane is 17 kJ/mol. From the calculation of the adsorption energy of S on C(OOOl) [31], it was concluded that the vertices of graphite hexagons (small circles in Fig. 20.1) or sites located between two hexagons (large circles in Fig. 20.1) are the most favorable adsorption sites, as shown by 1-butanethiol adsorption on C(OOOl). Predictions, however, become more uncertain because in these cases the tendency of C atoms to follow the C(OOOl) lattice prevails. On the basis of the adsorption energies of n-hexadecane (100 kJ I mol), n-hexane (22 kJ/mol) , and S on C(OOOl), the adsorption energy for dodecanethiol obtained from extrapolation is 70 kJ/mol. This value exceeds that ofthe adsorption energy of S on C(OOOl) and confirms the stability of the adsorbate on C(OOOl). The ordering of adlayers of alkanethiols on C(OOOl) indicates that the head-neighbor molecule chain interactions and, to a lesser extent, that of the head-head of molecular pairs prevail. Results from the adsorption of alkanethiols on C(OOOl) as well as on Au(lll) [32] show a strong influence of the substrate on the configuration of adsorbed molecules, regardless of the length of the aliphatic chain. 0

•

References

527

ACKNOWLEDGMENTS The authors thank the Consejo Nacional de Investigaciones Cientificas y Tecnicas (CONICET) and Agencia Nacional de Promoci6n Cientifica y Tecno16gica from Argentina for their financial support (PIP 0897, PICT 99-5030, and PICT 98 N°06-03251) to the research projects on which this chapter is based. MEV is a member of the research career of CIC.

REFERENCES 1. Binnig, G. and Rohrer, H. (1982). Surface studies by scannIng tunneling microscopy. Helv. Phys. Acta, 55, 726. 2. Rohrer, H. (1989). Scanning tunneling microscopy and related methods. NATO ASI Series, Series E, Applied Sciences, No. 184, Kluwer, p. 1. 3. Forbes, R.G. (1989). Scanning tunneling microscopy and related methods. NATO ASI E Series, No. 184, Kluwer, p. 163. 4. TersoH: J. and Hamann, D.R. (1983). Theory and application for scanning tunneling microscope. Phys. Rev. Lett., 50; Tersoff J. (1989). Scanning tunneling microscopy and related methods. NATO ASI E Series, No. 184, Kluwer, p. 77. 5. Leavens, C.R. and Aers, G.C. (1989). Scanning tunneling microscopy and related methods. NATO ASI E Series, No. 184, Kluwer, p. 27. 6. Siegenthaler, H. (1992). Scanning Tunnelling Microscopy II (R. Wiesendangerand and HJ. Guntherodt, eds) . Springer-Verlag. 7. Gewirth, A.A. and Siegenthaler, H. (1995). Nanoscale probes of the solid/liquid interface. NATO ASI Series, Applied Sciences, No. 288, Kluwer. 8. Lorenz, H.J. and Plieth, W. (1998). Electrochemical nanotechnology. In situ Local Probe Techniques at Electrochemical Interfaces. Wiley-VCH. 9. Itaya, K. (1998). In situ scanning tunneling microscopy in electrolyte solutions. Progr. Surf. Sci., 58, 121-47. 10. Capella, B. and Dieder, G. (1999). Force-distance curves by atomic force microscopy. Surf. Sci. Rep., 34, 1-3. 11. Binns, G., Baker, S.H., Demangeat, C., and Parlebas,J.C. (1999). Growth, electronic, magnetic and spectroscopic properties of transition metals on graphite. Surf. Sci. Rep., 34, 107-70. 12. Binnig, G., Quate, C.F., and Gerber, C. (1986). Atomic force microscope.Phys. Rev. Lett.,56, 930-3. 13. Mc.Creery, R.L. (1994). Carbon electrodes: structural effects on electron transfer kinetics, electroanalytical chemistry, Vol. 17 (A.J. Bard, ed.). Marcel Decker, p. 221. 14. Wiesendanger, R. and Anselmetti, D. (1994). Scanning Tunneling Microscopy 1. (HJ. Giintherodt and R. Wiesendanger, eds). Springer-Verlag. 15. Adamson, A.W. (1990). Physical Chemistry of Surfaces. Wiley-Interscience. 16. Chang, H. and Bard, AJ. (1991). Observation and characterization by scanning tunneling microscopy of structures generated by cleaving highly oriented pyrolytic graphite. Langmuir, 7, 1143-53.

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Chapter 20 Self-Assembled Monolayers on C(OOOl)

17. (a) Liu, C.-Y., Chang, H., and Bard, AJ. (1991). A large scale hexagonal domainlike structures superimposed on the atomic corrugation of a graphite surface observed by scanning tunneling microscopy. Langmuir, 7, 1138-42; (b) Albrecht, T.R., Mizes, H.A., Nogami, J., et al. (1988). Observation of tilt boundaries in graphite by scanning tunneling microscopy and associated multiple tip effects. Appl. Phys. Lett. ,52, 362-4; (c) Mizes, H.A. and Foster, J.S. (1989). Long-range electronic perturbations caused by defects using scanning tunneling microscopy. Science, 244, 559-62. 18. Coleman, R.V., Dai, Z., McNairy, W.W., et al. (1993). Methods of experimental physics. In Scanning Tunneling Microscopy. Vol. 27 G.A. Stroscio and WJ. Kaiser, eds). Academic Press. 19. Mizes, H.A., Park, S., and Harrison, W.A. (1987). Multiple-tip interpretation of anomalous scanning-tunneling-microscopy images of layered materials. Phys. Rev. B, 36, 4491-4. 20. Binnig, G., Fuchs, H., Gerber, Ch., et al. (1986). Energy-dependent state-density corrugation of a graphite surface as seen by scanning tunneling microscopy. Europhys. Lett., 1, 31-6. 21. Lin, F. and Meier, D J. (1994). Atomic-scale resolution in atomic force microscopy. Langmuir, 10, 1660-2. 22. McDermott, M.T. and McCreery, R.L. (1994). Scanning tunneling microscopy of ordered graphite and glassy carbon surfaces: electronic control of quinone adsorption. Langmuir, 10, 4307-14. 23. Somorjai, A.G. (1981). Chemistry in Two Dimensions: Surfaces. Ithaca: Cornell University Press, p. 178. 24. Findengg, G.H. (1972). Ordered layers of aliphatic alcohols and carboxylic acids at the pure liquid/graphite interface. J. Chem. Soc. Faraday Trans., 68, 1799-806; Ikai, A. (1996). STM and AFM of bioiorganic molecules and structures. Surf. Science Rep., 26, 261-332; Giancarlo, L.C. and Flynn, G.W. (1998). Scanning tunneling and atomic force microscopy probes of self-assembled, physisorbed monolayers: peeking at the peaks. Annu. Rev. Phys. Chem., 49, 297-336; Xie, Z.X., Xu, X., Mao, B.W., and Tanaka, K. (2002). Self-assembled binary monolayers of n-alkanes on reconstructed Au(111) and HOPG surfaces. Langmuir, 18, 3113-16. 25. (a) Zubimendi, J.L., Salvarezza, R.C, Vazquez, L., and Arvia, AJ. (1996). Scanning tunneling microscopy observation of sulfur electrodeposits on graphite single crystals. Langmuir, 12, 2-11; (b) Vicente, J.L. Mola, E.E., Appignanessi, G., et al. (1996). A quantum chemistry approach to possible sulfur adsorbate structures on the basal plane of graphite clusters. Langmuir, 12, 19-22. 26. Vericat, C., Andreasen, G., Vela, M.E., and Salvarezza, R.C. (2000). Dynamics of potential-dependent transformations in sulfur adlayers on Au(111) electrodes.]. Phys. Chem. B, 104, 302-7; Andreasen, G., Vericat, C., Vela, M.E., and Salvarezza, R. C. (1999) . Dynamics of sulfur adlayer transformations at metal/electrolyte interfaces.]. Chem. Phys., 111, 9457-60. 27. Venkataraman, B., Flynn, G.W., Wilbur, J.L., et al. (1995). Differentiating functional groups with the scanning tunneling microscope.]. Phys. Chem., 99, 8684-9. 28. Cyr, D.M., Venkataraman, B., Flynn, G.W., et al. (1996). Functional group identification in scanning tunneling microscopy of molecular adsorbates. J. Phys. Chem., 100, 13747-59.

References

29. Teran Arce, F., Vela, M.E., Salvarezza, R.C., and Arvia, A.J. (1996). Comparative study ofthiol films on C(OOOl) and Au(lll) surfaces by scanning probe microscopy. Surf. Rev. Lett., 4, 637-49. 30. Porter, M.D., Bright, T.B., Allara, D.L., and Chidsey, C.E.D. (1987). Spontaneously organized molecular assemblies. 4. Structural characterization of n-alkyl thiol monolayers on gold by optical ellipsometry, infrared spectroscopy, and electrochemistry. J. Am. Chem. Soc., 109, 3559-68. 31. Stranick, S.J., Parikh, A.N., Allara, D.L., and Weiss, P.S. (1994). A new mechanism for surface diffusion: motion of a substrate-adsorbate complex. J. Phys. Chem., 98, 11136-42. 32. Ulman, A. (1991). An Introduction to Ultrathin Organic Films:ftom Langmuir-Blodgett to Self-Assembly. Academic Press; Finklea H.G. (2000). Encyclopedia ofAnalytical Chemistry: Applications, Theory and Instrumentation (R.A. Meyers, ed.). Wiley; Schreiber, F. (2000). Structure and growth of self-assembling monolayers. Prog. Surf. Sci., 65. 151-257.

REMOVAL OF INORGANIC GASES AND VOCS ON ACTIVATED CARBONS Teresa

J. Bandosz

Department of Chemistry, City College

of New York,

New York, NY, USA

Contents Introduction 21.2 Adsorption of Inorganic Gases 21.3 Adsorption of Volatile Organic Compounds 21.4 Choice of Proper Carbon for a Desired Application References 21.1

533

534 549

553 556

21.1 INTRODUCTION Industrial revolution, along with development of new technologies to

improve everyday life, resulted in emission to the atmosphere vast quantities of athropogenic gases and toxic and cancerogenic volatile organic compounds (VOCs). Some of those species, as hydrogen sulfide or sulfur dioxide, have also their natural sources such as geothermal vents, volcanoes or other natural technologies where anaerobic digestion is the main bacterial activity. But it was a human addition to mother nature, which has resulted in detrimental environmental changes such as acid rains, photochemical smog, or global warming [1,2]. It is estimated that every year around 100 millions tons of 50 2 and N0 2 are emitted to the atmosphere from anthropogenic sources [1], mainly from power plants where fossil fuel is burned. The major sources of air pollution were, and still are, highly industrialized countries such as the United States or European nations. The situation changed in early 1990s when Clean Air Act of US government was introduced [2, 3]. The new regulations caused that in 2000 emissions ofacidic Adsorption by Carbons ISBN: 978-0-08-044464-2

© 2008 Elsevier Ltd.

All rights reserved.

533

Chapter

534

21

Removal of Inorganic Gases and VOCs on Activated Carbons

gases in the United States were 48 % lower than 1980 levels [3]. To complain with Clean Air Act, the new technologies engaged in desulfurization of fuel, cleaning the stock gases, or improving the efficiency of combustion have been developed and introduced. This resulted in a dramatic decrease in acidic gas emissions and significant improvements of the air quality. Nevertheless, the air quality is still controlled and the levels of pollutants such as sulfur dioxide, hydrogen sulfide, nitric dioxide, or VOCs are kept below certain thresholds considered as healthy for environment and human beings. Moreover, the stricter regulations are about to be introduced, which, for instance will require to limit the levels ofsulfur-containing species in gasoline and fuel oils to 30 and 15 ppm, respectively [4]. To follow the environmental law and to remove small but sometimes persistent concentrations of pollutants activated carbons seem to be the media of choice. They are relatively inexpensive, easily to obtain, and owing to their enormously high surface area and pore volume, they are able to remove and retain even traces of air and water pollutants. Activated carbons, due to their unique surface chemistry act not only as adsorbents but also as catalysts for oxidation of inorganic and organic species. Moreover, their surface can be modified and tailored toward desired applications. This chapter provides a comprehensive summary of surface science involved in the application of activated carbon for air cleaning from inorganic gases such as hydrogen sulfide, sulfur dioxide, nitric dioxide, hydrogen cyanide, and from VOCs. The emphasis is placed on the role of activated carbons surfaces, either unmodified or modified in the processes of adsorption and catalytic oxidationreduction of these pollutants.

21.2 ADSORPTION OF INORGANIC GASES 21.2.1

Removal of Hydrogen Sulfide

One of the leading malodorants arising from sewage treatment facilities and geothermal vents is hydrogen sulfide [5]. HzS emitted to the atmosphere is oxidized to sulfur dioxide, which results in the deposition of acid rain. Traditionally, activated carbons used for removal of high concentrations of HzS in sewage treatment plants are those impregnated with caustic materials such as NaOH or KOH [5-9]. Air currents around odor-generating facilities are initially washed in scrubbers, during which they intake high levels of humidity, and are then blown through the activated carbon vessels [7, 8]. The residual HzS quickly reacts with the strong base and is immobilized. The presence of humidity facilitates the reaction [10-12]. The carbon bed is mostly used as a support for the caustic material and storage of the oxidation products. The removal capacity of such carbon estimated using accelerated ASTM D6646-01 test [13] exceeds 0.140 g/cm3 of carbon bed. Recent study of the adsorption/oxidation mechanism on NaOH-impregnated activated carbons showed [12] that at least

21.2

Adsorption of Inorganic Gases

535

3 moles ofH2 S are adsorbed per 1 mole ofNaOH, which indicates the catalytic effect of NaOH. NaOH shifts the dissociation of hydrogen sulfide to the right increasing the content of HS- ions, which can be further oxidized either on adsorbed sulfur or on activated carbon surface. The reaction proceeds until all NaOH is consumed in the surface reaction and deposited in the form of salts, either sulfites or carbonates, and the regeneration of basic environment does not longer occurs. The shortcoming in the applications of caustic-impregnated activated carbon is the fact that impregnation decreases the ignition temperature of the carbon and poses a hazard of self-ignition [8, 9]. Another disadvantage is the oxidation of hydrogen sulfide to elemental sulfur [8, 9, 12], which cannot be removed from carbons by washing with water [14]. Moreover, the activity of caustic carbons toward H 2 S oxidation is exhausted when the caustic is consumed and the carbon pores are blocked by sulfur and sodium or potassium salts [12]. The catalytic action of NaOH-impregnated carbon can be summarized by the following reactions [12]: NaOH+H 2S

~

NaHS+H 2O

(21.1)

2NaOH+H 2S

~

Na2S+H2O

(21.2)

NaHS+0.50 2

~

S+NaOH

(21.3)

Na2S + 0.50 2 + H 2O

~

S+2NaOH

(21.4)

HS-+H 2 O

~

H 2S+OH-

(21.5)

S2- +H2O

~

HS-+OH-

(21.6)

2NaOH + H 2SO 4

~

Na2S0 4 +2H 2O

(21.7)

Both, advantages and disadvantages of caustic-impregnated carbons directed the attention of researchers toward other impregnantes, which can sustain basic

properties with less exothermic reaction in the system. An example is potassium carbonate, which was studied in details by Przepiorski and coworkers [15, 16]. According to them, hydrogen sulfide dissolves more favorably in aqueous solution of K2C0 3 than in water. H 2S, due to its small size, is able to access the small micropores as KHS (also KHC0 3 is formed), which instantly decomposes to H 2S. That H 2S located in small pores reacts with oxygen forming elemental sulfur. Important for surface catalysis is decomposition of KHC0 3 to K2C0 3 . Since oxidation of hydrogen sulfide to sulfur either in direct reaction or via dissociation to HS- and its oxidation releases significant heat, the risk of bed self-ignition still exists. This risk of self-ignition of the carbon bed along with hazardous conditions of working with high pH carbons caused that virgin (unimpregnated) activated carbons [17-49] or carbon with specific surface modifications, such as nitrogen functionality [50-57], started to be investigated as H 2S removal media. However, considerable removal capacities for hydrogen sulfide have been reported in the literature for carbons serving at temperatures around 473 K, the use of

536

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Removal of Inorganic Gases and VOCs on Activated Carbons

unmodified activated carbon for H 2 S removal at the ambient temperatures [40-45], is not yet common. This might be related to a relatively low capacity of virgin carbon compared to caustic-impregnated one, which for the best materials, coconut-based carbons is seven times smaller than that on the impregnated counterparts. Moreover, the mechanism on unimpregnated carbons seems to be more complicated and very detailed features of carbon surfaces play a role in adsorption and catalytic oxidation. This causes that most of the results reported so far have been based on an empirical analysis of specific types of carbon, which are sometimes difficult to reproduce [17-57]. A simple mechanism of adsorption/oxidation of hydrogen sulfide was first proposed by Hedden and coworkers [31]. According to them, dissociation of hydrogen sulfide occurs in the film of adsorbed water at the virgin carbon surface and then hydrogen sulfide ions, HS-, are oxidized by oxygen radicals to elemental sulfur. Since then many studies have been done to account for such factors as a role of water [26, 32, 34, 36, 37, 40, 48, 49], role of oxygen [18-27], autocatalysis by sulfur [27, 28], influence of pore sizes [19, 29, 33, 35, 38], role of carbon surface chemistry [41-44], the effects of ash [49, 58-60], and last but not least, speciation of surface oxidation products [41-46]. As mentioned above, the film ofwater is necessary for dissociation ofhydrogen sulfide, if pH of the surface allows it, and thus for its oxidation. It is well known that hydrophobic nature [61] of activated carbon surface is the result of high degree of aromatization and the presence of graphene-like sheets. Adsorption of water can be enhanced when functional groups containing oxygen or nitrogen (hetoreoatoms with the ability of hydrogen bonding) exist at the edges of graphene-like sheets [62, 63]. When the adsorption of hydrogen sulfide was studied at dry and wet conditions a dramatic difference in the performance of the carbon adsorbents was noticed [49]. The capacity at dry conditions is usually small and it represents mainly physical adsorption in the small pores of carbons. In some cases the presence of moisture in the air is not enough and to get the noticeable capacity prehumidification/preconditioning of samples is necessary. It was reported that on some carbons the prehumidification could improve the capacity as much as 80 times [49]. On the other hand, the amount of water adsorbed on the surface should not be too large. The studies suggested that the affinity for water adsorption should not be greater than 5 % [41, 49] to reach the maximum capacity. It is likely that, when the carbon surface becomes too hydrophilic, the small pores are filled by condensed water and the direct contact of HS- with carbon surface in the smallest pores is limited. Another factor that plays a role is the degree of carbon oxidation [41-44, 62, 63]. When more oxygen groups are present the surface becomes more acidic suppressing dissociation ofhydrogen sulfide. Although in the majority ofstudies the presence of water was found important to enhance hydrogen sulfide adsorption, Coskun and Tollefson [18] found that the presence of water at temperatures close to ambient decreases the catalytic activity of carbon surfaces. A role of oxygen in the kinetic of the H 2 S adsorption/oxidation were studied by Tollefson and coworkers [18-27], Steijns and Mars [29], and Meeyoo

21.2

Adsorption of Inorganic Gases

537

and coworkers [26]. In general, the experiments performed with low concentrations of H 2S «3 %) in wide temperature (398-473 K) and pressure ranges (230-3200 kPa). The results of Tollefson and coworkers [23] showed that optimum temperature for high H 2S conversion and low S02 production is 448 K with 0/H 2 S ration 10.05 times the stoichiometric ratio. The process was not impeded by high water vapor content, which might be related to relatively high temperature of the process, higher than boiling point of water. The rate-limiting step for catalytic oxidation reactions was defined as either adsorption of oxygen or hydrogen sulfide from the bulk phase on the activated carbon surface. The high heats of oxygen adsorption (73.8 kJ/mol) indicate its chemisorption on the surface whereas the low value of the heat of hydrogen sulfide adsorption suggests that the sorption at elevated temperature is physical in its nature [21]. Physical nature of adsorption was confirmed by Bagreev and coworkers [47] when adsorption on H 2S was studied at elevated temperature «400 K) in the absence ofair or water. At those conditions, the heat ofH2S adsorption (between 40 and 50 kJ/mol) depends only on the pore sizes. This was an indirect proof that oxygen chemisorbed on the surface or present as functional groups is not active enough active to oxidize hydrogen sulfide [47]. On the other hand, Mikhalovsky and Zaitsev [39] found using X-ray photoelectron spectroscopy (XPS) that surface oxygen-containing functional groups contribute significantly to the formation of S02 in H 2S oxidation. They suggest that at an inert atmosphere surface oxygen-containing complexes and elemental sulfur are formed during adsorption of H 2S. An interesting effect of autocatalysis by deposited sulfur was identified by Steijns and coworkers [27, 28]. Studying adsorption of hydrogen sulfide on various adsorbents, they found that deposition of sulfur at the beginning of the removal process increases the catalytic activity of the carbon. Then, when sulfur starts to block microporosity, a rapid decrease in activity follows. It was postulated that elemental sulfur is rather in the form of radical chains than S8 rings [28]. Steijns and Mars found that the catalytic activity per square meter of total surface area is approximately proportional to the amount of adsorbed sulfur. On the other hand, no evidence of sulfur autocatalysis was found by Ghosh and Tollefson [20, 21]. In all studies of hydrogen sulfide adsorption the presence of micropores is indicated as a important factor. Although the opinions about the first location of adsorbed sulfur vary [18, 19], the filling of micropores by elemental sulfur of sulfides seems to be the limiting factor of activated carbon capacity [41, 45, 46, 48]. Steijns and Mars [19] found that the strong sulfur adsorption is in carbons having pores between 0.5 and 1 nm, which is expected based on the size of sulfur chains and the overlapping of adsorption potential in pores similar in size to the adsorbate molecule. Moreover, when sulfur is adsorbed in such small pores the presence of large polymers is unlikely, and isolated adsorbed sulfur radicals are further oxidized to S02 and then S03. On such carbons, sulfuric acid is the important product of surface reaction [41]. It was also found that when the H 2S capacity of carbons is normalized to their pore volume, the similar

Chapter

21

Removal of Inorganic Gases and VOCs on Activated Carbons

values are obtained [41, 48]. This once gain indicates that the volume of pores where oxidation products are stored is the limiting factor for the amount ofH 2 S retained on the surface. A role of surface chemistry was for long time ignored in the study of hydrogen sulfide adsorption-oxidation. However, Kaliva and Smith [37] indicated that water likely forms complexes with oxygen thus taking part in the surface reaction, the effect of carbon surface chemistry, besides the influence of ash, was not discussed in details. Surface chemistry of carbons is rarely taken into account and it is even not considered as one of the required specifications for many applications. It is well known that the degree of acid dissociation depends on the pH of the system, and dissociation is feasible when pH is greater than pKa of an acid under study. Since hydrogen sulfide is a weak acid, analysis of the performance of carbons showed the dependence of the capacity on the acidity of carbon [38, 41, 48]. Moreover, threshold values were found on the dependence of the parameters describing the acidity of carbons and the normalized (for pore volumes) H 2 S breakthrough capacity values [48]. This clearly showed that the local pH in the pore system has a significant effect on the efficiency of hydrogen sulfide dissociation and thus its oxidation to various sulfur species. A moderately low average pH of the carbon surface is expected to suppress the dissociation of H 2 S and the formation of hydrogen sulfide ions. Those ions, when present at low concentration in small pores, are oxidized to sulfur oxides from which sulfuric acid is formed. On the other hand, a pH in the basic range promotes the dissociation ofH 2 S. This results in a high concentration ofHS- ions, which are then oxidized to sulfur radicals and polymers having chain or ring-like shapes. When the pH value is very low only physical adsorption can occur. The dependence of the normalized capacity on the pH of the carbon surface

is presented in Fig. 21.1 The threshold value derived from the analysis of the

,•

300 M

-

250

5

200

E () -.... 0)

•

•

•

~

"0

ca a. 150 ca ()

"0 Q)

"~ (ij

E 0

Z

100 50 0

0

2

4

6

8

10

12

Surface pH

Figure 21.1 Dependence of normalized H 2 S breakthrough capacity (per unit pore volume of carbon) on the surface pH (as described by Bandosz and coworkers [43, 48]).

21.2

Adsorption of Inorganic Gases

539

data occurs at the pH value around 4.5.The justification for the threshold in surface pH is based on the steps of hydrogen sulfide adsorption-oxidation on unmodified carbons [41, 48]. They are as follows: (1) H 2 S adsorption on the carbon surface, (2) its dissolution in a water film, (3) dissociation of H 2 S in an adsorbed state in the water film, and (4) surface reaction with adsorbed oxygen. The effect of ash can be considered as an extension of the effect of surface chemistry, since the pH of carbon expresses the average number and strength of acidic groups. While studying the hydrogen sulfide uptake on various carbons, it was found that presence of iron oxides or metals ions from group 6-8 has an effect on hydrogen sulfide adsorption [19, 49, 58, 59]. It is not only reflected in the amount adsorbed but also in the extent of oxidation. According to Steijns and Mars [19], the presence of iron oxide promotes formation ofS0 2 when removal process occurs at elevated temperatures. That effect was also noticed for removal of hydrogen sulfide on carbons at ambient conditions [32, 49]. The study of hydrogen sulfide removal on coal fly ash showed the noticeable adsorptionoxidation on those materials where active components for catalytic oxidation are mullite, hematite, and magnetite, all containing iron oxides [58, 59]. This effect was also clearly seen when carbonaceous materials derived from sewage sludge were tested as hydrogen sulfide adsorbents [64]. On them, an exceptionally high adsorption capacity, higher than that on coconut shell-based carbon was found. That superior performance was attributed to the catalytic reactions on ash, in particular on iron, copper and zinc oxides. When removal of hydrogen sulfide at 820 K was studied on carbons impregnated with zinc and copper a significant increase in the capacity was noticed; however, the activity diminished when the temperature of process was lowered [60]. Analysis of the above factors helped to formulate to the pH-dependent mechanism of hydrogen sulfide adsorption on activated carbons [41, 48]. It is summarized in Fig. 21.2 where the link exists between the extent of dissociation and the products of hydrogen sulfide adsorption. When the environment is moderately basic an increase in the concentration of HS- occurs. When the pH is distinctively acidic, the concentration of hydrogen sulfide ions is very low. In such situation hydrogen sulfide ions - when adsorbed in small pores are oxidized and converted to highly dispersed sulfur. These separated sulfur "islands" are susceptible to further oxidation to S02 and S03. This may happen since at such conditions the probability that an isolated sulfur atom will meet its own species is low. The main source of oxygen is likely oxygen from air. Its active radicals are adsorbed on the surface and accept electrons from sulfur. When the pH is less acidic (more basic) the concentration of HS- is much higher, which forces the created sulfur atoms to be close to each other, capable of forming polysulfides [28]. Then their polymerization to stable chain or cyclic sulfur molecules such as Ss occurs. It is apparent that further oxidation of such sulfur species is less probable than in the case of atomic sulfur. Summarizing, the results of the complex process of oxidation and its yield depend on the specific environment inside the porous structure of carbon. This environment consists of

Chapter

54°

21

Removal of Inorganic Gases and VOCs on Activated Carbons

S02(ads) + 0.5 O2 --+ S03(adS)

Cf free active sites Cf + 0.50 2 --+ C{O)

C(SSH) + 2HS- ~ C(S3SH) + H20

I Figure

21.2

pH-dependent mechanism of H 2 S adsorption-oxidation (as described by Adib

eta!' [43]).

the combination of pore sizes, degree of activated carbon hydrophilicity (related to surface functional groups), and local pH. The latter is the overall effect of carbon surface chemistry or applied chemical modifications. One can talk about the "local pH effect" only when the process occurs in pores where the existence of the water film is possible and surface groups can dissociate. The best conditions leading to oxidation of hydrogen sulfide to S4+ or S6+ exist when the concentration of HS- is just right (not too high, not too low) to be oxidized to highly dispersed sulfur. On the other hand, when the content of H 2 S0 4 rises in the course of the experiment" it suppresses the dissociation of hydrogen sulfide

21.2

Adsorption of Inorganic Gases

54 1

and inhibits the adsorption process. Under these conditions the small amount of H 2 S absorbed in the film of acid can be oxidized to elemental sulfur. The described above mechanism is also true when adsorption of hydrogen sulfide on nitrogen-containing carbons is discussed [50-57]. Such materials were introduced by Calgon Carbon in their proprietary process of Centaur® preparation [53]. Centaur®, a catalytic carbon that targets hydrogen sulfide removal is prepared by introducing the basic nitrogen functionality to the small pores of adsorbent. Although is done using impregnation with urea followed by high-temperature heat treatment, other nitrogen-containing organic compounds can be used [51, 54]. That treatment results in the presence of quaternary and pyridine-like nitrogen in the small pores [57]. As indicated above, basicity of such species, in the presence ofmoisture, enhances hydrogen sulfide dissociation, adsorption, oxidation, formation of radicals, and then their oxidation to sulfuric acid. However the total capacity of Centaur® is not exceptionally high (around 0.060 g/cm3 ) [57], its surface conversion of hydrogen sulfide to sulfuric acid is almost complete. This makes regeneration of spent materials using simple water washing feasible [50, 51]. Although nitrogen modification and oxidation to sulfuric acid makes Centaur® a superior product, high costs and risks related to the removal of concentrated acid from the surface limits its industrial and municipal applications in favor of caustic-impregnated or virgin activated carbons [9].

Table 21.1 H2 S breakthrough (ASTM 06646-01) capacities on few commercial activated carbons [65]

WVA 1100 (Westvaco) BAX 1500 Xtrusorb 60 (Calgon Carbon) Maxsorb (Kansai) 208c (Waterlink Barnabey and Sutcliffe) G55C (PICA) ROZ3 (Norit) Vapure 612 (Norit) R 2030(Norit) RB4 (Norit) STIX (Waterlink Barnabey and Sutcliffe) PCB-O (Calgon Carbon) BPL F3 (Calgon Carbon) MVP (Calgon Carbon) BPL 4xl0 (Calgon Carbon) FCA (Calgon Carbon) IVP (Calgon Carbon) Centaur HS® (Calgon Carbon) Centaur® (Calgon Carbon)

0.014 0.025 0.011 0.003 0.026 0.027 0.100 0.068 0.037 0.032 0.100 0.011 0.031 0.079 0.023 0.204 0.194 0.159 0.090

54 2

Chapter

21

Removal of Inorganic Gases and VOCs on Activated Carbons

Table 21.1 summarizes the HzS breakthrough capacity results obtained on few commercial activated carbons. The results are done using the same tests (ASTM D6646-01) so the comparison is meaningful. 21.2.2

Removal of Sulfur Dioxide

An increase in the acidity of natural water, fast rate of abrasion of buildings and monuments and health problems associated with this caused that desulfurization of fossil fuels and SOz removal from flue gases are technologies which have been developing rapidly during the last 20 years. Efficient media for removal sulfur dioxide are activated carbons [66-84] and activated carbon fibers [72,78,82]. Numerous studies indicate good efficiency of SOz removal on these materials either at low [72, 77, 78, 74, 76] or high temperatures [70,71, 80, 81]. Process ofSO z adsorption has been studied extensively and, like in the case of hydrogen sulfide, such parameters as porosity [68-77, 85, 86], surface chemistry [68, 71, 73, 75, 77, 78, 80, 82], and constituents of ash [81-89] were taken into consideration [5-16]. The products of surface reactions were analyzed from the point of view of removal efficiency and the feasibility of regeneration [74, 85]. Due to the higher oxidation state of sulfur in SOz than in HzS, the chemistry involved in immobilization is expected to be much less complex than that for oxidation of hydrogen sulfide. Since usually the process is carried out in the presence of moisture and oxygen, it is a generally accepted that sulfur dioxide is oxidized to sulfuric acid as a final product of the reaction. That acid is strongly retained in the pore system of activated carbons. Higher extent of oxidation usually results in more 50 z adsorbed [76]. Adsorption-oxidation of 50 z in oxygen atmosphere and in the presence of water occurs as follows [76]: SOZgas --+ SOZads

(21.8)

°Zgas --+ 20 ads

(21.9)

SOZads+Oads --+ S03ads

(21.10)

°

Hz gas --+ HZO ads S03ads + HZO ads --+ HZS04ads'

(21.11) (21.12)

where indices "gas" and "ads" refer to the presence of reactants in the gas phase and the adsorbed state, respectively. It was also found that three forms of adsorbed sulfur oxides could be present in such a situation. They are: weakly adsorbed SOz, physically adsorbed S03 (after oxidation of SOz), and strongly adsorbed H ZS0 4 [74-78]. It is well known that small pores, similar in size the adsorbate molecule, enhance the adsorption potential resulting in strong adsorption forces. Moreover, in the case of adsorption of sulfur dioxide it was demonstrated that oxidation to sulfur trioxide occurs mainly in the 7 A pores [76]. With an increase in the

21.2

Adsorption of Inorganic Gases

543

size of pores less 50 2 is converted, which results in smaller uptake of sulfur dioxide. No correlation was found between the amount of 502 adsorbed in the presence of oxygen and the volume of micropores. On the other hand, in the absence of oxygen the influence of pore volume was more pronounced. This can be explained by the extent of oxidation, which is enhanced when oxygen is present in the system. Supporting for this are the studies of the energetics of the adsorption where it was found that sulfur dioxide is adsorbed with two adsorption energies on activated carbons [68-77]. The low energy, about 50 kJ/mol, corresponds to weak physical adsorption, and the second, about 80 kJ/mol, to chemisorption [76], likely in the form of sulfuric acid. A significant effect of very small micropores on S02 adsorption was also noticed by Bagreev and coworkers [85]. The evidence on adsorption of sulfur dioxide in micropores in the absence of oxygen was found by Molina-Sabio and coworkers [77]. While calculating the micropore volumes of various carbons using CO 2, N 2, and S02' a relatively good agreement in the values was obtained. A small discrepancy found in the case of S02 was explained by its polarity. The strong adsorptive-adsorptive interaction in the gas phase caused weaker adsorbent-adsorbate interaction than in the case ofN2 and CO 2. Similar effect on micropore filling mechanism was also noticed by Wang and Kaneko [86]. Daley and coworkers [78] found that the S02 adsorption capacity on the activated carbon fibers was inversely proportional to pore size, pore volume, and pore size distribution. Although effects of porosity are crucial for physical adsorption, when weak adsorption forces exist, the importance ofthe catalytic effects ofsurface chemistry increases. In the case of acidic gases such as S02' the positive effect on adsorption should be observed when the basicity of surface increases. Numerous researches found that heat treatment of activated carbons or activated carbon fibers at temperatures about 1300 K results in an increase in the amount of sulfur dioxide adsorbed [68-74]. Such treatment, besides removal of oxygen-containing acidic groups, should increase carbon basicity [90]. It was specifically found that when basic groups containing oxygen are present on the carbon surface the adsorption ofS0 2 is significantly enhanced [73, 75]. In such a case basic groups (pyronic and pyronic-like type) are responsible for strong physical adsorption ofsulfur dioxide. Of course, those acid-base interactions do not introduce any catalytic effect leading to the formation of sulfuric acid and its chemisorption on the surface. The strong adsorption of sulfur dioxide is enhanced by the presence of oxygen [68, 71, 73, 75, 78]. These oxygen-containing sites are proposed to act as catalytic centers for oxidation ofS0 2 to S03 [79]. According to Davini [71, 73] oxygen present in the system plays an important role in the variations of S02 adsorbed. The negative role of oxygen in the amount of S02 adsorbed is linked to its ability to react with carbonaceous matrix, formation of surface groups, which decrease the surface area of adsorbent. A decrease in the S02 uptake upon the presence of oxygen-containing acidic groups was also noticed by Daley and coworkers [78]. They found the correlation between an increased S02 capacity and the amount of CO-C0 2 evolved during heat treatment of

544

Chapter

21

Removal of Inorganic Gases and VOCs on Activated Carbons

carbon fiber surfaces, which led to the formation of new active centers. Similar correlation was investigated by Mochida et al. [82]. On the other hand, Daley and coworkers [78] found that when dry S02 was adsorbed, the presence of oxygen-containing functional groups significantly enhanced the performance at temperature smaller than 348 K. That enhancement was explained by surface reactions of quinines with S02 and water forming diol and sulfuric acid. The effect of surface chemistry on S02 oxidation step was also discussed in details by Raymundo-Pinero and coworkers [76]. However, contrary to Daley and coworkers, they did not find any correlation between the amount of groups decomposed during heat treatment and an increase in the S02 adsorbed, they confirmed that removal of oxygen form the surface forms new high-energy adsorption-oxidation centers. An increase in the uptake of S02 upon oxidation of carbon was found by Lisovskii and coworkers [74]. It was postulated that surface acidic groups are the catalyst for S02 oxidation. Moreover, the presence of strong basic functionality was suggested as not beneficial for the process of sulfur dioxide removal due to an increase in the retention of sulfuric acid, which is undesirable form the point of few of adsorbent regeneration [74]. High adsorption on chars containing high surface acidity and basicity was also noticed by Rubio and Izquierdo [80]. Based on the performance of their materials, they concluded that not only the amount of surface groups but also their accessibility have an effect on S02 adsorption-oxidation. Besides empirical studies, ab initio molecular orbital calculations were performed on the possible pathways of S02 oxidation on activated carbon in the presence of water and oxygen. Yang and Yang [91] found that when surface oxides are present on the zigzag edge sites sulfuric acid is formed with sulfurous acid as an intermediate. On the other hand, chemisorption was found unfavorable on the edge sites containing twin oxides. Those findings can help to explain the discrepancies described above regarding the role of surface oxygen groups in 502 adsorption-oxidation on activated carbons. Basic nitrogen species present on the surface of activated carbons or carbon fibers, like in the case ofH25, were found to enhance the sulfur dioxide uptake. Polyacrylonitrile (PAN)-based activated carbon fibers are examples of good adsorbents for S02 removal [82, 92]. Although role of nitrogen present in the carbon matrix was not emphasized by Lee and coworkers [93] in their studies of S02 adsorption on PAN-based activated carbon fibers, [93] Kawabuchi and coworkers noticed a significant increase in the sorption capacity when activated carbon fibers were modified with pyridine and basic nitrogen functionalities were introduced to the surface [93]. Pyridine provided basic functionality, which increased catalytic removal of SO x. The effect ofintroducing nitrogen functionality to activated carbon surfaces on S02 removal was also studied in details by Raymundo-Pinero and coworkers [76] and Bagreev and coworkers [85]. Both group of researchers found that nitrogencontaining pyridinic species, which are placed at the edges of graphene layers, noticeably increase the amount of 50 2 adsorbed and its catalytic conversion to

21.2

Adsorption of Inorganic Gases

545

sulfuric acid. The effect is even more pronounced when those groups are present in small pores [85]. The only negative part related to the application of these materials is strong adsorption ofsulfuric acid leading to the difficulty in adsorbent regeneration, which was mentioned earlier by Lisovskii and coworkers [74]. As in the case of hydrogen sulfide, the presence of ash and its composition should have an effect on the amount of 50 2 retained on the surface. This effect was observed by Lu and Do [87] studying the 50 2 adsorption on activated coal rejected char. Its high content of inorganic matter-inorganic oxides was expected to affect the amount of 50 2 oxidized to sulfuric acid. As the most active ingredients, titanium oxide was identified. The enhancement in the oxidation of 502 due to the presence of active inorganic matter was also found by Bashkova et al. [89] on carbonaceous adsorbents derived from sewage sludge. In those materials, a high content of CaO was identified as a favorable factor. The effect of calcium was also studied when fly ash mixtures with calcium hydroxide were tested as 502 adsorbents [89]. It was found that Ca(OH)2 enhances the dispersion of calcium reagent and thus improves the efficiency of the adsorbent. 21.2.3 Adsorption of Hydrogen Cyanide

Another inorganic gas of extremely high toxicity is hydrogen cyanide (HCN). Besides its application as a warfare gas, called prussic acid (WWI) , or a massive extermination mean (WWII-cyclone B), it is an important industrial agent used in extraction of precious metals, in electroplating industry, metallurgy, and in the production of such materials as plastics, fire retardants, cosmetics, dyes, pains, and pharmaceuticals. As in the case of hydrogen sulfide and sulfur dioxide, physisorption of hydrogen cyanide on activated carbons is poor. Taking into account various chemical compounds, efforts were made to develop impregnated carbons, or carbon fibers (cloths) with efficient strength of the bonds between the irnpregnant(es) and the carbon surface [94-100]. On such materials chemisorption is the predominant process. Taking into account the toxicity of HCN, it is important that the removal process is irreversible and the adsorption capacity is sufficiently high. Usually efficient systems to remove HCN contain copper and an oxidizing salt such as sodium dichoromate [94]. Copper, either from nitrate or oxide is reduced to metal, then the oxidizing agent is added. Since the mixture is expected to exist in mesopores, they are active in the adsorption-chemisorption process. The chemistry of reactions in such systems was proposed by Alves and Clark [94]. It occurs in two stages: Cr+

Cr+

NC - CN + 2H 20 ~ CN - CONH 2 + H 20 ~ (CONH 2)2 cyanoformide oxamide (21.13)

They found that (CN)2 is an intermediate formed during HCN uptake on Cu-Cr-containing carbons. Then, in the presence of Cr6 + hydration occurs

546

Chapter 21 Removal of Inorganic Gases and VOCs on Activated Carbons

leading to oxamide, as the major product. On the other hand, on only copperimpregnated carbon the bulk of chemisorbed HCN is in the form of copper cyanide with no oxamide formation. In the case of Cu-Cr carbons the intermediate of the reaction, (CN)2 was found to be a factor enhancing the HCN removal capacity when compared to that on Cu carbon. Although copper, which is the most popular impregnant, results in a high HCN capacity (about 100 mg/g at 80 % humidity and 2 mg/L HCN in the challenge gas), the carbons containing the copper-chromate mixture are known to age with diminishing performance [95]. This directed the research efforts toward other metals-slats, which, when deposited on the carbon surface, can form complexes with HCN and cyanogens. The removal capacity on nickelor cobalt acetate-impregnated carbons was studied [95]. The uptake of90 mg/g was reached and the good breakthrough performance could be maintained for a year. The mechanism proposed was similar to that on Cu-impregnated carbons. It is believed that HCN dissolves in a saturated solution of metal acetate on the carbon surface and then metal-cyanide complexes and insoluble metal cyanides are formed [95]. Besides acetates, formates and propanoates of manganese, cobalt, nickel, copper, and zinc were used as impregnates ofactivated carbon cloth [96]. Although the exceptional capacities were not found, the results obtained supported the hypothesis that the reactions occurs in the film of water adsorbed on the surface and their pathways follow the reactivity of the impregnates with HCN in the solution. Determination of the participation of separate components of the systems in chemisorption and total adsorption was carried out by Rajakovic and coworkers [97]. They studied the performance of materials impregnated with compounds containing copper, silver (I), iron, magnesium, and aluminum in the forms of acetates, oxalates, tartrates, stearates, and citrates. Twofold structural activity of activated carbon cloth (ACC) was described. In spite of the fact that ACC is able to adsorb HCN without any impregnantes, adding metal salts acts chemically toward formation of complex compounds and precipitates. Although adsorptive and chemical forces are the most important factors, which affect the active bonding of pollutants, there are other important aspects influencing the performance of materials. They are the geometry of the system (porosity), diffusion rate, and the kinetics of surface reactions. Moreover, a significance of the type of metal salt was indicated. Application of organic salts with large organic moiety as impregnantes enhances the performance compared to the inorganic counterparts. This is the result of the affinity of the organic part to graphene layers and its strong retention on the surface. It was also found that at higher concentrations of pollutants formation of complex compounds predominates, whereas at lower concentration, the precipitates are formed.

21.2.4

Adsorption of NOx

The main source of nitric oxides (NO x) is combustion of fossil fuel where the concentration of NO x in the exhaust gases is usually smaller than 1000 ppm.

21.2

Adsorption of Inorganic Gases

547

First NO is formed and then it is oxidized in the atmosphere to N0 2 • Since in combustion, the origin of nitrogen is not only from N-rich fuel but also from air supplied for oxidation, in the elimination of NO x postcombustion methods are important. So far the most effective technique has been selective catalytic reduction of NO x on various catalysts. When the activated carbons are used as removal media, the elimination process includes also adsorption combined either with oxidation or reduction. Oxidation usually leads to the formation of nitric acid whereas N 2 is the product of NO x reduction. As in the cases of other pollutants addressed in this review, for NO x removal either unmodified or impregnated (caustics, catalytic metals) activated carbons have been used [101-114]. Adsorption of NO x on unimpregnated activated carbons has been studied at temperatures between 295 and 400 K and the pressure ranges between 100 and 3000kPa [101-105]. The reported amount of NO x adsorbed reached 150mg N0 2 per gram of carbon [101]. It was found that an increase in the pressure significantly increased the N0 2 uptake and that effect compensated the negative effect of an increasing temperature. As the mechanism of adsorption, the micropore filling was proposed with a significant amount of N0 2 adsorbed irreversibly. Nitric oxide was formed on the surface of carbon where catalytic reaction of oxidation of NO to N0 2 in the presence of oxygen was suggested to take place [101]. Adsorption of NO and its reduction on chars was studied by Izquierdo and Rubio [102]. The removal process was designed to work at the temperature range 373-473 K in the presence of oxygen and moisture. The removal capacity was between 100 and 150mg/g with around 30% of NO conversion. The conversion of NO via direct reduction with the carbon surface occurred as follows [102]: 2NO + C ---* N 2 + CO 2

2NO + O 2 + 2C ---* N 2 + 2C0 2

(21.14) (21.15)

It was found that surface chemistry affects the NO removal performance and an optimal amount of oxygen functional groups on the surface of char is needed. This amount has to be established experimentally. Izquierdo and Rubio [102] proposed that gas phase oxygen reacts with the carbon surface forming oxygen-carbon structures, which act as active centers for NO chemisorption. When the reduction proceeds, CO 2 is released and the new oxygen groups are formed. In the absence of oxygen, the conversion of NO decreases to zero when all active centers, functional groups are consumed. The effect of thermal surface treatment of carbons carried out in various atmospheres on the NO x adsorption-reduction was studied by Xia and coworkers [103]. They found that activated carbon heated at 1200K in hydrogen adsorbed NO without its oxidation to NO x • This happens as a result of a decreased affinity of the hydrogen reduced carbon to chemisorbed oxygen. It is interesting that such effect was not found on carbons treated in nitrogen.

548

Chapter

21

Removal of Inorganic Gases and VOCs on Activated Carbons

The amount of NO adsorbed on the hydrogen reduced carbons was about 1 mmoll g and the existence of strong (> 40 kcallmol) and weak chemisorption with various energies of adsorption was found. An enhancement in the process of NO x abatement with carbon adsorbents was proposed by Kong and Cha [104, 105]. Following the physical adsorption of NO x on unimpregnated carbons, treatment with microwave energy of 480 W was proposed. This process enhanced NO x reaction with carbon to produce nitrogen and carbon oxides. The few runs of microwave regeneration increased 10 times the surface area of spent char as a result of the activation process. Moreover, the nitrogen compounds were introduced to the carbon matrix changing its surface chemistry. Those stable compounds formed during dissociative chemisorption of NO were indicated to decompose to N 2 under microwave radiation. Kong and Cha concluded that in the presence of water and oxygen NO is converted to N0 2 and HN0 3 • During microwave treatment those species are reduced back to NO and the reaction with carbon occurs with formation of N 2 , CO, and CO 2 , A significant advantage of this process is that 90 % of NO x is reduced to N 2 and microwave treatment-regeneration can in fact be considered an activation method for low surface area chars. The effects of impregnation of activated carbons with potassium hydroxide on the efficiency of NO x removal was studied by Lee and coworkers [106, 107]. They found that KOH creates the selective adsorption sites (increases basicity of carbons by the presence of OH-) for NO x adsorption. As a result of the surface reaction, KN0 2 and KN0 3 are formed. Formation of salt crystals blocks the porosity of the materials and diminishes the NO x removal capacity. It was proposed that the surface basic OH- ions delay oxidation of KN0 2 to KN0 3 and thus result in an increase in the surface adsorptivity. The effect of potassium in the form of potassium carbonate or potassium silicate on reduction of NO x on coal chars was also investigated [108-111]. The best materials were prepared by pyrolysis of coal at 1300 K with high KOHl coal ratio [108]. On these adsorbents, at temperature smaller than 473 K, physical adsorption is predominant while the true NO x reduction by char occurs at T> 473K with formation ofN2 and CO 2 , The results indicated that a material with the high surface area should be used to promote adsorption of NO x and potassium remaining in chars catalyzes NO x reduction in the presence of oxygen [109]. The reduction of NO x on carbons can be also enhanced by the presence of ammonia [102, 112] or nitrogen-containing groups on the surface of carbons [104, 105, 113]. Mochida and coworkers [112] found that the presence of ammonia adsorbed on the surface of carbon fibers enhances the reduction of NO; however, the process is not efficient at humidity higher than 60% [113]. When ammonia is introduced to the reaction and oxygen is present the following reactions occur [102]: 6NO + 4NH3 -+ 5N2 + 6H 2 0

(21.16)

4NO + 4NH 3 + O 2 -+ 4N2 + 6H 2 0

(21.17)

21.3

Adsorption of Volatile Organic Compounds

549

Matzner and Boehm [113] found that the incorporation of nitrogen in activated carbons enhances their reduction activity toward nitric oxides. On such materials, reduction occurs at much lower temperature than that on undoped carbons and the conversion is higher. Moreover, the amount of NO adsorbed on nitrogen-doped carbon at room temperature increased with an increase in the content of nitrogen. As suggested, NO reacts with surface sites of chemisorbed nitrogen, C(N) and oxygen-containing site and nitrogen are formed: C(N) + NO -+ C(O) + N 2

(21.18)

It was proposed [113] that chemisorption reaction may also be associated with an electron transfer from the carbon surface to the NO molecule or (NO)2 molecule. The resulting species are diamagnetic and dimeric. Those hyponitrites are highly reactive and they can easy oxidize the carbon surface resulting in formation ofN2. Besides caustic and nitrogen modifications of the carbon surfaces, the reduction of NO x was extensively studied on carbons impregnated with transition metals [114-118] such as Ni, Fe, Co, or Cu. From all of those metals, copper was found as the most efficient catalysts toward reduction of NO into N 2 and O 2 either with or without oxygen. On the carbon - copper catalysts at temperature over 600 K 100 % conversion is reached with a high capacity of the adsorbent. It was found that a metallic catalytic system of NO-Cu reaction is very predominant and copper metal is activated for removing NO at high temperature even in the absence of oxygen [114]. As indicated above, in the studies of unmodified carbons, oxygen from NO-C reduction creates more active sites for NO adsorption via formation of high surface energy active sites on the surface.

21.3 ADSORPTION OF VOLATILE ORGANIC COMPOUNDS Volatile organic compounds commonly known as VOC are a group of various small molecule organic species with low boiling [119]. Among numerous organic species that can be considered as VOCs, US EPA lists 188 volatile organic compounds as the dangerous air and water pollutants. In these groups, one can find a broad spectrum of organic compounds from chlorinated species through ketones, aldehydes, carboxylic acids, and thiocompounds. Removal of those compounds occurs usually using condensation, absorption, oxidation, incineration, and adsorption. The last method with activated carbons as adsorbents is widely applied in industrial processes. This is owing to the predominantly hydrophobic nature of VOCs granting their interactions with activated carbon surfaces. Another important factor is a small size and high volume of activated carbon pores. They result in strong adsorption forces, even if traces of VOCs are present.

55°

Chapter

21

Removal of Inorganic Gases and VOCs on Activated Carbons

To study the adsorption of all listed VOCs on activated carbons is an overwhelming task. The experimental difficulties are linked to the long list of species to study and their high level of toxicity. This causes that the results described in the literature usually focus on one or few VOCs compounds as models, and those species are not necessary listed as the most dangerous pollutants by EPA. The tasks of research are usually established knowing the chemistry of the molecule to be studied and taking into account the existence of dispersive and specific interactions, which can playa role in the adsorption. Another important factor, which has to be taken into consideration is the concentration range, phase from which adsorption is supposed to occur and the temperature of the process. So far it has been determined that the equilibrium adsorption isotherms of such species as toluene, 1- butanol, and ethyl acetate can be described by the Langmuir-Freundlich or Toth equation [120]. The classical volatile organic compound whose adsorption was studied in details on activated carbon is benzene. In fact, before strict environmental regulations, benzene was used as a model compound to determine the porosity of activated carbons [121] owing to its stability, hydrophobicity, and symmetrical size of the molecule. The characteristic energy of adsorption used as a reference is calculated using the physiochemical properties of the benzene molecule. The interactions of various organic compounds, now considered as VOCs, with the surface of various activated carbons were also studied in details by Kiselev and Yashin [122]. Using inverse gas chromatography (IGC), they determined the energetic parameters (energy, enthalpy, entropy) of their interactions depending on the size of the molecule, sterical hindrances, and the heteroatoms present. The results obtained by them are very extensive and certainly can be used as a reference when adsorption of any VOCs is studied. The research of Kiselev and Yashin was done either on various nonporous carbon blacks or on porous activated carbons. Taking into account that the adsorption energy should double in micropores compared to the flat carbon surface, the accessibility of pores of the adsorbents for the molecules to be removed and thus the efficiency of the adsorption process can be estimated using these data. Since the fundamental studies of the Russian schools of Dubinin and Kiselev were carried out in the 1960s, the change in the approach of science toward application and concerns about environmental pollutions, directed the focus of scientific research toward studies of the adsorption of VOCs on carbons from the point of view of the feasibility of the removal process. Of course, this feasibility is related to the strength of the interactions, especially important at low concentrations, and the adsorption capacity (for high concentrations). Since that time also more has been done to understand specific interactions with the carbon surfaces, especially those decorated with functional groups containing heteroatoms [62, 63]. Recently, the effectiveness of removal of bromo-dichloromethane, benzene, carbontetrachloride, 1,1, i-trichloromethane, chloroform, and 1,1dichloromethane was studied on various laboratory-based and commercial activated carbons [123]. The pecan shell- and almond shell-based materials obtained

21.3

Adsorption of Volatile Organic Compounds

55 1

by either physical (steam, CO 2) or chemical (phosphoric acid) activation were used. For comparison, coconut shell and bituminous coal-based carbons were also studied. The obtained results showed, as would be expected, the superior adsorption of benzene compared to other species. The best performance for other VOCs studied was obtained for coconut and pecan shell physically activated carbons, which can be linked to their small pore sizes. All other VOC studied are halogenated compounds and they should interact with carbons only in a dispersive way. The removal of a broad range of environmentally detrimental VOCs on activated carbons was studied by Le Cloirec and coworkers [124]. Their extensive study led to quantitative relationship, which can be used to predict the energetic interactions resulting from either adsorption or desorption of VOCs on granulated activated carbons. To obtain that relationship, the adsorption of 40 VOCs was investigated using differential scanning calorimetry coupled to thermogravimetry. Multiple linear regressions were applied to correlate the data obtained to the physicochemical properties of the molecules. It was found that ionization potential, polarizability, and connectivity index have main influence on the adsorption energy of those species. Taking into account the difficulties in measuring the adsorption isotherms of VOCs, the obtained relationship, however simplified, can prove to be very useful in environmental engineering applications. The effects of physicochemical properties of VOCs on their adsorption capacity on activated carbons were also noticed by Chiang and coworkers [125]. Such properties as their boiling point, critical temperature, cross-sectional area, and dipole moment were found as the most important features governing activated carbon adsorption. Le Cloirec and coworkers [126] also studied the warming of the activated carbons adsorbent bed occurring during the removal process at high concentrations. The exothermal nature of the adsorption quite often results in bed ignition. It happens especially when very microporolls carbon is used, as for example coconut shell-based, or such species as ketones, aldehydes, carboxylic acids, or sulfur-containing species are to be removed. The heat effects in the cases of those species are not only related to the enhancement of adsorption potential due to physical adsorption but also are related to chemical reactions such as oxidation or dimerization taking place on the carbon surfaces at the temperatures even close to ambient [127]. To avoid self-ignition of the bed, the rise in temperature caused by oxidation of a solvent or carbon bed should be estimated and based on this, the proper maximum concentration of VOCs should be determined. It was also found that that at high VOCs concentrations, the moisture content of the air does not affect the carbon capacity for VOC removal or warming of the bed [126]. The reason for this lies likely in the difference in the affinity of water and VOC to be adsorbed on carbons. The latter, having a hydrophobic moiety interacts with graphene layers much stronger than water. Water, even if preadsorbed, is likely replaced with the organic molecule when the removal process proceeds. On the other hand, Chou and Chiou [128] in their research of the removal ofVOCs from exhausted gas stream found that

552

Chapter

21

Removal of Inorganic Gases and VOCs on Activated Carbons

moisture content in gas is unfavorable for the removal process. Similar effect was observed by Shin and coworkers [129] in their study of adsorption of benzene, toluene, and ethyl benzene. When relative humidity reached 60 % the adsorption of those species on activated carbon significantly decreased. For the multicomponent adsorption of VOC, displacement effects were noticed and adsorbates with strong interaction forced to displace weakly bounded species. The amount adsorbed was found to depend on the size of molecule (larger molecules - greater adsorption) and its polarity (less polar - greater adsorption). A detailed study of adsorption of aldehydes on activated carbons was performed by Domingo-Garcia and coworkers [130] and EI-Sayed and Bandosz [131, 132]. Using IGC at infinite dilution, it was found that formaldehyde is strongly adsorbed on activated carbons with isosteric heat between 15 and 33 kJ/mol [130] and the retention volumes increased with an increase in the surface areas of activated carbons. The results of the studies of adsorption of acetaldehyde [131] showed that the amount adsorbed depends strongly on the pore size distributions of carbons and their surface chemistry. When very small pores, close in size to the acetaldehyde molecule, and oxygencontaining groups are present (to certain extent), the heat of adsorption reaches its maximum value. A small density of surface groups can enhance the heat of adsorption whereas extensive oxidation leads to a decrease in the strength of adsorption forces. This happens due to the blocking of the pore entrances with functional groups and a decrease in the accessibility of the hydrophobic surface where the dispersive interactions of the hydrocarbon moiety with small pore walls can be enhanced. Oxidation of the carbon surfaces results in an increase in the amount of acetaldehyde adsorbed at saturation conditions indicating the importance of hydrogen bonding of adsorbate molecule with functional groups present on the activated carbon surface. Similar effect was noticed when the nitrogen enriched carbons were used as adsorbents [132]. Moreover, the adsorption capacity was found to depend strongly on the volume of pores in the adsorbents. The strong effect of dependence on the pore volume was also observed by Fuertes and coworkers [133]. For adsorption of n-butane and nhexane at room temperature it was found that at high adsorbate concentrations the amount adsorbed is a function of the pore volume, while at low concentrations, it depends mainly on pore size distributions of carbons. Moreover, at low relative pressure (P/Po < 0.004) the amount adsorbed can be correlated with the molecular parachor and the polarizability of adsorbates. The effects of surface properties of carbons on adsorption of amines [134, 135] and carboxylic acid were also investigated [136, 137]. For amines, at small concentrations, the acidic groups increased the amount adsorbed [135] whereas, in the case of valeric acid, the surface basic groups interacted with the adsorbate molecule [136, 137]. For the gross adsorption capacity, the volume ofmicropores, especially those smaller than loA governed the performance of materials. Study ofadsorption ofpolar methyl tertiary-butyl ether (MTBE) and nonpolar 1- methylbutane vapors on activated carbons in the dynamic conditions was carried out by Gironi and coworkers [138]. The maximum capacities ofactivated

21.4

Choice of Proper Carbon for a Desired Application

553

carbons for adsorption of air and MTBE or 1-methylbutane were equal to 0.55 and 0.45 gig, respectively. It was observed that during the adsorption of mixtures, MTBE is adsorbed preferentially on the carbon and the progressive saturation of the solid bed by MTBE causes the displacement of the previously adsorbed 1-methylbutane. Detailed investigation of interactions of MTBE and TCE (trichloroethane) with the surface of various activated carbon fibers was performed from aqueous phase by Li and coworkers [139]. Following differences in the sizes of the molecules, it was found that 7-10 A pores are preferable for TCE adsorption whereas MTBE is adsorbed primarily in 8-11 A pores. The authors concluded that the effective adsorbents to remove TCE and MTBE should be microporous with the pore sizes of about 1.3-1.8 times larger than the kinetic diameters of the target molecules. Moreover, the surface should be hydrophobic and the amount of heteroatoms such as oxygen and nitrogen should not exceed 3 mmol/g. The presence of surface functional groups is not favorable for adsorption of both those species due to the competition with water for high-energy sites. When adsorption was carried out from cyclohexane, surface of oxidized carbon was found to be preferable for MTBE adsorption. It was due to the preferential adsorption of MTBE on carboxylic acids and phenolic hydroxyl groups where hydrogen bonds could be formed between ether oxygen and hydrogen atoms of those groups. In water the adsorbents always exhibit a larger adsorptive capacity for TCE than for MTBE due to the greater aqueous solubility of MTBE. The importance of hydrogen bonding was also underlined in the studies of such volatile organic compounds as alcohols [140] or diethyl ether [141]. The strength of adsorption of those species increased when heteroatoms were incorporated to the matrix but for the gross adsorption capacity the volume of micropores was important. The chemistry of adsorbed VOCs molecules has also an effect on adsorption energy, which may increase with surface coverage when functional groups are present [142] due to the adsorbate-adsorbate interactions. Moreover, in some cases the chemical reactions of specific organic compounds with surface groups can occur in the presence of hot air as indicated by Popescu and coworkers [143].

21.4 CHOICE OF PROPER CARBON FOR A DESIRED ApPLICATION

The variety of activated carbons, carbon fibers, and carbon monoliths present on the market along with differences in the molecules to be adsorbedremoved causes that the choice of the adsorbents for a desired application becomes a difficult task. The capacities, for H 25, 502' NO x , HCN, or VOCs removal depend on the type of carbon used (Fig. 21.3). The problem is even more complex when multicomponent adsorption is expected to occur and the regeneration options have to be considered. Usually carbon specifications

Chapter

554

21

Removal of Inorganic Gases and VOCs on Activated Carbons

0.5 0.45 0.4

C> -...

.9

0.35

"C Q)

.0

0.3

"C ctS

0.25

(; en

C ~

0

E

«

0.2 0.15 0.1 0.05 0

Figure 21.3 Summary of the activated carbons-activated carbon fibers capacities for various species reported in the literature.

list such features as surface area (iodine number), density, hardness, and ash content, along with the specific test checking the target performance such as the hydrogen sulfide capacity or butane working capacity [13]. Those numbers, even if obtained following exactly the test procedures, should be compared with great precautions. For instance, in the case of hydrogen sulfide, to obtain meaningful results the experiments should be done at very low concentrations of H 2 S, taking into account the possibilities of the large differences in the rates oxidation on unmodified and impregnated carbons. Oxidation ofH 2 S on caustic carbon is a fast reaction while oxidation on unmodified carbon is rate limited due to the discussed above the complexity of the process. When the concentration is low and the contact times in the bed are long enough, both processes can go to completion. This means that the accelerated test, which is a standard procedure to evaluate the H 2 S breakthrough capacity of carbons, can be used for comparison of results only when the mechanisms of reactions are more or less similar. It follows that results can only be compared within the categories of unmodified carbons or caustic-impregnated ones. Moreover, it should be always taken into account that the conditions oflaboratory tests are different from those in real life. In the real environment, for instance, in sewage treatment plants, carbons are exposed to other species besides H 2 S, including many hydrocarbons, VOCs, and CO 2 • These species can enhance the breakthrough capacity by changing the pH of the carbon surface but they can also decrease the capacity by blocking the high-energy adsorption centers, small pores.

N ~

~

Table 21.2 Summary of important surface features governing the adsorption of inorganic species and VOCs at the temperatures close to ambient in the presence of air and humidity

()

::::r

or::;. (t)

S, ""'C

a

"'0

~

() Q)

H2S

S02 NO x

Physical adsorptiondissolution-oxidation

Physical adsorption-oxidation Adsorptionoxidation-reduction

HCN

Adsorptioncomplexationoxidation

VOC

Physical adsorption

Sulfur radicals, sulfur polymers, S02, H 2S0 4

S02, H 2S0 4 NO, N0 2, N 2, CO 2, CO, HN0 3 (CNh, CNCONH 2, (CONH 2)2 metal cyanides No reaction

Crucial component, adsorption in film of water, ensures dissociation

Volume of micropores, small size « 1 nm) promotes fonnation of S02 and H 2S0 4

Enhanced removal Should be less than 60%

Pore width <0.7 nm, volume of micropores

Enhanced removal

Mesopores where impregnant is present

Should be less than 60%

At small concentrations-small sizes are critical, for total capacity-high volume of micropores is needed

Basic surface (nitrogen or oxygen groups) promotes dissociation of H 2Sand oxidation of HS-, required pH> 4.5, basic nitrogen groups significantly increase basicity Active centers-oxygen- and nitrogen-containing groups Oxygen- or nitrogen-containing groups are centers for NO chemisorption

Fe 2 0 3 , CaO Cu, metals from group

6-8

co ::::s

~

Q)

o(t) ~.

roc.. »

"'0

""£. r::;.

CaO,

~

o·

::::s

Cu

Cu, Ag, Fe, Ni, Zn Oxygen and nitrogen groups important for adsorption of small concentration of polar VOCs

V1 V1 V1

Chapter

556

21

Removal of Inorganic Gases and VOCs on Activated Carbons

As described above, very important factors influencing the performance of carbons as adsorbents of either inorganic gases or VOCs are their surface area, pore volume, and pore size distributions. They are important not only as active centers for physical adsorption but also as storage space for chemically enhanced adsorption (oxidation or complexation) as happens in the case of hydrogen sulfide, sulfur dioxide, or hydrogen cyanide. The specific stress should be put here on the pore size distribution since the pore sizes are really critical for removal of pollutants at low concentrations. The sizes should be comparable to the size of the molecule to be adsorbed (one to twice larger) to impose the strong adsorption forces. Besides porosity, it is clearly demonstrated the surface chemistry of carbons is also a very important factor influencing the adsorption and it should not be neglected. Even subtle changes in surface acidity and basicity can have an effect on the amount adsorbed or on the extent of chemical reactions occurring on the surface. Moreover, the ash content or the content of the catalytic metals in ash has been also indicated as affecting the performance of adsorbents. In some cases, to reach the final goal of surface reaction as, for instance, reduction of NO x by carbon, NO has to be first adsorbed and oxidized, and for this step the surface oxygen groups are very beneficial. In the case of VOCs, the situation is even more complex. They are organic compounds so even though their affinity to be adsorbed on the hydrophobic surface of carbon is an unquestionable fact, the surface chemistry plays a critical role when concentrations are very small and the molecules exhibit various degrees of polarity as a result of the presence of heteroatoms such as oxygen, nitrogen, or chlorine. At such conditions, the strength of specific interactions via hydrogen bonding or an acid-base mechanism can be important to enhance the amount adsorbed. Table 21.2 summarizes the specific features of carbon surface, which have been demonstrated as important for the adsorption processes of species addressed in this chapter. These data can be used as a specific guideline to find the best adsorbents for the desired applications. As mentioned above, when the adsorbed phase contains more then one component, which occurs in the majority of reallife applications, the possibility of physical and chemical interactions between various molecules and the effect of those interactions on the enhancementinhibition and the feasibility of the removal process should be considered.

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Removal of Inorganic Gases and VOCs on Activated Carbons

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562

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21

Removal of Inorganic Gases and VOCs on Activated Carbons

97. Raj akovic, Lj.V., Hic, M.R., Jovanic, P.B., and Radosevic, P.B. (1995). Stoichiometric analysis of chemisorption of hydrogen-cyanide onto activated carbon cloth. Carbon, 33, 1433-41. 98. Hall, P.G., Gittins, P.M., Winn, J.M., and Robertson, J. (1985). Sorption of phosphine by activated carbon cloth and the effects of impregnation with silver and copper nitrates and the presence of water. Carbon, 23, 353-71. 99. Singh, B., Prasad, G.K., Suryanarayana, M.V.S., and Banerjee, S. (2001). The reaction of thiodiglycol on metal-impregnated carbon. Carbon, 39, 2131-42. 100. Freeman, F.G. and Reucroft, P.J. (1979). Adsorption of HCN and H 20 vapor mixtures by activated and impregnated carbons. Carbon, 17, 313-16. 101. Rubel, A.M and Stencel, J.M. (1996). Effect of Pressure on NO x adsorption by activated carbons. Energy Fuels, 10, 704-70. 102. Izquierdo, M. T. and Rubio, B. (1998). Influence of char physicochemical features on the flue gas nitric oxide reduction with chars. Environ. Sci. Technol., 32, 4017-22. 103. Xia, B., Phillips, J., and Chen, C-K. (1999). Impact of pretreatments on the selectivity of carbon for NO x adsorption/reduction. Energy Fuels, 13, 903-6. 104. Kong, Y. and Cha, C-Y. (1996). NO x abatement with carbon adsorbents and microwave energy. Energy Fuels, 9, 971-5. 105. Kong, Y. and Cha, C-Y. (1996). Microwave-induced regeneration of NOx-saturated char. Energy Fuel, 10, 1245-9. 106. Lee, Y-W., Park,J-W., Yun,J-H., et al. (2002). Studies on the surface chemistry based on competitive adsorption ofNO x -S0 2 onto a KOH impregnated activated carbon in excess 02' Environ. Sci. Techno!', 36, 4928-35. 107. Lee, Y-W., Choi, D-K., and Park, J-W. (2001). Surface chemical characterization using AES/SAM and ToF-SIMS on KOH-impregnated activated carbon by selective adsorption ofNO x ' Ind. Eng. Chern. Res., 40, 3337-45. 108. Ulan-Gomez, MJ., Salina-Martinez de Lecea, C., Linares-Solano, A., and Radovic, L.R. (1998). Potassium-containing coal chars as catalysts for NO x reduction in the presence of oxygen. Energy Fuels, 12, 1256-64. 109. Garcia-Garcia, A., Illan-Gomez, MJ., Linares-Solano, A., and Salinas-Martinez de Lecea, C. (2002). NO x reduction by potassium-containing coal briquettes. Effect of preparation procedure and potassium content. Energy Fuels, 16, 569-74. 110. Garcia-Garcia, A., Illan-Gomez, MJ., Linares-Solano, A., and Salinas-Martinez de Lecea, C. (1999). NO x reduction by potassium-containing coal briquettes. Effect of N0 2 concentration. Energy Fuels, 13, 499-505. 111. Bueno-Lopez, A., Caballero, J.A., and Garcia-Garcia, A. (2002). Analysis of the reaction conditions in the NO x reduction process by carbon with a view to achieve high NO x conversions. Residence time considerations. Energy Fuels, 16, 1425-8. 112. Mochida, I., Korai, Y., and Shirahama, M., et al. (2000). Removal of SOx and NO x over activated carbon fibers. Carbon, 38, 227-39. 113. Matzer, S. and Boehm, H.-P. (1998). Influence of nitrogen doping on the adsorption and reduction of nitric oxide by activated carbons. Carbon, 36, 1697-709. 114. Oark, B.-J., Park, S-J., and Ryu, S-K. Removal of NO over copper supported on activated carbon prepared by electroless plating. J. Colloid Interface Sci., 217, 142-5. 115. Davini, P. (2001). S02 and NO x adsorption properties of activated carbons obtained from a pitch containing iron derivatives. Carbon, 39, 2173-9.

References

116. Yamshita, H., Tomita, A., Yamada, H., et al. (1993). Influence of char surface chemistry on the reduction of nitric oxide with chars. Energy Fuels, 7, 85-91. 117. Ulan-Gomez, M.J., Linares-Solano, A., Radovic, L.R., and Salina-Martinez de Lecea, C. (1996). NO reduction by activated carbons. 7. Some mechanistic aspects of uncatalyzed and catalyzed reaction. Enetgy Fuels, 10, 158-68. 118. Illan-Gomez, M.J., Linares-Solano, A., Radovic, L.R., and Salina-Martinez de Lecea, C. (1995). NO eeduction by activated carbons. 2. Catalytic effect of potassium. Enetgy Fuels, 9, 97-103. 119. www.epa.gov/ttn/atw/188polls.html 120. Yu, F.D., Luo, L.A., and Grevillot, G. (2002). Adsorption isotherms of VOCs onto an activated carbon monolith: experimental measurement and correlation with different models.]. Chem. Eng. Data, 47, 467-73. 121. Dubinin, M.M. (1966). Porous structure and adsorption properties of active carbons, In Chemistry and Physics of Carbon, Vol. 2 (P.L. Walker, ed.). Marcel Dekker, pp. 51-120. 122. Kiselev, A.V. and Yashin, Y.I. (1969). Gas Adsorption Chromatography, Plenum. 123. Bansode, R.R., Losso, J.N., Masrshall, W.E., et al. (2003). Adsorption of volatile inorganic compounds by pecan shell- and almond shell-based granular activated carbons. Bioresource Technol., 90, 175-84. 124. Pre, P., Delage, F., Faur-Brasquet, C., and Le Cloirec, P. (2002). Quantitative structure-activity relationship for the prediction ofVOCs adsorption and desorption energies onto activated carbon. Fuel Process Technol., 77-8, 345-51. 125. Chiang, Y-C., Chiang, P.C, and Chang, E.E. (2001). Effects of surface characteristics of activated carbons on VOC adsorption.]. Environ. Eng., 127, 54-62. 126. Delange, F., Pre, P., and Le Cloirec, P. (2000). Mass transfer and warming during adsorption of high concentrations of VOCs on an activated carbon bed: experimental and theoretical analysis. Environ. Sci. Technol., 34, 4816-21. 127. Do, D.D. and Hu. X. (1993). An energy-distributed model for adsorption kinetics in large heterogeneous microporous particles. Chem. Eng. Sci., 48, 2119-27. 128. Chou, M-S. and Chiou, J-H. (1997). Modeling effects of moisture on adsorption capacity of activated carbon for VOCs.]. Environ. Eng., 1213, 437-43. 129. Shin, H-C., Park,]-W., Park, K., and Song, H-C. (2002). Removal characteristics of trace compounds of landfill gas by activated carbon adsorption. Environ. Pollut., 119,227-36. 130. Domingo-Garcia, M., Fernandez-Morales, I., Lopez-Garzon, F.J., et al. (1999). On the adsorption of formaldehyde at high temperatures and zero surface coverage. Langmuir, 15,3226-31. 131. EI-Sayed, Y. and Bandosz, T.J. (2001). A study of acetaldehyde adsorption on activated carbon. J. Colloid Interface Sci., 242, 44-51. 132. EI-Sayed, Y. and Bandosz, T.J. (2002). Acetaldehyde adsorption on nitrogencontaining activated carbons. Langmuir, 18, 3213-18. 133. Fuertes, A.B., Marban, G., and Nevskaia, D.M. (2003). Adsorption of volatile organic compounds by means of activated carbon fibre-based monoliths. Carbon, 41,87-96. 134. Perez-Mendoza, M., Domingo-Garcia, M., and Lopez-Garzon, F.J. (2000). Adsorption of methylamines on carbon materials at zero surface coverage. Langmuir, 16,7012-18. 135. Abe, M., Kawashima, K., Kozawa, K., et al. (2000). Amination ofactivated carbon and adsorption characteristics of its aminated surface. Langmuir, 16, 5059-63.

Chapter

21

Removal of Inorganic Gases and VOCs on Activated Carbons

136. EI-Sayed, Y. and Bandosz, T J. (2003). Effect of increased basicity of activated carbon surface on valerie acid adsorption from aqueous solution. Phys. Chern. Chern .Phys., 5, 4892-9. 137. EI-Sayed, Y. and Bandosz, TJ. (2004). Adsorption of valerie acid from aqueous solutions on activated carbons; role of surface basic sites. J. Colloid Interface Sci. 138. Gironi, F., Capparucci, C., and Marrelli, L. (2003). Adsorption ofMTBE vapors onto activated carbon. J. Chern. Eng. Data, 48, 783-8. 139. Li, L., Quinlivan, P.A., and Knappe, D.R.U. (2002). Effect of activated carbon

140. 141. 142. 143.

surface chemistry and pore structure on the adsorption of organic contaminants from aqueous solution. Carbon, 40, 2085-100. Salame, 1.1. and Bandosz, TJ. (2000). Adsorption of water and methanol on micro- and mesoporous wood-based activated carbons. Langmuir, 16, 5435-40. Salame, 1.1. and Bandosz, TJ. (2001). Study of diethyl ether adsorption on activated carbons using IGC at finite concentration. Langmuir, 17, 4967-72. Hsieh, C.-T. and Chen, J.-M. (2002). Adsorption energy distribution model for VOCs onto activated carbons, J. Colloid. Interface Sci., 255, 248-53. Popescu, M., Joly, J.P., Carre, J., and Danatoiu, C. (2003). Dynamical adsorption and temperature-programmed desorption of VOCs (toluene, butyl acetate and butanol) on activated carbons, Carbon, 41, 739-48.

GAS SEPARATION AND STORAGE BY ACTIVATED CARBONS Shivaji Sircar Department of Chemical Engineering, Lehigh University, Bethlehem, PA, USA

Contents Introduction Activated Carbons for Gas Separation and Purification 22.3 Mechanisms of Gas Separation by Activated Carbons 22.4 Examples of Gas Separation Processes 22.5 Adsorptive Process Design 22.6 Storage of Natural Gas on Activated Carbons 22.7 Conclusions References

22.1

22.2

22.1 INTRODUCTION

Separation and purification of gas mixtures by selective adsorption of one or more components of the mixture on a micro- and meso-porous adsorbent is a major unit of operation in the chemical, petrochemical, environmental, and pharmaceutical industries. The phenomenal growth in the development of this technology during the last 20 years is demonstrated by Fig. 22.1. It shows the number of the US Patents issued every year between 1980 and 2000 on "gas separation by adsorption" and "adsorption for air pollution control." More than Adsorption by Carbons ISBN: 978-0-08-044464-2

© 2008 Elsevier Ltd.

All rights reserved.

565

566

Chapter

Gas Separation and Storage by Activated Carbons

22

US Patents (1980-2000)

250

r---------'----------,

200

Co

Q)

150

<' en "E Q) Cii Q.

en

::J

'0 0

z

(a) Gas separation by adsorption (b) Pressure swing adsorption (c) Temperature swing adsorption (d) Adsorption for air pollution

100 Total = 1164

\ 50

0~~

1980

........---,----a"""~...I----J----I----L---I 1990 2000 Year

Figure

22.1

Results of the US Patent survey.

4000 patents were granted in these two areas and the patent estate continues to grow rapidly [1]. The main reasons for this are as follows: • Commercial availability of a spectrum of adsorbents like activated carbons, zeolites, aluminas, silica gels, and polymeric materials having a variety of pore structures and surface properties and exhibiting a variety of core adsorptive properties like equilibria, kinetics, and heats for the gas separation or purification application. • Large flexibility in the design and operation of the adsorptive separation and purification processes by taking advantage of the core properties. A successful separation process calls for the optimum marriage between the properties of the adsorbent and the process design. Thus, there can be many

22.2

Activated Carbons for Gas Separation and Purification

Table 22.1 Key applications of activated carbons in gas separation and purification

Trace impurity removal Solvent vapor removal and recovery Air separation Removal of CO 2 from flue gas Carbon dioxide-methane separation from landfill and biogases Hydrogen and carbon dioxide recovery from steam-methane reformer off-gas, coke oven gas, ethylene off-gas, coal gasification, etc.

TSA TSA and PSA PSA PSA PSA PSA

[3-6] [4-6] [7-13] [14] [15] [16, 17]

different combinations of materials and processes to achieve the same separation goal. This choice provides the driving force for innovations [2]. Activated carbons have played a major role in the development of adsorption technology. Table 22.1 is a brief list of key application areas where activated carbons are used. Removal oftrace organic and inorganic impurities from a gas stream by an activated carbon is one ofthe oldest applications ofadsorption technology. The other applications of Table 22.1 where the adsorbed components are present in dilute or bulk quantities in the feed gas mixture were developed during the last 30 years. Two generic process technologies are used for all of these applications. They are known as (1) the thermal swing adsorption (TSA) and (2) the pressure swing adsorption (PSA) processes. Both processes consist of a set of sequential unsteady state cyclic steps. These steps include the primary adsorption and desorption steps as well as a variety of complementary steps. They are designed to obtain the desired product gas purity and recovery while reducing the adsorbent inventory and the energy of separation. The adsorption steps in both processes are carried out by passing the feed gas mixture through a packed bed of the adsorbent at the highest pressure level of the cycle. Desorption of the adsorbed components in the TSA processes is achieved by heating the adsorbent. Desorption in the PSA processes is affected by lowering the superincumbent gas phase partial pressures of the adsorbed components without heating the adsorbent. Table 22.1 gives the most commonly used process choice for the applications.

22.2 ACTIVATED CARBONS FOR GAS SEPARATION AND PURIFICATION

Commercially used activated carbons for gas separation and purification are generally produced from coal, petroleum, vegetable, and polymeric precursors. The nature of the precursor, the method of carbonization, and the activation procedure determine the pore structure (volume and size distribution), the

568

Chapter

22

Gas Separation and Storage by Activated Carbons

surface chemistry (polarity, types of oxygen and hydroxyl group, presence of other elements), the particle and bulk densities, the hardness, the ash content, and the fraction of active adsorption surface area of the final product. These physicochemical properties dictate the overall core adsorptive properties of the activated carbon. Table 22.2 lists some of these properties for several activated carbons [18]. They were compiled from the manufacturers' data sheets. Commercial activated carbons are generally produced in granular, bead, pellet, or extrudate forms. The particles contain a complex network of meso-macro pores (pore diameters ranging between 30 A to several microns) and micropores (pore diameter <30 A) of different shapes and sizes. The larger pores act as arteries for the gas molecules to be transported from the external gas phase to the mouth of the micropores. Most of the adsorption capacity of a gas on the carbon is created by adsorption within the micropores. Figure 22.2 shows the cumulative pore size distribution of the carbons of Table 22.2 [18]. They were also obtained from the manufacturers' data sheet. The pore size distributions may vary over a large range (RB and XE 340), a medium range (BPL and Witcarb), or a very narrow range (MSC V and MSC). The last types of carbons are called molecular sieve carbons (MSC) because their mean pore diameters are comparable with the molecular diameters of gaseous adsorbates (3-5 A). The mean pore diameters of other carbons (20-50 A) are several times bigger than the gas molecular diameters. The large differences in the physicochemical properties of these carbons generate a large variation (and thus, choice) in the core adsorptive properties of these carbons for gas separation.

Table

22.2

BPL RB Witcarb 965 Amoco PX21 PCB Ambersorb XE340 MSCV MSC

Physical properties of activated carbons

2.1 2.3

Calgon Calgon Witco

Coal Coal Petroleum

1100 1250 1300

0.70 1.22 0.65

0.48 0.41 0.47

Amoco

Petroleum

3150

1.80

0.30

Calgon Rohm Haas

Vegetable Polymer

1200 400

0.72 0.34

0.44 0.60

2.2 1.3

Calgon Takeda

Coal Vegetable

0.50 0.43

0.67 0.67

2.1 2.2

8.0 23.0 1.0 2.0 6.0 < 0.5

22.3

6'

Mechanisms of Gas Separation by Activated Carbons

1.0

Pore volume distribution of various carbons

"" ()

~ 0.8

as E ::J

(5

I I

0.6

>

I I

Q)

0 0.4 a.

MSC'I

Q)

> ~ 0.2

I t

"3

t

E ::J

()

0.0

1.0

2.0

3.0

4.0 5.0

20.0

30.0

40.0 50.0

100.0

Pore diameter (A) -....

Figure 22.2 Pore size distributions of various activated carbons.

22.3 MECHANISMS OF GAS SEPARATION BY ACTIVATED CARBONS The separation of a gas mixture by an activated carbon is affected by

(a) Thermodynamic selectivity by which certain components of the gas mixture are preferentially concentrated near the solid surface due to the gas-solid molecular interactions. All components of the gas mixture, however, have access to the adsorption sites inside the carbon pores. (b) Kinetic selectivity by which certain components of the gas mixture diffuse into the carbon micropores faster than the other components creating a transient adsorbed phase having a composition different than that of the gas phase. This is dictated by the relative diameters of the gas molecules and the nucropores. (c) Molecular sieving where certain components ofthe gas mixture are essentially excluded from entering the micropores because of their shapes and sizes. Most practical gas separations using activated carbons are based on thermodynamic selectivity created by van der Walls', pole-pole, and pole-induced pole interactions between the gas molecules and the surface molecules at the walls of the carbon pores [19]. Examples of separation by kinetic selectivity are sporadic. True cases of molecular sieving by activated carbons are rare. The activated carbons can be energetically homogeneous or heterogeneous for adsorption of a gas. The homogeneous behavior is depicted if all of the adsorption sites within the adsorbent have the same gas-solid interaction energies. Otherwise, the adsorbent is heterogeneous. The heterogeneity can be caused by the presence of a distribution of (i) pores of different sizes and shapes and (ii) sites of different surface chemistry inside the adsorbent mass. Heterogeneity has

Chapter

570

22

Gas Separation and Storage by Activated Carbons

profound influence on the core adsorptive properties of the activated carbons for gas separation.

22.4 EXAMPLES OF GAS SEPARATION PROCESSES

The following sections describe a few cases of the gas separation applications listed in Table 22.1 in more details as well as several other emerging applications. 22.4.1

Trace or Dilute Impurity Removal

Activated carbon columns are frequently used to remove trace or dilute organic impurities from an inert nonadsorbing gas. These impurities may consist of toxic compounds, odor-forming compounds, solvent vapors, volatile organic compounds, etc. A TSA process is generally used for these applications. However, both TSA and PSA processes are used for the particular application of solvent vapor removal and recovery which are described in Section 22.4.1.1 22.4.1.1

Solvent vapor recovery

Many industrial operations use large quantities of organic solvents which contaminate the vent streams. Activated carbon columns are used for their removal and recovery. Figure 22.3(a) is a schematic drawing of a three-column embodiment of a TSA process for this application. (i) The contaminated gas is passed through the carbon column at a near ambient temperature (To) in order to produce a clean effiuent gas (less than 10 ppm impurity). (ii) The column is then countercurrently heated with a hot (temperature = T H ) solvent-free gas to desorb the solvent vapors. The effluent gas is cooled to To in order to condense out most of the solvents and the remaining gas is recycled as feed. (iii) The column is then cooled down to To by countercurrently flowing a solvent-free gas at To. The column effiuent from step (iii) is heated to TH and used as the heating gas for step (ii). A part of the clean gas produced during step (i) is used as the solvent-free gas for steps (ii) and (iii). The process is then repeated starting from step (i). Alternatively, superheated steam can be used as the regeneration fluid in step (ii) [5]. Three columns are needed for continuous operation of this cycle. Figure 22.3(b) is a schematic drawing of a two-column embodiment of a PSA process for solvent vapor recovery. (i) The solvent-laden feed gas is passed through the carbon column at a superambient pressure level (PA ) in order to produce a solvent-free effiuent gas at pressure PA. (ii) The column is then countercurrently depressurized to a near ambient pressure level (FD ) to desorb a part of the adsorbed solvents. It is then (iii) countercurrently purged at pressure PD with a part of the solvent-free gas produced by step (i) in order to further desorb the solvent. (iv) Finally, the column is countercurrently pressurized from PD to PA with another part of the solvent-free gas produced during step (i). The

22.4

Examples of Gas Separation Processes

(a)

Thermal swing adsorption (TSA) system

57 1 (b) Pressure swing adsorption (PSA) system

Solvent + inert gas .....

Cooler Separator

Solvent + inert gas Solvent-free gas

(c)

Rotary adsorber O·Solvent-riCh gas

Solvent-free gas

Q

fan for regeneration

Figure 22.3 Schematic drawings of solvent vapor recovery systems: (a) conventional thermal swing adsorption, (b) conventional pressure swing adsorption, and (c) rotary adsorber.

process is then repeated starting from step (i). At least two columns are needed

for continuous operation of the PSA cycle by balancing the duration of step (i) with the combined durations of steps (ii)-(iv). The solvent can be recovered by condensing it out from the desorbed gases. This PSA cycle is a modified version of the classical Skarstrom cycle [20]. The separation efficiency can be increased by using a subatmospheric pressure level (FD ) for desorption of the solvents. A rotary bed adsorber (also called the adsorption wheel), which provides a truly continuous TSA system, has also been employed for solvent vapor recovery [21]. Figure 22.3 (c) is a schematic representation of this arrangement. It uses a shallow wheel-shaped adsorption bed that continuously turns about an axis inside a fixed supporting frame. A section of the wheel is continuously used for adsorbing the impurities (organic solvents) from an inert gas in order to produce a solvent-free gas stream while the other section of the wheel is continuously regenerated by heating it with a part of the solvent-free gas. The solvents can be recovered by condensation from the regeneration effluent gas. The adsorbent wheel is made from a honeycomb-shaped alumina substrate which can be coated with layers of activated carbons.

Chapter

57 2

22

Gas Separation and Storage by Activated Carbons

Table 22.3 Adsorption of dilute hydrocarbons on BPL carbon at 298 K

n-Hexane

Acetone

1.29 x 10-4 1.58 x 10- 4 2.00 x 10- 4 0.154 1.275

74.9 79.3 78.0 70.8 76.0

0.82 1.47 2.12 2.65 4.20

0.50 1.03 1.99 1.92 3.63

The hydrophobic nature of the activated carbons is best suited for the solvent vapor recovery applications because most industrial waste gas streams containing organic solvents are saturated with water vapor. Activated carbons can retain a large fraction of their dry adsorption capacities for organic compounds in presence of high humidity. Table 22.3 shows a few examples of this behavior [22]. Most polar adsorbents (zeolites, alumina, and silica gels) will not be effective for this application. 22.4.2

Production of Nitrogen from Air

Carbon molecular sieves (CMS) are often used for production of 98+ % nitrogen-enriched gas from ambient air. The separation is based on a kinetic selectivity of0 2 over N 2 . The pore mouths of certain types ofthese microporous CMS materials are altered in such a way that they cause faster diffusion of relatively smaller O 2 molecules (diameter rv3.46 A) into the pore cavities than the N 2 molecules (diameter rv3.64 A). Consequently, a transient 02-enriched adsorbed phase is formed when the CMS is contacted with air for a short period of time. The material has practically no thermodynamic selectivity for air separation and prolonged contact with air eventually allows the N 2 molecules to diffuse into the pore structure of the CMS. The kinetic adsorption selectivity and capacity for O 2 is time dependent. Figure 22.4(a) shows the differences in the kinetic uptakes of0 2 and N 2 from air on such a CMS sample [23]. Numerous PSA processes have been developed for production of98+ % N 2 from ambient air using CMS materials [7-13]. Figure 22.4(b) shows a simple two-column embodiment of a PSA process developed by the Bergbau Forschung Corporation of Germany. It consists of (i) flowing compressed air (rv 80-110 psig (650-860 kPa)) at near ambient temperature through a CMS column for partially pressurizing the column and selective adsorption of O 2 in order to produce the N 2-enriched product gas at feed gas pressure, (ii) pressure equalization of the column with the companion column which has completed the next step, (iii) countercurrent depressurization of the column to near ambient pressure for desorbing 02' and (iv) partial pressurization by pressure equalization with the companion column. The cycle is then repeated starting from step (i). Figure 22.4(c) describes the

22.4

Examples of Gas Separation Processes

573

1.1 1.0

0.9

• Experiment - - Equation (34)

~ 0.8

~ 0.7 :::J

0.6

§

·u

0.5 0.4

u..

0.3

(ij

~

n~2 = 0.68 moles/g k~~4 = 0.0044 sec-1 n~2 =0.18 moles/g k;~4 =0.0684 sec-1

0.2

0.1 0.0 ~=---,---_-I-_--*'-_--L._---.a--.L-,.._-'----~ o 10 20 30 40 Square root time (s 1/2)

(a)

200 ~-------------.. N2

---..,..-0Q00........ product

1:I

150

u..

()

~ ~

'S;

u -a e a.

100

Desorbed gas

(b)

3

4

(c)

Figure 22.4 Air separation by carbon molecular sieve (eMS): (a) uptakes of 0z and N z from air on a eMS sample, (b) schematic drawing of a N z pressure swing adsorption (PSA) system, (c) performance of a N z PSA process.

performance of a N 2 PSA process similar to the one described above [13]. The N 2 productivity (standard ft 3 of N 2 product/ft3 of carbon in system I h (m3 1m3 Ih)) is plotted against the % 02 impurity present in the N 2 product gas. The 02-enriched desorbed gas from the process contained 30-45 % 02' The N 2 productivity decreases as the purity of the product gas is increased. PSA processes have also been designed to produce a 99.99+ % N 2 product using CMS adsorbents, albeit at a reduced N 2 productivity[l 0-12].

22.4.3 Production of Hydrogen and Carbon Dioxide from Reformer Off-Gas The most common industrial process for making H 2 is by catalytic reformation of natural gas (mostly CH 4 ) or naphtha by reacting with steam. The

574

Chapter

22

Gas Separation and Storage by Activated Carbons

reformed gas is then subjected to a water-gas shift reaction to produce a crude H 2 -enriched gas stream containing '""75 % H 2 , 20 % CO 2 , 4 % CH 4 , 1 % CO, and trace N 2 (dry basis) at a pressure of '""lS0-3S0psig ('""1.13-2.51 MPa) [16, 17]. The gas is then purified in a multicolumn PSA system to produce 99.999+ % H 2 at the feed gas pressure with a H 2 recovery of 75-90 %. Activated carbons are the preferred adsorbents for CO 2 adsorption from the crude reformer off-gas because (a) CO 2 is moderately strongly adsorbed on the carbons compared to the zeolites, (b) they provide high selectivities for adsorption of CO 2 over CO, CH 4 , N 2 , and H 2 , and (c) CO 2 is much easier to desorb from the carbons than the zeolites. The last point is a critical issue because the ease of desorption of CO 2 in the PSA process often determines the ultimate H 2 recovery by the process. On the other hand, the SA zeolite is preferred for removal of dilute CO, CH 4 , and N 2 impurities from H 2 in the process because of the zeolite's higher capacity and selectivity of adsorption for these gases. Figure 22.S(a) shows the variety of isotherms (Type I by Brunauer classification [19]) available for adsorption of pure CO 2 on the activated carbons of Table 22.3 and on SA zeolite [18]. Table 22.4 gives the corresponding Henry's law constants and selectivities for adsorption of CO 2 and H 2 at 303 K as well as the isosteric heats of adsorption of pure CO 2 in the Henry's law regions [18]. These data show that (a) the strength of CO 2 adsorption and the coadsorption of H 2 from CO 2 + H 2 mixtures can vary significantly, and (b) the adsorption of CO 2 on the SA zeolite is too strong to be useful in a PSA process. Figure 22.S(b) describes the adsorption isotherms of various gases on the BPL carbon. Table 22.5 gives the Henry's law selectivities for various binary gases on the BPL carbon and the SA zeolite at 303 K [18]. These data indicate that (a) CO 2 is more selectively adsorbed on the BPL carbon than CO, CH 4 , N 2 , and H 2 , and (b) the SA zeolite exhibits much higher selectivities for adsorption of CO, CH 4 , and N 2 from H 2 than the BPL carbon. Figure 22.S(c) describes the isothermal and isobaric desorption characteristics of CO 2 from columns packed with various activated carbons and SA zeolite. The columns were initially saturated with pure CO 2 at 1 atm (101.3 KPa) and 303 K and then purged with pure H 2 at the same conditions [24]. The figure plots the fraction of CO 2 desorbed as a function of H 2 used. The strength of adsorption of CO 2 on these adsorbents increases in the order SA» MSCV>BPL>RB and thus, the ease of desorption of CO 2 from these carbons increases in the order RB>BPL>MSCV»SA [24]. These data clearly validate the logic for the selection of adsorbents for this application. Figure 22.6(a) is a schematic representation of a nine-column "Poly Bed" PSA process developed by the Union Carbide Corporation, USA, for the H 2 purification application [16]. The parallel columns are packed with a layer of an activated carbon in the feed end followed by a layer of SA zeolite at the product end. The PSA cycle has 11 sequential steps consisting of (i) adsorption at feed pressure to produce the H 2 product at the same pressure, (ii) four cocurrent

22.4

Examples of Gas Separation Processes

575

100.0 - - - - - - - - - - - - - - - . . , Pure CO2 adsorption isotherms at 30°C

t

PX21

10.0

C) .........

en

Q)

1.0

(5

E

S c:

0.1 0.1

1.0

10.0

100.0

P(atm) --..

(a) 100.0 Adsorption isotherms of various gases on BPL carbon at 30°C

10.0

t 0> ...........

1.0

en

CD

"0

E

E, c::

0.1 0.1

1.0

10.0

100.0

P(atm) --.....

(b) 1.0 c

E ~

(5

0.9 0.8

(,)

0.7 E ,g 0.6 1:) Q)

> E

0.5

~

0.4

C\I

0.3

0

0

()

'0 0.2 ~ 0

0.1

Pure CO2 desorption by purge at 30°C

0.0 50

(c)

100

Hydrogen purge SUkg

150 -...

Figure 22.5 Ad(de)sorption characteristics ofactivated carbons: (a) isotherms for adsorption of pure CO 2 on various activated carbons, (b) isotherms for adsorption of various gases on the BPL carbon, (c) desorption of pure CO 2 from various adsorbents.

576 Table

Chapter

22.4

22

Gas Separation and Storage by Activated Carbons

Adsorptive properties of CO 2 and H2 at 303 K ...

.

,

.Henry's law . C02~H2· · .

~ .....1sta

..

selectivity..

••••••••

. .

BPL

3.45 2.38 7.14 4.54 2.94 3.92 3.10 138.9

RB MSCV PCB PX21 Witco 965 XE 340 5A zeolite

Table 303 K

22.5

CO 2 + CH4 CO 2 + CO CO 2 + N 2 CO 2 + H 2 CO + CH 4 CO + N 2 CO + H 2 CH4 + N 2 CH 4 + H 2

N2 +H 2

0.038 0.027 0.026 0.046 0.060

24.28 22.61 38.94 20.10 23.03 25.12

91 90 275 98 49

0.188

39.36

7400

Binary Henry's law adsorption selectivities at

2.5 7.5 11.1 90.8 0.33 1.48 12.11 4.5 36.6 8.2

195.6 59.1 330.7 7400.0 3.3 5.6 125.0 1.7 37.8 22.3

depressurization steps to produce essentially pure H 2 streams at various pressures lower than that of the feed gas, (iii) countercurrent depressurization to partly desorb the adsorbed impurities, (iv) countercurrent purge with a H 2 -enriched stream at a near ambient pressure to further desorb the impurities, and (v) four countercurrent pressurization steps using various lower pressure H 2 -enriched streams as well as using a part of the high-pressure H 2 product gas. The cycle is then repeated. Another multicolumn PSA system called "Gemini-9" process was developed by the Air Products and Chemicals, Inc., USA, for purification of H 2 from the crude reformer off-gas [17]. This process was designed to simultaneously

22.4

Examples of Gas Separation Processes

577

Hydrogen

Adsorbed gas plus hydrogen (a)

Crude H2 feed --,....-----------~,.,..,........-~

Product CO 2

(Fuel gas)

Product H2 (b)

Figure 22.6 Schematic flow sheets of (a) Polybed and (b) Gemini-9 pressure swing adsorption (PSA) processes for production of H 2 from reformer off-gas.

Chapter

578 Table 22.6

22

Gas Separation and Storage by Activated Carbons

Comparative performance of two PSA processes

~::s~:

"'...

W~

Polybeda Gemini-9 b

2.10 1.82

~e

99.999 99.999

:

~

86.0 87.1

aFeed gas: 77.1 % H 2 + 22.5% CO 2 + 0.35% CO bFeed gas: 75.4% H 2 + 19.9% CO 2 + 0.96% CO

None 99.4

94.0

CH4 32.0 65.4

66.8 8.1

1.0 5.6

0.04 20.8

+ 0.013% CH4 • + 3.73% CH 4 .

produce a stream of 99.999+ % H 2 and a stream of 99+ % CO 2 from the feed gas. Figure 22.6(b) is a schematic representation of the process. It contains six parallel "A" beds in series with three parallel "B" beds. The A beds are packed with activated carbons for removal of CO 2 from the feed gas. The B beds are packed with SA zeolite primarily for removal of the other impurities. The A and B beds remain connected in series during the adsorption step and then they are decoupled to undergo two completely different sequences of regeneration and pressurization. The cycle steps for A beds include (i) adsorption at feed pressure, (ii) CO 2 rinse at feed pressure and recycle of eilluent gas as feed, (iii) countercurrent depressurization to ambient pressure to desorb a CO 2 -enriched gas to be used in step (ii) after recompression, (iv) evacuation to desorb and produce the CO 2 -enriched product gas, and (v) two pressurization steps. The B beds undergo (i) adsorption to produce the H 2 product at the feed gas pressure, (ii) pressure equalizations with an A and a B bed, (iii) countercurrent depressurization to ambient pressure, (iv) countercurrent purge with a part of the H 2 product gas, and (v) two pressurization steps. Table 22.6 gives a comparative performance of the two processes. The "Poly Bed" process or its variations are frequently used to produce pure H 2 from different H 2 containing feed gases. It, however, produces a CO 2 containing waste gas which is vented after combustion. The Gemini-9 process may be attractive in view of climate (greenhouse gas) control because the CO 2 is produced as a by-product gas for sequestration or use as a chemical feed [16, 17].

22.4.4 Nanoporous Carbon Membranes for Gas Separation Two types of nanoporous activated carbon membranes have been developed for continuous gas separation applications [25]. They are (i) the MSC membrane produced by the Carbon Membranes Limited, Israel [26], and others [25, 27, 28], and (ii) the selective surface flow (SSF) membrane produced by the Air Products and Chemicals, Inc., USA [29]. Both membranes consist

22.4

Examples of Gas Separation Processes

579

of a thin layer « 10 J.Lm) of a nanoporous (3-10 A pore diameter) carbon film supported by a porous solid structure (e.g., carbonized polymeric hollow fiber for MSC and tubular alumina for SSF). They are both produced by judicious pyrolysis of a polymeric film at a temperature of 873-1273 K. However the mechanisms of gas transport through these membranes are very different. The MSC membranes are produced by carbonization of polyacrylonitrile, polymide, and phenolic resins [30]. They contain nanopores (typically <5 A in diameter) that allow some of the molecules of a feed gas mixture to enter the pores at the high-pressure side, adsorb, and then diffuse to the low-pressure side where they desorb into the gas phase. The other molecules of the feed gas are excluded from entering the pores and they are enriched in the high-pressure side. Thus the separation is based on the differences in the molecular sizes and shapes of the feed gas components. The smaller molecules preferentially diffuse through the membrane as schematically depicted by Fig. 22.7(a). Table 22.7 gives the permeance and the permselectivity of the smaller species (component 1) of several binary gas mixtures by the MSC membrane [25, 26, 30]. The SSF membranes are produced by carbonization of polyvinylidene chloride (PVDC) [29]. They contain nanopores (5-7 A in diameters) which allow all of the molecules of the feed gas mixture to enter the pore structure. However, the larger (higher polarizability) and the more polar molecules are selectively adsorbed on the pore walls at the high-pressure side. Then they selectively diffuse on the pore surface to the low-pressure side, where they desorb into the gas phase. The adsorbed molecules effectively block the transport of the smaller molecules through the void space within the pores, if any. Figure 22.7 (b) schematically depicts the transport mechanism through an SSF membrane. Thus, the SSF membrane preferentially permeates the larger molecules of a feed gas mixture whereas the smaller molecules are enriched at the highpressure side. This is a significant advantage because the smaller molecules of a feed gas are often the desired components, and they are produced at the feed gas pressure by the SSF membrane. The selective adsorption-surface diffusion mechanism of transport simultaneously permits high flux and high selectivity of the permeating gases by these membranes as well as operation using relatively low-pressure gradients across the membrane [25]. The SSF membrane can be used to enrich H 2 from C 1-C 4 hydrocarbons or from mixtures with CO 2 and CH 4 [21]. It can also be used to separate H 2 S, which is selectively permeated, from H 2 or CH 4 as shown in Fig. 22.7(c). The figure plots H 2 S rejection (fraction of H 2 S feed that is removed in the low-pressure product gas) as a function of H 2 recovery (fraction of H 2 feed that exits with the high-pressure product gas) for a feed gas containing ""'25 and 50 % H 2 S at a pressure of 0.79 MPa. The membrane was at ambient temperature and the lowpressure side of the membrane was maintained at 0.115 MPa [21]. About 80 % H 2 S could be rejected with a H 2 recovery of ""'80 % from an equimolar feed gas. Figure 22.7(d) shows a flow sheet for a novel two-stage SSF membrane arrangement which can be used to produce a ""'98 % H 2 stream at feed gas

o

80 70 60 50 40 30 20 10

100 90

o

25%H2 S • 50% H2 S I I 10 20 30

j+

40

t'2---

50

--

.-B

60

70

80

,,

90

100

\"\\

"\.\ \

,"

"- ~

i ' . "~

i'":'---.

H2 Recovery (%)

I

PL=0.115MPa I

I

HPH=O.791 MPa I

••

Low Pressure

•

B-rich Product

(d)

SSF Stage I

H 2 S Enriched gas

H2 S + CH 4 (or H2 )

(b)

• -B

Low Pressure

"•• • ••••

~LPore

..

A-rich Product

SSF membrane

Waste

Figure 22.7 Descriptions of nanoporous carbon membranes: (a) mechanism of transport through the molecular sieve carbon (MSC) membrane, (b) mechanism of transport through the selective surface flow (SSF) membrane, (c) separation performance ofHzS-H z mixtures by the SSF membrane, (d) schematic drawing ofa two-stage SSF membrane operation for H zS-Hz/CH 4 separation.

(c)

:£

(J)

~

~

g

'°;

~

(a)

.-A

Hi:h. Pressure

••••

•• ••• • •

A-rich Product

MSC membrane

VI

::s

ao

tu

()

rD c..

tu

» ~ <.

rD 00<

CIQ

o@

V>

c..

::s

tu

::s

?l o·

tu

rD "0

V>

VI

tu

G")

N N

~

"0

tu

:::r

()

o

00

U"1

22.4

Examples of Gas Separation Processes

Table

22.7

O 2 (1)

581

Separation performance of MSC membranes

+ N2

(2)

H 2 (1) + CH 4 (2) CO 2 (1) + CH4 (2) C 3 H 6 (1) + C 3 H s (2)

16.0 365.5 91 183

13,6 500 50 12-15

[23] [22] [22]

[22]

pressure from a gas contaInIng 50 % H 2 + 50 % H 2 S [25]. This remarkable separation is achieved by operating the first stage of the membrane with a low H 2 recovery (r-v30 %) and the second stage with a high H 2 recovery (r-v90 %) [25]. The net H 2 S rejection by the membrane is 98.3 %. The H 2 can be further enriched to make a 99.99+ % pure H 2 product by using a conventional TSA system using an activated carbon adsorbent. The overall H 2 recovery by the SSFTSA hybrid process is r-v77 %. The SSF membrane has been scaled up and pilot tested [31].

22.4.5 Sorption-Reaction Process for Removal of Trace VOC Stricter environmental regulations often require thermal or catalytic incineration oftrace hydrocarbons at a temperature of600-1600 K from contaminated air before venting [32]. This usually consumes a large quantity of fuel (energy) to heat the air mass. A cyclic sorption-reaction (SR) process concept developed by the Air Products and Chemical, Inc., USA, can reduce the energy need for this application [33]. The process consists of (i) adsorption of trace hydrocarbons from the air at ambient temperature and pressure in a bed packed with a mixture of an activated carbon and an oxidation catalyst to produce a clean air stream, (ii) in situ oxidation of the hydrocarbons by directly or indirectly heating the packed bed to about 425 K, and (iii) cooling the bed to near ambient temperature and venting the combustion products. The cycle is then repeated. Only the adsorber vessel and the adsorbent-catalyst mixture are heated to the reaction temperature which reduces the energy need. The adsorption of trace hydrocarbons and their subsequent batchwise thermal desorption substantially increase their concentrations in the gas phase which facilitate the reaction rates. Figure 22.8(a) shows the schematic drawing of a two-column embodiment of the SR process. Figure 22.8(b) shows a shell and tube reactor design for the process using indirect heating and cooling during the cycle. Table 22.8 compares the performance of the SR process for cleaning a 1 MM SCFD (million standard cubic feet per day) (0.0283 x 106 m 3 / day) air stream containing 260 ppm vinyl chloride monomer (VCM) to a level of 1 ppm with that of a conventional plug-flow reactor using a standard oxidation catalyst at a reaction temperature of 600 K [18]. The adsorbent in the SR process was RB

582

Chapter

22

Gas Separation and Storage by Activated Carbons

Time (h) To vent

o 20 1A_A_ H

40

lei

leMA_ 1A

1B

Adsorbent and catalyst Clean air

..........

.....---~

"--"'I~I"""'----.l----"Clean

Blower

Blower

Air -+- )

air Heating fluid

Heating fluid

(a)

(b) 0.3

,.-------------------"'!"'l • Experiment p= 1.0 atm -

t

Langmuir model

0.2

100

200

y(ppm) --...

(c)

Figure 22.8 Sorption-reaction (SR) process for removal of trace organic contaminants: (a) schematic drawing of a two column SR process, (b) shell and tube reactor configuration for the process, (c) isotherms for adsorption of trace vinyl cWoride monomer (VCM) on an activated carbon.

Table 22.8

Energy savings by sorption - reaction process

Power requirement (kW) Adsorbent - catalyst inventory (kg)

3.52 2590

120 364

22.4

Examples of Gas Separation Processes

carbon that was impregnated with 1.5 wt % palladium chloride as the oxidation catalyst. Figure 22.8(c) shows the isotherms for adsorption of trace VCM from air on the RB carbon at three temperatures. The table shows that energy savings of an order of magnitude can be achieved by the SR process.

22.4.6 Chemically Modified Activated Carbons for Gas

Separation Molecular engineering of an activated carbon surface provides a very interesting opportunity to beneficially alter the carbon's core adsorptive characteristics for gas separation. Polar groups can be introduced to the surface of a weakly polar carbon by judicious surface oxidation. Thus, a hydrophobic carbon can be converted to a hydrophilic adsorbent. Figure 22.9(a) shows the water vapor adsorption isotherms at 297 K (specific amount of water adsorbed 11 as a function of relative water vapor pressure x) on the original Ceca carbon (Type V

100

[1'1'

,.

1""'1

99

Water adsorption isotherms at 24 0 C 0.3·

98 97

~ >.

~ ~

0.2

.9

o()

96 95

~

94

« '-

93 92

0.1

91 90

o

0.2

0.4

0.6

0.8

(a)

r'\'

"

i\

r\

.

;

\

\

\

M !\

~. :~~~~~j~~g:~5 40

il1\ •

J

60

50

1.0

x-

"-

70

80

90

100

H20 rejection (%)

(b)

0.35....------------------, - Y - MSC-30 -x- NO.5 0.30 - - NO.7 -a->- NO.8 0.25

~

0.20

(5

E E

o

0.15 0.10 0.05

o.00

~-l...--\.-__J.___J.._-J--...1,.".......JI..___.1.___1.._.I.__.L_,.....L_...L._...1.._J....,_1--l..:...-...L--J

0.0

(c)

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Pressure (bar)

Figure 22.9 Examples ofmolecular engineering of carbon surface: (a) isotherms for adsorption of H 2 0 vapor on various chemically modified carbons, (b) gas drying characteristics of the modified selective surface membrane (SSF) membrane, (c) high-temperature chemisorption of CO 2 on MgO-doped activated carbon.

Chapter

22

Gas Separation and Storage by Activated Carbons

isotherm shape by Brunauer classification [19]) and on carbon samples which have been oxidized by heating in fuming HN0 3 and 45 % HN0 3 solution with or without the presence of copper acetate catalyst at 353 K [34]. Oxidation progressively changed the shape of the water isotherms from Type V to Type IV to Type I indicating that the surface has changed from hydrophobic to mildly hydrophilic. The figure also gives the water adsorption isotherms on NaX zeolite (Type I with very strong adsorption) and Alumina (Type IV with moderately strong adsorption). The Type I water isotherm on the oxidized carbon produced by HN0 3 oxidation in presence of the catalyst exhibits higher water capacity than the alumina in the low-pressure region but it holds water much less strongly than the zeolite. The Henry's law constants for water adsorption on the NaX zeolite, the modified Ceca carbon, and the alumina at 297 K are ~140, 5.3, and 2.1 kg/kg, respectively [34]. These properties are very desirable for a desiccant to be used in a PSA gas drying process (moderate water adsorption capacity and ease of desorption by partial pressure reduction). The modified activated carbon can serve as an improved desiccant for a PSA drier. The carbon surface oxidation procedure described above was also applied to introduce hydrophilicity to the pore walls of the SSF membrane [25]. The oxidized membrane could remove water vapor from air at a moderate feed gas pressure of ~305-405 kPa. Water was selectively adsorbed and permeated through the membrane. The adsorbed water essentially blocked the flow of air molecules through the void space of the modified membrane. Figure 22.9(b) shows the performance of the modified SSF membrane. Air recovery (fraction of air feed that is produced as the high-pressure product gas) is plotted against water rejection (fraction of feed water that is permeated to the low-pressure side) in the figure. The low-pressure side of the tubular SSF membrane was purged with N 2 . The parameter S/F represents the ratio of purge gas flow rate to that of feed gas. It can be seen that 70-80 % of feed water can be rejected with very little air loss (~99 % of feed air is recovered at the feed pressure). The original membrane was totally unselective toward water. The modified SSF membrane can be used as a continuous drying apparatus. Activated carbon surfaces have also been modified by doping them with various metal oxides, such as CaO or MgO or their combinations, in order to produce chemisorbents which are selective toward CO 2 at high temperatures (600-700K) [35]. Figure 22.9(c) shows isotherms for adsorption of CO 2 at 573 K on various doped samples of Maxsorb carbon (MSC-30) produced by the Kansai Coke and Chemical Company ofJapan [35]. Of particular interest is the isotherm No.6 which is a MgO-doped carbon. It exhibits large CO 2 working capacity. Reversible high-temperature CO 2 chemisorbents can be used in the newly developed "Sorption Enhanced Reaction Process" by the Air Products and Chemicals, Inc., USA. The process can produce COx-free H 2 (fuel cell grade) by carrying out the equilibrium-controlled steam methane reforming reaction at a much lower temperature than the conventional processes without sacrificing the conversion of CH 4 to H 2 [36].

22.5

Adsorptive Process Design

585

The above examples demonstrate that activated carbons can be chemically modified for different new gas separation applications and the possibilities are many.

22.5 ADSORPTIVE PROCESS DESIGN The state of the art procedure for design of cyclic PSA or TSA processes using activated carbon adsorbents is to simultaneously solve the partial differential equations describing the mass, the heat, and the momentum balance equations for each step ofthe process using the appropriate initial and boundary conditions. These numerical calculations are carried out over many cycles for the process until a cyclic steady-state performance solution is achieved. Many different numerical integration algorithms are available for this purpose. The core input variables for the solution are multicomponent gas adsorption equilibria, heats, and kinetics for the system of interest [37]. The separation of20 % C 2 H 4 (1) + 80 % CH 4 (2) gas mixture was mathematically simulated using the four-step Skarstrom PSA cycle consisting of adsorption, depressurization, product purge, and product pressurization steps [37]. The feed gas pressure and temperature were 2.08 MPa and 298 K, respectively. The Nuxit charcoal was employed as the adsorbent. An essentially pure stream of CH 4 product (99.87 %) could be produced with a recovery of 28.4 %. The CH 4 productivity was 0.088 kg moles of product/kg of carbon in system/day [37]. Figure 22.10(a) shows the profiles of gas phase mole fractions of C 2 H 4 inside the adiabatic adsorber as functions of column positions at the end of each step of the PSA cycle. Figure 22.10(b) shows the corresponding C 2 H 4 loading profiles on the carbon normalized to the C 2 H 4 capacity at the feed gas conditions. The shaded area in the figure represents the net cyclic working capacity for C 2 H 4 as a function of the column position. These profiles demonstrate the complexity of the process created by nonlinearity of the adsorption equilibria, adsorbent heterogeneity, and column nonisothermality. Most of the working capacity of the carbon for C 2 H 4 is located in the first half of the column (feed end). The second half of the column is used to achieve the high purity of the product gas. These results may not be intuitive. Table 22.9 compares the performance of the above-described PSA process for two extreme cases: (a) isothermal operation and (b) assumption of constant heats of adsorption for the components or ignorance of adsorbent heterogeneity. The severe influence of the energetic heterogeneity of the carbon and the corresponding thermal effects on the separation process is self-evident.

Chapter 22 Gas Separation and Storage by Activated Carbons

586

0.40

c

r-....._--r--__r_--r-....--.--_._--......-..ro--'t"'-"

r-

-_

(i) Repressurize (ii) Adsorb - - _. (iii) Depressurize (iv) Purge

0.30

0

U jg Q)

(5

E 0.20 Q)

c

Q)

~

.c [j

0.10

0.2

0.4

0.6

0.8

1.0

Normalized column axial position, Z*

(a)

iCc: ..... c:

1.00

0> c

:.cco .Q

(i) Repressurize (ii) Adsorb (iii) Depressurize (iv) Purge

0.75

Q)

c

Q)

~

.c Ci5

"0

0.50

Q)

.~

co

E

o

z

0.25

0.00 '--""-""'-....a--"""'.......r..--'--l""-I--""---'---t-~_..a..__L__t'--J..._""__~ . . .iiiilllI 1.0 0.2 0.4 0.6 0.8 0.0

Normalized column axial position, Z*

(b)

Figure 22.10 Adsorption column profiles for C 2 H 4-CH 4 separation by a pressure swing adsorption (PSA) process using activated carbon: (a) gas phase C 2 H 4 mole fractions, (b) C 2 H 4 loadings on the adsorbent.

22.6

Storage of Natural Gas on Activated Carbons

Table 22.9

Performance of the PSA process for (2 H4 + (H 4 separation

CH 4 purity (mol %) CH4 recovery (%) CH 4 productivity (kg moles/kg/day)

99.87 28.4 0.088

99.87 60.16 0.376

99.88 18.92 0.057

22.6 STORAGE OF NATURAL GAS ON ACTIVATED CARBONS The abundance of natural gas, its relatively lower price, and its potential to be a cleaner fuel has promoted much interest in its use as motor fuel. Numerous vehicles around the world have been adapted to use "compressed natural gas (CNG)" as fuel. The gas is typically stored at a pressure of200 atm (r-v20.2 MPa) in heavy steel cylinders. The net deliverable capacity for the CNG tank between 20.2 and 0.137 MPa is 215 standard literslliter of storage volume (m3 /m 3 ). The energy density of CNG is, however, only 29 % of that of gasoline. Replacing CNG by storing methane in a vessel packed with an activated carbon has been a subject of much work during the last 20 years. This concept of using "Adsorbed Natural Gas (ANG)" can potentially reduce the gas storage pressure without sacrificing deliverable capacity. The target pressure is r-v35 atm (r-v3.5 MPa) that can be obtained by a single-stage compressor. The key question is whether the deliverable capacity of ANG can match that ofCNG. Research in this area has been directed toward (a) finding or preparing activated carbons with high micropore volume (or BET surface area) in order to increase the CH 4 adsorption capacity, and (b) to increase the bulk density of the carbon (reduce void volume of the storage vessel) to minimize the amount of unadsorbed CH 4 in the tank. Chemical activation of carbon precursors by heating in alkali solutions and phosphoric acid to create micropores as well as surface activation of microporous carbons by heating in CO 2 and steam are common techniques used for this purpose [38, 39]. Table 22.10 summarizes the published values of isothermal deliverable CH 4 capacities for several activated carbon samples[18, 40-42]. The Amoco PX 21 carbon has the highest BET surface area of all carbons listed in Table 22.3. Yet, the isothermal deliverable CH 4 capacity for this carbon is about 100 m 3 /m 3 [18]. This is due to its low bulk density (high external void). If this carbon can be produced in a monolith form so that the external void in the ANG tank is negligible, then the isothermal deliverable capacity (r-v21 0 m 3 /m 3 ) approaches that of the CNG [18]. Recently, a carbon monolith was fabricated by Lozano-Castello and coworkers, but it produced an isothermal deliverable capacity of r-v126 m 3 /m 3 only [40]. The carbon temperature increases during filling the cylinder with methane and it decreases during methane discharge due to the release and consumption of

588

Chapter

22

Gas Separation and Storage by Activated Carbons

Table 22.10 Isothermal deliverable CH 4 capacities of activated carbons (CNG == 21 5 m3 1m 3 ). . .

I

. .

...

.

.

UU>U

I

Amoco PX 21 at 303 K Amoco PX 21 at 303 K Amoco PX 21 at 298 K Amoco PX 21 at 298 K Activated carbon fiber (C0 2 activated) Activated carbon

Granular (bulk density == 0.3 kg/I) Monolith (no external void) (bulk density == 1.08 kg/I) Granular Bonded with polymer

Monolith

82.0 (calculated) 210.0 (calculated) 101.0 144.0 143.0

[42]

126.0

[40]

[18] [18]

[41 ] [41]

the heats of ad(de)sorption, respectively. Instantaneous heat removal or supply from or to an ANG system may not be practically possible. Consequently, the real deliverable capacity of the activated carbon system may be much less than the isothermal numbers given by Table 22.10 if a rapid fill-up or supply of CH 4 is required. The adiabatic delivery capacity (ADC) of the carbon may be a more appropriate variable in absence of a heat supply/removal mechanism. Figure 22.11 (a) shows CH 4 adsorption isotherms on PX21 activated carbon at different temperatures [18]. The isosteric heat of adsorption of CH 4 (q) is 16.7kJ/mole. Figure 22.11(b) shows the CH 4 adsorption isobars at 35.0atm (3.54 MPa) and 1.35 atm (0.137 MPa) on the same carbon as well as the adiabatic fill-discharge operating lines, which have slopes equal to the ratio of the heat capacity of the adsorbent (Cp = 0.25cal/g/C (1.046k]/kg/K)) to the isosteric heat of adsorption of CH 4 . Accordingly, a temperature rise and a drop of 66 and 77 K from a base temperature of 303 K will occur during adiabatic filling and discharge of CH 4 , respectively, when operated between these two pressure levels. The corresponding ADC for the granular carbon will be ~36.5 m 3 /m 3 only [18]. Attempts have been made to incorporate phase change materials with the activated carbons inside the ANG tanks in order to remove (or supply) the heat from (or to) the carbon so that the carbon remains isothermal during the filldischarge process [41]. This, however, lowers the carbon inventory in the tank and increases system cost. Instantaneous heat transfer between the carbon and the phase exchange material may also not be practically feasible. Several theoretical studies of natural gas storage on activated carbons have been undertaken. A molecular simulation of CH 4 adsorption predicts that the maximum storage capacity by a palletized and a monolith activated carbon will be 146 and 209 m 3 1m3 , respectively [43]. Nonisothermal fill-discharge and dynamics ofCH 4 ad(de)sorption in ANG systems have also been evaluated [44].

22.7

Conclusions

100.0 - - - - - - - - - - - - - - - - - - - - - - . . . ,

Methane adsorption isotherms on PX 21 carbon

t

10.0

C)

en Q)

"'6 E

5

1.0

c::-

qO =4.0 kcal/mole

0.1

---------------"'--------1 1.0 10.0 100.0

0.1

P(atm)

(a)

---.......

r----------------------.. . . . . .

15

10

~ Q)

"'6

E

5 c:

5

I - ....1--1.. . . Slope =Cp t

P=1.35AI

o

-50

o

30

100

q 150

(b)

Figure 22.11 Adsorption of CH 4 on PX 21 activated carbon for storage: (a) adsorption isotherms at various temperatures, (b) adsorption isobars and operating lines for CH4 fill and discharge.

22.7 CONCLUSIONS Activated carbons produced from different precursors provide a large spectrum of pore structures and surface chemistry for gas separation and purification. The wide range of core adsorptive properties like adsorption equilibria, heats, and kinetics exhibited by these activated carbons encourages the design and

Chapter

59°

22

Gas Separation and Storage by Activated Carbons

development of novel pressure swing and temperature swing adsorption processes for gas separations. Many successful commercial applications in the areas of trace impurity removal from a contaminated gas, solvent vapor recovery, production of nitrogen from air, production of hydrogen and carbon dioxide from reformer off-gases, etc., already employ activated carbon adsorbents almost exclusively. Potential novel applications include nanoporous carbon membranes, combined sorption and reaction in a single unit operation, and natural gas storage. Molecular engineering of carbon pore structures and surface chemistry can open many new doors for application of this fascinating material in the gas separation industry.

REFERENCES 1. Sircar, S. (2000). Publications on adsorption science and technology. Adsorption, 6,359-65. 2. Sircar, S. (2001). Potential applications of gas separation by adsorption for the future. Adsorp. Sci. Tech., 19, 347-65. 3. Keller, G.E., Anderson, R.A., and Yon, C.M. (1987). Adsorption. In Handbook of Separation Process Technology (R.W. Rousseau, ed.). John Wiley, Chapter 12, pp. 644-96. 4. Lovett, W.D. and CunnifL F.T. (1974). Air pollution control by activated carbon. Chern. Eng. Prog., 70(5), 43-7. 5. Logsdon, P.B. and Basu, R.S. (1993). Recovery and recycle ofHCFCs by activated carbon adsorption. JIES, 36(2), 33-6. 6. Takeuchi, Y. (1991). Recent Advances in Solvent Recovery by Fixed-Bed Adsorption. Proceedings ofSeiken Symposium (M. Suzuki, ed.). Institute of Industrial Science, pp.87-94. 7. Schroter, H.J. andJiintgen, H. (1989). Gas separation by pressure swing adsorption using carbon molecular sieves. In Adsorption: Science and Technology, NA TO ASI Series, Vol. 158 (A.E. Rodrigues, M.D. Levan, and D. Tondeur, eds). Kluwer Academic, pp. 269-83. 8. Jiintgen, H., Knoblauch, K., Reichenburger, J., et al. (1981). Recovery of nitrogen rich gases from gases containing nitrogen and oxygen such as air. US Patent 4,263,339. 9. Knoblauch, K., Heimbach, H., and Harder, B. (1985). Preparation of nitrogen. US Patent 4,548,799. 10. Lacava, A.I. and LemcofL N.G. (1996). Single bed pressure swing adsorption process to generate high purity nitrogen. Gas. Sep. Purij., 10(2), 113-15. 11. Shirley, A.I and Lacava, A.I. (1992). Pressurization pressure swing adsorption (psa) systems for the production of high purity product gas. US Patent 5,082,474. 12. Lemco~ N.G. and Gmelin, R.C. (1993). Pressure swing adsorption method for separating gas mixtures. US Patent 5,176,722. 13. Golden, T.C. Battavio, P.J. Chen, Y.C., et al. (1993). Carbon-based oxygen selective desiccant for use in nitrogen PSA. Gas. Sep. Purij., 7, 274-8.

References

59 1

14. Litvinov, V.N. (1993). Removal of carbon dioxide from flue gases. Russian Patent 1,790,981. 15. Kapoor, A. and Yang, R.T. (1989). Kinetic separation of methanecarbon dioxide mixture by adsorption on molecular sieve carbon. Chern. Eng. Sci., 44, 1723-33. 16. Fuderer, A. and Rudelstorfer, E. (1976). Selective adsorption process. US Patent 3,896,849. 17. Sircar, S. (1979). Separation of multi-component gas mixtures. US Patent 4,171,206. 18. Sircar, S. Golden, T.C., and Rao, M.B. (1996). Activated carbon for gas separation and storage. Carbon, 34(1), 1-12. 19. Young, D.M. and Crowell, A.D. (1962). Physical Adsorption of Gases. Butterworths. 20. Skarstrom, C.W. (1960). Method and apparatus for fractionating gaseous mixtures by adsorption. US Patent 2,944,627. 21. Hirose, T. and Kuma, T. (1990). Honeycomb rotor continuous adsorber for solvent vapor recovery and dehumidification. 2nd Korea-Japan Symposium on Separation Technology. 22. Rudisill, E.N. Hacskaylo, J.J., and Levan, M.D. (1992). Co-adsorption of hydrocarbons and water on BPL activated carbon. I & E C Res., 31(4), 1122-30. 23. Rynders, R.M. Rao, M.B., and Sircar, S. (1997). Isotope exchange technique for measurement of pure and multi-component adsorption equilibria and kinetics. AIChEJ., 43, 2456-70. 24. Sircar, S. and Golden, T. C. (1995). Isothermal and isobaric desorption of carbon dioxide by purge. I & EC Res., 34, 2881-8. 25. Sircar, S. and Rao, M.B. (2000). Nano-porous carbon membranes for gas separation. In Recent Advances on Gas Separation by Micro-Porous Membranes (N. Kanellopoulos, ed.). Elsevier, pp. 473-6. 26. Carbon Membranes Ltd. Israel. Trade Literature. 27. Jones, C.W. and Koros, W.J. (1994). Carbon molecular sieve gas separation membrane: I - preparation and characterization based on polyamide precursors. Carbon, 32, 1419-25. 28. Tanihara, N.H., Shimazaki, Y., Hirayama, S., et al. (1999). Gas permeation properties of asymmetric carbon hollow fiber membranes prepared from asymmetric polyamide hollow fiber. J. Membrane Sci., 160(2), 179-86. 29. Rao, M.B. Sircar, S., and Golden, T.C. (1992). Gas separation by adsorbent membranes. US Patent 5,104,425. 30. Soffer, A. and Koresh, J.E. (1987). Separation device. US Patent 4,685,940. 31. Naheiri, T. Ludwig, K.A., Anand, M., et al. (1997). Scale-up of selective surface flow membrane for gas separation. Sep. Sci. Technol., 32, 1589-602. 32. Spivey, J.J. (1987). Complete catalytic oxidation of volatile organics. I & E C Res., 26, 2165-80. 33. Dalton, A.1. and Sircar, S. (1977). Method for removing low concentration of oxidizable organic contaminants from an oxygen containing inert gas. US Patent 4,025,605. 34. Golden, T.C. and Sircar, S. (1990). Activated carbon adsorbent for drying gases by pressure swing adsorption. Carbon, 28, 683-90. 35. Yong, Z., Mata, V.G., and Rodrigues, A.E. (2001). Adsorption of carbon dioxide on chemically modified high surface area carbon-based adsorbents at high temperature. Adsorption, 7, 41-50.

59 2

Chapter

22

Gas Separation and Storage by Activated Carbons

36. Waldron, W.E. Hufton, J.R., and Sircar, S. (2001). Production of hydrogen by cyclic sorption enhanced reaction process. AIChE J., 47, 1477-9. 37. Hartzog, D.G. and Sircar, S. (1995). Sensitivity of PSA process performance to input variables. Adsorption, 1, 133-51. 38. Ling, L. Song. Y. Liu, L., and Li. K. (2001). Method for preparing activated carbon for storing methane. Chinese Patent 1,303,732. 39. Baker, F.S. (1997). Low pressure methane storage with highly micro-porous carbons. US Patent 5,626,637. 40. Lozano-Castello, D., Cazoria-Amoros, D., Linares-Solano, A., and Quinn, D.F. (2002). Activated carbon monoliths for methane storage: Influence of binder. Carbon, 40, 2817-25. 41. Blazek, C.F., Jasionowski, W.J., Tiller, A.J., and Gauthier, S.W. (1990). Paper Presented at 25th Intersociety Energy Conversion Engineering Conference. Reno, Nevada. 42. Sejnoha, M., Chahine, R., Yaici, W., and Bose, T.K. (1994). Adsorption storage of natural gas. Paper presented at AIChE Annual Meeting, San Francisco, California. 43. Matranga, K.R., Myers, A.L., and Glandt, E.D. (1992). Storage of natural gas on activated carbon. Chern. Eng. Sci., 47, 1569-79. 44. Barbosa-Mota, J.P., Rodrigues, A.E., Saatdjian, E., and Tondeur, D. (1997). Dynamics of natural gas adsorption storage system employing activated carbon. Carbon, 35(9), 1259-70.

ELECTROCHEMICAL ENERGY STORAGE Fran~ois Seguin 1 and Elzbieta Frackowiak2 Centre de Recherche sur /a Matiere Divisee, CNRS-Universite, 1 B rue de /a Ferol/erie, 45071 Orleans Cedex 02, France 2 Institute of Chemistry and Technical Electrochemistry, Poznan University of Technology, ul. Piotrowo 3, 60-965 Poznan, Poland 1

Contents 23.1 Introduction 23.2 Lithium Insertion in Carbon Materials 23.3 Nanostructured Carbons as Components of Supercapacitor Electrodes 23.4 General Conclusion and Perspectives References

593 595 607 621 623

23.1 INTRODUCTION

The great demand for portable electronic devices supplied by light electric power sources as well as an increasing interest for electrically powered vehicles results in a continuous development of high-performance energy systems. Lithium-ion (Li-ion) and nickel-metal hydride batteries, fuel cells, and supercapacitors [1] belong to such promising energy sources. An intense research effort is focused on the development and/or improvement of electrode materials for these electrochemical systems. It is now well-demonstrated that carbons constitute a versatile class ofmaterials for the development of high-performance power sources [2, 3]. The important Adsorption by Carbons ISBN: 978-0-08-044464-2

© 2008 Elsevier Ltd.

All rights reserved.

593

594

Chapter 23 Electrochemical Energy Storage

factors that dictate the selection of carbon for this target are its accessibility, easy processability, and low cost. Moreover, the great versatility of the forms attainable allows to use carbons in composite electrodes or as a main electrode component when self-standing films, fabrics, felts, or aerogel blocks are used. Carbon as electrode is a well-polarizable material, chemically stable in different solutions (acidic, basic, aprotic) and in a wide range of temperatures. Because of its amphoteric character, carbon can be electron donor and acceptor as well, and its substitution by neighbor elements from the periodic chart (e.g., boron, nitrogen) allows the electronic properties to be adjusted, which broadens the panel of its electrochemical applications. Moreover, intercalation-insertion processes into carbon can proceed easily because of the weak van der Waals forces between graphitic layers and/or domains [4]. Hence, different carbons (e.g., graphites, cokes, mesophase, activated carbons, aerogels, xerogels, carbon blacks, nanotubes) have been extensively considered as active material for energy storage [5-8]. The nanotextural/structural and chemical properties of carbons determine their efficiency in electrochemical application as electrodes. A strict control of the carbonization process (time, temperature, gas flow), the kind of natural or synthetic precursor and/or chemical vapor deposition conditions allow to prepare carbons with almost defined structure/nanotexture. Various advanced forms of carbon can be designed and prepared by a careful selection of templates, in such a way that one-, two-, or three-dimensional carbons can be easily obtained [9-12]. The modification of carbon by an activation process gives a further possibility of affecting the properties, especially by high developing of the specific surface area [13]. The main demanded characteristics of carbon for all the electrochemical applications are good electrical conductivity and wettability, the latter being strongly affected by the surface functionality. The electrical conductivity significantly depends on the thermal treatment conditions, nanotexture, hybridization, and content of heteroatoms. Certainly, each electrochemical application involves completely different nanotextural properties of carbon characterized by the specific surface area, the presence of micro- and mesopores, their ratio, pores shape, and so on. Often literature claims about a correlation between some electrochemical parameters of a cell and the Brunauer, Emmett, Teller (BET) specific surface area. However, it is noteworthy that the electrochemically active surface area (ASA) of carbon, which takes part in the electrochemical processes, differs significantly from the physical surface area determined by nitrogen and/or carbon dioxide sorption. Therefore, the estimation of the ASA [14] connected with the special reactivity of carbon with di-oxygen can supply an additional and extremely useful information on the electrochemical properties of carbons in energy storage systems. In this chapter, the electrochemical applications of various carbon materials in energy conversion, mainly lithium storage and supercapacitors, will be critically discussed taking into account their structure/nanotexture and surface functionality, with some attention for future perspectives.

23.2

Lithium Insertion in Carbon Materials

595

23.2 LITHIUM INSERTION IN (ARBON MATERIALS The new generation ofLi-ion batteries combines a high power and energy density, hence, they appear as the most promising system for portable devices as well as for electrical vehicles. However, there is still a need to improve the electrode materials for getting the highest capacity, while keeping good electrochemical characteristics, especially a good calendar life. A relatively high reversible capacity (372mAh/g, i.e., one lithium for six carbon atoms in standard conditions) at a potential close to metallic lithium and a moderate irreversible capacity can be obtained with graphite-based anodes. A higher degree of reversible lithium insertion than in graphite, but also an important irreversible capacity, is observed with various kinds of nanostructured carbons. Therefore, an intensive research effort is focused on the optimization of the anodic carbon materials, with the objectives to enhance the reversible capacity and to reduce as much as possible the irreversible capacity and hysteresis, which are often important drawbacks of these materials. The next section will discuss the correlations between the electrochemical performance of nanostructured carbons and their nanotexture/structure and surface functionality. Taking into account the key parameters that control the electrochemical properties, some optimizations proposed in literature will be presented. 23.2.1

Principle of a Li-ion Battery

The electrodes of Li-ion batteries are based on intercalation materials between which lithium ions are transferred through an aprotic electrolytic medium during charge and discharge. The general principle of a Li-ion battery is presented in Fig. 23.1. The cathodic (positive electrode) materials are lamellar oxides such as LiCo0 2 and LiNi0 2 represented by the general formula Li yM0 2 (y ~ 1), whereas carbon (more generally graphite) is used for the negative electrode (anode). The following equations represent the reversible redox reactions in the cell:

6C + xLi+ + xe- {:} Li x C 6 Li y M0 2

{:}

Li y_x M0 2 + xLi+ + xe-

(23.1) (23.2)

Using graphite, such a battery operates at almost constant voltage of about 3.5 V during discharge, which makes this system very attractive for its highenergy density [15]. In the case of graphite, lithium penetrates between the graphene layers through an intercalation process with charge transfer to carbon. The successive formation of stages 3, 2, and 1 derivatives [16] during the reduction of graphite is demonstrated by well-defined plateaus at constant potential on the galvanostatic curves (Fig. 23.2), reaching the composition LiC 6 at saturation. It is remarkable for graphite that insertion and extraction proceed very close to the potential of metallic lithium, allowing the Li-ion battery to discharge at

Chapter 23 Electrochemical Energy Storage

~e-

~e-

+

•

Li+

~.

Li+

Electrolyte

Figure 23.1 Principle of a lithium-ion battery. This scheme shows the case of charge, i.e., graphite is reduced, while the oxide LiyMO z is oxidized. The part of lithium which is irreversibly lost during the first cycle is represented schematically as a layer surrounding graphite.

Carbon layer

--.--.. -••

Lithium 3

0.3

2.5

0.25

---

--.

••

0.2 2

Stage III

0.15 ::J

en >

1.5

--

----

••

•• ••

•• ••

••

••

Stage II

Sta el

0.1

~

0.05 0 0.2

0.5

0.4

0.6

1.2

0.8

x in Li xC6

o o

0.2

0.4

0.6

0.8

1.2

x in Li xC6

Figure 23.2 Galvanostatic intercalation-deintercalation of lithium in graphite using a twoelectrode lithium-graphite cell. The inset is a magnification of the curve at low potential, which shows the existence ofdifferent stage domains. The potential plateaus during reduction represent the successive transitions from stages III to II and to I.

23.2

Lithium Insertion in Carbon Materials

597

high and almost constant value of voltage. Nevertheless, it must be pointed out that a part of lithium, being involved in the so-called solid electrolyte interphase (SEI) [17] as LiF, Li2 0, LiOH, Li 2 C0 3 , ROC0 2 Li [18-20], formed during the first reduction cycle, is not recovered during deintercalation (oxidation) giving rise to a noticeable irreversible capacity. The SEI represented schematically in Fig. 23.1 as a layer surrounding graphite, is electron insulating, but behaves as an ionic conductor, allowing only nonsolvated lithium ions to migrate from the electrode surface to the bulk of graphite. The SEI formation is extremely profitable because it coats carbon preventing from further electrolyte decomposition on its surface [17]. Although graphite is the most used anodic material in commercial batteries, it has some drawbacks, especially because of the risks of exfoliation during cycling, which considerably affects the long-term life ofthe system. It is generally accepted that exfoliation is due to solvated lithium intercalation during the reduction step [17, 21]; therefore, it is important to control the initial formation of the SEI that is further supposed to allow only nonsolvated lithium to be intercalated.

23.2.2

Properties of Nanostructured Carbon Anodes

Lately, many efforts have been devoted to develop electrodes based on the use of hard carbons, because of the high reversible capacity which can be reached with some of these materials, without the inconvenience of exfoliation during the insertion-deinsertion processes. Beside these advantages, the drawbacks are an important irreversible capacity Cirr and a varying voltage during lithium deinsertion, giving rise to the so-called hysteresis. An example of charge-discharge characteristics of such a material in the form of carbon cloth from viscose is shown in Fig. 23.3 [22]. An optimal nanostructured carbon for Li-ion batteries should have a higher reversible capacity than graphite, while keeping a small irreversible capacity and its main part of discharge (oxidation) close to 0 V vs Li. Only a good knowledge of the physicochemical parameters that control the electrochemical properties of hard carbons can provide a chance to improve the materials and to reach ideal properties.

23.2.2.1

Origins of the irreversible capacity in nanostructured carbons

The possible origins ofirreversible capacity Cirr have been carefully studied by a number of authors. Some papers claim that lithium could be irreversibly trapped by the surface functional groups of carbon [23], e.g., by electrostatic forces such as -COO-Li+, or that it could react with di-oxygen or water molecules adsorbed on the carbon surface [24]. A linear dependence has been found between the irreversible capacity ofa series of carbons and their micropore volume [25], and 7Li NMR experiments lead to the conclusion that metallic

598

Chapter 23 Electrochemical Energy Storage

2.4

~--.,r------------------------.

2.2 2

0.71

1.34

1.8 :.:J

1.6

~

1.4 1.2

~

co ·E Q)

(5 (L

1

0.8 0.6 0.4 0.2

o -0.2 +&--&-.....I......I..~L...J..+.I....L.-I-...I....i-I-..L-L-L-+-L-I....&.......L-1f--L.L-.a........L.+.1..L-L...J....+-L....L...J-1-+-L-JL....L-L-f-J--l-.L.....L+...L..L-J...J...+-L...L..L.J-+-J-J~ -0.2 0 0.2 0.4 0.6 0.8 1.2 1.4 1.6 1.8 2 2.2 2.4

xin Li xC6

Figure 23.3 Galvanostatic insertion-deinsertion of lithium into hard carbon from viscose. Current load of20mA/g. (Adapted from Re£ [22]).

lithium could be irreversibly trapped in the micropores of the materials [26]. However, the main contribution to the irreversible capacity seems to be the formation of the SEI during the first reduction cycle at ca. 0.8 V vs Li. Some papers claim that the extent of the decomposition reaction is directly related to the BET specific surface area of carbon measured by nitrogen adsorption at 77 K [27-29]. In fact, this relationship between Cirr and the BET surface area is not always verified, as shown, e.g., in Fig. 23.4 for graphite ball-milled in different atmospheres and for the same samples coated by pyrolytic carbon after milling, confirming that other parameters control the value of C irr • This is not surprising, because the BET specific surface area is essentially a geometric parameter based on nitrogen physisorption on the basal carbon planes, whereas the SEI formation involves higher energies. Therefore, it has been suggested [22] to correlate the irreversible capacity to so-called ASA [14], which depends on the number of active sites on the carbon surface. The ASA of carbon materials corresponds to the cumulated surface area of the different types of defects present on the carbon surface (stacking faults, single and multiple vacancies, dislocations) [14, 30]; these sites are responsible for the interactions with the adsorbed species. A perfect linear relationship between the irreversible capacity and the value of ASA has been documented for different series of carbon samples [22]. While C irr can be possibly not correlated with the BET area, Fig. 23.4 shows that it is linearly dependent of the ASA [31]. Moreover, all the samples coated with a thin carbon layer by pyrolytic decomposition of propylene demonstrate the lowest values of irreversible capacity and ASA (Fig. 23.4) [22, 31]. Figure 23.5 illustrates the positive effect of such a coating on the charge-discharge characteristics of carbon fibers from viscose,

23.2

lithium Insertion in Carbon Materials

~

S

500

599

(9).

450

(I)

m 400 (ij 350

(a).

~ 300

(c).

«S 't: 250 ::J

en 200

(e).

(.)

~

(.)

150

~ 100

en ~

w

m

50

(h) (d) .(f) ,(b)

0 0

0.5

1.5

1

2.5

2

xin Li xC6 '@

70

N'

60

«S

50

S Q)

(ij Q) (.)

«S 't:

(c) (II)

•

(e) (9)

40

(a)

30

•

::J

en Q)

>

U «

20 10 0.5

1

1.5

2

xin Li xC6

Figure 23-4 Relation between the BET specific surface area (curve I) or the active surface area (ASA) (curve II) and the irreversible capacity x of graphite samples ball-milled in different conditions, or ball-milled and subsequently coated by pyrolytic carbon. (a) 10 h in vacuum; (b) 10 h in vacuum + pyrolytic carbon deposition; (c) 10 h under H 2 ; (d) 10 h under H 2+ pyrolytic carbon deposition; (e) 10 h under 02; (f) 10 h under 02+ pyrolytic carbon deposition; (g) 20 h in vacuum; (h) 20 h in vacuum + pyrolytic carbon deposition. (Adapted from Re£ [31].)

whose irreversible capacity diminishes to only x = 0.25 (x = 1 for a capacity C = 372 rnA h/g) , whereas before coating the same material showed a value x = 0.7 (Fig. 23.3) [22]. A similar improvement was mentioned after coating of graphite and subsequent carbonization, either with a blend ofpitch and resin [32] or with coal-tar pitch (CTP) [33]. Figure 23.6(a) shows the transmission electron microscopy (TEM) image of the cross section of a fiber coated with pyrolytic carbon. One can easily differentiate the fiber core with a highly disordered nanotexture from the more dense coating with a preferentially ordered nanotexture [22]. A schematic representation of this composite material is represented in Fig. 23.6(b). Because of its oriented nanotexture with only few edge planes accessible for adsorbed species, the thin carbon coating forms a barrier preventing an easy diffusion of the large solvated lithium ions to the active sites of the fibers. For the same reasons, in the ASA determination experiment, di-oxygen

600

Chapter 23 Electrochemical Energy Storage

2.4 . . . . - - . , - - - - - - - - - - - - - - - - - - - - - - - - - - , 2.2 2

0.25

1.51

1.8

:.:J 1.6 ~

~

1.4 1.2

(ij

1

Q)

0.8

E "0

a.

0.6 0.4 0.2

o -0.2 -t-L-'.....L.....J-~.L.......I..4_...L-L..L..L..f_L....&.......I.._+__L_'L-L-L-+_&__I_..L.....L..+~...L..+J.....L....J....L_+_'__.L-L...L..+_&__I_....L.....I..4...L....L..1.....L.+_JL-L-L-J....+_I_.L...L-L...I -0.2 o 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2.2 2.4 2

xin Li x C 6

Figure 23.5 Galvanostatic insertion-deinsertion of lithium in a composite constituted from hard carbon from viscose coated by a pyrocarbon film. Current load of 20 mAl g. (Adapted from Ref. [22].)

cannot easily diffuse to reach the active sites through the pyrolytic carbon layer, therefore the ASA is apparently low in the coated samples. 23.2.2.2

Properties of anodes from carbon nanotubes

Besides the typically microporous hard carbons, essentially mesoporous carbons such as nanotubes and nanofilaments were also extensively investigated for lithium storage [34-37]. A significant reversible capacity has been found, up to 780mAh/g for multiwalled nanotubes (MWNTs) and 1000mAh/g for ball-milled single wall nanotubes (SWNTs), however with some drawbacks. Figure 23.7 presents a galvanostatic insertion-deinsertion curve for nanotubes in 1 mol/L LiPF 6 in EC-DEC (ethylene carbonate-diethylcarbonate) mixture which is quite typical for all this family of materials, including SWNTs, MWNTs, and nanofilaments. In all the cases the irreversible capacity measured after the first discharge-charge cycle is extremely high and varies proportionally to the mesopore volume for the different types of nanotubes investigated [3]. The central canal and/or the mesopores formed by the nanotubes entanglement are surely favoring the SEI formation, allowing an easy access of the voluminous solvated lithium cations to the active surface where they can be transformed into the decomposition products. A similarly high value of Cirr is demonstrated by the mesoporous carbons prepared by a templating procedure in clay minerals [38]. Moreover, during subsequent cycling of the electrodes from nanotubes, an additional passivation layer is formed, demonstrated by a continuous increase of C irr [3, 34]. It means that, in the case of carbons with open mesopores, solvated ions can still penetrate to the interior of the electrode where they can

23.2

Lithium Insertion in Carbon Materials

601

(a)

(b)

Figure 23.6 (a) 002 lattice fringes image on a cross section of a carbonized viscose fiber coated with pyrolytic carbon by CVD from propylene at 900°C. The continuous line shows the separation between a microporous carbon at the bottom (fiber) and the lamellar pyrocarbon at the top. The two insets represent a magnification of selected areas in these two parts. (b) Model showing the disordered nanotexture of the fiber and the lamellar and dense nanotexture of the coating. The coating acts as a barrier which hinders an easy diffusion of species to the core of the fiber. (Adapted from [22]).

be further decomposed. Simultaneously, the reversible capacity also diminishes, and the loss is estimated as ca. 30 % after 10 cycles. For all types of nanotubular materials, a high divergence is observed between the values of insertion and extraction potentials [34, 35], that is commonly called hysteresis. The almost

602

Chapter 23 Electrochemical Energy Storage

3.5 3 2.5

~

:.J en >

2 1.5

lJ.J

0.5

a -0.5

a

500

1000 1500 Capacity (rnA h/g)

2000

Figure 23.7 Representative curve of galvanostatic insertion-deinsertion of lithium into carbon nanotubes. Current load of 20 rnA/g. (Adapted from Ref. [3].)

linear increase of the oxidation potential above ca. 0.5 V vs Li (Fig. 23.7) indicates a progressive evacuation of a wide variety of sites, where lithium has different kinds of interactions with the carbon network. Additionally, the fully lithiated nanotubes represent a well-conducting material due to the charge transfer to carbon, whereas the delithiated materials are significantly less conductive than pristine because of the huge amount of electrically insulating SEI; therefore, the cells' resistance changes rapidly depending on the degree of lithium insertion. The comparison of lithium insertion into rnicroporous and mesoporous carbons, definitively leads to the conclusion that ultrarnicroporous carbons of small ASA are required for limiting the extent ofSEI formation. Although mesoporous carbons look to be attractive on the point of view of their large reversible capacity, the important irreversible capacity and the associated hysteresis preclude their use as active material in Li-ion batteries. Regarding a practical application of carbon nanotubes in these systems, recent results obtained with supercapacitor electrodes demonstrate that they could be useful as a percolating additive (below 10 wt%) to the active carbon material [39]. Moreover, the good mechanical properties of the nanotubular materials allow to preserve a good resiliency of the final anodic material during cycling.

23.2.2.3 Effects of doping on the performance of nanostructured carbons The presence of heteroatoms (boron, nitrogen, oxygen, silicon, phosphorus) substituted to carbon in the graphene layers or occurring as functional groups has been considered for changing the electrochemical performance [40, 41]. The foreign atoms modify the electron donor-acceptor properties of the graphene layers [42], and are consequently expected to affect the interactions

23.2

Lithium Insertion in Carbon Materials

603

during insertion and deinsertion of lithium. The main dopants studied in literature are nitrogen and boron. However, because of the difficulty to determine surely whether the heteroatoms are substituted to carbon, or if they are simply located in interstitial sites, a correct interpretation of the data is impossible. In the case of the nitrogen doped materials, various synthesis procedures have been used in order to study the dependence of the electrochemical characteristics with the nitrogen content. Anodes from nitrogen-containing carbons prepared by chemical vapor disposition (CVD) from acetonitrile, pyridine, and acetyleneammonia mixture demonstrate a reversible capacity ca. 250-300 rnA hi g. The irreversible capacity increases with the nitrogen content whereas the cell capacity shifts to lower voltages compared to pure carbon electrodes [43]. In these CxN materials, a part of nitrogen is substituted for carbon ("lattice nitrogen") and the other is chemically bound to organic molecules ("chemical nitrogen"). The lattice nitrogen acts as a donor, weakening the lithium host bond compared with a pure carbon that explains the lowering of cell voltage. The study of disordered polyacrylonitrile derived carbons revealed a reduction in charge capacity from 380 to 254 rnA hi g but a distinctly faster kinetics of the lithium insertion as the heat treatment temperature increased between 500°C and 1000°C [44]. As the nitrogen content is expected to decrease with the increase of heat-treatment temperature, the reversible capacity seems to be correlated with the amount of nitrogen present in this isotropic carbon material. A similar decrease of reversible capacity is observed when quinoline pitch (QPC) obtained at temperatures from 700°C to 1000°C. However, in the same conditions, the capacity of naphthalene pitch carbons (NPC) decreases more rapidly with temperature, and becomes smaller at 1000°C than their QPC counterpart. The better performance of QPC has been attributed to vacancies left after nitrogen evolution, which create new sites for lithium insertion [45]. The disordered carbonaceous materials prepared by pyrolysis of various nitrogen-containing polymers at 600°C contain graphene nitrogen and conjugated nitrogen which cannot be involved in the irreversible reaction with lithium [46]. The higher the content of nitrogen in the pristine polymeric carbon, the higher the reversible capacity. This increase of capacity mainly results from the graphene nitrogen (N 1s binding energy 398.5 eV). Carbonaceous materials ranging from soft carbons of moderate nitrogen content (up to 2.5 wt%) to typical hard carbons with an excess of nitrogen (up to 6 wt%) have been produced by carbonization of CTP - polyacrylonitrile blends with various ratio of the components [47]. The nitrogen-enriched hard carbons demonstrate a relatively low value of reversible capacity, because of the absence of available nanopores. On the other hand, the irreversible capacity increases with the proportion of nitrogen, especially in the form of pyridinic groups. The lone pair of electrons contribute to the trapping of solvated lithium cations on these groups which act as active sites for the electrolyte decomposition during the first reduction, leading to an enhanced irreversible capacity.

604

Chapter 23 Electrochemical Energy Storage

The slight inconsistency in the results presented above seems to arise from overlapping the contributions of the structural-nanotextural characteristics and the nature of the nitrogen functionality. Taking into account that the N ls X-ray photoelectron spectroscopy (XPS) spectra of the materials must be fitted by four components assigned to pyridinic (N6), pyrroliclpyridonic (N5), quaternary (NQ) , and oxidized nitrogen (NX) functionalities [48], respectively, only a correlation of the electrochemical properties with the proportions of each form could give more reliable information. Nevertheless, for all the nitrogen-enriched carbons, the general tendency from the literature data is an increase ofirreversible capacity with the proportion of nitrogen. If one takes into account that in the best cases the reversible capacity is comparable to that of graphite, this leads to the conclusion that the presence of nitrogen in the carbonaceous materials should be rather precluded for this application. Boron is one of the few elements which are known to be surely substituted to carbon into the carbon lattice. Having one electron less than carbon, boron in substitution can act as an electron acceptor and should be able to facilitate the insertion of electron donors [42, 49], such as lithium. This specific aspect of the nature of boronated carbons has attracted recently a particular attention with respect to the possible performance improvement of carbons used as anode material for rechargeable Li-ion batteries [40, 50]. Boron-substituted carbons, B z C 1- z , with 0 < z < 0.17 were prepared by the CVD method using boron trichloride-benzene mixtures at 900°C, and tested in lithium cells [51]. For z = 0, the reversible capacity is x = 0.65, and it increases with z reaching a value of x = 1.17 (435 rnA hi g) for z = 0.17. Because of the presence of boron, the Fermi level is lowered in a rigid band model, allowing more lithium (which plays as electron donor) to be intercalated. When boron-substituted carbons are produced from acetylene and boron trichloride precursors at 1140°C, the amount of lithium reversibly intercalated increases with the boron content up to a limit close to 13 at% of boron [52]. Lithium intercalation is not so efficient beyond this value ofdoping, suggesting that boron can be substituted in the carbon lattice only up to 13 at%. For a given value of lithium concentration, all the cells with boronated carbons show an increase of voltage of about 0.5 V compared to that in the cell with z = 0 [51, 52] that represents an important drawback. This is interpreted by a strengthening of the chemical bond between the lithium and the boronated carbon host compared with a pure carbon host that contributes to increase the lithium potential in this kind of electrode. Taking into account that the irreversible capacity of the boronated carbons is higher than in the corresponding carbons, it does not seem that this kind of doping is profitable for improving the performance of lithium cells anodes. Almost similar results were found when copyrolysis of QI-free CTP with the borane-pyridine complex (BPC) is used to prepare boronated carbon materials [53]. For a series of cokes calcined at 1000°C, the most striking effect of increasing the boron content is an increase of irreversible capacity ~rr from 0.2 to 0.7. Because a high amount of oxygen is found even in the graphitized boronated carbons, it proves that the incorporated boron and

23.2

Lithium Insertion in Carbon Materials

605

nitrogen (from BPe) induce a strong chemisorption activity ofthe material when exposed to air, which is responsible for the high irreversible capacity in all these materials.

23.2.3 Mechanism of Reversible Li Insertion/Deinsertion in Disordered Carbons Although a very realistic model for lithium intercalation in graphitic materials is proposed since many years [16], the lithium insertion mechanism in disordered carbons remains still not completely documented. The main reason is the complex structure-nanotexture of these carbons which practically makes impossible to propose a unique model applicable for all the materials. Many papers try to interpret the values of reversible capacity in these carbons and to identify the kinds of sites occupied by lithium. An almost linear correlation has been found between the HI C ratio ofvarious polymers pyrolysed below 1000°C and the reversible capacity [54]. The lithium atoms may bind on the hydrogen-terminated edges at the periphery of the basal structural units (BSUs) , causing a change of carbon hybridization from Sp2 to Sp3 during insertion, and from Sp3 to Sp2 during deinsertion [55]. The additional energy which is required for the hybridization change during lithium removal would be the cause of the large potential hysteresis observed with these materials. However, some disordered carbons can maintain capacities higher than 400 rnA hi g, even though their hydrogen content is considerably reduced by a heat treatment [56]. In addition, they demonstrate a low-voltage plateau and little hysteresis [54, 57]. Therefore, several structural-microtextural models have been presented to interpret the reversible insertion behavior of these carbons. From X-ray diffraction and small-angle X-ray scattering measurements, it has been suggested that lithium is adsorbed reversibly onto the internal surfaces of nanopores formed by single-, bi-, and tri-layer groups of graphene sheets arranged like in a "house of cards" [58]. The nanopores size estimated from small-angle X-ray scattering is close to 7 A [59]. In the hypothesis that all the graphene sheets are isolated, the reversible capacity would be twice larger than with graphite [54]. This adsorption on the surface of nanopore walls is similar to the cavity filling by lithium [60]. In the latter case, lithium can as well form clusters in the cavities between the walls, and be intercalated between the graphene layers [61]. Much progress has been done in better determining the location and state of lithium by using ex situ 7Li nuclear magnetic resonance (NMR) at different steps of reduction or oxidation of disordered carbons [62, 63]. This technique supplies also information about the sequence of pores filling by lithium and their empting depending on the potential. However, some doubts may result from the experimental procedure that is used for the realization of ex situ experiments. In particular, the equilibrium composition of the samples can be altered after their extraction from the cell, either by washing or by moisture and oxygen

606

Chapter 23 Electrochemical Energy Storage

from the atmosphere of the glove box. Additionally, each value of cell potential requires the preparation of a new sample, which limits the number of possible experiments. In order to circumvent all these inconvenience, in situ 7Li NMR has been performed on a supple ultrathin plastic carbon-lithium cell at various steps of galvanostatic cycling [57, 64]. The carbon electrode was a composite from ex-viscose carbon fibers coated by a thin layer of pyrolytic carbon, which demonstrate a small irreversible capacity and a reversible capacity 50 % higher than graphite. During the reduction, two lines related with lithium insertion were observed, the minor one at 18 ppm attributed to intercalated lithium (with a charge transfer to carbon), while the position of the most important is downfield shifted during lithium insertion to reach values of ca. 120 ppm, characteristic of quasi-metallic lithium, at full reduction of carbon. After the oxidation step, these two lines disappear and only two other lines remain at 263 and 0 ppm, attributed to metallic lithium from the counter electrode and to the electrolyte-passivation layer, respectively. Figure 23.8 presents a model for the lithium insertionextraction in the carbon fiber, which takes into account the 7Li-NMR data and the structural-nanotextural data provided by high-resolution transmission electron microscopy (HRTEM) observation of the host carbon. Lithium first intercalates in the small intervals between the nanometer-size graphitic type

Insertion

--<-~~~

.', •

Deinsertion

o

Li+

o

Intercalated Li Quasi-metallic Li

•

0

.~ •••.

............

'-~

~ ~ , t• • ~~

~~.I'

Figure 23.8 Schematic model showing the sequence of lithium insertion-deinsertion into the carbon fiber-pyrolytic carbon composite. During reduction, once the solid electrolyte interphase (SEI) is formed, ionic lithium penetrates at first in the smallest intervals. Then it diffuses to the largest intervals where the ions are screened by delocalized electrons through a backdonation process: quasi-metallic clusters are formed in the largest intervals. During oxidation, the opposite process occurs. (Adapted from Re£ [57].) ~

23.3 Nanostructured Carbons as Components of Supercapacitor Electrodes

layers and then penetrates in the nanopores where growing quasi-metallic clusters are formed.

23.2.4 Conclusion An anodic material for lithium-ion batteries must posses low ASA and BET specific surface areas that reflects a limited number of defects. The harmful role of mesopores for lithium storage was perfectly illustrated with nanotubes. The entangled nanotubular network facilitates the access of solvated Li ions to the electrode interface, leading to a high irreversible capacity and a significant pseudocapacitive effect. Although relatively high values of reversible lithium insertion are reached with mesoporous carbons, the lack ofvoltage plateau during lithium deinsertion precludes these carbons from any practical application as electroactive material for lithium-ion batteries. A well-developed nanostructure with small ultramicropores that ensure a high insertion degree of nonsolvated lithium ions without hysteresis is required for an optimal performance of carbon anodes. It has been also proved that coating carbon materials by a pyrocarbon film gives a beneficial improvement of the electrochemical behavior for Li-ion cells by a decrease of irreversible capacity. In that sense, it seems preferable to preclude the presence of any foreign atom, even when substituted in the carbon lattice.

23.3

NANOSTRUCTURED CARBONS AS COMPONENTS OF

SUPERCAPACITOR ELECTRODES

23.3.1 General Properties of Supercapacitors Electrochemical capacitors, also called supercapacitors, are very attractive electricity sources because of their high power, very long durability, and intermediate energy between the classical dielectric capacitors and batteries. The performance of a typical electrochemical capacitor is based on the accumulation of charges in the electrical double layer without faradaic reactions (no electron transfer). The electrons involved in double layer charging are the delocalized conduction-band electrons of the electrode material. As shown in Fig. 23.9, an electrochemical capacitor contains one positive electrode with electron deficiency and the second one with electron excess (negative). The capacitance C of one electrode due to a pure electrostatic attraction of ions is proportional to the surface area S of the electrode-electrolyte interface, according to the formula (23.3):

eS

C=-

(23.3) d where e is the permittivity or dielectric constant of the solution and d represents the thickness of the electrical double layer (which is generally less than one

608

Chapter 23 Electrochemical Energy Storage

+ + + + + + Current collectors Separator •

anions of the electrolyte

cations of the electrolyte;

Figure 23.9 Schematic representation of an electrochemical capacitor. EB cations of the electrolyte;

e

anions of the electrolyte.

nanometer), i.e., the distance where the maximal charge density is located in the electrode-electrolyte interface. The technological advantage of supercapacitors over conventional capacitors lies on the small value of d that leads to a specific capacitances of the order of 0.1 F/m2 . Taking into account that the supercapacitor electrodes are mostly constituted from activated carbons, with a specific surface area in the range of 1000 m 2 / g, a capacitance of 100 F/ g of carbon is easily reached [2, 6]. It is noteworthy that the overall capacitance C of the

device is determined by the series connection of two electrodes of capacitance C 1 and C2 according to formula (23.4): 111

-=-+C C C 1

(23.4)

2

Hence, in the case of a capacitor built from two electrodes with different capacitance, the component of smaller capacitance will contribute more to the total value because of the reciprocal dependence. The capacitance is expressed in farad (F), which is the charge (in coulombs) accumulated in a defined range of voltage (1 F = 1 Cll V). The specific capacitance can be related to the electrode mass (F/ g), to the electrode volume (F/ cm3 ), or to the electrode surface (F I cm2 ). The amount of electrical energy W accumulated in electrochemical capacitor is proportional to the capacitance C and to the square of voltage U, according to formula (23.5): 1

W= -CU 2 2

(23.5)

Hence, the application of an organic electrolyte is of great interest because of its wider stability than aqueous electrolytes. A capacitor in organic electrolytic

23.3 Nanostructured Carbons as Components of Supercapacitor Electrodes

60 9

solution can easily operate in a range of2.5 V, whereas in aqueous electrolytes it is generally below 1 V. The main advantage of the capacitor device is the ability of a high dynamic of charge propagation that allows a rapid withdrawing of energy, simply because the electrodes do not undergo any phase transformation as in accumulators. Such a high power can be adapted in the hybrid power sources for electrical vehicles, computers, UPS, and pulse laser technique. The electrochemical capacitors are of two types, i.e., the electrical double layer capacitors where only a pure electrostatic attraction between the ions and the charged surface of an electrode takes place, and pseudo-capacitors based additionally on pseudo-faradaic charge transfer reactions [65]. In this case, the electrons involved in the additional faradaic reactions are transferred to or from valence-electron states of the redox reagent, e.g., transition metal oxides (RuO z, MnO z, etc.)[66-68] or conducting polymers [69-73]. Pseudocapacitance might be also realized through a special doping via the presence of heteroatoms, e.g., oxygen and/or nitrogen [74, 75]. The values ofcapacitance are strictly connected with the nature and surface area of the electrodelelectrolyte interface as well as the amount of pseudocapacitive additive.

23.3.2 Activated Carbons for Supercapacitor Application Generally, the more developed specific surface area of carbon, the higher the ability for charges accumulation in the electrode-electrolyte interface. It is well-known that the micropores (with a diameter less than 2 nm) play an essential adsorption role for the formation of the electrical double layer. However, these micropores must be electrochemically accessible for the ions; therefore, the presence of mesopores (diameter from 2 to 50 nm) is necessary for an efficient charge propagation to the bulk of the electrode material, allowing the so-called frequency response to be fulfilled, i.e., the energy to be extracted at higher frequencies (e.g., 1 Hz). Hence, the availability and wettability of pores with dimensions adapted to the size of solvated anions and cations that have to be transported from the electrolytic solution, is crucial for a high performance of capacitor. For capacitor application, activated carbons from different precursors and prepared by different activation processes have been widely used [76, 77]. It is often assumed in literature that the higher the BET specific surface area, the higher the capacitance value. Figure 23.10, which shows a plot of values taken from Refs [76, 78] for a wide variety of activated carbons, demonstrates that this trend is not perfectly followed. In fact, the narrow micropores may not contribute to the total double layer capacitance due to a sieving effect depending on the size of the electrolyte ions [79], which justifies the absence of proportionality with the BET surface area. This is confirmed by a recent study which shows that capacitance values as high as 175 Fig in aqueous medium can be reached using a carbon with a surface area of only 1300 m ZI g, if the pore size is optimized by chemical activation [80]. Usually, the capacitance values of activated carbons range from 100 to 200 Fig in aqueous medium, and

Chapter 23 Electrochemical Energy Storage

610

250

I:

200

H. Shi, Electrochem. Acta 1996, 41, 1633-1639 D. Qu, H. Shi, J. Power Sourc 1998,74,99-107

0)

~

150

(1) ()

c

'0

~

ca

100

o

...

50

.

. . . . ..

.. . , . . ,. .. .- . • .. • • • ~

S

I

-

•

.

. .. . . . •

-

•

•

o o

500

1000

1500

2000

2500

3000

BET specific surface area (m 2/g)

Figure 23.10 Capacitance of various activated carbons in 30 % potassium hydroxide (KOH) aqueous medium as a function of their Brunauer, Emmett, Teller (BET) specific surface area. Values taken from Refs [76, 78].

from 50 to 150 Fig in organic medium. The larger values in aqueous electrolyte are essentially justified by a smaller size of solvated ions and a higher dielectric constant than in organic medium. However, the organic electrolyte is generally preferred for the applications, because of its high potential window that allows more energy to be stored than in aqueous solution. An interesting solution for optimizing the performance in organic medium consists in the selection of activated carbons with pores adapted to the size of the ions. Therefore, it has been suggested to use different carbons for the positive and the negative electrodes, taking into account that the ionic radii of the cations and anions are different [81]. Table 23.1, which presents data obtained using tetraethylammonium tetrafluoroborate, (C 2 H s)4 N + BF 4 -, in acetonitrile, demonstrates that capacitance is high and resistance is low when the pores size is smaller at the positive electrode than at the negative one [81]. Reversing the electrodes, capacitance decreases and resistance highly increases. It proves clearly that some compromise must be found between the sizes of ions and the carbon pores. Lately, potassium hydroxide (KOH) activation has been used to produce activated carbons from cheap and available natural precursors, such as coals and pitch-derived carbonaceous materials. This method efficiently develops the micropores, and allows to get various pore size distributions depending on the kind of precursor and activation conditions [82-85]. The nitrogen adsorption isotherms (Fig. 23.11) at 77 K of activated carbons obtained from coal (C), coal semicoke (CS), pitch semicoke (PS), pitch mesophase (PM), and a commercial activated carbon (AC) , using KOH and carbon in the 4:1 ratio, reveal that a

611

23.3 Nanostructured Carbons as Components of Supercapacitor Electrodes

Table 23.1 Effect of the pore size on the volumetric capacitance and the internal resistance of capacitors made from two carbons A and B. The pores of carbon B are smaller than those of carbon A (Adapted from Ref. [81].)

Capacitor Capacitor Capacitor Capacitor

1 2 3 4

A A B B

26.6 20.8 27.5 18.8

B A B A

24 23 257 243

1200 - r - - - - - - - - - - - - - - - - - - - - - - - - - - - - ,

1000

~

a..

800

l-

en

I

Z

600

'0 Q)

E

-/::}- A-C

::l

o>

400

~A-CS

______ A-PM -G- A-PS

---+-

200

A-AC

O------r---.---------r-----r--~-__,__-__r--_r___-__,__-___f

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

plpo

Figure 23.11 Nitrogen adsorption isotherms at 77 K for potassium hydroxide (KOH) activated carbons (A-) from various precursors. C = coal; CS = coal semicoke; PM = pitch mesophase; PS = pitch semicoke; AC = commercial activated carbon. (Adapted from

Re£ [84].)

wide distribution of micropores can be obtained by this method [84]. A typical galvanostatic charge-discharge characteristic, with a correct triangular shape without a significant ohmic drop, is shown in Fig. 23.12 for the activated carbon from PM. Table 23.2 presents a comparison of the porous characteristics of a series of KOH activated carbons, together with their capacitance values in 1 mol/L

Chapter 23 Electrochemical Energy Storage

612

0.9 0.8 0.7 0.6 0.5 ~ .........

llJ

0.4 0.3 0.2 0.1 0 -0.1 0

1000

2000

3000

4000

5000

6000

7000

t/ s Figure 23.12 Galvanostatic charge/discharge in 1 mol/L H 2 S0 4 of a supercapacitor built from the carbon A-PM obtained by potassium hydroxide (KOH) activation of pitch mesophase. 1=2 mAo (Adapted from Ref. [84].)

Table 23.2 Porosity parameters of potassium hydroxide (KOH) activated carbons prepared from various precursors and their capacitance values estimated by galvanostatic discharge in 3:1 mol/L H2 S0 4 solution. The precursors are coal, coal semicoke, pitch mesophase, pitch semicoke, and a commercial activated carbon for A-C, A-CS, A-PM, and A-PS, A-AC, respectively (Adapted from Ref. [84].)

A-C A-CS A-PM A-PS A-AC

3150 3190 2660 2750 1900

0.951 0.936 0.839 0.859 0.609

312 223 294 261 198

9.9 7.0 11.0 9.5 10.4

H 2 S0 4 medium. In general, the results obtained on these kinds of activated carbons, as well in organic and in aqueous electrolyte, confirm that capacitance is not directly related to the BET specific surface area [83, 84]. Considering samples of comparable specific surface area, the wider the micropore size distribution, the higher the capacitance. Additionally, the existence of some mesopores favors the accessibility of narrow micropores by the electrolytic solution. It has been shown also that some large values of capacitance obtained with KOH activated carbons are related with an important surface functionality. The presence of a large amount of oxygenated groups can be profitable either because they improve the wettability on the carbon surface or they contribute to an additional

23.3 Nanostructured Carbons as Components of Supercapacitor Electrodes

6 13

pseudocapacitance. Finally, the nanotextural-structural ordering of the activated carbon may also affect its electrochemical performance [84]. For example, the high value of capacitance observed in Table 23.2 for the sample A-PM probably results from its good electrical conductivity. One can also suspect that pores of well-adapted size are produced as a consequence of potassium intercalation during KOH activation. All these contributions justify that even for materials obtained in identical conditions, the specific capacitance ranges from 7 to 11 f.1F/cm2 in Table 23.2 [84]. In conclusion, KOH and NaOH activation is certainly able to provide activated carbons with the most adapted nanotextural characteristics for supercapacitors, at a reasonable cost. However, it must be pointed out that before to state definitively on the interest of these materials, long-term capacitor performance should be investigated. In order to fulfill the practical demand, only carbons with a small RC constant, low leakage current, and limited self-discharge should be selected. The important research work which has been performed lately, especially by the companies developing supercapacitors, seems to indicate that impurities, even at a low level, or particular functional groups on carbon may strongly affect the calendar life of these devices.

23.3.3 Mesoporous Carbons as Supercapacitor Electrodes Lately, a fascinating strategy has been successfully developed for the preparation of ordered mesoporous carbons. The synthesis procedure of these advanced carbons consists in the infiltration of an organic precursor into the pores of silica or aluminosilicate templates, followed by the subsequent pyrolysis of the precursor and dissolution of the template framework by HF [9-12]. In another process, carbon is directly introduced in the template by a CVD method [86]. The method gives a highly ordered and interconnected network of meso- and micropores [87], where the size of carbon mesopores is defined by the walls thickness of the pristine silica matrix. Such materials are very suitable for better understanding the relationships between the porous characteristics and the supercapacitors performance [88, 89]. Template carbons have been prepared from the MCM-48 and SBA-15 hosts and investigated as supercapacitor electrodes. The carbon precursors were propylene (Pr), pitch (P), and sucrose (S), supplying CPr48, CP48, CS48 and CPr15, CP15, CS15, respectively from the two precursors [90]. The nanotextural data together with the capacitance performance for aqueous and organic media are reported in Table 23.3. The total surface area of the template carbons prepared by sucrose impregnation is significantly higher than the surface area of the corresponding silica template. The formation of micropores during the carbonization is attributed to the release of water and gases. Just an opposite tendency is observed when propylene is used as carbon precursor. In the latter case, the pore volume of the template carbon is consistent with a uniform pore filling, and the values of surface area are easily justified by different pores and walls diameters in the pristine template.

614

Chapter 23 Electrochemical Energy Storage

Table 23.3 Characteristics of the template carbons used as electrode in supercapacitors

CPr48 CS48 CP48 CPr15 CS15 CP15

850 2000 1300 713 1470 923

ClOH1.500.1 C lO H1.900A C lOH1.4 0 0.25 C lO H1.300.1 C lO H1.900A C lO H1.000.2

0.25 0.58 0.29 0.21 0.45 0.25

0.19 0.36 0.18 0.11 0.30 0.19

3.7 2.7 2.4 3.4 3.1 2.8

109 202 96 66 167 87

62 115 50 48 93 57

TSA - total surface area detennined by N 2 adsorption (BET method); V(N 2 ) and V(C0 2 ) - micropore volumes calculated by the application of the Dubinin-Radushkevitch equation to N 2 adsorption at 77 K and CO 2 adsorption at 273 K; pore size detennined according to the BJH method - maximum value of the BJH pore size distribution peak calculated from the adsorption branch of the N 2 isotherm; capacitance values detennined in 1 mollL H 2 S0 4 and 1.4mollL TEABF 4 in acetonitrile (Adapted from Ref [90].)

A mirror-like shape of the voltammetry characteristics is observed for all template carbons both in the aqueous and organic medium [86, 88, 90]. Table 23.3 shows that the values of capacitance reach 200 Fig in aqueous electrolyte and 115 Fig in organic medium, although the total surface area is not higher than 2000 m 2 I g. Such data demonstrate that an interconnected network of mesopores and micropores together with a developed microporosity is very profitable for a quick charge propagation to the surface of micropores. A complementary information is provided by Fig. 23.13, which presents the capacitance-frequency dependence from impedance spectroscopy measurements for CS48 and CS15 in acidic and organic medium [88]. In the low-frequency region (from 1 to 100 mHz) , the quite stable values of capacitance indicate the domination of the capacitive behavior at the electrolyte-carbon interface and nearly a complete penetration of the ions into the pores. The drop of capacitance with frequency becomes significant only at frequencies higher than 1 Hz. In the case of the sample CS15 (curves (b) and (d) in Fig. 23.13), the decrease of capacitance is shifted to slightly higher frequency compared to CS48, both in the aqueous and organic medium. It means that, for a given frequency, the ions diffusion to the active surface is more efficient in the case of CS15. This better frequency behavior of CS15 could be due to the presence of slightly larger mesopores than in CS48 (see Table 23.3) or mesopores of appropriate shape that favor a better efficiency of ions access to the active surface, although the mesopore diameter is larger than the size of the solvated ions in both cases. Table 23.3 shows also that there is not any tight correlation between the capacitance in aqueous or organic medium and the BET specific surface area [76, 78]. On the contrary, in Fig. 23.14, a good linear relationship can be observed between the capacitance values for both media and the micropore volume

23.3 Nanostructured Carbons as Components of Supercapacitor Electrodes

250

1.0E-Q4

1.0E-03

1.OE-Q2

1.0E-Q1

1.0E+00

1.0E+01

1.0E+02

1.0E+03 1.0E+04

1.0E+05

Frequency (Hz)

Figure 23.13 Capacitance-frequency dependence of capacitors based on template carbons (a) CS48 in 1 mol/L H 2 S0 4 , (b) CS15 in 1 mol/L H 2 S0 4 , (c) CS48 in TEABF4 , (d) CS15 in TEABF 4 • The frequency is expressed in logarithmic scale. (Adapted from Re£ [88].)

250

200

-I ...........................•.....................

150 -+ ................................................................................................................... .•............................•...... ~t"

:

.

I"0)

u..

o

100

-I

50

~

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;

~~

,

:.~".""..~A\~,·····························

.. ··············· .................

,

,

r---------,

A. organic O+----.----.------.----r----.----i-----l:=-=;:=====l 0.05 0.1 o 0.15 0.2 0.25 0.3 0.35 0.4

V (C0 2 )/cm 3 g-1

Figure 23.14 Capacitance values in aqueous (+) and organic (Ai) media of the nanotextured carbons synthesized with different carbon precursors and templates vs their micropore volume determined by CO 2 adsorption. (Adapted from Ref. [90]).

Chapter 23 Electrochemical Energy Storage

determined by CO 2 adsorption. Such a trend indicates that ultramicropores, i.e., pores with a size smaller than 0.7 nm, contribute to the formation of the double layer. If one takes, e.g., the case of the organic electrolyte, it is obvious that such a pore size is smaller than the diameter of the solvated ions [91]. From various literature data, the diameter of the nonsolvated ions ranges from 0.7 nm [92] to 0.8 nm [93] for (C2Hs)4N+, and is in the range from 0.44 nm [94] to 0.49 nm [91] for BF4-. Hence, under the application of an electrical polarization, the solvated ions easily diffuse in the mesopores and in the supermicropores for being finally trapped as nonsolvated in ultramicropores. It has been shown that in aqueous medium, most of the ultramicropores of these templated carbons are available for charging the electrical double layer [90]. Such a good efficiency can only be obtained if ultramicropores are interconnected by a well-developed network of mesopores and supermicropores. This nanotexture seem to be especially adapted for capacitor with organic electrolytic solutions and fast charge propagation demanded.

23.3.4 Carbon Nanotubes - A Unique Electrode Component The power P of a supercapacitor is given by Eqn (23.6):

v2

P=-

4R

(23.6)

where R is the internal resistance, i.e., commonly the equivalent series resistance (ESR) R s • As the main function of supercapacitors is to be used for high-power applications, it is essential to lower the series resistance ~. Because of their entangled network of open mesopores that favors a quick transportation of ions to the active surface, carbon nanotubes as electrodes components are very promising for this function of electrochemical capacitors [95]. Additionally, as their graphitic type layers are well-extended, nanotubes are also characterized by a high electrical conductivity which can also contribute to decrease R s • Lately great efforts have been devoted to develop large scale production methods of high-purity carbon nanotubes (CNTs) [96]. Therefore, it becomes now reasonable to consider more carefully their usage directly as electrode material and/or as backbone for electrochemically active materials.

23.3.4.1 Nanotubes as active electrode materials Nanotubes as a typical mesoporous material were carefully investigated for supercapacitor applications [2, 3, 95, 97-105]. Supercapacitors built with electrodes from self-standing mats ofHyperion™ MWNTs have been investigated by impedance spectroscopy, showing a frequency "knee" at about 100 Hz, which suggests that most of the energy stored is accessible at high frequencies [95]. This value, which is much higher than that reported for capacitors from activated

23.3 Nanostructured Carbons as Components of Supercapacitor Electrodes

617

carbon electrodes, confirms the advantages of the nanotubes backbone to provide a well accessible active surface. As a consequence, a power density as high as 8000 W /kg of total cell weight could be measured [95]. Most of the nanotubes-based capacitors give a regular box-like shape of the voltammograms, which denotes an entire electrostatic attraction. In general, the higher the BET specific surface area and oxygen content of the nanotubes, the higher the capacitance values, however, with some discrepancies that can be easily explained by different nanotextures and compositions. For example, values as high as 80 Fig of carbon have been found with MWNTs prepared by decomposition of acetylene at 700°C on a Co-supported catalyst, although the BET specific surface area of these MWNTs is only 411 m 2 I g. In the latter case, a thin layer of pyrolytic carbon on the nanotubes with a high number of surface active sites is at the origin of the high value of capacitance. Capacitance could even be increased to 130 Fig through the functionalization of these nanotubes by nitric acid at 80°C [98]. A reversible ill-defined redox peak due to the oxygenated surface functionality is noted at ca. 0.2 V in the voltammetry curve (Fig. 23.15), whereas the nonoxidized nanotubes material gives a regular boxlike shape of voltammograms. However, a noticeable capacitance fading occurs with cycling typical for this type of pseudocapacitance due to irreversible redox reactions of the surface groups. Another kind ofpseudocapacitance effect, varying with the kind ofelectrolytic solution, was observed with the Hyperion™ catalytic nanotubes [99]. Capacitance varies from 14F/g in 6moi/L KOH to 78F/g in 1moi/L H 2 S0 4 [99] and even to 104 Fig in 38 wt% H 2 S0 4 on a free-standing mat of these nanotubes [95] . Well-visible humps on the voltammetry curves clearly show

6 4

2

<' E.-

-

o -2

-4

-6 -0.2

0

0.2

0.4

0.6

0.8

U(V)

Figure 23.15 Voltammetry characteristics (10 mV Is) of a supercapacitor built from multiwalled carbon nanotubes modified by hot nitric acid. Electrolyte - 6 M KOH. (Adapted from Ref. [2].)

618

Chapter 23 Electrochemical Energy Storage

that this behavior is not strictly connected with the charging of an electrical double layer. Redox pseudocapacitive reactions, related with iron from the catalyst (1.2 wt %) trapped in the material, contribute noticeably to the observed values [99]. The SWNTs prepared by laser ablation (Rice University) or by the HiPco™ process (Carbon Nanotechnologies) supply capacitance values in the range of 20-45 Fig [99, 104, 106]. Taking into account their BET specific surface area of 500 m 2 I g, the specific capacitance per unit surface area is around 4-9 f.1F I cm2 that is rather less than the value given by activated carbons [6]. After annealing at 1650°C, the capacitance of SWNTs from Rice University diminishes to 18 Fig because of a better arrangement of the tubes in the bundles that hinders the diffusion of solvated ions toward the active surface [99]. Interestingly, the capacitance of the HiPco SWNTs does not decrease at a high current density of 150 mAl g. This is attributed to the large external surface area of this material rv ( 400 m 2 I g) on which ions adsorptionldesorption proceeds quickly because of the absence of sieving effect [104]. Hence, the open mesoporous network of SWNTs is profitable for a quick charge propagation especially when an organic medium is used as electrolytic solution. Raw materials containing 30 % of SWNTs have been also used for the preparation of super capacitor electrodes after mixing with poly(vinylidene chloride) (PVDC) and pyrolysis of the mixture at 1000°C. The authors attribute the high capacitance value of 180 Fig measured in 7.5 M KOH to the SWNT material [103]. However, in reality, the carbonization ofPVDC at 1000°C produces microporous carbon [107], and as a consequence the high capacitance values are certainly because of the carbon obtained from the polymeric binder but not of SWNTs.

23.3.4.2 Activated carbon nanotubes as active electrode materials Most of the data recently reported for pure MWNTs range from 20 to 40 Fig during long-term cycling. Since MWNTs are essentially mesoporous, it has been suggested to produce micropores in the walls by KOH activation in order to enhance capacitance [85, 108, 109]. In some cases, the specific surface area increased four times and the values of capacitance from 15 to 90 Fig in aqueous medium. This interesting phenomenon can be explained by the insertion or intercalation of potassium in the walls of nanotubes and the subsequent formation of micropores. Generally, the opening of nanotubes takes place together with the development of their microporosity. In organic electrolyte, the capacitance of the activated material reached 65 Fig with a box-like shape of the cyclic voltammograms (Fig. 23.16) [108]. Although these values are interesting, they are lower than for the commercial activated carbons used in capacitors. Moreover, because ofthe relatively high cost of the pristine material, activated nanotubes cannot be produced at a competitive pnce.

23.3 Nanostructured Carbons as Components of Supercapacitor Electrodes

100 80

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I

2mV/s

,-"'''''--,~ 10 mV/s

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I

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·0

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()

rrI

f

20

c

~

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0 (,2

l

~

~

f

~ ~

I

olp

0.2

0.4

0.6

0.8

1.0

-20

1.4

1.6

1.8

,1°

22

J

-40 -60

1.2

I

lJ

i-..."""----""""""'" ,., "'-'

-~

....----

-80 Voltage (V)

Figure 23.16 Voltammetry characteristics of a capacitor built from activated nanotubes at scan rates of 2 and 10mV/ s. Electrolyte 1.4 M TEABF 4 in acetonitrile. (Adapted from Ref. [108].)

23.3.4.3 Use of nanotubes as a support for materials with pseudocapacitance properties Because of their good electrical conductivity and their high mesoporous character, MWNTs are better adapted as a support for electroactive materials with pseudocapacitance properties, e.g., conducting polymers or transition metal oxides. Pseudocapacitance is an intermediate situation where a faradaic charge transfer occurs with a continuous voltage change during charging or discharging, as in a real capacitor [2]. In the case of polypyrrole (PPy) this can be described by the following reaction:

(23.7) where an electron transfer reaction is coupled with the counter ions exchange during the electrochemical oxidation and reduction of the polymer. Capacitance properties of composites from nanotubes with conducting polymers [69, 70, 110-112], e.g., polypyrrole (PPy), polyaniline (PANI), or a polythiophene derivative (PEDOT) have been studied. Polypyrrole (PPy) is the most promising for its high conductivity, stability in the oxidized form and ability to be electrochemically switched between the conducting and the isolating states. PPy can supply a high specific capacitance, because of its high doping level; however, it is valid only for thin films that has a limited practical application. Generally, the thick layers of PPy undergo shrinkage and swelling

620

Chapter 23 Electrochemical Energy Storage

what is the cause of film degradation and conductivity loss. Moreover, bulk PPy supplies very low capacitance values (below 20 Fig) at current loads of 200-400 mAl g. The combination of the two components, using chemical or electrochemical polymerization to get a layer of PPy on the nanotubes, allows all these problems to be overcome and to use efficiently the mesoporous nanotubular network for supplying a perfect three-dimensional volumetric charge distribution [70]. In the case of the electrochemically obtained nanotubeslpolypyrrole (PPy) composites, the values of capacitance reached ca. 170 Fig [69, 70]. Such composite electrodes could be easily cycled at 350 mAl g current load without any performance aggravation over 2000 cycles [100]. Recently, similar composites have been prepared by electrochemical deposition of PPy on well-aligned carbon nanotube electrodes [113, 114]. However, as the values of capacitance presented in this work are given per surface of electrode, it is difficult to estimate the possible applications of this material in a real capacitor. The highest values of capacitance, i.e., 200 Fig with a long durability if a limited voltage range (0.6 V) is selected [115], were obtained from composites containing 80 wt% of PPy deposited chemically on highly entangled catalytic MWNTs. In this case, the PPy layer is more porous, less compact, allowing the diffusion of ions to proceed more easily. Several kinds of polymers were deposited on MWNTs by chemical polymerization and used for supercapacitors. The scanning electron microscopy (SEM) image presented in Fig. 23.17 shows

Figure 23.17 SEM micrograph showing the morphology of a polyaniline/multiwalled nanotubes (PANI/MWNTs) composite material which contains 80 wt % of chemically deposited polyaniline. (Adapted from Ref. [115].)

23.4 General Conclusion and Perspectives

621

the example of the composite with 80 % of deposited PANI which is quite homogeneous. SWNT IPPy nanocomposites have been also investigated in alkaline solution [111]. However, it seems that the nickel foam used for the current collector supplies an additional capacity in this medium. It is also well-known that PPy in alkaline solution degrades quickly, hence, these results have a limited practical application.

23.3.5 Conclusion Contrarily to Li-ion batteries, the supercapacitor application requires highly developed surface area carbons with micropores adapted to the size of the ions involved in the formation of the electric double layer. In this case, the additional presence of mesopores is crucial to fulfill the demand of fast charge propagation with a minimal time constant. It seems that the most suitable would be to increase the amount of mesopores in KOH activated carbons or to increase the microporosity of the essentially mesoporous template carbons. A further improvement of the materials could be a special carbon doping by the incorporation of heteroatoms able to provide useful pseudocapacitance effects. From a careful analysis of the results given by nanotubular materials, it seems that nanotubes can be a perfect component of the electrodes, generally as a support. Carbon nanotubes have a higher rate of electron transfer than conventional carbons due to the curvature of the graphene layers and to their specific open mesoporous texture offering an accessible electrode/electrolyte interface. The novel nanocomposite electrodes, combining the complementary properties of nanotubes and conducting polymers or oxides such as amorphous MnO z [39] are very promising due to the very efficient three-dimensional charges distribution.

23.4

GENERAL CONCLUSION AND PERSPECTIVES

In a nonexhaustive way, this chapter shows that Li-ion batteries and supercapacitors are very important electrical energy storage systems, where the carbon material plays a central role in the performance. Lately, many types of carbons have been investigated more or less empirically in these cells. However, the works performed recently pay a special attention to find correlations with specific parameters of nanostructured carbons, which is rather difficult because of the highly disordered state of these materials.

622

Chapter 23 Electrochemical Energy Storage

From the above presented data, it is obvious that the storage properties are highly influenced by the surface functionality and the porous texture of the materials. For example, we have shown that the irreversible capacity of lithium batteries is mainly related to the (ASA) of the materials. The surface groups play also a significant role in supercapacitors by providing an additional pseudocapacitance, and by reducing considerably the calendar life. The porosity of carbon, i.e., the pore size and the total pore volume, strongly affects the capacity of both the energy storage systems, and some trends show that the performance could be considerably changed by a perfect control of the pore size. Although devices based on carbon electrodes are commercially available, they have to be improved. In the case of lithium anodes, efforts to optimize the surface functionality have to be continued, even for graphite where exfoliation during cycling is a real drawback of graphite-based electrodes. The high values of reversible capacity given by some disordered carbons show promise for future developments. However, it is necessary to find a way to cure the noticeable overvoltage for lithium extraction, which more or less precludes a practical use of these materials. This overpotential, which corresponds to the additional energy requested to extract lithium, could certainly be partly reduced by an optimization of porosity to render lithium withdrawing more easy. In that sense, techniques such as CO 2 adsorption should be more extensively used to investigate the porous texture of these carbons. Regarding the supercapacitors, the real problem is not to increase the capacitance of the materials. Indeed, there are enough commercial carbons giving high values of capacitance. The most fundamental problem for solving is to determine the proportion of the total pore volume that is really used for the process of charge storage. In other words, what are the optimal pore size and shape required for efficient transportation and sorption of ions in a given electrolyte? Answering to this question is ofprime importance, because all the useless volume should be excluded from the material, in order to enhance as much as possible the specific capacity. The nanostructured carbons prepared from templates are certainly a good issue for providing useful information on pore size effects. Another important factor that determines the possible use of supercapacitors is their cycle life. They are supposed to operate for millions of cycles without considerable aging. Actually, this is not the case for supercapacitors operating in organic medium, mainly because of electrolyte decomposition on the surface functionality. Hence, harmful surface groups must be better determined and also the strategies which allow their elimination. Taking into account the underestimated advantages to operate in aqueous electrolyte, it seems also important to look for other applications of carbon materials where the unique combination of electrical conductivity, surface functionality and porous texture may be useful. Such applications as electrochemical hydrogen storage [116, 117], asymmetric supercapacitors [118] open future perspectives where all the information previously collected on other systems will be useful.

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626

Chapter 23 Electrochemical Energy Storage

57. Chevallier, F., Letellier, M., Morcrette, M., et al. (2004). In situ 7Li Nuclear Magnetic Resonance observation of reversible lithium insertion into disordered carbons. Electrochem. Solid State Lett., 6, A225-8. 58. Zheng, T., Xue, J.S., and Dahn J.R. (1996). Lithium insertion in hydrogencontaining carbonaceous materials. Chem. Mater., 8, 389-93. 59. Gibaud, A., Xue, J.S., and Dahn, J.R. (1996). A small angle X ray scattering study of carbons made from pyrolyzed sugar. Carbon, 34, 499-503. 60. Tokumitsu, K., Mabuchi, A., Fujimoto, H., and Kasuh, T. (1996). Electrochemical insertion of lithium into carbons synthesized from condensed aromatics. ]. Electrochem. Soc., 143, 2235-9. 61. Mabuchi, A., Fujimoto, H., Tokumitsu, K., and Kasuh, T. (1995). Chargedischarge characteristics of the mesocarbon microbeads heat-treated at different temperatures.]. Electrochem. Soc., 142, 1041-6. 62. Gautier, S., Leroux, F., Frackowiak, E., et al. (2003). Influence of the pyrolysis conditions on the nature of lithium inserted in hard carbons.]. Phys. Chem. A, 105, 5794-800. 63. Tatsumi, K., Akai, T., Imamura, T., et al. (1996). 7Li-Nuclear magnetic resonance observation of lithium insertion into mesocarbon microbeads.]. Electrochem. Soc., 143, 1923-30. 64. Letellier, M., Chevallier, F., Clinard, C., et al. (2003). The first in situ 7Li nuclear magnetic resonance study of lithium insertion in hard-carbon anode materials for Li-ion batteries.]. Chem. Phys., 118,6038-45. 65. Conway, B.E. (1991). Transition from "supercapacitor" to "battery" behavior in electrochemical energy storage.]. Electrochem. Soc., 138, 1539-48. 66. Toupin, M., Brousse, T., and Belanger, D. (2002). Influence of microtexture on the charge storage properties of chemically synthesized manganese dioxide. Chem. Mater., 14, 3946-52. 67. Wu, N.L. (2002). Nanocrystalline oxide supercapacitors. Mater. Chem. Phys., 75, 6-11. 68. Miller, J.M., Dunn, B., Tran, T.D., and Pekala, R.W. (1999). Morphology and electrochemistry of ruthenium/carboniaerogel nanostructures. Langmuir, 15, 799-806. 69. Frackowiak, E., Jurewicz, K., Delpeux, S., et al. (2002). Synergy of components in supercapacitors based on nanotube/polypyrrole composites. Mol. Cryst. Liq. Cryst., 387, 73-8. 70. Jurewicz, K., Delpeux, S., Bertagna, V., et al. (2001). Supercapacitors from nanotubes/polypyrrole composites. Chem. Phys. Lett., 347, 36-40. 71. Laforgue, A., Simon, P., Sarrazin, Ch., and Fauvarque, J-F. (1999). Polythiophene-based supercapacitors.]. Power Sourc., 80, 142-8. 72. Arbizzani, C., Mastragostino, M., and Soavi, F. (2001). New trends in electrochemical supercapacitors.]. Power Sourc., 100, 164-70. 73. Mastragostino, M., Arbizzani, C., and Soavi, F. (2002). Conducting polymers as electrode materials in supercapacitors. Solid State Ionics, 148, 493-8. 74. Jurewicz, K., Babel, K., Ziolkowski, A., et al. (2002). Ammoxidation of brown coals for supercapacitors. Fuel Process. Tech., 77-78, 191-8. 75. Jurewicz, K., Babel, K., Ziolkowski, A., and Wachowska, H. (2003). Ammoxidation of active carbons for improvement of supercapacitor characteristics. Electrochim. Acta, 48, 1491-8.

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96. Delpeux, S., Szostak, K., Frackowiak, E., et al. (2002). High yield of pure multiwalled carbon nanotubes from the catalytic decomposition of acetylene on in-situ formed cobalt nanoparticles. J. Nanosci. Nanotech., 2, 481-4. 97. Ma, R.Z., Liang, J., Wei, B.Q., et al. (1999). Study of electrochemical capacitors utilizing carbon nanotube electrodes. J. Power Sourc., 84, 126-9. 98. Frackowiak, E., Metenier, K., Bertagna, V., and Beguin F. (2000). Supercapacitor electrodes from multiwalled carbon nanotubes. Appl. Phys. Lett., 77, 2421-3. 99. Frackowiak, E., Jurewicz, K., Delpeux, S., and Beguin, F. (2001). Nanotubular materials for supercapacitors. J. Power Sourc., 97-98, 822-5. 100. Frackowiak, E., Jurewicz, K., Szostak, K., Delpeux, S., and Beguin, F. (2002). Nanotubular materials as electrodes for supercapacitors. Fuel Process. Tech., 77-78, 213-9. 101. Chen, J.H., Li, W.Z., Wang, D.Z., et al. (2002). Electrochemical characterization of carbon nanotubes as electrode in electrochemical double-layer capacitors. Camon, 40,1193-7. 102. Zhang, B., Liang, J., Xu, C.L., et al. (2001). Electric double-layer capacitors using carbon nanotube electrodes. Mater. Lett., 51, 539-42. 103. An, K.H., Kim, W.S., Park, Y.S., et al. (2001). Supercapacitors using single-walled carbon nanotube electrodes. Adv. Mater., 13, 497-500. 104. Shiraishi, S., Kurihara, H., Okabe, K., et al. (2002). Electric double layer capacitance of highly pure single-walled carbon nanotubes (HiPco™ BuckytubesTM) in propylene carbonate electrolytes. Electrochem. Commun., 4, 593-8. 105. Frackowiak, E. (2004). Carbon nanotubes for storage of energy: supercapacitors. Encyclopedia of Nanoscience and Nanotechnology. Marcel Dekker, pp. 537-46. 106. Barisci, J.N., Wallace, G.G., and Baughman, R.H. (2000). Electrochemical quartz crystal microbalance studies of single-wall carbon nanotubes in aqueous and nonaqueous solutions Electrochim. Acta., 46, 509-17. 107. Endo, M., Kim, Y.J., Osawa, K., et al. (2003). High capacitance EDLC using a carbon material obtained by carbonization of PVDC: the effect of the crystallite size of the pristine PVDC. Electrochem. Solid State Lett., 6, A23. 108. Frackowiak, E., Delpeux, S., Jurewicz, K., et al. (2002). Enhanced capacitance of carbon nanotubes through chemical activation. Chem. Phys. Lett., 361, 35-41. 109. Jiang, Q., Qu, M.Z., Zhou, G.M., et al. (2002). A study of activated carbon nanotubes as electrochemical super capacitors electrode materials. Mater. Lett., 57, 988-91. 110. Lota, K., Khomenko, V. and Frackowiak, E. (2004). Capacitance properties of poly(3,4-ethylenedioxythiophene)/carbon nanotubes composites J. Phys. Chem. Solids, 65, 295-301. 111. An, K.H., Jeon, K.K., Heo, J.K., et al. (2002). High-capacitance supercapacitor using a nanocomposite electrode of single-walled carbon nanotube and polypyrrole. J. Electrochem. Soc., 149, Al058-62. 112. Fan, J., Wan, M., Zhu, D., et al. (1999). Synthesis, characterizations, and physical properties of carbon nanotubes coated by conducting polypyrrole.J. Appl. Polymer Sci., 74, 2605-10. 113. Chen, J.H., Huang, Z.P., Wang, D.Z., et al. (2001). Electrochemical synthesis of polypyrrolelcarbon nanotube nanoscale composites using well-aligned carbon nanotube arrays. Appl. Phys. A Mater. Sci. Process, 73, 129-31.

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114. Chen, J.H., Huang, Z.P., Wang, D.Z., et al. (2002). Electrochemical synthesis of polypyrrole films over each of well-aligned carbon nanotubes. Synth. Met., 125, 289-94. 115. Khomenko, V., Frackowiak, E., Szostak, K., and Beguin, F. (2005). Determination of specific capacitance of conducting polymers/nanotubes composite electrodes using different cell configurations. Electrochim. Acta, 50, 2499-506. 116. Jurewicz, K., Frackowiak, E., and Beguin, F. (2001). Enhancement of reversible hydrogen capacity into activated carbon through water electrolysis. Electrochem. Solid State Lett., 4, A27-9. 117. Jurewicz, K., Frackowiak, E., and Beguin, F. (2004). Towards the mechanism of electrochemical hydrogen storage in nanostructured carbon materials. Appl. Phys. A, 78, 981-7. 118. Brousse, T., Toupin, M., and Belanger. (2004). A hybrid activated carbonmanganese dioxide capacitor using a mild aqueous electrolyte. J. Electrochem. Soc., 151~ 614-22.

ADSORPTION OF INORGANIC SPECIES FROM

AQUEOUS SOLUTIONS Pierre Le Cloirec and Catherine Faur-Brasquet Ecole des Mines de Nantes, Nantes cedex, France

Contents 24.1 Introduction 24.2 Metal Ion Removal 24.3 Anion and Cation Removal 24.4 Reaction Between Activated Carbon and Oxidants 24.5 Catalytic Reactions with Modified Activated Carbon 24.6 Conclusions and Trends References

24.1 INTRODUCTION Water and wastewater can be considered as complex mixtures of suspended solids, colloids, and dissolved organic or inorganic pollutants due to natural discharges or human activities. The contaminant levels are quite low in drinking water sources compared to pollutant concentrations found in industrial wastewater. However, to obtain clean water, several physicochemical or biological processes are available and commonly carried out, such as sedimentation, coagulation, flocculation, filtration, adsorption, oxidation, and free or fixed microorganisms [1]. To control and limit the impact of inorganic species on human health and the environment, treatment processes have to be defined and proposed. The methods for the removal of cations or anions from water are precipitation, membrane processes (nanofiltration or reverse osmosis), oxidation, biotreatments, ion exchange, and adsorption [2]. Activated carbon in Adsorption by Carbons ISBN: 978-0-08-044464-2

© 2008 Elsevier Ltd. All rights reserved.

631

Chapter 24 Adsorption of Inorganic Species from Aqueous Solutions

the form of powder, grains and, more recently, fibers (cloth or felt) [3] is a universal adsorbent and, in particular, some interactions occur with inorganic species present in water. The purpose of this chapter is to address the mechanisms of these interactions and to describe the processes for the removal of inorganic materials onto activated carbon. First, metal ion removal will be considered for the example of virgin activated carbon or precoated with organic matter. In this case, the regeneration of saturated materials will be described. The second section will be dedicated to cation and anion removal by adsorption, ion exchange, or biological activated carbon (BAC). The activated carbon can react with residual oxidant concentrations in water. In the third part, oxidation-reduction reactions in the presence or absence of catalysts will be presented. Finally, the interactions of porous carbon with metal or metal oxides to give catalytic or photocatalytic reactions will be approached in terms of the production of such material and its use in specific organic treatments.

24.2 METAL ION REMOVAL Environmental pollution due to the significant release of heavy metals by several industries is of major concern because of their toxicity and the threat to human life and to the environment, especially when tolerance levels are exceeded [4]. Besides ion exchange or reverse osmosis, adsorption onto activated carbon is one of the tertiary processes that may be used to remove low concentrations of metals from waste streams or drinking water. Adsorption has been shown to be economically favorable, compared with ion exchange, and technically easy, compared with reverse osmosis [5]. However, although adsorption by activated carbon is a common treatment for organic compound removal, it has been rarely used for metal ion elimination in an industrial setting, despite the fact that its performance has been demonstrated by numerous researchers [6]. Generally speaking, metal ion adsorption onto activated carbon may be studied in terms of distinct but interrelated phenomena: adsorption, surface precipitation, complexation, and ion exchange [7]. The maximum extent of adsorption depends on the nature of the metal ion, given by its speciation in aqueous solution, and on the activated carbon surface chemistry (see Chapter 13). This section aims to give an overview of adsorption processes of metal ions by activated carbon. Three cases are detailed: (1) the adsorption of metal ions onto virgin activated carbon; adsorption capacities are given in static and dynamic reactors, and the influence of various operating conditions is shown; (2) the adsorption of metal ions onto activated carbon preloaded with organic matter; (3) the saturation of activated carbon by organic matter and metal hydroxides after its use in wastewater treatment. The influence of metal hydroxides on activated carbon regeneration is demonstrated.

24.2

Metal Ion Removal

24.2.1

633

Adsorption of Metal Ions by Virgin Activated Carbon

24.2.1.1

Adsorption mechanism

A variety of distinct but interrelated phenomena may be involved in the adsorption process of metal ions onto activated carbons: adsorption (physical adsorption or chemisorption), surface precipitation, ion exchange, and surface complexation. The metal sorption is often not the result of one mechanism but of several reactions. The mechanisms involved and their degree of importance seem to depend on the materials and the operating conditions used. • Different studies have shown, during metal ion removal by activated carbon, a decrease in final pH as metal ion concentration is improved [8]. This fact may be due to a release of H 3 0+ ions and may indicate an adsorption mechanism by ion exchange, expressed by the following reaction where Mm+ is the metal ion and S-OH is a surface functional group of activated carbon [9]:

Ion exchange consists of the replacement of one adsorbed, readily exchangeable ion by another. The involvement ofoxygen surface groups in the sorption mechanism by ion exchange was confirmed by an improvement in adsorption onto oxidized adsorbents [10]. Carboxylic surface groups have been shown to be especially involved in the adsorption process [8], but this phenomenon may also occur with other ions such as [11] Ca2+, K+, and Na2+. • The formation of suiface complexes may also happen, by assuming an amphoteric behavior of activated carbon, according to the following reactions [11]:

for bidentate complexes:

2

OH + M 2+ ~== S - OM+ + H+ S - OH+M 2+ ~ (== S - 02M+2H+)

== S -

for monodentate complexes:

==

• In the presence of a high cation· to sorbent ratio, and at high sorbate concentrations, surface sites become saturated and surface complexation may be replaced by suiface precipitation, which involves the formation of a new solid or gel metal hydroxide at the surface [12]. • An adsorption process may also occur by surface reaction between the cation M 2+ and the negatively charged surface of the activated carbon, without exchange of ions or electrons. The variety of mechanisms that may be involved in the sorption process of metal ions onto activated carbon induces a great number of factors that control the adsorption: the surface oxygen complex content, the pH of point of zero charge, the pore texture of carbon, the solution pH and its ionic strength, the adsorption temperature, the nature of the metal ion given by its speciation diagram, its solubility, and its size in adsorption conditions. The influence of these various conditions is detailed in Section 24.2.1.4.

Chapter 24 Adsorption of Inorganic Species from Aqueous Solutions

24.2.1.2

Adsorption capacities in a batch reactor

Monocomponent adsorption capacities

Although activated carbon is rarely used for metal ion removal in an industrial setting, various works have shown its ability to remove these inorganic pollutants from water. Table 24.1 summarizes some adsorption capacities of activated carbon obtained for different metal ions in a static reactor. Depending on the operating conditions and the activated carbon and metal ion characteristics [6], the adsorption capacity ranges between 2 and 200 mg/g. These values are higher than those obtained with clay, and of the same order as those of sorbents like biomass or peat, the maximum adsorption capacities (up to 1000 mg/g for H~+ or Pb 2+) being reached with chitosan or lignin [13]. Table

24.1 Adsorption capacities of different metal ions onto activated carbon in a static reactor

Co (mg/L) (g/L) pH Q (mg/g) Reference wAC

1 0.2 7 2.6 [14]

Co - initial concentration, na - not available.

10-40 2 5 5-200

100 1 7

[8] WAC -

8

10-40 2 5 5-30

10-40 2 5 2-60

[15]

[8]

[8]

20-1000 10

20-1000 10

na

na

3-11 [16]

20-70 [16]

activated carbon weight, Q (mg/g) - adsorption capacity,

Multicomponent adsorption capacities

The competitive adsorption of metal ions is dependent on both the metal ions and the adsorbent, its magnitude being related to the adsorption mechanism. In the case of competition between metal ions for the same adsorption sites, it has been shown that the favored metal ion is that which presents the faster adsorption kinetics on the same activated carbon in a monocomponent solution. This is the case for the adsorption of Cu(II) and Pb(II) onto activated carbon cloths [17]. When metal ions present in solution do not interact with the same adsorption sites, the removal of both ions is not affected compared with monocomponent adsorption. For example, in a study performed with different activated carbons, nickel removal was not affected by the presence of cadmium, because the sites that interact with nickel do not strongly interact with cadmium [18]. Finally, due to the strong relationship that exists between the metal ion adsorption mechanism and pH (see Section 24.2.1.4), it as been demonstrated that competitive adsorption is also influenced by pH [19]. 24.2.1.3

Adsorption capacities in a column

The adsorption performance of activated carbon was confirmed in an activated carbon column for various metal ions like Cd(II), Pb(II), Hg(II), and

24.2

Metal Ion Removal

Table

24.2

635

Adsorption properties of metal ions by activated carbon in a

column [6]

Co (mg/L) WAC (g) pH U (m/h) Adsorption

112 40 7 4.9 BV = 2.6

52 30 2.5 4.9 BV = 400

50 50 4 3.7 BV= 20

2 na 8 4.6 60% removal

43 120 7 na V=2L

Co - initial concentration, WAC - activated carbon weight, U - hydraulic loading rate, BV - bed volumes treated at breakthrough, V - volume treated at breakthrough, na not available.

Zn(II) as presented in Table 24.2 [6], or Cr(VI), more than 99% of which was removed from industrial electroplating wastewater [20]. The modeling of the experimental breakthrough of lead (II) onto activated carbon fibers in a fixed bed, using axial dispersion and diffusion equations solved by the orthogonal collocation method, demonstrated that the intraparticle and external mass transfer is not the rate-controlling step, due to the short diffusion path for the adsorbate in activated carbon fibers [21].

24.2.1.4 Influence of operating conditions The stronger effect on the adsorption capacities ofmetal ions onto activated carbon is due to the pH contribution, which can be attributed to interactions between ions in solution and complexes formed at the adsorbent surface. The fact that a metal ion in aqueous solution can form different species whose presence depends on the solution pH is well documented [22]. Furthermore, the surface charge of an activated carbon surface also depends on solution pH: the surface charge is positively charged when the solution pH is below the pH of point of zero charge (pHpzc ) and negatively charged when the pH is above pHpzc (see Chapter 13). Different surveys show that a pH increase leads to an improvement in metal ion adsorption. Figure 24.1 presents copper adsorption onto an activated carbon cloth at different concentrations [8]. This result shows that the removal of heavy metals increases from about 10 to 90 % in a narrow pH range, known as the "pH adsorption edge," which is shifted to more alkaline regions as the molar metal concentration increases [19]. The coinfluence of metal ion removal by precipitation is also presented in Fig. 24.1. Table 24.3 summarizes the values of pH adsorption edges for different metals and given operating conditions. The adsorption increase of Cu(II) in a GAC column for a pH increase from 2 to 6 was explained by a shift of the equation (Mm+ + SOH -+ SOM(m-l)+ + H+) from left to right, which results in the production of more surface complexes SOM (m-l)+ or a higher removal of metal ions [9].

636

Chapter 24 Adsorption of Inorganic Species from Aqueous Solutions

100 90 80 70 (ij

60

> 0 E

50

0>R.

40

~

30 20 10

-+---------J'--I--------....--4----l

---+-

% adsorbed - 20 ppm

-+--------J~------4---J-----l ----0---

%

---+-

%

-+-----~---------I'---7'-----l _

-0- -

%

precipitated - 20 ppm adsorbed - 40 ppm precipitated - 40 ppm

0 2

0

4

6

8

10

12

Initial pH

Figure 24.1 Influence of pH on copper adsorption onto an activated carbon cloth [8].

Table 24.3 pH adsorption edges for the adsorption of different metal ions onto activated carbon (AC)

Zn(II) Cu(II) Pb(II) Ni(II)

100

1

40 40 40

2

2-7 2-6

2 2

4-9

3-4

[15] [8,9] [8] [8]

Because of a mechanism by ion exchange or surface complexation, the influence of other ions in solution cannot be neglected. An increase in the ionic strength of the solution reduces the electrostatic interaction, either repulsive or attractive, between the activated carbon surface and the metal ions due to a screening effect of the electrolyte. When the initial electrostatic interaction is repulsive (respectively attractive), an increase in ionic strength induces an increase (respectively a decrease) in adsorption [23]. The type of background electrolyte (NaN0 3 or NaCI0 4) does not significantly affect metal removal [18]. Among other factors that may influence the removal ofmetal ions by activated carbon, different surveys have pointed out the combined effect of initial metal concentration and activated carbon dosage with a decrease in adsorption as the metal/carbon ratio increases [24,25], or of temperature [26].

24.2.1.5 Modeling by surface complexation models Surface complexation models (SCM) are surface chemical equilibrium models that originate from work with metal oxides. The basic premise of SCM

24.2

637

Metal Ion Removal

is that adsorption of ions onto hydrous solids is analogous to the formation of soluble complexes, according to the following single metal-surface complexation reaction:

Various types of SCM have been assessed; namely, the diffuse-layer model (DLM) [27], the constant-capacitance model [28], the Stern model [29], and the triple-layer model (TLM) [30]. They differ in complexity from the simplest, DLM, which has four adjustable parameters, to the most complex, TLM, which includes seven adjustable parameters. The number ofparameters is dependent on the hypothesis relative to the model. In various researches, the DLM is selected because of its simplicity and its applicability to various solution conditions [31]. It takes into account ionic strength effects on protolysis equilibria through the Gouy-Chapman-Stern-Grahame charge-potential relationship:

where (J"o is the surface charge (C/m 2 ), 8 is the dielectric constant of water (78.5 at 25°C), 8 0 is the permittivity of free space (8.854 x 10- 12 C/V1m), Z is the valence of the electrolyte, and I is the ionic strength (moI/L). The DLM model needs to determine four parameters to enable surface complexation computation using the FITEQL program from adsorption vs pH curves [32]. These parameters are • both surface acidity constants of the ionization reaction of surface sites defined by the following equations:

== SOH2+ ~== SOH+H+ == SOH ~== SO- +H+ • the total number of acidic surface sites assessed by the Boehm method (see Chapter 13); • the specific surface area determined by nitrogen adsorption at 77 K. Because of a sorption mechanism of metal ions onto activated carbon that involves surface complexation, the DLM model was successfully applied to describe adsorption of metal ions onto this adsorbent. For example, the adsorption of Cd2+ and Zn2+ onto activated carbon in the form of powder or granules was modeled [19]. The modeling of the adsorption of Cu2+, Ni2+, and Pb 2+ onto activated carbon cloths allowed complexation constants to be calculated:

.

K~ =SOM+

{== SOM+}{H+}

= {== SOH}{M2+} exp

(-F'RTIJ: ) 0

Chapter 24 Adsorption of Inorganic Species from Aqueous Solutions

Table 24.4 Surface complexation constants of metal ion adsorption onto two activated carbon cloths, calculated using the DLM model [33]. na: not available

cu2+ Pb 2 + Ni2 +

20 40 20 40 20 40

2.909 2.102 4.137 2.545 0.068 -0.021

na

0.293 na na

-0.382 -0.606

These values are given in Table 24.4 for two initial concentrations of metal ions, 20 and 40 mg/L [33]. Values obtained for complexation constants are of the same order of magnitude as that obtained for copper adsorption onto a GAC, K:~OM+ ~ 6 [34]. 24.2.2 Adsorption of Metal Ions onto Activated Carbon

Preloaded with Organic Matter The influence of activated carbon preloaded with organic matter (see Chapter 25 for the adsorption of organics in aqueous solution) on the adsorption of metal ions is dependent on the operating conditions and on the properties of both the activated carbon and the organic matter [18]. The comparison of copper adsorption onto different activated carbons (in the form of cloth, ACC; and granules, GAC) preloaded with benzoic acid [17] shows that, whereas adsorption of Cu(II) onto loaded ACCs is greater than onto virgin ACCs, the loading of GAC by benzoic acid induces a decrease in adsorption capacity of 66 % (Fig. 24.2). As porosity and surface functional groups are similar for ACCs and GAC, this behavior difference may originate from pH conditions, initial pHo = 5 for ACC and 3.5 for GAC. At pHo = 5, adsorbed benzoic acid is in benzoate form C 6 H sCOO- (pKa = 4.2) and may form some ligands with metal cations Cu 2+, cationic species being dominant with hydrolyzed species at pH = 5. A previous work carried out with virgin activated carbon demonstrated an adsorption mechanism by ion exchange [8]. In the case of an activated carbon surface coated by benzoate ions, the following reaction may occur (where "S" is the activated carbon and "M" the metal ion), which induces an increase in metal ion removal from solution (Ce = 0 mmol/L in all cases): S-C 6 H sCOO- +M 2+ -+ S-(C 6 H sCOO-M)+.

24.2

Metal Ion Removal

+ Cu/ACC1 0.3 0.25

& Cu/ACC2 6. Cu/ACC2*BA

• Cu/GAC o Cu/GAC*BA

¢ ¢

0.2

Cu/ACC1*BA

¢

Qe (mmol/g) ¢

¢

+

¢

0.15

¢

+ ¢ ¢ +.. +. ~ <>~ • •

0.1

.

+

6.

6.

~

• 0

0.05

o 0

0

•

+

•

&6..

0

• 0

0

0

0

0

0 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Ce(mmol/L)

Figure 24.2 Adsorption of Cu(II) metal ions onto activated carbons in the form of cloths (ACC) and granules (GAC) , and onto the same activated carbons preloaded with benzoic acid [17].

The improvement in adsorption was more marked as the equilibrium concentration increased, due to the constant concentration of benzoic acid. At pHo = 3.5, adsorbed benzoic acid is in C 6 H sCOOH form and there is no ligand formation, so no increase in adsorption. The size of the organic molecules coating the activated carbon may also have an influence on the metal ion adsorption. Gold cyanide adsorption onto granular activated carbon loaded with different organic compounds (phenol, sodium ethyl xanthate, and ethanol) showed that the long-chain organic compounds had a higher degree of inhibition of gold cyanide mass transfer compared to the low-molecular-weight compounds [35]. For this reason, high-molecular-weight organic molecules, like fulvic acids, induce a reduction of Cu(II) binding by activated carbon due to either the blockage of pores or the interaction of the surface sites with fulvic acid molecules [36].

24.2.3 Saturation of Activated Carbon by Organic Matter and Metal Hydroxides After its use in wastewater treatment (see Chapter 26), activated carbon is saturated by organic matter and may contain some metal hydroxides that have been formed because of the presence of metal ions (like iron, aluminum, and calcium) in chemicals used in the coagulation and flocculation steps. Table 24.5 shows that high levels of calcium are accumulated by a field-spent activated carbon while accumulation of other metal ions occurs at much lower concentrations [37]. Usually, thermal processes using CO 2 or steam are employed for the regeneration of this field-spent activated carbon at temperatures that commonly exceed 700°C. However, the quality ofregenerated activated carbon for organics removal may be negatively affected by the presence of these metal hydroxides,

Chapter 24 Adsorption of Inorganic Species from Aqueous Solutions

Table 24.5 Ash content and inorganic composition of virgin and field-spent activated carbon Chemviron F400 [37]

M~tal 'otttent

.

~ JI r_ 1."#

Virgin GAC Spent GAC

4.8 12.6

0.089 4.045

0.618 0.480

0.467 0.543

0.026 0.029

0.069 0.061

0.020 0.062

0.002 0.006

which could catalyze the oxidation reaction between the regeneration agent (C0 2 or steam) and the solid carbon. The catalytic metals, by promoting localized oxidation of the carbon base, cause excessive mass loss due to the destruction of narrow micropores and thus a conversion of micropores into mesopores [38]. The catalytic effect of accumulated metals is especially marked with calcium [39, 40]. The presence of 2.3 % calcium increases the mass loss for steam regeneration at 850°C by a factor of 5 and for CO 2 by a factor of 25 at the same temperature compared to the respective rates observed in the absence of calcium [41]. The catalytic effect of iron was also shown on the thermal regeneration of granular activated carbon, with an increase of mass loss from 4.2 to 5.7 % in the presence of chelated Fe(III) but without an alteration of the pore structure. However, this catalytic effect of iron is no longer significant in the presence of sulfur at concentrations (0.01-0.03 %) naturally occurring in granular activated carbon [42]. To overcome calcium catalysis, a methodology has been assessed that uses specific reactivation parameters in terms of temperature ramp and duration [39, 40]. In any case, an acid washing seems to be a good way to remove the majority of metal ions before thermal regeneration of activated carbon [43].

24-3 ANION AND (ATION REMOVAL Most common ions (sodium, calcium, nitrate, phosphate, chlorine, bromide, and iodine) found in natural or wastewater are not really adsorbed onto activated carbons. An exception is fluoride that can be removed by activated carbon as well as by activated alumina. Table 24.6 gives some indications of the adsorption potential of some inorganic cations and anions onto carbonaceous porous material. Recently, the reduction by activated carbon filters of bromate (Br0 3 -), an ozone disinfection molecule produced by reactions between ozone and bromide initially present in water, has received increasing attention. Bromate reduction (Br0 3 - /Br-) was effective in a virgin activated carbon grain filter or in a BAC filter. The presence of natural organic matter (NOM) or inorganic ions (nitrate,

24.4 Reaction Between Activated Carbon and Oxidants

Table 24.6 Weak adsorption of common ions present in water onto activated carbon [2]

Adsorption potential

Low

Low

Low

Low

Low

Low

Low

High

phosphate, chloride, sulfate) caused a decrease in the mass of bromate removed by activated carbon grains as a result of the competition for adsorption-reduction sites. Increasing the empty bed contact time (EBCT), about 20 min, improves Br0 3 - removal [44-46]. In the specific case of perchlorate (CI0 4 -), a strong oxidant present in water at several micrograms per liter due to the utilization ofNH 4 CI0 4 in solid rocket fuel or components of munitions, Brown et al. [47] showed that: • in an abiotic GAC filter, percWorate was removed by ion exchange rather than by chemical reduction. The removal capacity in a column was found to be 0.172 mg/CI0 4 /g GAC. However, perchlorate was often displaced from the GAC by other ions present in the raw water. • in a biotic GAC filter, a low concentration of perchlorate was reduced biologically (less than 50 g/CIO 4 - / J..LL). The microorganisms convert perchlorate to chloride. The same operating conditions as for denitrification are required. However, this reduction was highly sensitive to nitrate. As N0 3 - concentration increased, perchlorate removal decreased. BAC filtration is a feasible option for perchlorate and nitrate treatment in drinking water. In order to improve perchlorate elimination from groundwater, granular and fibrous activated carbons preloaded with iron were used and compared to virgin GAC [48]. The activated carbon treatment was performed with ferric chloride and oxalic acid according to the procedures described in Section 24.4.1. The perchlorate adsorption capacity was found to be 0.34 mg/g in the preloaded carbon compared to 0.24 mg/g for the virgin activated carbon. The experiments were developed in a lab pilot unit and in a full-scale bed with an EBCT of 40 min. Sodium borohydride solution (100 mg/L) at about 5 % of the treated groundwater volume was able to restore the adsorption capacity of the GAC filter. The perchlorate mass flow ratio ranged from 100 to 215.

24-4

REACTION BETWEEN ACTIVATED (ARBON AND

OXIDANTS

The reactions between an oxidant and the activated carbon surface have been investigated in different ways. The first is to obtain a high level of surface functional groups to improve the interactions between these chemical functions

Chapter 24 Adsorption of Inorganic Species from Aqueous Solutions

and the pollutants (see Section 24.2 for heavy metal ion removal). The second way is to remove the residual oxidant from the aqueous solutions.

24.4.1 Direct Reaction with High Concentration Oxidants In aqueous solution, activated carbon (C), considered as a reductant, in contact with an oxidant (OX) reacts to give volatile molecules such as CO, CO 2 , H 2 0, and/or an oxidized carbon surface (C*O). This exothermal redox reaction is represented by the following general equation:

C*+OX+0 2 ~ CO+C0 2 +H 2 0+C*O Yang [49] describes some acidic surface functional groups bonded to aromatic rings present in the carbon surface. A simplified approach shows the presence of chemical groups such as carboxyl (G1), lactone (G2), phenol (G3), and carbonyl (G4). Infrared spectroscopy, X-ray photoelectron spectroscopy or ESCA, temperature programed desorption or TPD, and electrokinetic measurements have been carried out to identify and quantify these surface functional groups. However, acid-basic titration has been the most useful technique to determine the acidity (or basicity) of porous carbon [50]. More details on the surface chemistry characterization of carbons can be found in Chapter 13. Different activated carbons in contact with oxidants have been analyzed. Table 24.7 presents the oxidized material characteristics. The drastic treatments induce an increase in the chemical functions and then a better removal of heavy metal ions in aqueous solutions (Section 24.2.1). Some organic molecules, such as humic substances or more generally NOM, present in surface water have also been reported as being removed by oxidized activated carbon [51].

24.4.2 Reaction with Free Chlorine or Chlorine Dioxide One of the first mechanisms proposed for the interaction between chlorine and activated carbon is a hydrolysis, either in solution or in the adsorbed state, with the following simple reaction:

At high concentrations, free chlorine reacts directly with activated carbon to produce high-molecular-weight color-forming organics. Snoeyink et al. [52] also found chlorinated by-products in solutions such as chloroform, trichloroethane, and chlorinated aromatics. Montgomery [2] mentioned that, during a drinking water treatment, the concentration of residual chlorine in water is low and thus the level of the chlorinated compounds produced by these reactions is insignificant. Free chlorine reacts also with organic matter adsorbed onto activated carbon grains, which catalyze the reactions. Chlorinated compound precursors are, for example, NOM such as humic substances [53], proteins,

tv

~

.h-. ::::c (1) cu

Table 24.7

Characteristics of activated carbon after an oxidation reaction, Gi are the surface functional groups determined by Boehm's method, Gl for carboxylic acid, G2 for lactone, G3 for phenol, and G4 for carbonyl. These groups are differentiated by neutralization with solutions (o.oSN) of NaHC0 3 , Na 2 C0 3 , NaOH, and CH 3 CH 2 0Na [50]. 100 g of activated carbon in 500 mL of water with or without an oxidant

~

o' ::3 OJ

(1)

~ (1) (1)

::3

»

~

<' ~

(1)

0-

n cu

Microporous carbon (PI) PI in contact PI in contact S20S2PI in contact KMn0 4 PI in contact H 2SO 4

virgin

C-

468

995

0.155

0

0

0.45

0

0.45

o

885 927

0.106 0.154

0.02 0.04

0 0

0.68 0.86

0 0

0.70 0.90

0-

::3

cu ::3

with 03 with

50mg/03/min, t = 2h 98 g Na2S20 s /L, 2 h

447 588

with

0.065 g KMn0 4 /g PI

650

0.18

0.08

0.52

0

0.78

with

0.054g H 2S0 4 /g PI

510

0.72

0.07

0.42

0

1.21

Mesoporous virgin carbon (PO) PO in contact with 0 3 PO in contact with HN0 3 PO in contact with NaOCI

50 mg 03/min, t = 2 h HN0 3 10N 450mL NaOCI + 50mL H 2S0 4 36N, t = 2 h

290

1250

0.554

0.48

0.03

1.04

0

1.55

300

937

0.483

0.40 1.30

0.25 0.15

1.30 2.00

0 0

1.95 3.45

0.68

0.18

1.45

0.05

2.13

o

>< c.:: cu ~ (J)

0\

~

w

644

Chapter 24 Adsorption of Inorganic Species from Aqueous Solutions

amino acids, sugars, polysaccharides [1, 54], or xenobiotic molecules (aromatics, esters, aldehydes, ketones, organic acids) trapped in the porous volume. Byproduct molecular structures and concentrations are similar to those found with the reaction between chlorine and dissolved organics in solution. Thus, trihalomethane, chlorinated acids, nitriles, and aldehydes have been found [1, 52, 55-57]. Current regulations (US EPA regulations or European Union directives for example) impose a maximum concentration of halogenated compounds of less than 0.1 ,ug/L. Chlorine dioxide (CI0 2) reacts quickly with activated carbon but the nature of the by-products and the reactions is a function of pH [58]: • at pH = 3.5, CI- (chloride) is predominant but CI0 2 - (chlorite) and CI0 3 (chlorate) are also found. • at pH = 7.9, CI0 2 - is the predominant species while CI- and CI0 3 - are also present at low concentrations. The different reactions are discussed in terms ofpH and species concentrations by Faust and AIy [58] for batch reactors and full scale plant GAC columns.

24.4.3 Dechlorination-dechloramination Dechlorination can be performed with activated carbon. Chlorine or hypochlorite, OCI- for example, react with the carbon surface to give chloride, an acidification of the solution and oxidized groups on the carbon surface. These chemical functions may be decomposed into carbon monoxide or dioxide. A schematic overall reaction is written:

Monochloramine (NH 2 CI), produced during disinfection of water or oxidation of soluble organic molecules with chlorine, reacts more slowly than HOCl with activated carbon. In this case, the carbon acts as a reducing agent but also as a catalyst in producing ammonia (NH 3 or NH4 + depending on the solution pH) chlorine and gaseous nitrogen following the reactions: C* + NH 2 CI + H 2 0 ~ NH 3 + CIC*O + 2NH 2 CI ~

+ H 3 0+ + C*O N 2 + 2CI- + H 2 0+ + C*

Dichloramine (NHCI2) reacts more rapidly than HOCI to give nitrogen and chlorine:

The kinetics of the reactions between free or combined chlorine have been extensively described and modeled for bed adsorbers by Suidan et al. [59].

24.5 Catalytic Reactions with Modified Activated Carbon

24.5

645

CATALYTIC REACTIONS WITH MODIFIED ACTIVATED

CARBON

In order to improve the efficiency ofactivated carbon in organic compound removal, catalytic reactions are favored by modifications of the activated carbon surface. The functional groups are increased by oxidation treatment (see section on impregnation with metals or metal oxides). The metal coating the porous surface plays the role of catalyst or reacts with soluble organic compounds.

24.5.1 Catalytic Reactions in the Presence of an Oxidant In this approach, the use of the activated carbon surface, the functional groups or metal oxide on the surface and the presence of an oxidant, such as ozone or hydrogen peroxide, is combined to remove recalcitrant organic pollutants from water or wastewater. Rivera-Utrilla and Sanchez-Polo [60] mentioned a fast degradation of 1,3, 6-naphthalenetrisulfonic acid at low pH (about 2.3) by a large number ofactivated carbons in contact with ozone. The catalytic activities ofactivated carbon quantified by the ash constituents are shown to give highly oxidative species in solution. With a similar approach, a catalytic decomposition of hydrogen peroxide and 4-chlorophenol (4-CP) in the presence of modified activated carbons was described by Huang et al. [61]. After oxidation of the activated carbon surface (Section 24.4.1), there are more acidic groups. They retard H 2 0 2 loss and reduce the effect of surface scavenging, resulting in an increase in the efficiency of 4-CP degradation. A kinetic approach to H 2 0 2 consumption is proposed with mechanisms integrating the catalytic effect.

24.5.2 Metal or Metal Oxide Impregnation Different metals, metal ions, or metal oxides (such as copper, nickel, iron, or titanium oxide) are used to impregnate activated carbon in order to obtain a surface useful for specific compound removal or catalytic or photocatalytic applications. Impregnation is performed before or after the activation step. Before activation, the metal distribution is uniform at the carbon surface and plays the role of catalyst, for example between CO 2 and the surface, during the activation. An impregnation after activation allows the deposit of a larger amount of metal but with an inhomogeneous distribution on the solid surface. Various procedures are used to impregnate the activated carbon. The porous solid is stirred with saturated solutions for 1-3 h and dried. Another direct impregnation is achieved by contact with a solution of metal ions. The aqueous solution is removed by vacuum distillation. Then, the impregnated materials are activated again by heating under an inert, reducing (hydrogen), or oxidative (air) atmosphere to obtain a metal or a metallic oxide loading the activated carbon. A recent procedure has been proposed using an ionized cluster beam method

Chapter 24 Adsorption of Inorganic Species from Aqueous Solutions

to prepare activated carbon fibers covered by titanium oxide [62]. The crystal nature (anatase for Ti0 2 ) of the coating is important in terms of performance and reaction specificity.

24.5.3 Applications of Photocatalysis Numerous researchers have paid special attention to the photocatalytic degradation of organic pollutants on activated carbon loaded with metal or metal oxides. Titanium dioxide is the main compound used as a catalyst for the mineralization of organic substances in water. Ti0 2 -activated carbon was prepared by impregnation as described previously (Section 24.5.2) or mixed directly into the solution before irradiation. Generally, UV lamps with wavelengths ranging between 300 and 400 nm with a main radiation close to 365 nm were used. Experiments were performed on different organics in diluted aqueous solutions. UV irradiation of the Ti0 2 loaded onto activated carbon fiber was applied to a solution of2-propanol or 1,2-dichloroethane. These organics were decomposed into CO 2 , H 2 0, and HCI [62] A suspended mixture of Ti0 2 and activated carbon was UV irradiated to oxidize phenol, 4-chlorophenol and herbicide 2,4-D (2,4-dichlorophenoxy-acetic acid) [63]. The kinetics of disappearance followed an apparent first-order rate. A synergy factor was determined ranging from 1.3 to 2.5 depending on the activated carbons and the soluble molecules. Experiments were performed with solar irradiation in the same operating conditions giving similar results in terms of kinetics and synergy factors. Hybrid photocatalysts consisting of Ti0 2 and an adsorbent such as activated carbon were used in the photoinduced mineralization ofbromoform and propyzamide dissolved in water. In the first step, the target substrates were adsorbed onto the adsorbent support. Next, due to the presence of Ti0 2 , they were photodestructed [64, 65]. The effect of Ti0 2 photocatalyzed oxidation on the degradation and decolorization of humic substances was investigated and the by-products studied in terms of their adsorptivity onto activated carbon [66]. A significant decolorization was found with an increase of the BOD (biological oxygen demand)/COD (chemical oxygen demand) ratio due to the formation of more biodegradable substances. After the irradiation period, no real change in adsorption was noted.

24.5.4 Specific Treatment of Sulfide or Hydrogen Sulfide For sulfide or hydrogen sulfide removal (the species depends on the solution pH), found, for example, in wastewater networks or industrial aqueous eilluents, activated carbon preloaded with iron (AC-Fe) or copper was used. In this case, an AC-Fe-S complex is formed on the activated carbon surface following the simple reaction: However, in the presence of oxygen, the sulfur is thought to be removed according to another mechanism involving an oxidation of sulfide to sulfur (SO) or sulfate (SO 42-) at the surface of the activated carbon. The level of oxygen on

647

References

the carbon is a function of the acidic surface functional groups as determined by Boehm's method [50].

24.6

CONCLUSIONS AND TRENDS

Activated carbon is a universal adsorbent with a wide variety of adsorption capacities depending on the inorganic compound structure. The capability of carbons precoated by organic material to remove metal ions is highlighted. The impregnation of the porous solid leads to catalytic or complexation mechanisms with some soluble molecules and seems to be promising. Activated carbon is also a reducing agent for oxidant residues present in drinking water giving some by-products at very low levels. However, some perspectives and trends in terms of research and technology developments could be suggested: • new porous carbons have recently been proposed and commercialized, such as activated carbon fiber cloths, felts, or spherical porous carbonized polymers. Their utilization in water treatment and especially in inorganic species removal could be promoted. • surface functional groups seem to play an important role in inorganics removal and more specifically in heavy metal ion removal. Special activated carbons with a large number of functional groups could be designed in order to have a synergy in terms of mechanism between adsorption and ion exchange. • interactions between organic matter coating activated carbon and metal ions need to be studied more in water treatment not only to elucidate mechanisms but also to determine possible leachate during drinking water production. • the catalytic or photocatalytic effects of activated carbon preloaded with metal or metal oxide, and especially with Ti0 2 , seem to be promising. More research is needed to explore mechanisms, kinetics, and to identify and quantify reaction by-products. • a multiscale approach (molecule behavior, reactions, kinetics, fluid mechanics, diffusion, mass balance) to these treatments has to be developed for a better understanding of mechanisms and an optimal design of these processes. • multifunction systems to remove both organics and inorganics present in water could be designed to reduce process size and improve performance.

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1.

Chapter 24 Adsorption of Inorganic Species from Aqueous Solutions

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650

Chapter 24 Adsorption of Inorganic Species from Aqueous Solutions

41. Knappe, D.R.U., Snoeyink, V.L., Dagois, G., and DeWolfe, J.R. (1992). Effect of calcium on thermal regeneration of GAC. J. Am. Water Works Assoc., 84(8), 73-80. 42. Cannon, F.S., Snoeyink, V.L., Lee, R.G., and Dagois, G. (1997). Effect of iron and sulfur on thermal regeneration of GAC. J. Am. Water Works Assoc., 89(11), 111-22. 43. Pilard, M., Dagois, G., Montagnon, P., and Chesneau, M. (1996). Influence of minerals on the regeneration of activated carbon used in drinking water treatment. Water Supply, 14, 263-70. 44. Kirisits, MJ. and Snoeyink, V.L. (1999). Reduction of bromate in a BAC filter. J. Am. Water Works Assoc., 91(8), 74-84. 45. Kirisits, MJ., Snoeyink, V.L., and Kruitho£J.C. (2000). The reduction of bromate by granular activated carbon. Water Res., 34(17), 4250-60. 46. Bao, M.L., Griffini, 0., Santianni, D., et al. (1999). Removal of bromate ion from water using granular activated carbon. Water Res., 33(13), 2959-70. 47. Brown, J.C., Snoeyink, V.L., and Kirisits, MJ. (2002). Abiotic and biotic perchlorate removal in an activated carbon filter. J. Am. Water Works Assoc., 94(2), 70-9. 48. Na, C., Cannon, F.S., and Hagerup, B. (2002). Perchlorate removal via iron-preloaded GAC and Borohydride regeneration. J. Am Water Works Assoc., 94(11), 90-102. 49. Yang, R.T. (2003). Adsorbents, Fundamental and Applications. Wiley Interscience. 50. Boehm, H.-P. (2002). Surface oxides on carbon and their analysis: a critical assessment. Carbon, 40, 145-9. 51. Lemarchand, D., Le Cloirec, P., Gaid, K., and Martin, G. (1983). Etude de l' adsorption des substances humiques sur charbon actif Environ. Technol. Lett., 4, 297-310. 52. Snoeyink, V.L., Snoeyink, V.I., Clark, R.R., McCreary, JJ. and McHie, W.F. (1981). Organic compounds produced by aqueous free chlorine-activated carbon reaction. Environ. Sci. Technol., 15, 188-92. 53. Christman, R.F., and Gjessing, E.T. (1983). Aquatic and Terrestrial Humic Materials. Ann Arbor Science Publishers. 54. American Water Works Association (1990). Water Quality and Treatment, 4th edn. McGraw-Hill. 55. Le Cloirec, C. and Martin, G. (1985). Evolution of amino acids in water treatment plants and the effect of chlorination on amino acids, In Water Chlorination, Vol. 5 Golley, R.L., et aI., eds). Lewis Publishers, pp. 821-34. 56. Hureiki, L., Croue, J.Ph., and Legube, B. (1994). Chlorination studies of free and combined amino acids. Water Res., 28(12), 2521-31. 57. White, G.C. (1999). Handbook of Chlorination and Alternative Disinfectants. John Wiley & Sons. 58. Faust, S.D. and Aly, O.M. (1998). Chemistry of Water Treatment, 2nd edn. Lewis Publishers. 59. Suidan, M.R., Kim B.R., and Snoeyink, V.L. (1980). Reduction of free and combined chlorine with granular activated carbon. In Activated Carbon Adsorption of Organics from the Aqueous Phase, Vol. 1 (I.H. Suffet and MJ. McGuire, eds). Ann Arbor Science Publishers.

References

60. Rivera-Utrilla, J. and Sanchez-Polo, M. (2002). Ozonation of 1,3, 6-naphthalenetrisulphonic acid catalysed by activated carbon in aqueous phase, Appl. Catal. B: Environ., 39(4), 319-29. 61. Huang, H.H, Lu, M.C., Chen,J.N., and Lee, C.T. (2003). Catalytic decomposition of hydrogen peroxide and 4-chlorophenol in the presence of modified activated carbons. Chemosphere, 51(9), 935-43. 62. Yamashita, H., Harada, M., Tanii, A., et al. (2000). Preparation of efficient oxide photocatalysts by an ionized cluster beam (ICB) method and their photocatalytic reactivities for the purification of water. Catal. Today, 63(1), 63-9. 63. Matos, J., Laine, J., and Hermann, J.M. (2001). Effect of the type of activated carbons on the photocatalytic degradation of aqueous organic pollutants by UV-irradiated titania.J. Catal., 200(1), 10-20. 64. Yoneyama, H. and Torimoto, T. (2000). Titanium dioxide/adsorbent hybrid photocatalysts for photodestruction of organic substances of dilute concentrations. Catal. Today, 58(2-3), 133-40. 65. Hermann, J.M., Matos, J., Disdier, J., et al. (1999). Solar photocatalytic degradation of 4-chlorophenol using the synergistic effect between titania and activated carbon in aqueous suspension. Catal. Today, 54(2-3), 255-65. 66. Berkbolet, M., Ce~en, F., and Ozkosemen, G. (1996). Photocatalytic oxidation subsequent adsorption characteristics of humic acids. Water Sci. Technol., 34(9), 65-72.

ADSORPTION OF ORGANIC SOLUTES FROM

DILUTE AQUEOUS SOLUTIONS Carlos Moreno-Castilla Departamento de Qufmica Inorganica, Facultad de Ciencias, Universidad de Granada, Granada, Spain

Contents 25.1 25.2 25.3 25.4 25.5 25.6 25.7

Introduction Factors that Control the Adsorption Process Adsorption of Nonelectrolytes Adsorption of Electrolytes Adsorption of Natural Organic Matter Adsorption of Bacteria Conclusions References

653 655 658 660 668 671 673 674

25.1 INTRODUCTION

Activated carbon is the most important carbon material used to adsorb organic solutes from aqueous solutions, although the use of activated carbon fibers and activated carbon cloths has been continuously growing in recent years. These carbon materials are applied across a wide spectrum of systems such as drinking water and wastewater treatments and are used in the food, beverage, pharmaceutical, and chemical industries. Furthermore, activated carbon adsorption has been cited by the US Environmental Protection Agency as one of the best available environmental control technologies [1]. Adsorption by Carbons ISBN: 978-0-08-044464-2

© 2008 Elsevier Ltd. All rights reserved.

653

654

Chapter 25 Adsorption of Organic Solutes from Dilute Aqueous Solutions

Activated carbons can be manufactured in powder and granular form from a large variety of raw materials [2], and their highly developed porosity, large surface area, and variable surface chemistry make them unique and versatile adsorbents. Powdered activated carbon is usually added as an aqueous slurry to the tank containing the water to be treated, whereas granular activated carbon is used in column beds in which water usually flows downward, driven by either pressure or gravity. A major advantage of granular activated carbons is that they can be regenerated for reuse when their adsorption capacity is exhausted. In spite of the large market for activated carbon, the specific mechanisms of the adsorption of many compounds, especially organic compounds, on this adsorbent remain uncertain. This is because liquid-phase adsorption is a more complicated process than gas- or vapor-phase adsorption [1]. The main differences between adsorption from the gas phase and that from liquid phase are as follows [3]. First, adsorption from solution is essentially an exchange process, and hence, molecules adsorb not only because they are attracted by solids but also because the solution may reject them. A typical illustration is that the attachment of hydrophobic molecules on hydrophobic adsorbents from aqueous solutions is mainly driven by their aversion to the water and not by their attraction to the surface. Second, isotherms from solution may exhibit nonideality, not only because oflateral interactions among adsorbed molecules but also because of nonideality in the solution. Third, multilayer adsorption from solution is less common than from the gas phase, because of the stronger screening interaction forces in condensed fluids. The study of a particular adsorption process requires the knowledge of equilibrium data and adsorption kinetics [4]. Equilibrium data are obtained from adsorption isotherms and are used to evaluate the capacity of activated carbons to adsorb a particular molecule. They constitute the first experimental information that is generally used as a tool to discriminate among different activated carbons and thereby choose the most appropriate one for a particular application. Statistically, adsorption from dilute solutions is simple because the solvent can be interpreted as primitive, that is to say as a structureless continuum [3]. Therefore, all equations derived from monolayer gas adsorption remain valid. Some of these equations, such as the Langmuir and Dubinin-Astakhov, are widely used to determine the adsorption capacity of activated carbons. Batch equilibrium tests are often complemented by kinetics studies, to determine the external mass transfer resistance and the effective diffusion coefficient, and by dynamic column studies. These column studies are used to determine system size requirements, contact time, and carbon usage rates. These parameters can be obtained from the breakthrough curves. In this chapter, I shall deal mainly with equilibrium data in the adsorption of organic solutes. Adsorption measurements should preferably be amplified by microcalorimetry, such as immersion and flow microcalorimetry. These techniques can give additional information about the surface nature of the adsorbent and the mode or mechanism of the adsorption.

25.2

Factors that Control the Adsorption Process

655

25.2 FACTORS THAT (ONTROL THE ADSORPTION PROCESS Adsorption is a spontaneous process that takes place if the free energy of adsorption is negative. There is a wide range of energies contributing to the free energy of adsorption, which can be divided between nonelectrostatic and electrostatic. Although at the atomic level all ionic and molecular interactions can be interpreted as "electric," this term is restricted to coulombic interactions, and all other interactions are termed nonelectrostatic, whatever their origin. Electrostatic interactions appear when the adsorptive is an electrolyte that is dissociated or protonated in aqueous solution under the experimental conditions used. These interactions, which can be either attractive or repulsive, strongly depend on the charge densities of both the carbon surface and the adsorptive molecule and on the ionic strength of the solution. The nonelectrostatic interactions are always attractive and can include van der Waals forces and hydrophobic interactions. The factors that influence the adsorption process are the characteristics of the adsorbent and the adsorptive, the solution chemistry, and the adsorption temperature. Among the characteristics of the adsorbent are its pore texture, surface chemistry, and mineral matter content. The characteristics of the adsorptive are its molecular size, solubility, polarity, pKa (for electrolytes), and nature of the substituents if it is aromatic. Finally, the solution chemistry factors are the pH and the ionic strength [5]. I shall focus in this section only on the role of the characteristics of the adsorbent, especially its carbon surface chemistry, on the adsorption processes, because although its importance has long been recognized [6, 7], the exact nature of this importance has often been controversial and misunderstood [1]. The adsorption capacity of carbon materials is not related in a simple manner to their surface area and porosity. The adsorption capacity will depend on the accessibility of the organic molecules to the inner surface of the adsorbent, which depends on their size. Thus, under appropriate experimental conditions, small molecules (e.g., phenol) can access micropores, natural organic matter (NOM) can access mesopores, and bacteria can access macropores. Activated carbon fibers have attracted increasing attention in recent years as a better adsorbent than granular activated carbons, because they normally present much higher adsorption kinetics and adsorption capacity. Activated carbon fibers only have micropores, which are directly accessible from the external surface of the fiber. Thus, adsorptive molecules reach adsorption sites through micropores without the additional diffusion resistance of macropores, which is usually the rate-controlling step in granular adsorbents. The surface chemistry of activated carbons essentially depends on their heteroatom content, mainly their surface oxygen complex content, which determines the charge of the surface, its hydrophobicity, and the electronic density of the graphene layers. Thus, when a solid such as a carbon material is immersed in an aqueous solution, it develops a surface charge that derives from the

Chapter 25 Adsorption of Organic Solutes from Dilute Aqueous Solutions

dissociation of surface groups or the adsorption of ions from the solution [1]. The surface charge will depend on the solution pH and the surface characteristics of the carbon. A negative charge results from the dissociation of surface oxygen complexes of acid character such as carboxyl and phenolic groups. Therefore, these surface acid sites are of Bronsted type. The origin of the positive surface charge is more uncertain because, in carbons without nitrogen functionalities, it can be due to surface oxygen complexes of basic character like pyrones or chromenes, or to the existence of electron-rich regions within the graphene layers acting as Lewis basic centers, which accept protons from the aqueous solution. An indication that surface basicity can be mainly due to these electronrich regions is that the net enthalpy of neutralization of the total basic sites decreases with the oxygen content of the surface, whereas the net enthalpy of neutralization of total acid sites increases [8], as shown in Fig. 25.1. These results, obtained with activated carbons of different origins, can be explained by the fact that surface oxygen complexes of acid character reduce the electronic density of the graphene layers and consequently reduce the basicity of the carbon surface. More experimental evidence on these effects has recently been reported by Darmstadt and Roy [9], who showed a linear decrease in the full width at half maximum of the graphite peak in the XPS spectra of carbon blacks with an increase in their concentration of surface basic sites, determined by titration. This linear correlation strongly suggests that basic sites are largely associated with basal planes of graphene layers. This is because a narrow graphite peak indicates a small concentration of defects and a large delocalization of the 'IT electrons, which increases the Lewis basic character of the graphene layers. The surface charge can be determined by electrokinetic or titration methods. These are complementary methods, especially in the case of granular porous

120

:§ ::3CD

~

U I

f' <]-

80

I

0

I

CD c:

40

0

ctS

~

:t

if

0

0

2

3

4

5

6

7

8

[0] (mmol/g)

Figure 25.1 Variation of the net enthalpy of neutralization aiH(NaOH)net, a; and aiH(HCI)net' ., with the total amount of oxygen. (Adapted from Re£ [8].)

25.2

Factors that Control the Adsorption Process

657

carbons [1, 10]. The first method primarily measures the surface charge at the more external surface ofthe particles, whereas the second one provides a measure of the total surface charge. The pH at which the external surface charge is zero is referred to as the isoelectric point, pH IEP ' while the total surface charge is zero at the point of zero charge, pHpzc ' In addition, surface oxygen complexes also affect the surface hydrophobicity, which determines the hydrophobic interaction. Hydrophobic interaction or, more specifically, hydrophobic bonding describes the unusually strong attraction between hydrophobic molecules and hydrophobic carbon surfaces. The surface hydrophobicity of carbon materials is not determined in many research works. However, knowledge of the surface hydrophobicity is of great value for a more complete characterization of the surface chemistry of carbons to be used as adsorbents in aqueous solutions. Surface hydrophobicity can be known by determination of the total surface energy, which can be carried out either by measuring the contact angle with test liquids of known surface tension [11], by inverse gas chromatography [12], or by water adsorption [13, 14], among other methods. Hydrophobic bonding occurs exclusively in aqueous solution: in fact, it mainly comes from the strong tendency of water molecules to associate with each other by hydrogen bonding and from the characteristic structure of water molecules. Hydrophobic bonding plays an important role in interface and colloid science [15]. For instance, the increasing adsorbability of aliphatic acid molecules with increasing hydrocarbon length, also known as Traube's rule, is essentially due to the increasing hydrophobic effect [6]. Therefore, it is important to plot the adsorption isotherms obtained for adsorptives with different solubilities against the concentration relative to the saturated solution. This normalization eradicates the differences in hydrophobicity between the adsorptive molecules, so that the normalized isotherms more truly reflect the affinity for the surface [3, 6]. An increase in the surface oxygen content of carbon produces a decrease in its hydrophobicity. Thus, total carbon surface energy can be divided into polar and dispersive components. Carbon oxidation with air and ozone greatly increases the polar contribution and to a lesser extent the dispersive component [11], as shown in Table 25.1. Hence, the net effect of oxidation is a rather large increase in total surface energy, which normally produces an increase in the strength of the interfacial forces. This improves the wetting by polar liquids and diminishes the hydrophobic effect. In addition, it brings about the H-bonding of water molecules to surface oxygen complexes, especially carboxylic groups, which reduces the accessibility of the adsorptive molecules to part of the carbon surface. Surface oxygen complexes also affect the electronic density of the graphene layers [16], which in turn affects the dispersion interactions between the carbon surface and the adsorptive molecules. For instance, carboxyl groups fixed at the edges of the graphene layers have the ability to withdraw electrons, whereas phenolic groups release them. Thus, Tamon and Okazaki [17] determined by

Chapter 25 Adsorption of Organic Solutes from Dilute Aqueous Solutions

Table 25.1 Surface energies of furnace carbon black

Untreated Air oxidized Ozone treated

20.9 22.7 24.4

M120

0.9 4.3 8.1

21.8 27.0 32.5

Adapted from Ref [11].

a semiempirical quantum chemical method the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) levels of a nonsubstituted phenanthroperylene cluster, considered as a model aromatic molecule, and of the same cluster substituted with two phenolic groups and with two carboxyl groups. The results obtained indicate that the withdrawing groups, such as carboxyl groups, decrease HOMO and LUMO levels with respect to the original carbon cluster, whereas the donating groups increase these levels. Finally, another characteristic of the adsorbent that controls the adsorption process is its mineral content. This has a generally deleterious effect on the adsorption because it can block the porosity of the carbon matrix and can preferentially adsorb water due to its hydrophilic character, which reduces the adsorption of the adsorptive. In the following sections I attempt to offer a consistent explanation of the importance of the carbon surface properties that influence the adsorption processes, which is valid for different organic solutes, from nonelectrolytes to polyelectrolytes and bacteria.

25.3

ADSORPTION OF NONELECTROLYTES

The recent work by Li and coworkers [18] provides a good illustration of the importance of the surface chemistry and pore texture of carbon materials on nonelectrolyte adsorption. They studied the adsorption of trichloroethene (TCE) and methyl tert-butyl ether (MTBE) on different commercial activated carbons and activated carbon fibers with different porosity and surface chemistry. TCE is a relatively hydrophobic planar molecule. MTBE is tetrahedron-like and relatively hydrophilic. The results of the adsorption from aqueous solutions on the more hydrophobic carbons showed that TeE adsorption was controlled by a pore volume ranging from 0.7 to 1 nm width, as shown in Fig. 25.2. MTBE was primarily adsorbed in pores with widths between 0.8 and 1.1 nm. These micropore ranges were between 1.3 and 1.8 times the kinetic diameter of the adsorptives.

25.3 Adsorption of Nonelectrolytes

40......----------------.....,

'C)

-...

C>

S

30

uQ)

.0

0en

u ca 'E ::::J 0

20

E


10

•

AAW

• •

AW HAW

6.

G219

o

F600

-f---------.------......-------t 0.1

0.15

0.2

0.25

Pore volume in the 0.7-1 nm width range (cm 3jg)

Figure 25.2 Effect ofpore volume on tricWoroethene adsorption. (Adapted from Ref. [18].)

Introduction of surface oxygen complexes on the carbons negatively affected the TCE and MTBE adsorption from aqueous solution. However, the MTBE adsorption from cyclohexane solution was greatly increased (by a factor of about 5-6) for oxidized samples. This was explained by preferential MTBE adsorption on carboxyl and phenolic groups, which form H-bonds with the ether functionality of MTBE. These H-bonds in aqueous solution would be preferentially formed with water molecules, producing water clusters that would reduce the accessibility to the rest of the carbon surface. The results of TCE adsorption from cyclohexane solution showed that the effect of the surface chemistry was negligible, indicating that TCE was not preferentially adsorbed on the surface oxygen complexes. However, these complexes reduced TCE adsorption from the aqueous solution with respect to the nonoxidized carbon, due to the formation of water clusters, as in MTBE adsorption. All these results show the importance of the carbon surface chemistry and pore texture on the adsorption of nonelectrolytic organic solutes. Thus, for hydrophobic carbons, which generally have a low content of surface oxygen complexes, the adsorption oforganic molecules is by dispersion and hydrophobic interactions, and the pores involved in the adsorption depend on the molecular size of the adsorptive. Conversely, when the adsorbent's content of surface oxygen complexes increases or its hydrophobicity decreases, there is a preferential adsorption of water on these complexes, which reduces the adsorption capacity of the adsorbent.

660

Chapter 25 Adsorption of Organic Solutes from Dilute Aqueous Solutions

25.4

ADSORPTION OF ELECTROLYTES

The adsorption of organic electrolytes is a more complicated process than that of nonelectrolytes because it is a complex interplay between electrostatic and nonelectrostatic interactions. In this section, I present results obtained with three representative types of organic electrolytes: phenol and its derivatives, dyes, and surfactants. These observations demonstrate the importance of the surface chemistry of carbons on the adsorption processes. The adsorption of phenol and phenolic compounds is by far the most studied of all liquid-phase applications of carbon adsorbents [1]. This is because phenol is used as a model aromatic molecule and has been declared a priority pollutant. Therefore, this chapter devotes more attention to the adsorption of phenol and substituted phenols than to the adsorption of other organic solutes. It has long been known [16], and has more recently been confirmed by many authors [1], that phenol adsorption presents certain complexities, such as the occurrence of two distinct plateaus in the isotherm. In addition, the phenol uptake decreases upon oxidation of the activated carbons. To demonstrate this phenomenon (Table 25.2), sample A was oxidized in order to increase its surface acidity. Heat treatment of the oxidized sample progressively decreased the surface acidity, mainly through the removal of carboxyl and phenolic groups [19]. A sample heat-treated at 950°C had no acidity, and its surface area was lower than that of an as-received sample. Phenol adsorption isotherms on these carbons are shown in Fig. 25.3. There was a large decrease in phenol uptake after oxidation. This phenol uptake progressively increased as the surface acidity decreased, and the oxidized sample heat-treated at 950°C had the same adsorption capacity as the as-received one, despite the lower surface area of the former sample compared with the latter.

Table

25.2 Surface area and surface acidity of activated carbons with different degrees of oxidation

As received As received oxidized Oxidized and heat-treated at (0 C)

975

503

0.12 5.93

300 400 500

603 606

4.79 2.74

681

1.60

700

640

900

675

0.34 Nil

Adapted from Ref [19].

661

25.4 Adsorption of Electrolytes

1.5 C> ......... "'6 E

.6 1.0 Q)

.:::£

ctS

Q. :::J

"'6 0.5 c Q)

.c.

a..

0.0

o

100

200

300

400

500

Equilibrium concentration (ppm)

Figure 25.3 Adsorption isotherms of phenol on activated carbons with different degrees of oxidation. (Adapted from Re£ [19].)

Three main mechanisms have been proposed to explain this behavior: the 1T-1T dispersion interaction mechanism, the H-bonding formation mechanism, and the electron donor-acceptor complex mechanism. The first two mechanisms were proposed by Coughlin and Ezra [16] in 1968, and the third mechanism was proposed by Mattson and coworkers [20] in 1969. At that time, phenol was known to be adsorbed in a flat position on the graphene layers, and in this situation the adsorption driving forces would be due to 1T-1T dispersion interactions between the aromatic ring of phenol and the aromatic structure of the graphene layers. Thus, Coughlin and Ezra proposed that acidic surface oxygen groups, which are located at the edges of the basal planes, remove electrons from the 1T-electron system, creating positive holes in the conducting 'IT-band of the graphitic planes. This would lead to weaker interactions between the 1T-electrons of the phenol aromatic ring and the 1T-electrons of the basal planes, thereby reducing the phenol uptake. Coughlin also proposed that the H-bonding of water molecules to the oxide functional groups can play an important role in the uptake of phenolic compounds. In this case, Coughlin adopted Dubinin's proposal that water molecules adsorbed to oxygen groups become secondary adsorption centers, which retain other water molecules by means of H-bonds. As a result, complexes of associated water form within the pores of a carbon adsorbent. These complexes could prevent the migration of organic molecules to a large portion of the active surface area. This mechanism was ruled out by Coughlin, whose results indicated that surface oxygen complexes had no influence on phenol uptake from concentrated solutions (in the second plateau of the isotherms). Mattson and coworkers suggested that aromatic compounds adsorb on carbons by a donor-acceptor complex mechanism, with the carbonyl oxygen of the carbon surface acting as the electron donor and the aromatic ring of the adsorbate acting as the acceptor. Once the carbonyl groups are exhausted, the

662

Chapter 25 Adsorption of Organic Solutes from Dilute Aqueous Solutions

aromatic compounds form donor-acceptor complexes with the rings of the basal plane. Thus, Mattson and coworkers explained that the decrease in phenol uptake after carbon oxidation was due to the oxidation of carbonyl groups to carboxyl groups. As a result, the electron donor-acceptor complexes cannot be formed. One of the weak points of the Mattson mechanism is that there is much experimental evidence that although oxidation of carbons increases their concentration of CO 2 -evolving groups, the CO-evolving groups also increase or remain essentially unchanged [19]. A quote from the conclusions of the key paper published by Coughlin and Ezra [16] is apposite at this point: "evidence for any single explanation [of the decrease of phenol uptake with increase in surface acidity] is not overwhelming ... it is hoped that continuing research will shed more light on this question." Unfortunately, however, this was not often the case, as can be seen in the recent review published by Radovic and coworkers [1]. Since the initial proposals by Coughlin and Mattson, many published papers have attempted to elucidate the most appropriate mechanism to explain the adsorption of phenolic compounds and of aromatic compounds in general on carbon materials. Perhaps the first experimental evidence of the 1T-1T dispersion interaction mechanism was provided by Mahajan and coworkers [19] in their study ofphenol adsorption on graphite and boron-doped graphite samples. They reported that the presence of substitutional boron in the lattice of polycrystalline graphite, which removes 1T-electrons from the solid, results in a lowering of the phenol uptake from water. These authors also indicated that both phenol and water can compete to form H-bonds with surface oxygen groups, such as carboxyl groups. In this competition, water molecules are preferentially bound by H-bonds [19]. This idea of competition between phenol and water molecules for H-bonding to surface oxygen groups suggested that phenol uptake from its cyclohexane solution would be favored by the surface oxygen complexes. Thus, when phenol adsorption per unit cyclohexane area was plotted for two heat-treated carbons, the carbon with higher surface acidity exhibited a greater phenol uptake. More recently, Franz and coworkers [21] revisited this issue by studying the adsorption of phenol aniline, nitrobenzene, and benzoic acid from both aqueous and cyclohexane solution. Their experimental results seem to indicate that the adsorption mechanism is both by water H-bonding with carboxyl groups and by 1T-1T dispersion interactions between the aromatic ring of the adsorptive and the graphene layers. These authors also concluded that Mattson's mechanism is not the driving force for the adsorption of aromatics on activated carbons. Nevskaia and coworkers [22] also concluded, in a kinetics study of phenol adsorption on oxidized and nonoxidized activated carbons, that the specific competition of water molecules with surface oxygen groups inhibits phenol adsorption from dilute solutions. Additional experimental evidence of the influence of water adsorption comes from the enthalpy of immersion into water of activated carbons, which reflects the specific and nonspecific interactions between the liquid and the solid [23], as

25.4 Adsorption of Electrolytes

110

. ..

90 0> ........ J ........

0

~

•

70

C\l

~

J:

•

•

•

50

if

.~

30 10 10

30

50

70

90

110

12.1 [0] + 10.3[meq HCI] + + 0.8(Nam - 2.0[0] - 1.0[meq HCI]) + Sa X 0.031

Figure 25.4 Correlation between the enthalpy of immersion into water, the total surface oxygen, the basic groups titrated with HCI, the micropore filling, and the wetting of the nonporous surface area. (Adapted from Re£ [23].)

shown in Fig. 25.4. The study of a large number of carbons oxidized to different degrees revealed a simple correlation between the enthalpy of immersion, the oxygen content of the surface, the basic groups titrated by HCI, the micropore filling, and the wetting of the external surface. Thus, the specific interaction between the surface oxygen and water is 12.1 kJ/mol oxygen, involving an average of two water molecules per oxygen. More experimental evidence comes from the work of MacDonald and Evans [24]. These authors measured the enthalpy of exchange of phenol-water from diluted aqueous solutions on BPL carbons with different oxygen contents and found that phenol exchange enthalpy is inversely proportional to the net molar enthalpy of immersion in water. This indicates that the strong preference of water to H-bond to surface oxygen complexes lowers the phenol exchange enthalpy in aqueous solution. Fernandez and coworkers [25] recently showed, by adsorption from solution and immersion calorimetry, that water is preferentially adsorbed on oxygencontaining surface complexes with an energy of -10 kJ/mol[O]. In the case of dilute solutions, phenol is adsorbed on the remaining surface, with a specific enthalpy of -0.105 ± 0.004]lm2 • These authors conclude that the preferential blocking of the surface oxygen complexes by water explains the reduction of phenol uptake with increasing surface oxidation. In the case of concentrated solutions, water was still preferentially adsorbed by the surface oxygen complexes, and phenol filled the fraction of micropore volume not occupied by water. The two mechanisms proposed by Coughlin can better explain many of the experimental results obtained to date. However, an electron donor-acceptor mechanism cannot be completely ruled out because it could explain the irreversible or chemical adsorption of phenolic compounds. Thus, it is well known that the adsorption ofphenolic compounds is partly physical and partly chemical.

664

Chapter 25 Adsorption of Organic Solutes from Dilute Aqueous Solutions

The reversibility of phenol adsorption was first discussed in detail by Magne and Walker [26], who reported that the physisorbed phenol can become chemisorbed in the course of time or by increasing the temperature. These authors also conclude that the sites responsible for phenol chemisorption are carbon sites of the active surface area, i.e., oxygen-free sites located primarily at the edges of the graphene layers, whereas physisorption takes place on the entire surface. Physisorbed phenol can be desorbed by treating with different solvents or by heat treatments in inert atmosphere. However, the chemisorbed part cannot be desorbed, even at high temperatures, and is converted to light gases and heavy products that evolve from the surface of the carbon, and also to a polymeric carbon residue that remains on the surface [27]. This residue can be related to the condensation of large aromatic radicals into an extended Sp2 structure, and to the H 2 evolution. Furthermore, this residue reduces the adsorption capacity of thermally regenerated activated carbons. These authors [27, 28] have also pointed out that the surface oxygen complexes play an important role in the production of light gases because they act as cracking centers for the phenolic compound molecules. The irreversibility of phenol adsorption was also studied by Grant and King [29], who proposed that irreversible adsorption was caused by oxidative coupling reactions of phenol on the carbon surface in the presence of dissolved molecular oxygen. These reactions, which were slow compared with physisorption at 25°C, produced polymeric compounds. Vidic and coworkers [30] demonstrated that the presence of dissolved oxygen in the adsorptive solution increased the adsorption of phenolic compounds on activated carbons. This adsorption enhancement was due to the abovementioned polymerization reactions, which were accompanied by a significant oxygen consumption and by a reduction in the recovery of the adsorbents by solvent extraction. The polymerization reaction seems to be catalyzed by basic carbon surfaces and suppressed by increasing surface acidity [30, 31]. It has also been reported [30] that these basic groups were pyrone-type and not those associated with electron-rich regions within the graphene layers of the adsorbent. In addition, the ash and metal content of the carbon did not significantly affect the above reaction [30], although some metals are suspected [31] of acting as promoters without being considered essential for polymerization. More recently, Terzyk [32] also suggested that the irreversibility of phenol adsorption is due to the creation of strong complexes between phenol and surface carbonyl and lactone groups and to phenol polymerization. Salame and Bandosz [33] studied phenol adsorption at 30 and 60°C on oxidized and nonoxidized activated carbons. They concluded, from analyses of the isotherms by the Freundlich equation and the surface acidity of the carbons, that phenol was physisorbed by 1T-1T dispersion interactions, whereas it was chemisorbed via ester formation between the OH group of phenol and surface carboxyl groups. All these data indicate that chemisorbed phenolic compounds are strongly bound by other forces than those of dispersion. These could likely involve

665

25.4 Adsorption of Electrolytes

charge-transfer complexes in which the direction of the electron transfer could be either similar or opposite to that proposed by Mattson and could involve polymerization under certain circumstances. However, other kind of bonds cannot be ruled out. Therefore, further research on the irreversible character of phenolic compound adsorption is required to clarify its mechanism. On the other hand, the solution pH is one of the key factors that control the adsorption process of weak organic electrolytes and polyelectrolytes on carbon materials, because it controls the electrostatic interactions between the adsorbent and the adsorbate. Thus, the solution pH determines the carbon surface charge and the dissociation or protonation of the electrolyte. At a solution pH lower than the pH pzc or the pH IEP ' the total or external surface charge, respectively, will be on average positive, whereas at a higher solution pH they will be negative. In addition, the solution pH also controls the dissociation or ionization of the electrolyte through its pKa • Thus, acidic electrolytes are dissociated at pH > pKa • Therefore, the solution pH controls the adsorptive-adsorbent and adsorptiveadsorptive electrostatic interactions, which can have a profound effect on the adsorption process [34, 35]. Thus, the adsorption of substituted phenols on activated carbon depends on the solution pH [36,37]. Results found [37] (Table 25.3) showed the uptake to be maximal at acidic pH because the phenols are undissociated and the dispersion interactions predominate. At basic pH, however, the uptake is lower because of electrostatic repulsions between the negative surface charge and the phenolate anions and between phenolate-phenolate anions in the solution. The pH at which the uptake decreases depends on the adsorptive pKa and the difference between the pHpzc and the pH IEP . Radovic and coworkers [38] recently investigated the effects on the adsorption process of the pH and the nature of the functional groups on the aromatic adsorptive and the adsorbent. For this purpose, they used an as-received activated carbon oxidized with nitric acid and nitrided with ammonia to study the adsorption of aniline and nitrobenzene, which are, respectively, electron-donating and electron-withdrawing groups. Results found by these authors, together with Table 25.3 Amount of phenolic compounds adsorbed (mg/g) on carbon CP-10 (pH 1EP = 5.0 and pH pze = 10.4) at different solution pH

Phenol m-CWorophenol p- Nitrophenol p-Cresol m-Aminophenol

9.96 10.17 8.80 8.16 7.13

123 148 155 143 123

136 150 154 145 125

120 100 130 103 91

Initial concentration 150 mg/l, adsorption temperature 25°C. Adapted from Ref [37].

86 60 58 80

666

Chapter 25 Adsorption of Organic Solutes from Dilute Aqueous Solutions

others found in the literature, indicate that the functionalization of either the adsorptive or the adsorbent, which increases the 11'-electron density, leads to enhanced or stronger adsorption when the adsorption process is governed by dispersion forces. The converse is also true. When the adsorption of aromatic weak electrolytes is governed by nonelectrostatic interactions, such as 11'-11' dispersion or hydrophobic interactions, the area of the adsorbent occupied by the adsorbate depends on the porosity of the former and the molecular size of the latter. Thus, adsorption from diluted aqueous solution and immersion calorimetry measurements [39] showed that phenol and m-chlorophenol are adsorbed as monolayers by both porous and nonporous carbons with basic surface properties, provided that the adsorptive is undissociated at the solution pH. This did not apply where molecular sieve effects reduced the accessibility of the micropore system. Other important organic electrolytes are the dye molecules. The adsorption of dyes is of interest largely because they are pollutants frequently found in textile wastewaters and because some of them were proposed as molecular probes to characterize the pore texture of carbon adsorbents. However, this last application should be viewed with caution [1] because dye adsorption is profoundly affected by the carbon surface chemistry and solution pH. Thus, Graham [40] found a good linear relationship between a decreased uptake of the anionic metanil yellow and an increased carbon surface acidity. This author concluded that acidic groups on the carbon surface tend to reduce the capacity for anionic adsorbates in general. The adsorption of dyes was subsequently investigated by other authors [1]. For instance, Nandi and Walker [41] studied the adsorption of acid and basic dyes on different carbon materials and found that the area covered by a dye molecule depended on the nature of the solid surface. The studies published by Dai [42, 43] made an important contribution to the dye adsorption issue. He used two cationic dyes (methyl green and methyl violet) and three anionic dyes (phenol red, carmine, and titan yellow). According to this author, the solution pH affects the adsorption because it affects the zeta potential of the carbon surface, and he distinguished three states. When the zeta potential is zero, the electrostatic interactions between the carbon surface and dyes are negligible, and the adsorption forces are mainly dispersion forces. In the positive or negative zeta potential states, there is an electrostatic attraction or repulsion between the carbon surface and the ionic dyes. For instance, at a solution pH higher than the pHpzc , when the zeta potential is negative, the carbon surface is suitable for the adsorption of cationic dyes. Dai concluded that adsorption forces were either the sum of or difference between dispersion and electrostatic forces. This is in broad agreement with previous findings for phenol and substituted phenols. More recently, Pereira and coworkers [44] found a close relationship between anionic dye adsorption and carbon surface basicity due to oxygen-free Lewis sites. Surface oxygen complexes of acid character inhibited anionic dye adsorption. However, the latter complexes had a positive effect on cationic dye adsorption. The removal of these groups by heat treatment in H 2 at high temperature

667

25.4 Adsorption of Electrolytes

also yielded a good performance for cationic dye adsorption, leading the authors to suggest the existence of two parallel adsorption mechanisms involving electrostatic and dispersion interactions. Surfactants will be the last type of organic electrolyte to be studied in this section. These molecules are amphiphilic, due to their dual hydrophobic/hydrophilic character. This produces their accumulation at solid-water interfaces, where both the hydrophobic and the hydrophilic parts participate in favorable intermolecular interactions. Surfactants are widely used in many industrial and commercial products and processes and have an environmental impact on wastewaters. In recent years, several studies have been published on the adsorption of surfactants on carbon materials [11, 45-48], and the main results obtained in these works are presented below. Pendleton and coworkers [46] showed (Fig. 25.5) that the adsorption of dodecanoic acid on different activated carbons linearly decreased when the oxygen content of the carbonaceous adsorbent increased and that the adsorption was not related to the micropore volume of the adsorbent. They concluded that the surface chemistry more accurately predicted the adsorption of dodecanoic acid in aqueous phase compared with the surface area or micropore volume. In addition, carbon surface chemistry also had a significant influence on dodecanoic acid adsorption kinetics. Thus, the adsorption rate was reduced by the high surface oxygen content of the carbon adsorbent, whereas its pore volume made a smaller contribution [47]. In another recent study, Chen and coworkers [11] also investigated the effect of surface oxygen complexes, introduced by air and ozone treatments, on the adsorption of the commercial surfactants SDS, Darex II (anionics), and Tergitol (nonionic). Results revealed that the surfactant adsorption was strongly suppressed by surface oxidation. These authors proposed that surfactant adsorption primarily occurs on nonpolar carbon surface patches by hydrophobic interactions. Therefore, the oxidative suppression of surfactant adsorption was

Micropore volume (ml/g) 0.4 200

0.5

0.6

0.7

~------&...----......I---------I

"0 (J.)

-e

~C>

"0 ..........

co c>

.... E So

100

E


O+------.,...----~-----.--I

o

5

10

15

0/0 Oxygen content

Figure 25.5 Relationship between the maximum amount of dodecanoic acid adsorbed on carbons with different oxygen contents and micropore volumes. (Adapted from Re£ [46].)

668

Chapter 25 Adsorption of Organic Solutes from Dilute Aqueous Solutions

due to the destruction of the nonpolar carbon surface area, with contributions from micropore blockage and an increased negative charge in some systems. The effect of the solution pH on octanoic and dodecanoic acid adsorption has also been studied [48]. A larger surfactant uptake was observed from aqueous solutions than from strong caustic solutions. The authors attributed this finding to oxidation of the carbon surface, promoted by the high solution pH, and to anionic surfactant dissociation, which brings about electrostatic repulsions between the carbon surface and the adsorbate, leading to a decreased uptake of surfactants under these conditions.

25.5

ADSORPTION OF NATURAL ORGANIC MATTER

Dissolved NOM is mainly formed by the decay of vegetation and animal residues in the environment. It is, therefore, present in most surface waters used for drinking. The composition of this mixture is complex and depends on the environmental source. NOM composition ranges from small hydrophilic acids, proteins, and amino acids to larger molecular weight compounds. The latter compounds predominate in the mixture and are mainly fulvic, tannic, and humic acids that derive from the polymerization of gallic acid (3,4,5-trihydroxybenzoic acid) with different sugars. Hence, most of the compounds present in NOM can carry a negative charge attributed to the dissociation of carboxyl and phenolic groups. This causes them to behave as polyelectrolytes in aqueous phase, and therefore, the degree of dissociation of their functional groups depends on the solution pH. Study of the factors that control NOM adsorption from aqueous phase on activated carbons is of great importance for two reasons. First, NOM adsorption can, under certain circumstances, be the primary objective in some water treatment plants to avoid the formation of halogenated compounds during water chlorination. Second, NOM is usually present at concentrations that are three to six or more orders of magnitude higher than those of the micropollutants of interest, such as pesticides, surfactants, polycyclic aromatic compounds, phenolic compounds, and halocompounds. These are designated synthetic organic compounds (SOCs). In this case, the NOM competes directly with the SOC for adsorption sites on activated carbons or can block their porosity. This brings about a significant reduction in the adsorption capacity for micropollutants. Considerable research has been carried out to identify both the factors that control NOM adsorption and the mechanisms of competitive adsorption between NOM and SOC. Some of these studies are cited here [1, 49-52]. However, in this brief chapter, I only address NOM adsorption on activated carbons. Adsorption of a complex mixture such as NOM, in which polyelectrolytes predominate, involves both electrostatic and nonelectrostatic interactions as well as molecular sieving effects. Several researchers [53-55] reported that the adsorption of humic substances altered the surface properties of carbons because their

25.5 Adsorption of Natural Organic Matter

surface charge properties are largely determined by the adsorbed material rather than by the carbon surface itself In addition, the solution pH has a major effect on NOM adsorption [55-62], as could be expected because it determines the charge on both the NOM and the carbon surface. Thus, it was found [61] that a rise in the pH from 3 to 9 decreased the adsorption of NOM (with size range from 500 to 3000 Da) due to increased electrostatic repulsions. Maximal NOM adsorption was reached at pH 3, when the charge of the NOM was very low or zero. The negative charge of the NOM increased with a rise in the solution pH [61], and although the carbon surface charge was positive at certain pHs (below the pHpzc ), when electrostatic attractions would appear, the adsorption capacity was decreased. This is because the charge of the whole carbon-NOMadsorbed would be negative when polyions are adsorbed on the carbon surface, as commented above. The influence ofthe pore size distribution ofcarbon on NOM uptake has been recognized by several researchers [57,63]. Likewise, Karanfil and coworkers [64] and Kilduffand coworkers [65] concluded that the adsorption ofhumic substances was largely governed by molecular size distribution in relation to pore size. Moreover, a good linear relationship (Fig. 25.6) was found between the amount adsorbed by different carbons and their pore volume between 0.8 and 50 nm [61, 66] when the adsorption was carried out at pH 3. This is because electrostatic effects are minimized under these experimental conditions and nonelectrostatic interactions predominate. The adsorption mechanism would be due to hydrophobic and/or 1T-1T-electron interactions, and in this case as with other electrolytes (see above),

400

• C> ........ 0>

S U

Q)

.0

0en

200

u

co 'E

::J

0

E

<

O-t-----r----~---__.,..-----I

o

0.2

0.4

0.6

0.8

Pore volume (em 3/g) between 0.8-50 nm

Figure 25.6 Relationship between natural organic matter (NOM) adsorption capacity and available adsorption volume for different activated carbons at solution pH = 3. (Adapted from Ref. [61].)

Chapter 25 Adsorption of Organic Solutes from Dilute Aqueous Solutions

the adsorption would be affected by a pore volume of appropriate size range. In other carbon-NOM systems, however, the same authors [62] found that the results could not be explained by the available pore volume and surface charge alone. The authors very ambiguously pointed out that this was due to the complexity of this adsorption process and the importance of the carbon surface chemistry. The effect of the solution ionic strength on NOM adsorption has also been studied [58-62]. This parameter plays an important role in the adsorption ofelectrolytes because it controls the electrostatic interactions between the adsorbent and the adsorptive by means of a screening effect [3, 15]. This screening effect reduces the electrostatic interactions, whether attractive or repulsive. Therefore, when the electrostatic interaction between the surface and the adsorptive is repulsive or the surface concentration is sufficiently high, an increase in ionic strength will increase the adsorption. Conversely, when the electrostatic interactions are attractive, or the surface concentration is sufficiently low, an increase in the ionic strength will diminish the adsorption. To illustrate the effects of the ionic strength, Fig. 25.7 depicts the results [61] of NOM adsorption on an activated carbon C (pHpzc 7.5) at a solution pH of 4. Under these conditions, the carbon surface will be positively charged, whereas the NOM will be negatively charged. The adsorption isotherms show an intersection point indicating a transition from a screening-reduced to a screening-enhanced regime. At low surface concentrations below the intersection point of the isotherms, attractive interactions between the adsorbent and the adsorbate are screened by an increase in the salt concentration, decreasing the adsorption. Above the intersection point, when the surface concentration is higher, salt screens the repulsion between

80

0.30 M NaCI 0)

.........

60

C)

S "0 Q)

.c

0 en

40

"0

ca C ~

0

E

«

20

O-l------r-------r-------,------f

o

4

8

12

16

Solution concentration (mg/I)

Figure 25.7 Adsorption of natural organic matter (NOM) on carbon C (pHpzc = 7.5) at two ionic strengths and at solution pH = 4. (Adapted from Re£ [61].)

25.6 Adsorption of Bacteria

671

charged segments of the polyelectrolyte and between the adsorbed NOM and the NOM in solution, increasing the adsorption.

25.6

ADSORPTION OF BACTERIA

In many liquid-phase applications, the bacterial colonization of activated carbons can occur quite readily [67]. This colonization [68] is considered to result from (i) the adsorptive properties of carbon, which produce an increase in the concentration of nutrients and oxygen as well as the removal of disinfectant compounds; (ii) the pore texture of the carbon particles, which provides the bacteria with a protective environment; (iii) the presence of a large variety of functional groups on the carbon surface, which enhances the adhesion of microorganisms; and (iv) the nature of the mineral matter content of the carbon, which can favor bacteria adhesion. In general, bacteria attached to carbon particles are very resistant to disinfectants. The establishment of these microorganisms in biologically activated carbon (BAC) beds during water treatment can have some beneficial effects. The life of the carbon beds is prolonged because the microorganisms can convert biodegradable organic matter into biomass, carbon dioxide, and residual products, thus preventing saturation of the carbon. However, there are also drawbacks to carbon colonization. Thus, excessive bacterial growth can raise the pressure drop through fixed beds, or microorganisms can enter into the effiuent stream. In addition, pathogens can grow on the carbon bed and the presence of microorganisms can inhibit the adsorption of other molecules. The biofilm that forms on the carbon when the microorganisms are adsorbed produces changes in the porous texture of the carbon and in its surface charge, which in some cases can affect the adsorption of different contaminants on the carbon bed. Since the average dimensions of individual bacterial microorganisms generally fall within the range of "'-'0.3-30 f.,Lm, their adsorption on carbons only produces direct changes on the largest macropores and brings about indirect changes by blocking the entrances to smaller pores. Microbial colonization of a solid-liquid interface may occur in the following sequence [69]. First, there is the transport to the cell surface. The next step is the initial adhesion, which is mainly a physicochemical process. Adhesion can be reversible or irreversible. Irreversibly adhering bacteria exhibit no Brownian motion and cannot be removed unless by a strong shear force. Adhesion is followed by firm attachment, which is reached by forming strong links between the cells and the solid surface. The final sequence is the surface colonization. A bacterial suspension can be interpreted as a living colloidal system, and the initial step of adhesion involves, at a first approximation, an adsorption phenomenon that takes place between the organic macromolecules that constitute the bacteria outer shell and the carbon surface. Hence, bacteria adsorption can be explained by colloid and surface chemistry theories, which is why this section

672

Chapter 25 Adsorption of Organic Solutes from Dilute Aqueous Solutions

has been included in the present chapter. Bacteria adsorption on solid surfaces has been understood in terms of hydrophobic and electrostatic interactions [6973]. The term hydrophobicity is often used in the interpretation of bacteria adsorption on surfaces [70]. Hydrophobicity and van der Waals interactions are related through the Hamaker constant of the system. This constant is a material property that expresses the interaction energy between two bodies. Thus, the van der Waals interaction depends linearly on the Hamaker constant of the system. When the hydrophobicity of a bacterial or carbon surfaces increases, the difference between their Hamaker constants and the Hamaker constant of water becomes larger. As a consequence, the van der Waals attraction will be stronger [70, 71]. The influence of the surface characteristics of activated carbons and of the pH and ionic strength of the solution on the adsorption of Escherichia coli (E. colt) was recently studied [74, 75]. The main results obtained are summarized in Table 25.4 and show that the adsorption capacity of carbon S was much higher than that of carbon M. This result was due to the lower oxygen content or higher surface hydrophobicity of carbon S compared with carbon M. In addition, from an electrostatic point of view, E. coli would be negatively charged at the solution pH of lOused in these adsorption experiments, because the pHpzc is 3, and carbon S (pH pzc 12.1) would be positively charged, whereas carbon M (pHpzc 7.5) would be negatively charged. Thus, attractive interactions would predominate between bacteria and carbon S, whereas repulsive interactions would predominate in the case of carbon M. Therefore, both hydrophobic and electrostatic interactions would be more favored in the former carbon than in the latter. At a solution pH of 10, the bacteria adsorption on carbon S-HCl was negligible. However, when the solution pH was 4.5, the bacteria adsorption was very similar in both Sand S-HCl samples. These results demonstrate the importance of the electrostatic interaction between bacteria and carbon surfaces. The mean size of E. coli is around 3 x 103 nm, so that pores larger than this size would be accessible to bacteria. Thus, the greater the macropore volume of an activated carbon, the greater is its capacity to adsorb E. coli. This further explains the higher adsorption capacity of sample S compared with sample M.

Table 25.4 Surface characteristics of activated carbons and adsorption of Escherichia coli from a solution containing 5.0 x 107 CFU/cm 3 at solution pH 10 and at 25°C

S M S-HCl

1182 1089 1237

0.481 0.259 0.448

9.8 16.5 16.0

aValue in parentheses is at solution pH 4.5. Adapted from Ref [74].

6.1 1.7 4.7

12.1 7.5 8.7

8.6 6.6

100 20 5 (90)a

673

25.7 Conclusions

Table 25.5 Adsorption of Escherichia coli from a solution containing 1.0 x 107 CFU/cm 3 at solution pH 10 and at 25°C in the presence of Fe(lll) and Ca(ll) added as chlorides (2.5 x 10- 3 M)

FeCl3 CaCl2 None

1.5 7.5

X X

10- 2 10- 3

88 55 8

Adapted from Ref [74].

The above considerations indicate that E. coli adsorption would be enhanced in carbons with low oxygen content to increase their hydrophobicity, with an appropriate pHpzc to increase electrostatic attractions and a large macropore volume. With regard to the ash content, it was detected that some metallic oxides present in the mineral matter of carbon S were good adsorbents for bacteria adsorption, enhancing the total uptake of bacteria. On the other hand, an important feature of bacteria adsorption on activated carbons was that the pH pzc of the overall activated carbon-bacteria complex decreased due to the lower pHpzc of the bacteria (Table 25.4). This would influence the interaction between the activated carbon-bacteria complex and other electrolytic solutes. In addition, bacteria adsorption reduced the porosity of the carbons. When adsorption of E. coli on sample S-HCI was carried out in the presence of different electrolytes, the adsorption capacity markedly increased (Table 25.5). These data can be explained by the DLVO colloid chemical theory [71, 72], which takes into consideration the screening of the surface charge by the electrolyte. In this case, the solution pH was around 10 and the surface charge of both carbon and bacteria would be negative, which would prevent adsorption. In the presence of electrolytes, the repulsive electrostatic interactions would be reduced due to a screening effect favoring bacterial adsorption. More bacteria were adsorbed in the presence of FeCl3 than with CaC12 because of the greater ionic strength of the former.

25.7

CONCLUSIONS

This chapter shows that a unified explanation can be given of the adsorption from dilute aqueous solutions of different organic solutes, from nonelectrolytes to electrolytes, polyelectrolytes, and bacteria. Thus, the adsorption process is a complex interplay between electrostatic and nonelectrostatic interactions. Electrostatic interactions depend on the solution pH and ionic strength. The former controls the charge on the carbon surface and on the adsorptive

Chapter 25 Adsorption of Organic Solutes from Dilute Aqueous Solutions

674

molecule, and the second screens the electrostatic interactions, either attractive or repulsive. The electrostatic interactions mainly appear with electrolytes, polyelectrolytes, and bacteria when they are ionized under the experimental conditions used. N onelectrostatic interactions are mainly due to dispersion and hydrophobic interactions. The surface chemistry of carbons has a great influence on both electrostatic and nonelectrostatic interactions and can be considered of major importance in the adsorption mechanism of all organic solutes from dilute aqueous solutions. The surface chemistry of carbons largely depends on their heteroatom content, especially their surface oxygen content. These determine the charge of the surface, its hydrophobicity, and the electronic density of the graphene layers. A negative surface charge is due to the dissociation of acidic groups, whereas a positive charge is more likely due to the existence of electron-rich regions within the graphene layers acting as Lewis basic centers, which accept protons from the aqueous solution. Both charges depend on the solution pH and influence electrostatic interactions. A high surface hydrophobicity (low surface oxygen content) increases the hydrophobic interaction with hydrophobic solutes, increasing the uptake and avoiding the preferential attachment of water molecules by H-bonds that reduces the adsorption capacity of the carbon surface. The electronic density of the graphene layers mainly influences the adsorption of aromatic solutes because it affects the 'IT-'lT dispersion interaction. Adsorption will take place into pores that are appropriate to the molecular size of the adsorptive when nonelectrostatic interactions are the driving forces that control the adsorption process. This condition can be attained by controlling the surface chemistry of the carbon and the pH and ionic strength of the solution. The irreversible adsorption of organic solutes, which is of great importance in the regeneration of the adsorbents, is due to stronger interactions than dispersion or hydrophobic interactions. In the case of aromatic compounds such as phenol, it could involve a charge-transfer mechanism between the carbon surface and the adsorbate and/or its polymerization under certain experimental conditions. Therefore, further research is warranted in this area.

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Chapter 25 Adsorption of Organic Solutes from Dilute Aqueous Solutions

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References

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42. Dai, M. (1994). The effect of zeta potential of activated carbon on the adsorption of dyes from aqueous solution. I. The adsorption of cationic dyes: methyl green and methyl violet. J. Colloid Interface Sci., 164, 223-8. 43. Dai, M. (1998). Mechanism of adsorption for dyes on activated carbon. J. Colloid Inteiface Sci., 198, 6-10. 44. Pereira, M.F.R., Soares, S.F., Orfao, JJ.M., et al. (2003). Adsorption of dyes on activated carbons: influence of surface chemical groups. Carbon, 41, 811-21. 45. Garcia-Delgado, R.A., Cotoruelo, L.M., and Rodriguez, J.J. (1992). Adsorption of anionic surfactant mixtures by polymeric resins. Sep. Sci. Technol., 27, 1065-76. 46. Pendleton, P., Wu, S.H., and Badalyan, A. (2002). Activated carbon oxygen content influence on water and surfactant adsorption. J. Colloid Interface Sci., 246, 235-40. 47. Pendleton, P. and Wu, S.H. (2003). Kinetics of dodecanoic acid adsorption from caustic solution by activated carbon. J. Colloid Inteiface Sci., 266, 245-50. 48. Wu, S.H. and Pendleton, P. (2001). Adsorption of anionic surfactant by activated carbon: effect of surface chemistry, ionic strength and hydrophobicity. J. Colloid Inteiface Sci., 243, 306-15. 49. Pelekani, C. and Snoeyink, V.L. (1999). Competitive adsorption in natural water: role of activated carbon pore size. Water Res., 33, 1209-19. 50. Li, Q., Snoeyink, V.L., Marinas, BJ., et al. (2003). Elucidating competitive adsorption mechanisms of atrazine and NOM using model compounds. Water Res., 37, 773-84. 51. Li, Q., Snoeyink, V.L., Marinas, BJ., et al. (2003). Pore blockage effect of NOM on atrazine adsorption kinetics of PAC: the roles of PAC pore size distribution and NOM molecular weight. Water Res., 37, 4863-72. 52. Matsui, Y., Fukuda, Y., and Inoue, T. (2003). Effect oforganic matter on powdered activated carbon adsorption of trace contaminants: characteristics and mechanism of competitive adsorption. Water Res., 37, 4413-24. 53. Morris, G. and Newcombe, G. (1993). Granular activated carbon: the variation of surface properties with the adsorption of humic substances. J. Colloid Inteiface Sci., 159, 413-20. 54. Newcombe G. (1994). Activated carbon and soluble humic substances: adsorption, desorption, and surface charge effects. J. Colloid Inteiface Sci., 164, 452-62. 55. La France, P. and Mazet, M. (1989). Adsorption ofhumic substances in the presence of sodium-salts. J. Am. Water Works Assoc., 81, 155-62. 56. McCreary, J.J. and Snoeyink, V.L. (1980). Characterization and activated carbon adsorption of several humic substances. Water Res., 14, 151-60. 57. Lee, M.C., Snoeyink, V.L., and Crittenden,J.C. (1981). Activated carbon adsorption of humic substances. J. Am. Water Works Assoc., 73, 440-6. 58. Randtke, S.J. andJepse, C.P. (1982). Effects of salts on activated carbon adsorption of fulvic acid. J. Am. Water Works Assoc., 74, 84-93. 59. Summers, R.S. and Roberts, P.V. (1988). Activated carbon adsorption of humic substances. I. Heterodisperse mixtures and desorption. J. Colloid Interface Sci., 122, 367-81. 60. Summers, R.S. and Roberts, P.V. (1988). Activated carbon adsorption of humic substances. II. Size exclusion and electrostatic interactions. J. Colloid Inteiface Sci., 122, 382-97. 61. Newcombe, G. and Drikas, M. (1997). Adsorption of NOM onto activated carbon: electrostatic and non-electrostatic effects. Carbon, 35, 1239-50.

Chapter 25 Adsorption of Organic Solutes from Dilute Aqueous Solutions

62. Bjelopavic, M., Newcombe, G., and Hayes, R. (1999). Adsorption of NOM onto activated carbon: effect of surface charge, ionic strength, and pore volume distribution. J. Colloid Interface Sci., 210, 271-80. 63. Ogino, K., Kaneko, Y., Minoura, et al. (1988). Removal of humic substance dissolved in water. J. Colloid Interface Sci., 121, 161-9. 64. Karanfil, T., Schlautman, M.A., Kilduff: J.E., et al. (1996). Adsorption of organic macromolecules by granular activated carbon. 1. Influence of molecular properties under anoxic solution conditions. Environ. Sci. Technol., 30, 2187-94. 65. Kilduff: J.E., Karanfil, T., and Weber, WJ., Jr (1996). Competitive interactions among components of humic acids in granular activated carbon adsorption systems: effects of solution chemistry. Environ. Sci. Technol., 30, 1344-51. 66. Newcombe, G., Drikas, M., and Hayes, R. (1997). Influence of characterized natural organic material on activated carbon adsorption: II. Effect on pore volume distribution and adsorption of 2-methylisoborneol. Water Res., 31, 1065-73. 67. Derbyshire, F., Jagtoyen, M., Andrews, R., et al. (2001). Carbon materials in environmental applications. In Chemistry and Physics of Carbon, Vol. 27 (L.R. Radovic, ed.). Marcel Dekker, pp. 1-66. 68. Camper, A.K., LeChevalier, M.W., Broadaway, S.C., et al. (1986). Bacteria associated with granular activated carbon particles in drinking water. Appl. Environ. Microbiol., 52, 434-8. 69. Van Loosdrecht, M.C.M., Lyklema, J., Norde, W., et al. (1990). Influence of interfaces on microbial activity. Microbiol. Rev., 54, 75-87. 70. Van Loosdrecht, M.C.M., Lyklema, J., Norde, W., et al. (1987). The role of bacterial cell wall hydrophobicity in adhesion. Appl. Environ. Microbiol., 53, 1893-7. 71. Van Loosdrecht, M.C.M., Norde, W., and Zehnder, AJ.B. (1990). Physical chemical description of bacterial adhesion. J. Biomater. Appl., 5, 91-106. 72. Van Loosdrecht, M.C.M., Norde, W., Lyklema, J., et al. (1990). Hydrophobic and electrostatic parameters in bacterial adhesion. Aquat. Sci., 52, 103-14. 73. Rijnaarts, H.H.M., Norde, W., Lyklema,J., et al. (1999). DLVO and steric contributions to bacterial deposition in media of different ionic strengths. Colloid Surf. B, 14, 179. 74. Rivera-Utrilla, J., Bautista-Toledo, I., Ferro-Garcia, M.A., et al. (2001). Activated carbon surface modifications by adsorption of bacteria and their effect on aqueous lead adsorption. J. Chern. Technol. Biotechnol., 76, 1209-15. 75. Moreno-Castilla, C., Bautista-Toledo, I., Ferro-Garcia, M.A., et al. (2003). Influence of support surface properties on activity of bacteria immobilised on activated carbons for water denitrification. Carbon, 41, 1743-9.

ADSORPTION FROM AQUEOUS SOLUTIONS: WATER PURIFICATION Gayle Newcombe Cooperative Research Centre for Water Quality and Treatment, Salisbury, South Australia, Australia

Contents 26.1 Introduction 26.2 Factors Influencing the Application of Activated Carbon in Drinking Water Treatment 26.3 Removal of Microcontaminants of Concern to the Drinking Water Industry 26.4 Removal of Natural Organic Material 26.5 Conclusions Acknowledgments References

679 681 689 702 703 704 704

26.1 INTRODUCTION The use ofcarbon in drinking water treatment is thought to date back more than 4000 years, as there is archaeological and written evidence that filtration through charcoal was used to improve the taste of drinking water as far back as 2000 Be. In modern times, since the 1920s, activated carbon has been used in conjunction with conventional water treatment processes to improve the esthetic quality (taste, odor, color) and to reduce the probability of potentially toxic compounds reaching the consumer [1]. 26.1.1

Conventional Water Treatment Processes

Although many water authorities are now utilizing more advanced treatment processes to overcome the issue of contaminants in drinking water, still the Adsorption by Carbons ISBN: 978-0-08-044464-2

© 2008 Elsevier Ltd.

All rights reserved.

679

680

Chapter 26 Adsorption From Aqueous Solutions: Water Purification

most common treatment for drinking water is seen in the "typical" conventional drinking water treatment plant. Generally the processes used are: 1. Coagulation followed by flocculation with a metal-based coagulant such as aluminum sulphate or ferric chloride. This process removes most particulate materials and some dissolved organic compounds. 2. Sedimentation or flotation. In this step the coagulated material is either allowed to settle to the bottom of the sedimentation tanks, or floated to the top using dissolved air, and skimmed from the surface. 3. Filtration through filters consisting of sand, anthracite, or a combination of media. 4. Disinfection using chlorine, chloramine, ozone, or UV to deactivate pathogenic organisms. 26.1.2

Adsorption Processes

In addition to the conventional processes described above, activated carbon is often used to address water quality issues. Activated carbon is generally utilized in drinking water treatment plants in two forms, powdered activated carbon (PAC) and granular activated carbon (GAC). 26.1.2.1

Powdered activated carbon

The aim of PAC addition is often the removal of unpleasant tastes and odors or, in some cases, toxins produced by blue-green algae (cyanobacteria). In Europe and the United States PAC is also used to help control high levels of pesticides or other man-made industrial micropollutants in the source water. Powdered activated carbon can be added before coagulation, during chemical addition, or during the settling stage, prior to sand filtration. It is removed from the water during the coagulation process, in the former cases, and through filtration, in the latter. As the name implies, PAC is in particulate form, with a particle size typically between 10 and 100 f-.Lm in diameter. It is usually dosed as slurry, mixed with water, and doses can range from 2 to over 200 mg of PAC per liter of water (mg/L). However, the high end of this range would not be commonly used over a prolonged period due to the cost and the difficulty of handling large volumes of fine black powder. One of the advantages of PAC is that it can be applied for short periods, when problems arise, then ceased when it is no longer required. With problems that may arise only periodically, for example algal metabolites, or accidental industrial chemical spills, this can be a great cost advantage. One of the major influences on the effectiveness of PAC is the contact time, i.e., the time the PAC is in suspension, allowing efficient bulk diffusion of the target compound to the particle surface. In a conventional water treatment plant, this will be dependent on the point of application, and the hydraulic flow. To increase the contact time, the PAC can be used in combination with membrane

26.2

Factors Influencing the Application of Activated Carbon in Drinking Water Treatment

681

filtration. In this process the carbon is added prior to a membrane, usually a micro- or ultrafiltration membrane (pore sizes in the ranges 0.1 to 10 and 0.001 to 0.1 f.Lm, respectively), to remove target contaminants. The membranes retain the PAC, the contact time of the PAC is therefore greater than the hydraulic retention time, and more ofthe adsorption capacity of the carbon can be utilized. Another process that can be used to maximize the use of the PAC capacity is the floc blanket reactor. In this process the water flows upward through a blanket of flocculated particles and organic material and, as with the PAC membrane process, the contact time of the PAC will be longer than the hydraulic residence time and the capacity of the adsorbent will be utilized to a greater extent.

26.1.2.2

Granular activated carbon

Granular activated carbon is used extensively in Europe and the United States for the removal of micropollutants such as pesticides, industrial chemicals, and tastes and odors. It is also sometimes used to remove natural organic material (NOM), such as humic and fulvic acids, which is present in all water bodies, and reacts with chlorine in the disinfection process to form potentially harmful disinfection by-products. The particle size is larger than that of PAC, usually between 0.4 and 2.5 mm. GAC is generally used as a final polishing step, after conventional treatment and before disinfection, and is often used in conjunction with ozone. When used in conjunction with ozone it is sometimes called BAC, or biological activated carbon; however, this is a misnomer as all GAC filters function as biological filters within a few weeks to months of commissioning. Granular activated carbon is also sometimes used as replacement for sand in conventional treatment filters as this is a low-cost alternative to retrofitting GAC filters in an existing plant, where space constraints may not allow additional filters to be built. The effectiveness of this method of application is determined by the flow of the water and depth of the filters, and sometimes the contact time with the activated carbon is too low to allow prolonged adsorption of problem compounds.

26.2 FACTORS INFLUENCING THE ApPLICATION OF ACTIVATED CARBON IN DRINKING WATER TREATMENT 26.2.1

Characteristics of the Adsorbent and Adsorbate

The significant differences between activated carbons are often forgotten by drinking water utilities interested in keeping costs to a minimum. There are hundreds of activated carbons currently in the market suitable for drinking water treatment, and they are far from equivalent in their ability to remove problem compounds.

682

Chapter 26 Adsorption From Aqueous Solutions: Water Purification

Some of the major factors influencing adsorption onto activated carbon during water purification are similar to those acting in other systems described previously in this book, namely: 1. Activated carbon surface structure (pore sizes and shapes) and surface chemistry 2. Adsorbate shape, size, charge, solubility, hydrophobicity, and aromaticity 3. Water quality, pH, and ionic strength. The net effect, the adsorption of target compounds, is obviously a complex interaction of all these factors. Primarily, as reported many times in the literature (e.g., [2, 3]), the highest energy pore for adsorption is one where the adsorbate has more than one contact point with the surface, i.e., a pore slightly larger than the adsorbing molecule. Therefore, the most favorable carbon for a particular target compound will have a large volume of pores in the size range slightly larger than the adsorbate. It is also understood that the chemistry of the activated carbon surface plays a role in adsorption [4, 5]. However, it is important to note at this stage that attempting to distinguish between the predominance of any of these factors in a particular system involving activated carbon is not a trivial exercise. For example, many studies have attempted to relate the adsorption of particular compounds to the surface chemistry of the activated carbon [6-8]. In most cases, the pore volume distributions are measured, and this is taken into account in the interpretation of the adsorption data, resulting in conclusions drawn regarding the effects of surface chemistry. These conclusions are all dependent on the accuracy of the pore volume measurements, and these can vary from laboratory to laboratory. This discrepancy is illustrated in Fig. 26.1 that shows the adsorption of an odor compound, 2 methyl isoborneol (MIB) onto a range of activated carbons plotted against the pore volume in a particular size range. Figure 26.1 (a) indicates that the adsorption is a function of pore volume below 1.0 nm. Figure 26 .1 (b) shows the same plot using pore size data obtained from a different laboratory. The data in this figure suggests that, for two of the activated carbons, factors other than pore size are influencing adsorption, and such behavior has been attributed by several authors to surface chemistry effects [7, 8]. In this case the discrepancy was due to the inaccurate pore distributions used in Fig. 26 .1 (b). Pore volume distributions are calculated from gas adsorption isotherms, most commonly nitrogen. Very low relative pressures are required to analyze pores in the range plotted in Fig. 26.1. If extremely low pressures are not realized, carbons with high volumes of larger pores may appear to also have high volume of primary micropores (pore size < 0.8 nm). Figure 26.2 shows the nitrogen adsorption isotherms of two activated carbons, one with high primary micropore volume (PAC A), and the other with a high secondary micropore (0.8 nm < w < 2.0 nm) and mesopore volume (2.0 nm < w < 50 nm) (PAC B). The inset shows the expansion of the isotherm at low relative pressures. Clearly if the pressures reached are not sufficiently low, pore volume calculations will result in erroneously high micropore values for carbon B. Such results illustrate the

26.2

683

Factors Influencing the Application of Activated Carbon in Drinking Water Treatment

3000

R=0.97, P<0.0005

2500

C)

•

E

...........

e>

S

•

2000

OJ

./

3000

. /

/

2500

/

,'(1

/

•

/

2000

/ / /

~

/

'0

1500

c:

,'.

1500

/ /

0

• /

a(;

/

1000

en

'0

«

1000

• •

500

0 0.00

/

(I

500 (I

0 0.05

0.10

0.0

0.15

0.1

0.2

0.3

0.4

0.5

0.6

Pore volume below 1.0 nm (cm 3/g)

Figure 26.1 Adsorption of MIB as a function of pore size for seven activated carbons.

200 150 100

800

50

700 O+---..----r-----.---r-----.-----,---.-~----,,.--..__......_____,

0.0000 0.0002 0.0004 0.0006 0.0008 0.0010 0.0012

600

-g

.c

500

(; en

'0 ctS

400

C\J

Z

/

300

/

1=

I

200 100

PAC A PACB

O-+----r--..,.----r----,-..,...----,--~....,_~-~___r__r_____r___._-..,.____r____,-__r____.______,

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Relative pressure

Figure 26.2 Nitrogen adsorption isotherms on two activated carbons. The insert illustrates the importance of reaching low relative pressures.

684

Chapter 26 Adsorption From Aqueous Solutions: Water Purification

importance of accurate pore distributions, and the difficulties confronted by the scientist wishing to interpret the effect of surface chemistry vs pore volume distribution. In fact this is the reason for the discrepancy shown in Fig. 26.1. In 2002 an international interlaboratory trial commenced, initially involving 19 laboratories, from 12 countries, routinely undertaking pore analysis of activated carbons. Samples of four carbons were sent, in duplicate, to all laboratories. Pore volume analyses were undertaken using nitrogen or argon adsorption and the results were analyzed using density functional theory [9], commonly used for analysis of gas adsorption data. The results are presented on the Carbon Round Robin Web site (http://www.waterquality.crc. org.au/carbon_rr/round_robin_index.htm) and clearly indicate that there is significant variability between laboratories in the measurement of pore volumes of activated carbons. These results also suggest that caution is required in the interpretation of solution adsorption studies in relation to pore size and surface chemistry effects. 26.2.2

Prediction of Adsorption Behavior

Two major considerations for the water supplier using activated carbon are:

1. What dose of PAC is necessary to reduce the target to the required level? and 2. For what length of time will a GAC filter function to the required level? 26.2.2.1

Powdered activated carbon

The cost-effective use of PAC depends on the application of the correct dose to reduce the target compound to an acceptable level. Computer modeling has helped water suppliers address this important issue. For adsorption to take place, several steps must occur. These are:

1. 2. 3. 4.

Bulk diffusion to the particle surface Diffusion through the boundary layer to the external carbon surface Diffusion through the pore structure to the most favorable adsorption site Adsorption.

These steps will be influenced by a range of factors. Step 1 is affected by molecular dimensions and shape. With sufficient mixing these effects will be minimized. Step 2 could also be affected by molecular dimensions and shape, although it is generally considered to be rapid under conditions of sufficient mixing. Step 3 is affected by pore structure, both external and internal, and molecular dimensions and shape, and step 4 is generally considered to be instantaneous. In practical situations in drinking water treatment, step 3 is most likely to be rate determining. For the adsorption of microcontaminants onto activated carbon this step is often modeled using the homogeneous surface diffusion model (HSDM). The HSDM has been successfully applied for the prediction of the kinetics of adsorption ofa range of compounds onto activated carbon [1, 10, 11]. For the HSDM, the activated carbon particles are considered to be spherical and

26.2

Factors Influencing the Application of Activated Carbon in Drinking Water Treatment

685

of homogeneous structure, and Fick's first law of diffusion is applied for the calculation ofthe adsorbent surface concentration as a function of the radial position within the particle. The change in bulk liquid-phase concentration with time is then calculated using a mathematical model appropriate for the configuration of the system, e.g., batch, plug flow, or completely stirred tank reactors [10]. A derivation of the model and description of its use can be found elsewhere [12]. Due to the effects of molecular size and shape and pore structure on the kinetics, the model cannot be used for general predictive purposes. In practice, in order to predict PAC adsorption, a series of experiments must first be carried out using the compound of interest, the activated carbon to be applied, and the water in which it is to be used. Equilibrium parameters, determined from the Freundlich adsorption isotherm equation, are used as input into a computerbased HSDM, which uses the method ofleast squares to minimize the difference between the experimental kinetic data points and the HSDM fit of the data [10]. When the best fit is achieved, the resultant kinetic parameters (liquid film mass transfer coefficient, kf , and the surface diffusion coefficient, D s) can then be used for the prediction of adsorption behavior under different conditions. When appropriate theoretical adsorption models are used for PAC dose prediction, cost-benefit analyses can be undertaken for the application of various carbons. Using predictive tools it is often found that a more expensive PAC (per ton) will provide better value over time. The combination of lower PAC dose, and smaller areas required for storage of bulk adsorbent, is very attractive to treatment by plant managers. For example, Table 26.1 shows the requirements for the removal of the odor compound MIB from reservoir water to an acceptable level under particular conditions of water quality and contact time for four PACs. As shown, the dose required for each carbon is different, reflecting the differing capacities for the compound. Due to the different raw materials and activation conditions of the carbons, the costs are also different. In the past, water authorities have often made the mistake of buying the cheapest activated carbon, in this case it would be PAC 4. As we can see from Table 26.1, due to the high dose required this carbon would not be the most cost effective, and would also pose the difficultly of storage and handling very large amounts of PAC. In contrast, one of the most expensive carbons, PAC A, could be used at a cost slightly lower than the cheaper carbon, with the advantage of much lower volumes of PAC required for prolonged dosing. The HSDM is now widely used for such analyses in the drinking water industry. Table 26.1 Activated carbon doses required to reduce the concentration of odour compound MIS to a level acceptable to consumers

PAC dose (mg/L)

16

31

26

38

PAC required for 10 days dosing (ton)

8.0

15.5

13.0

19.0

Cost for 10 days dosing (U5$)

19600

17300

29100

20000

686 26.2.2.2

Chapter 26 Adsorption From Aqueous Solutions: Water Purification

Granular activated carbon

Similar to PAC, the cost-effective application of GAC is dependent on the ability of the water supplier to estimate the "lifetime" of the filters, or the time over which the filters will reduce the target compound concentrations to the desired level. After this time, the GAC must either be replaced, or regenerated. The large mass of GAC used in water treatment plant filters results in high costs for regular replacement, and the latter process involves an energy intensive (and therefore expensive) reactivation process to volatilize adsorbed compounds. The ideal experimental design would reproduce the GAC filters on a smaller scale, where the target compound could be spiked into the filter, and data collected to determine the length of time the filters would function adequately. Unfortunately, this is a very time-consuming and expensive process, as GAC filters can run efficiently for months or years, depending on the criteria for determining the replacement, or regeneration of the carbon. As a result, a number of short-term tests have been designed with the aim of gathering the same information in a much shorter timescale. There is a range of predictive tools in use for the optimization of GAC [13]. Two of the most widely used are the short bed adsorber test (SBA), which has, a similar basis to the HSDM, requiring similar laboratory data input, and the rapid small-scale column test (RSSCT), which relies on the "scaling down" of the conditions in the full-scale plant to laboratory scale. Detailed information is available in the literature [1, 10, 13, 14], a short description is given below: Short bed adsorber test

This test has a similar basis to the PAC predictions described previously. In this case the kinetic parameters are determined using a small-scale GAC column, run over several hours. The equilibrium parameters are used in the HSDM to fit the experimental column data and the derived kinetic parameters are then applied to predict the adsorption in the column under different conditions of flow, initial concentration, etc. [10]. Rapid small-scale column test

These are designed on the theory of similitude, i.e., GAC filter conditions can be scaled down to laboratory columns and represent the adsorption behavior of the target compound, but over a reduced time frame [14]. The scaling factors, used to determine the operational parameters of the RSSCT, are derived from the mathematical models used to describe mass transfer in the full-scale filters. In this case the dispersed flow pore surface diffusion model (DFPSDM, described in detail in [15]) is used. The scaling factors are determined from dimensionless parameters in the model describing partition between solution and surface, surface diffusion, pore diffusion, film transfer, and axial dispersion of the target compound. These dimensionless parameters must remain constant in the scaling down of the full-scale to laboratory-size column. If the same parameters are applied to the smaller column, scaling factors between the operational parameters

26.2

Factors Influencing the Application of Activated Carbon in Drinking Water Treatment

687

in the full- and laboratory-scale can be found [16]. The scaling factors are then used to determine the appropriate particle size, hydraulic loading, and empty bed contact time (EBCT) of the small column. If the scaling parameters provide sufficient similitude, the breakthrough curve of the RSSCT should represent that shown by the full-scale filters [1]. Disadvantages of the laboratory-scale GAC predictive tools These tests cannot take into account several important factors, and are therefore not considered to be precise for the prediction of all GAC adsorption behavior. These issues include:

1. Ongoing "fouling" of the GAC surface with NOM. 2. The RSSCT relies on crushing the carbon to the calculated size range. If this is undertaken on carbon sampled from a filter that has been in use for several months (carbon preloaded with NOM), this process may open blocked pores and allow the target compound access to previously unavailable adsorption sites. 3. Most target compounds will only challenge GAC filters intermittently, not continuously as represented by these tests. 4. Biological activity can increase the lifetime of GAC filters. However, tools such as these can be used successfully to compare the performance of different activated carbons and to give an indication of the expected lifetime of the filters, and therefore provide a caution to water authorities when increased monitoring offilter eilluent water quality might be warranted. Another type of test, the mini-column test, was used successfully by Gillogly et al. [17] to simulate the removal of the musty odor compound MIB in a pilot-scale GAC filter over a period of several years. This simple test, described in more detail in a later section, cannot be used to predict the lifetime of a GAC filter, but it can indicate how well a filter would function at the time of sampling if challenged by an unexpected microcontaminant influx. Thus predictive tools such as SBA or RSSCT can be used in conjunction with a monitoring tool, such as the minicolumn test, to allow the confident use of GAC for the removal of problem compounds.

26.2.3 Biological Removal Microorganisms present in water rapidly colonize GAC filters within a short time after the filters are brought on line. The particles of GAC are particularly favorable to the adhesion of microorganisms. They have a rough surface, with cavities of the appropriate size to offer protection from the shear caused by normal water flow and the additional shear occurring during regular backwashing of the filters. Studies have shown that a surprising variety and abundance of microorganisms adhere to the GAC surface, taking advantage of the protection and constant nutrient source it provides [18]. Biological activity

688

Chapter 26 Adsorption From Aqueous Solutions: Water Purification

on a GAC filter can significantly enhance its effectiveness for removal of target contaminants if the compounds are readily assimilable, as the removal can be accomplished through dual mechanisms, physical and biological.

26.2.4 Natural Organic Material Natural organic material consists of a mixture of dissolved substances such as humic and fulvic acids, lignins, carbohydrates, proteins, and simple hydrophilic acids [19]. As it consists of such a complex mixture of compounds the chemical structure of NOM can never be fully characterized, although some typical features of NOM chemistry have been established. From a wide range of spectroscopic and elemental analyses it is known that humic acids contain aliphatic, aromatic, and oxygen-containing functional groups (predominantly carboxylic, hydroxyl, and methoxyl moieties), and to a lesser extent nitrogen and sulfur containing functional groups. Containing a large proportion of its oxygen in carboxyl groups, NOM also has a high negative charge at neutral pH [2022]. Although in the past NOM was considered to be very high in molecular weight, with modern techniques of molecular weight determination, it has been shown that most drinking water sources contain NOM in the range 300-4000 g/mol [23]. Chemical characteristics of NOM are influenced by the source material and the biogeochemical processes occurring within the various components of the environment [24]. Clearly such a complex mixture is impossible to fully characterize, and therefore the effect of NOM on activated carbon adsorption is difficult to fully define. While problem compounds in drinking water are typically found in concen-

trations of nanograms or micrograms per liter, NOM is virtually always three to six orders of magnitude higher in concentration, and always offers significant competition for adsorption sites. This usually substantially reduces the adsorption capacity for the target compound [25, 26]. An important issue in the understanding of the competitive effect is the determination of the composition and concentration of directly competing compounds. With a complex mixture such as NOM this is not a trivial exercise as the commonly utilized characterization techniques such as dissolved organic carbon (DOC) concentration and ultraviolet absorbance at 254 nm (UV254) are bulk parameters describing the total amount of carbon in NOM and the UV-absorbing species, respectively. These parameters give no information regarding the specific NOM components competing with a particular target contaminant, as this is likely to be only a small portion of the entire NOM "soup" [27]. Ideal adsorbed solution theory (lAST) was developed using thermodynamic considerations to describe multicomponent adsorption from solution onto activated carbon [28]. The model can be used to predict the adsorption of individual components in a mixture if the single solute isotherms are known [29]. Researchers have attempted to apply the model to describe the competition observed between NOM and microcontaminants [5]. This process is not always successful, mainly due to the fact that competing NOM may only be a small portion of the total. The measurable parameter used to apply the lAST

26.3 Removal of Microcontaminants of Concern to the Drinking Water Industry

to this system is the DOC concentration, which may not be representative of the actual concentration of competing compounds. The equivalent background compound (EBC) model can be used to obtain the concentration of competing compounds when the adsorption of the target compound is known in the presence and absence of the competing NOM [10, 27, 30]. The EBC is not considered to be the entire NOM present in natural waters, as only an unknown portion of the NOM will compete. The model uses lAST to obtain the EBC adsorption parameters (Freundlich K, lin, and initial EBC concentration) by the minimization of the error between the experimental adsorption isotherm in the presence of NOM and the adsorption isotherm obtained from the lAST model. The EBC isotherm determined through this procedure can then be used to predict the adsorption isotherms of the target compound in the same NOM solution at a range of initial concentrations. As well as this direct competitive effect, which occurs on both PAC and GAC, NOM is responsible for "fouling" of GAC [1, 31]. When activated carbon is used in this form it is continuously exposed to water containing NOM, whereas the target compounds are often only present for particular periods; e.g., water sources are more prone to taste and odor problems during the warmer months. During the fouling process the NOM adsorbs onto the carbon surface, a process called preadsorption, and occupies adsorption sites that are no longer available when the filter is challenged by the target compound. The NOM compounds can also block or restrict activated carbon pores, resulting in hindered diffusion through the pore structure [31]. In addition, when NOM adsorbs onto the activated carbon surface it significantly changes the surface properties, in particular the charge [7, 32].

26.3

REMOVAL OF MICROCONTAMINANTS OF CONCERN

TO THE DRINKING WATER INDUSTRY

One of the major uses of activated carbon is the removal of chemicals present in the environment due to human activity. These include pesticides, industrial chemicals and pharmaceuticals, and personal care products that can enter drinking water sources through indirect reuse of treated wastewater. The latter, as well as some pesticides, are of particular concern as many are known to act as endocrine disruptors. Another major use of activated carbon is the removal of tastes and odors as, although they are not of health concern, they are of concern to consumers, and will result in complaints to water authorities. A lesser, but very important, use of activated carbon is the removal of toxic metabolites of blue-green algae (cyanobacteria). These compounds can cause a range of illnesses including liver and nerve damage. Although they are not present in high concentrations in most waters, they are of considerable importance to the water industry for their potential adverse health effects.

Chapter 26 Adsorption From Aqueous Solutions: Water Purification

26.3.1 Pesticides This range of compounds consists of the many chemicals that are used to control pests worldwide. Target species include insect, animal, or plant species. Examples of the hundred or so pesticides that have been studied to determine their removal during drinking water treatment processes include s-triazines (atrazine, simazine, cyanazine, propazine), lindane, DDT, 2, 4-D, atachlor, metolachlor, asulam, hymexazol, methomyl, imidacloprid, carbaryl, linuron, thiobencarb, and diquat. Clearly there is a wide range of pesticide compounds and they are of significant concern to the water industry as they can cause a variety of health problems. A number of pesticides are known carcinogens, endocrine disruptors, or nerve toxins. As a result, many countries have strict regulations regarding their concentration in drinking water. The European Directive on drinking water quality defines pesticides as any organic chemicals used as insecticides, herbicides, fungicides, nematocides, acaricides, algicides, rodenticides, slimicides, and related products [33]. The maximum acceptable level of any individual pesticide is 0.1 f.,Lg/L with the total allowable up to 0.5 f.,Lg/L. Exceptions to this regulation are aldrin, dieldrin, heptachlor, and heptachlor epoxide; the maximum allowable concentration for each of these compounds is 0.03 f.,Lg/L. In contrast, the United States has nominated over 20 specific pesticides, and stipulates maximum contaminant levels for each, ranging from 0.2 to 700 f.,Lg/L. Atrazine has been one of the most commonly applied pesticides worldwide, although its use is now somewhat curtailed due to the problems it causes in drinking water. It is used to control weeds in crops such as corn, sorghum, and sugar cane, and has a high water solubility, which has resulted in its presence in many drinking water sources. It is moderately hydrophilic, and is known to be recalcitrant to degradation in the environment. It is also recalcitrant to oxidation, therefore activated carbon is considered by the water industry to be the best available technology to achieve the low levels stipulated by many health authorities. As a result of these considerations, atrazine is also the most widely studied by drinking water researchers. As with all target microcontaminants, the adsorption capacity ofatrazine varies between activated carbons [34, 35]. This has been attributed to surface area, but more realistically it has been attributed to the micropore structure of the carbons [34, 36] as the size of the molecule (molecular weight 216 g/mol) indicates it would adsorb into primary micropores. The kinetics of adsorption of atrazine can also be strongly affected by the mesopores, acting as transport pores [34]. The effect of NOM on the adsorption of atrazine has been comprehensively studied, with the aim of understanding, and perhaps, therefore minimizing the effect. This would result in substantial cost savings to the international water industry. Figure 26.3 shows the adsorption isotherm of atrazine in the absence of NOM, and in Seine River water, with a moderate DOC concentration of 3.8 mg/L [10]. As can be seen in the figure, the surface concentration of atrazine is reduced considerably in the presence of NOM, by approximately 80% at

26.3 Removal of Microcontaminants of Concern to the Drinking Water Industry

-*"100

Single-solute isotherm K= 18.8 (mg/g)(L/~g)1/n 1/n=0.516 o

0

o o

10

o

o

o

o

o

o

o

0

0

o

Co =82.7 ~g/L

o

o

o Co =41 .2 ~g/L

0.1

10

100

C(lJg/L)

Figure 26.3 Adsortion of atrazine in the presence and absence of NOM. (Reproduced with permission from Re£ [10].)

a solution concentration of 1.0 ~g/L, and an atrazine initial concentration of 82.7 ~g/L. Using the EBC model, Knappe [10] calculated the concentration of competitive NOM to be approximately 3.2 ~mol/L. If we assume the competing NOM has a molecular weight of 300 g/mol, and carbon makes up approximately 50 % of the mass of NOM, this represents a DOC concentration of around 0.96 mg/L, or less than a third of the DOC present in Seine River water. It should also be noted that 3.2 ~mol/L represents a competitive fraction approximately 10 times the molar concentration of the target compound. It is clear from these calculations that only a small proportion of the NOM need compete with the target compound to have a significant effect on the adsorption. Pelekani and Snoeyink [25, 36, 37] developed a conceptual model for competitive effects between atrazine and a series of dyes, as well as natural organic material from one groundwater source. The authors concluded that the competitive mechanism depends strongly on the pore size distribution of the carbon, as well as the relative sizes of the target and competing compounds. In particular, they suggested that the smaller NOM compounds could also participate in pore blockage, or pore restriction without pore blockage. They found that a wider pore size distribution in the adsorbent resulted in less pore blockage and consequently less evidence of competition. A later study, using model compounds thought to simulate the behavior of large molecular weight NOM (polystyrene sulfonate, 1800 g/mol) and small molecular weight NOM (p-dichlorobenzene) confirmed these conclusions [38], as did similar work using NOM in a natural water [39]. The HSDM has been successfully used to predict the adsorption of atrazine onto PAC [40]. Figure 26.4 shows the removal of atrazine as a function of time [10]. Also shown is the HSDM fit of the data, and the surface diffusion coefficient derived from the fit (Ds). This coefficient was then used to successfully predict adsorption of atrazine onto this PAC at different initial atrazine concentrations and carbon doses [10].

Chapter 26 Adsorption From Aqueous Solutions: Water Purification

• Experimental data - - HSDMfit

0.8

Co =36.8 IJg/L Cc =12.5 mg/L K =2.20 (mg/g)(UlJg) 1/n 1/n= 0.516 Ds =1.99 x 10-12 cm 2/s

0.6

0.4 0.2

o.0

L........Io-"'"-.&..........................&..-.""--&.......\,-"'"-.&..........................&..-..&.-&.......\,----'-----L...--I

o

100

200

400

300

Time (min)

Figure 26.4 Kinetics of adsorption of atrazine and the application of the HSDM. (Reproduced with permission from Re£ [10].)

The combination of membranes and PAC has proved to be very effective for the removal of atrazine, at the laboratory and full-scale plant [41]. Modeling of the process has been effective in the prediction of atrazine removal, although laboratory studies have shown that the longer retention time in this system can result in displacement of the pesticide from the surface by NOM, and this must be taken into account when applying the model for full-scale predictions [42, 43]. The RSSCT and SBA tests have also been applied to predict GAC bed life for atrazine removal, with mixed success [10, 44]. Figure 26.5 shows the RSSCT predictions of atrazine removal compared with the full-scale removal at a water treatment plant in France, at two empty bed contact times [45]. The RSSCT overestimated the removal to a significant extent for the 7 min contact time, also for the 14 min contact time for large-scale

Specific throughput (Ug)

o 0.5

100

300

........ Pilot (EBCT =7 min) --1(--

0.4

200

Specific throughput (Ug)

o 0.4

100

150

.......... Pilot (EBCT =14 min)

CD-RSSCT

ICo, avg. = 3.7 ~g/L I

50

r----..----~-~-~-_r__--r--I

---k-

CD-RsseT

0.3

ICo,

avg.

= 3.7 Jlg/L

I

0.2 0.1

0.1 0.0 ....-~...Io.-----J,_--'--_....L----'-_--'--_"""--' 100 200 300 o

Large-scale time (days)

0.0

_-x----

o

x x-----x--

100 200 Large-scale time (days)

300

Figure 26.5 Comparison ofpilot plant removal of atrazine with RSSCT data at two contact times. (Reproduced with permission from Re£ [45].)

26.3 Removal of Microcontaminants of Concern to the Drinking Water Industry

time > 200 days. In both cases the use of the RSSCT predictions would have overestimated the effective life of these full-scale columns. Many other pesticides have been studied [46, 47] and although removal efficiencies are varied, activated carbon is considered an essential treatment process for water affected by these chemicals. In general, as for atrazine, it has been found that the effectiveness of the adsorption process depends on the volume of micropores of the activated carbon [48], and the hydrophobicity of the adsorbate [49].

26.3.2 Industrial Chemicals The range of chemicals that can make their way into drinking water sources is enormous. Many major cities are sited on large rivers, with the possibility of cleaning materials, solvents, fuels etc., entering waterways through urban stormwater runoff Many industries are also situated where they can cause damage to the aquatic environment due to accidental spills of chemicals. Storage of a range of chemicals in underground tanks that have developed leaks has led to contamination of underground water sources. With growing awareness of the impact on the environment, and quality of drinking water, these practices have improved greatly over several decades. However, many of these industrial micropollutants are persistent in the environment, and are therefore still an issue for water suppliers. Two chemicals that have been the subject of a number of studies are methyl tertiary-butyl ether (MTBE) and trichloroethylene (TCE). In an effort to reduce lead emissions into the environment, MTBE has been introduced into petrol as an alternative in a number of countries. Since its introduction in the late 1980s it has become one of the top four chemicals in terms of mass production in the United States. Unfortunately, by the beginning of the twenty-first century many drinking water sources, in the United States in particular, had become contaminated with this chemical, which is of concern for both health and esthetic considerations [50]. In a comprehensive study of the adsorption of MTBE onto a range of activated carbon fibers, Knappe et al. [51] related the capacity of the adsorbents to the volume of pores in the range 0.8-1.1 nm. This corresponded to pores approximately 1.6 times the kinetic diameter of the MTBE molecule. It was also found that, if the requirement for pores in the correct size range was met by the carbons, the more hydrophobic carbon showed the highest capacity. Shih et al. [50] used RSSCTs to compare GACs for their ability to remove MTBE, and to compare the effects of different waters. Figure 26.6 illustrates the strong sensitivity to the background water quality of the adsorption of MTBE. The removal in the three waters follows the trend of the DOC concentration, i.e., the lower the DOC, the higher removal of MTBE. From these results it is difficult to determine the effect, if any, of the character of the NOM.

Chapter 26 Adsorption From Aqueous Solutions: Water Purification

1.2...----------------------------. o

o~

•• o

o

g

••··tIItII

o

0.8

cP

0.6

ad::tiJ [LJ ~o

/.,., ....

0.4

•• •

til

•••

o

0.2

0

....

•

'

.__ _ cP~_ ...., · -

o

5

10

15

20

25

30

35

40

45

Liters of water treated per gram of PCB GAC • 20 ppb MTBE with Lake Tahoe groundwater at 10 min EBCT o 50 ppb MTBE with Arcadia Wellfield groundwater at 10 min EBCT A

20 ppb MTBE with Lake Perris surface water at 10 min EBCT

Figure 26.6 RSSCT results for the removal of MTBE in three waters. (Reproduced with permission from Re£ [50].)

Due to its high solubility in water (50 giL) [52] it is unlikely that activated carbon will be considered the best available technology for this contaminant. In contrast, TCE is relatively hydrophobic, and adsorbs well on activated carbon [51]. For example, in a comprehensive study of the adsorption of both compounds, Knappe et al. [51] found that, in one of the waters studied, and for the most effective activated carbon, removal of 90% of TCE and MTBE would require 8 and 160 mglL of PAC respectively. Trichloroethylene is widely used in industry for cleaning metal parts. It is also an ingredient in adhesives, paint removers, typewriter correction fluids, and spot removers. Its water solubility (1 giL) ensures that, if contamination occurs near a water source, it is possible it will be present in drinking water at unacceptable levels. Knappe et al. [51] tested the range of activated carbon fibers mentioned above for the removal of TCE, and found the carbons with a higher volume of pores in the range 0.7-1.0nm were the most effective for removing the compound. These pores are approximately 1.5 times the kinetic diameter of TCE. Also similar to MTBE, given a similar pore volume in the appropriate range, the more hydrophobic carbon demonstrates the higher adsorption of MTBE. A number of studies have focussed specifically on the effect of NOM on the adsorption ofTCE, particularly those by Kilduff and coworkers [31,53-56]. In summary, they concluded that the greatest effect on adsorption of TCE was achieved by preloading the activated carbon with low-molecular-weight NOM. They suggested the NOM occupied the high-energy adsorption sites, thus

26.3 Removal of Microcontaminants of Concern to the Drinking Water Industry

decreasing site heterogeneity, and the decrease in adsorption ofTCE was due to \ the decrease in suitable adsorption sites rather than a pore-blockage mechanism.

26.3.3 Pharmaceuticals and Personal (are Products In many parts of the world, it is common practice to release treated wastewater to inland waterways. As a result, many pharmaceuticals (such as antibiotics and hormonal medicines) and personal care products such as soaps, shampoos, and moisturizing lotions (e.g., substances containing phenols and phthalates), are present in drinking water sources. These have relatively recently become an important issue for the drinking water industry as many are known to disrupt the endocrine systems of animals, including humans. Of the 10 000 or so chemicals in the environment that are suspected of endocrine disruption, several are of particular importance due to their potential significant impact on human health, and the prevalence ofuse ofthe compounds. These are the range of antibiotics for human and veterinary uses and hormones, synthetic and natural, known to affect the reproductive system of humans. Although the studies have been relatively few in number, activated carbon adsorption appears to be one of the best available technologies for the removal of these compounds [57-60]. Two human hormones that have received considerable attention are 17[3-estradiol (a natural estrogen) and 17a-ethynyl estradiol (a synthetic hormone used in contraceptive medicines) both of which have been found in wastewater treatment plant effiuents. Y oon et al. [61] reported a comprehensive investigation of activated carbon adsorption for the removal of 17[3-estradiol, 17a-ethynyl estradiol, and bisphenol A (a common plasticizer). They found a range of capacities when several activated carbons were tested for removal of these compounds, and the ease of removal of the three compounds corresponded quite well to their octanolwater coefficients. Table 26.2 shows some of these results, which also suggest quite a strong effect of water quality, with water 2 having almost twice the concentration of DOC as water 1. The important conclusion for water authorities was that these compounds could be successfully removed by activated carbon.

Table 26.2 Removal of endocrine disrupting chemicals with PAC [61]

Carbon 1 Carbon 2

88 98

98

99

>99

>99

73 95

94 >99

5

51

96

89

49

87

15

87

97

95

78

94

5 15

78 95

50 81

Chapter 26 Adsorption From Aqueous Solutions: Water Purification

26.3.4 Algal Metabolites Worldwide, a major issue for the drinking water industry is the esthetic quality of water, in particular the taste and smell of the water at the consumer's tap. Apart from chlorine added to most water supplies to ensure microbiological safety, the most common cause of taste and odor problems are algal metabolites in the source water, and the two most common of these are MIB (MIB can also be produced by actinomycetes bacteria) and geosmin, an earthy odor compound. Some blue-green algae or cyanobacteria can also produce a range of algal toxins that can cause harmful health effects from skin irritation, liver damage, tumor promotion, and death by nerve damage if consumed in sufficient quantity. Detailed information on the structures, occurrence, and toxic effects of these compounds can be found in Y 00 et al. [62].

26.3.4.1 Tastes and odors Geosmin and MIB are small (0.6-0.8 nm), moderately polar alicyclic tertiary alcohols. From their size it could be predicted that they would adsorb in pores in the primary or smaller secondary micropore range, (approximately < 1.0 nm) or pores slightly larger than the size of the molecules. Geosmin has been found to be more readily adsorbed by activated carbon than MIB [63,64]. This could be due to several factors, such as the shape of the geosmin molecule (flatter in shape and possibly more amenable to adsorption in the slit-shaped pores in the activated carbon) resulting in a higher adsorption energy - its slightly lower solubility [65], lower competition with NOM, or a combination of these factors. The removal of MIB and geosmin from potable water has been the focus of many studies. Most studies have shown large differences between activated carbons [66]. Figure 26.1 indicates that the volume of pores on the range <0.1 nm is the controlling factor in the adsorption of MIB, although some research has shown surface chemistry also plays a role [8, 67]. The effect of NOM on MIB adsorption is significant, and it has been reported in the literature to reduce adsorption by up to 98% [27]. Similar to TCE, the smaller NOM compounds compete to the greatest extent for MIB adsorption sites. Figure 26.7 shows a series of MIB adsorption isotherms on one activated carbon in a reservoir water, and four molecular weight fractions of the same NOM. The DOC concentrations were the same, and it is clear that the greatest competition is provided by the low-molecular-weight compounds. Newcombe et al. [27] reported this effect and concluded from their investigations that the low-molecular-weight NOM competed directly for adsorption sites and had the greatest effect on adsorption of MIB, while the higher molecular weight NOM caused some pore blockage, resulting in hindered kinetics for the MIB molecule. Similar to the findings ofPelekani and Snoeyink [36, 37] for atrazine, the authors reported that the significance of the effect varied between activated carbons, although the controlling effect of pore size distribution far outweighed the variation of NOM competitive effects between carbons.

26.3 Removal of Microcontaminants of Concern to the Drinking Water Industry

50

• Reservoir water • Diluted reservoir water .. <0.3kDa o <0.5kDa o 0.5-3kDa 6. >30kDa

C)

E -...

40

C>

-S c 0

~

30

:/~

"E Q)

6.

()

c 0

()

Q) ()

ctS

't:

~~,,~:'::• • •

10

::J

. .0··

iooOOn~.n.g~.~

20

en

20

40

III

60

80

100

Equilibrium solution concentration (ng/L)

Figure 26.7 Adsorption isotherms of MIB in six types of NOM.

1.0 PAC dose = 25 mg/L

C>

c

'c

'(ij

0.9

MIS •

0.8

HSDMfit Geosmin • Co =39 ng/L -------- HSDMfit

e\

0.6

E ~

c

-\

0.5

\~

0

U ctS

u:

•

0.7

Co =49 ng/L

\\~,

0.4

"'~,

0.3

.

0.2

-.

0.1 0.0 0

50

100

150

200

250

Time (min)

Figure 26.8 Fraction of MIB and geosmin remaining as a function of time.

The practical application of PAC for the removal of MIB and geosmin has been aided by the application of the HSDM [63, 64, 68]. Figure 26.8 illustrates the difference in the adsorption of the two compounds, and the fit that the HSDM can give to the data. Diffusion coefficients derived from these fits can then be used to predict the adsorption of the taste and odor compounds, and consequently the PAC doses required under particular water treatment plant situations [63, 68, 69].

Chapter 26 Adsorption From Aqueous Solutions: Water Purification ..c

0)

100

::J

Cinf =50nglL MIB

e

80

..c ~

co

~

0

60

.0

c:c

40

"E Q)

20

~

0

~

Q)

0

a..

0

2

4

6

Service time (years)

(a)

..

1.99 min EBCT 2.71 min EBCT

Os =7.86 x 10-12 em 2/s

4.28 min EBCT HSDM Fit - 2.71 min EBCT

~ = 2.23 x 10-4 em/s

HSDM Prediction - 1.99 min EBCT

mc =0.4195g

HSDM Prediction - 4.28 min EBCT

Bed depth = 1.00 em

..c

0)

::J

100

~

80

~

60

e ..c co

.0

c:c ~ "E Q) ~

Q)

a..

40 20 0

0

1000

2000

3000

Time (min)

(b) Figure 26.9 Removal of MIB using laboratory GAC techniques. (a) Comparison of minicolumn results with pilot plant [17]. (Reprinted from Journal AWWA, Vol. 91, No.8 (August 1999), by permission. Copyright © 1999, American Water Works Association). (b) HSDM fits and predictions compared with SBA data. (Reproduced with permission from Re£ [68].)

Figures 26.9(a) and (b) show how laboratory techniques can assist in the application of GAC for the removal of geosmin and MIB. Figure 26.9(a) shows the results of a mini-column test on GAC removed at various intervals from a GAC pilot plant [17]. The percent removal of MIB was measured in the laboratory by running a mini-column test at the same empty bed contact time as that used in the pilot. Further details can be found in [68]. The results indicate that GAC filters could be tested at regular intervals for the removal of MIB using a simple laboratory trial. Figure 26.9(b) compares the experimental data points obtained during a SBA test with the HSDM fit and predictions [68]. The carbon had been preloaded for 2 years in a pilot plant. The predictions and the

26.3 Removal of Microcontaminants of Concern to the Drinking Water Industry

fit agree well with the data, therefore it could be expected that the results, when applied to full scale, could give a good indication of the potential performance of GAC filter for the removal of MIB.

26.3.4.2 Algal toxins Although a range of algal toxins has been identified, the most common worldwide, and therefore the most widely studied, is the microcystin group of compounds. They are cyclic compounds, consisting of seven amino acid groups, and are of around 1000 g/mol molecular weight. More than 60 variants of the microcystin toxin have been identified, differing from one another mainly in variations of two of the amino acid groups, although minor variations to the other amino acids are also seen in some variants [62]. All microcystins contain the Adda side chain, the structural unit largely responsible for the toxicity of the compounds through protein phosphatase inhibition. The most common of the over 60 known variants of the toxin, microcystin LR (mLR) , incorporates leucine and arginine in the variable positions. Although mLR is the most commonly reported of the microcystins, it is very seldom the only microcystin found in a bloom situation, and is often not present at all, with the other variants predominating. The information available in the literature on the adsorption of mLR onto activated carbon indicates that, as with the adsorption of most microcontaminants, the removal efficiency is dependent on the type of activated carbon and the water quality conditions [70-72]. Newcombe and Nicholson [73] have reported a direct linear relationship between the adsorption of the toxin and the volume ofpores between 2 and 50 nm, with a linear regression giving parameters R 2 = 0.97, P < 0.0001, and N = 9. Microcystin LR is seldom the only microcystin present in a toxic algal bloom, and in many regions mLR is not the most commonly occurring variant [74]. Very little information is available in the literature on the effect of water treatment processes on other variants. The only published investigation of the adsorption of microcystin variants other than mLR used relatively impure toxin extracts [75]. The authors suggested differences seen in the adsorption of the microcystin variants could have been due to different contaminant levels in the spiking material. The UK Water Industry Research (UKWIR) undertook a computer modeling study to compare the octanol-water partition coefficients of nine microcystin variants [76]. With this information, and molecular size data, the authors concluded that the variants should respond similarly to water treatment processes; and, in particular, that the variants would adsorb onto activated carbon to the same, or greater, extent as the commonly studied variant microcystin LR. Studies since, on four microcystin variants, have shown large differences in the adsorption of the variants [71, 77, 78]. Surprisingly, the largest and the most hydrophilic of the toxins studied, mRR with two arginine groups in the variable positions, showed the highest adsorption on a range of PACs, contrary

Chapter 26 Adsorption From Aqueous Solutions: Water Purification

700

to expectations for adsorption onto activated carbon. The reason for this effect is still not clear. The adsorption of microcystins has been shown to be strongly affected by NOM [78]. In this work the effect, for four microcystin variants, was shown to be a function of the DOC concentration. This is probably a result of the direct competitive effect, where the competitive NOM, those compounds approximately the same molecular weight as the microcystins, makes up the bulk of the NOM. Therefore the bulk characterization parameter, DOC, gives an indication of the concentration of competing compounds, where for MIB and geosmin it could not [27, 63, 69]. Figure 26.10 displays the large difference in the adsorption ofmLR and microcystin LA (mLA) as a function of time. Microcystin LA (comprising alanine, rather than arginine as one of the variable groups) is a smaller, more hydrophobic molecule than mLR, but adsorbs to a much lower extent. The HSDM was used to fit the data, and predict kinetics of adsorption under different conditions. As can be seen from the figure, the predictions are excellent. Computer modeling of kinetics of adsorption was used to predict the PAC doses required to reduce the two compounds to below the WHO guideline of 1.0 f.1g/L in 60 min. The results are given in Table 26.3. Clearly, the differences in adsorption between microcystin variants will have a significant effect on treatment options available to water suppliers. Some previous studies showed that GAC is effective in the removal of the microcystin hepatotoxins [79, 80]. These studies were undertaken on new, or virgin, activated carbon, which has a very large pore volume available for

mLA

mLR 1.1

•

1.0

-

C)

c

'c '(ij

E ~

\

0.9

~

\

1.0 0.9

-. -.~.-.-.

HSDM prediction

\

0.8

Co =17.3 mg/L Cc =15 mg/L HSDMfit Co =14.0 mg/L Cc =25 mg/L

\

....

0.8

•. •

ti~

0.7

e

0.6

0.7

() ()

'E c

0.5

~

0.4

"-

T '. ,

•

T.,

0

~

....

....

\

C

-

• ...

Co =19.2 mg/L Cc =15 mg/L

HSDMfit Co =15.6 mg/L Cc =25 mg/L _. _.. HSDM prediction

0.6 0.5

',T.-

T T

u.

0.4

0.3 0.3 0.2 0

10

20

30

40

Co = initial concentration

50

60

0

10

20

30

40

50

60

Time (min)

Cc=PAC dose

Figure 26.10 Adsorption ofmicrocystins LR and LA as a function of time, showing HSDM fits and predictions. (Reproduced with permission from Ref. [71].)

26.3 Removal of Microcontaminants of Concern to the Drinking Water Industry

701

Table 26.3 Predicated PAC doses required to obtain a concentration of 1 J-Lg/L after 60 min contact

38

10 5 2

»100 95 50

29 15

adsorption and is capable of adsorbing a wide range of organic compounds. When similar studies were conducted over a longer timescale, or on activated carbon which had been in use for a period, it was found that breakthrough of toxin can occur in the eilluent from the filter [81, 82]. This is most likely due to both direct competition for adsorption sites and fouling of the GAC surface by NOM compounds of approximately the same size as the microcystins. As mentioned above, this NOM represents the majority of the DOC, and thus results in significant fouling effects. It has also been shown that breakthrough occurs at a different rate, depending on the DOC concentration of the inlet water [82]. Predictive tools have been used in an attempt to predict breakthrough of microcystins, but in these cases the results were not accurate due to biological degradation occurring, as well as adsorption [83, 84]. Figure 26.11 illustrates both forms of removal on a laboratory-scale GAC column. Initially the GAC,

.-.-.-.-.-==---.-.-..- ..-.-.

Sterilization

100

80

,.ll~'J/~~

~

o>

E ~

II1\ 60

/ \ /;

..

c

\,'

·x .9 C Q) ~

."w

.1I

uQ)

I

•/\

I

II

/ \

/

\ I\ ~

40

\: II"

.~

/ \/ \ I \I

\

Q)

a..

•

20

I

\/ •

•

1-_-mLR I -.-mLA

l II

•

Adsorption

+llII-----------------1.~~---~

Biodegradation

Adsorption

O-+----,--.....__----r--.-----r---,-~----r-.....__----r--~-,.---,r----+-____r-....,..........---.

o

10

20

30

40

50

60

70

80

Days

Figure 26.11 Adsorption and biodegradation taking place on a GAC laboratory column.

Chapter 26 Adsorption From Aqueous Solutions: Water Purification

702

preloaded with NOM, adsorbed both toxins to a certain extent. The fact that mLR was removed to a greater extent than mLA indicated the removal mechanism was mainly physical adsorption. However, after an "acclimation" period of 16 days, the toxin was no longer detected in the effiuent from the column. When the GAC was removed from the column, sterilized and replaced, adsorption was again the main mechanism. This is an excellent illustration how physical and biological processes working together can optimize the use of GAC.

26.4

REMOVAL OF NATURAL ORGANIC MATERIAL

As mentioned earlier, activated carbon is not commonly employed specifically to remove NOM. When PAC is applied, the removal of NOM is usually very low compared with the bulk DOC concentration. However, the removal of NOM through GAC filters can be high when the filter is first commissioned, and can reach a steady state removal ofbetween 10% and 20%. This is often considered to be due solely to biodegradation of the more readily degradable NOM, but is probably due to a combination of physical adsorption and biological processes. The removal of NOM, even at relatively low levels, is advantageous to the water supplier as it results in lower formation of disinfection by-products, as well as lower consumption of disinfectant, and a longer maintenance of the disinfectant residual in the distribution system. Due to this fact, and the significance of NOM as a competitor in the removal of other target compounds, a great deal of literature has been published on the adsorption behavior of N OM onto activated carbon. Many workers have shown that the pore size distribution has a significant effect on the adsorption of NOM [5, 6, 53, 85, 86] with some surface chemistry effects also noted [7, 87, 88]. Unlike the contaminants mentioned previously in this chapter, NOM can be highly charged, therefore the surface charge and solution conditions can have a significant effect on the adsorption of NOM. Several authors have shown that electrostatic effects, both between adsorbed NOM molecules, and between the carbon surface and the adsorbate, influence the adsorption, perhaps to as great an extent as the pore volume [6,7,31]. Figure 26.12 shows combined data for 10 activated carbons (described elsewhere [89, 90]), and two different NOM molecular weight fractions [91]. The average hydrodynamic diameters for each NOM fraction were measured using flow field flow fractionation and these values were related to the pore volume available for adsorption in that size range. The amount of DOC adsorbed at a solution concentration of DOC = 100 mg/L was plotted against available pore volume. The results show that the adsorption of NOM, at pH 3, is governed solely by the size of the adsorbate, and is due to dispersion forces, unaffected by the surface chemistry of the carbon. On the other hand, the adsorption of NOM at pH 7, also shown in Fig. 26.12, cannot be attributed to the available pore volume alone. Bj elopavlic et al. [92] showed that electrostatic effects between the surface and the adsorbate were important at low surface

703

26.5 Conclusions

400

'Oi .........

C)

•

pH 3, R=0.99, P<0.0001

•

pH 7

•

300

•

-S "C

Q)

.0

0en

"C

as

•

200

()

0 0

100

•

~

•

• •

0.2

0.4

0.6

0.8

Available pore volume (em 3/g)

Figure 26.12 Adsorption of NOM at two pH. (Reproduced with permission from Re£ [91].)

concentrations, whereas the repulsion between adsorbed ions was important at high surface concentrations.

26.5

CONCLUSIONS

Activated carbon is used extensively in drinking water treatment for the removal of problem contaminants. Presently it is the best available technology to reduce the concentration of problem chemicals, man-made and natural. As with all applications of adsorption onto carbon, the processes taking place are complex and interrelated. In the treatment of drinking water this is exacerbated by the wide range of structures of the contaminants of interest, and the presence of the complex mixture of natural organic material. Whether the aim is to remove NOM or a microcontaminant, the complexity of NOM and the inability to completely characterize the mixture is by far the greatest influence on the application of the adsorbent. Predictive tools, for the effective application of activated carbon, can be ofgreat benefit, but must be used with the knowledge that the systems under investigation change on a daily basis (e.g., temperature, concentration and character of NOM, concentration and type of contaminant), and such tools will almost always be only an estimate of the adsorption behavior in practice.

Chapter 26 Adsorption From Aqueous Solutions: Water Purification

7°4

ACKNOWLEDGMENTS

The author would like to acknowledge the significant contributions to this chapter by Lionel Ho, Najwa Slyman, and David Cook.

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706

Chapter 26 Adsorption From Aqueous Solutions: Water Purification

35. Ayele,J., Leclerc, V., and Couillault, Ph. (1998). Efficiency of three powdered activated carbons for the adsorption of atrazine and diuron - use of some models.Aqua, 47(1), 41-5. 36. Pelekani, C. and Snoeyink, V.L. (1999). Competitive adsorption in natural water: role of activated carbon pore size. Water Res., 33(5), 1209-19. 37. Pelekani, C. and Snoeyink, V.L. (2000). Competitive adsorption between atrazine and methylene blue on activated carbon: the importance of pore size distribution.Carbon, 38(10), 1423-36. 38. Li, Q., Snoeyink, V.L., Marinas, B.J., and Campos, C. (2001). Role of NOM molecular weight in PAC adsorption equilibrium and kinetics of atrazine: a simulation study using model compounds. Proceedings of the American Water Works Association Water Quality Technology Conference, November 12-14, 2001, Nashville, TN. 39. Li, Q., Snoeyink, V.L., Marinas, BJ., and Campos, C. (2003). Pore blockage effect of NOM on atrazine adsorption kinetics of PAC: the roles of PAC pore size distribution and NOM molecular weight. Water Res., 37, 4863-72. 40. Knappe, D.R.U., Matsui, Y., Snoeyink, V.L., et al. (1998). Predicting the capacity of powdered activated carbon for trace organic compounds in natural waters. Environ. Sci. Technol., 32(11), 1694-8. 41. Campos, C., Marinas, BJ., Snoeyink, V.L., et al. (1998). Adsorption of trace organic compounds in CRISTAL@ processes. Desalination, 117(1-3),265-71. 42. Li, Q., Snoeyink, V.L., Campos, C., and Marinas, BJ. (2002). Displacement effect of NOM on atrazine adsorption by PACs with different pore size distributions. Environ. Sci. Technol., 36, 1510-15. 43. Li, Q., Marinas, BJ., Snoeyink, V.L., and Campos, C. (2003). Three component competitive adsorption model for flow through PAC systems 1 Model development and verification with a PAC/membrane system. Environ. Sci. Technol., 37, 2997-3004. 44. Schmidt, KJ. (1994). Prediction of GAC column performance using bench-scale techniques. M.S. Thesis, University of Illinois, Urbana, USA. 45. Knappe, D.R.U., Snoeyink, V.L., Roche, P., et al. (1997). The effect ofpreloading on RSSCT predictions of atrazine removal by GAC adsorbers. Water Res., 31(11), 2899-909. 46. Sotelo, J.L., Ovejero, G., Delgado, J.A., and Martinez, I. (2002). Comparison of adsorption equilibrium and kinetics of four chlorinated organics from water onto GAC. Water Res., 36, 599-608. 47. Hua, J.-Y., Aizawa, T., Ookubo, Y., et al. (1998). Adsorptive characteristics of ionogenic aromatic pesticides in water on powdered activated carbon. Water Res., 32(9), 2593-600. 48. Donner, C., Remmier, F., Zullei-Seibert, N., et al. (2002). Enhanced removal of herbicides by different in-site barrier systems (GAC, FAC, anthracite, lignite coke) in slow sand filtration. Water Sci. Technol.: Water Supply, 2(1), 123-8. 49. Hua, J.-Y., Aizawaa, T., and Magara, T. (1997). Evaluation of adsorbability of pesticides in water on powdered activated carbon using octanol-water partition coefficient. Water Sci. Technol., 35(7), 219-26. 50. Shih, T.C., Wangpaichitr, M., and Suffet, M. (2003). Evaluation of granular activated carbon for the removal of methyl tertiary butyl ether (MTBE) from drinking water. Water Res., 37, 375-85.

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51. Knappe, D.R.U., Li, L., Quinlivan, P.A., and Wagner, T.B. (2003). Effects of activated carbon characteristics on organic contaminant removal. American Water Works Association Research Foundation Research Report No. 90926. 52. Nichols, E.M., Einarson, M.D., and Beadle, S.C. (2000). Strategies for Characterising Subsurface Releases of Gasoline Containing MTBE. Publication No. 4699, American Petroleum Institute. 53. Kildu£I: J.E., Karanfil, T., Chin, Y.P, and Weber, W., Jr (1996). Adsorption of natural organic polyelectrolytes by activated carbon: a size exclusion study. Environ. Sci. Technol., 30(4), 1336-46. 54. Kildu£I:J.E., Karanfil, T., and Weber, W.,Jr (1998). Adsorption by GAC preloaded with humic substances: effects of molecular weight.]. Am. Water Works Assoc., 90, 76-89. 55. Kildu£I:J.E., Karanfil, T., and Weber, W.,Jr (1998). Competitive effects of nondisplacable organic compounds on trichloroethylene uptake by activated carbon. I. Thermodynamic predictions and model sensitivity analysis.]. Colloid Interface Sci., 205,271-9. 56. Kildu£I:J.E., Karanfil, T., and Weber, W.,Jr (1998). Competitive effects of nondisplaceable organic compounds on trichloroethylene uptake by activated carbon II - Model verification and applicability to natural organic matter.]. Colloid Interface Sci., 205(2), 280-9. 57. Yoon, Y., Westerho£I: P., Snyder, S., and Song, S. (2002). A review on removal of EDCs and pharmaceuticals by drinking water processes. Proceedings of the American Water Works Association Water Quality Technology Conference, November 11-13, 2002, Seattle, USA. CD ROM. 58. Ijpelaar, G.F., Beerendonk, E.F., and Siegers W.G. (2003). EDCs in water: a quick scan of the removal efficiency of practical water treatment processes. Proceedings of the IWA Leading Edge Conference Drinking Water & Wastewater Treatment Technologies, Amsterdam. 59. Thermes, T., Meisenheimer, M., McDowell, D., et al. (2002). Removalofpharmaceuticals during drinking water treatment. Environ. Sci. Technol., 36, 3855-63. 60. Petrovic, M., Diaz, A., Ventura, F., and Barcelo, D. (2003). Occurrence and removal of estrogenic short chain ethoxy nonylphenolic compounds and their halogenated derivatives during drinking water production. Environ. Sci. Technol., 37,4442-8. 61. Yoon, Y., Westerho£I: P., Snyder, S., and Esparzo, M. (2003). HPLC-fluorescence detection and adsorption of bisphenol A, 17r3-estradiol and 17a-ethynyl estradiol on powdered activated carbon. Water Res., 37, 3530-7. 62. Yoo, R.S., Carmichael, W.W., Hoehn, R.C., and Hrudey, S.E. (1995). Cyanobacterial (blue-green algal) toxins: a resource guide. American Water Works Association Research Foundation Report No. 90693. 63. Cook, D., Newcombe, G., and Sztajnbok P. (2001). The application of powdered activated carbon for MIB and geosmin removal: predicting PAC doses in four raw waters. Water Res., 35(5), 1325-33. 64. Graham, M., Summers, R., Simpson, M., and Macleod, B. (2000). Modelling equilibrium adsorption of 2-methylisoborneol and geosmin in natural water. Water Res., 34(8), 2291-300. 65. Pirbazari, M., Borow, H., Craig, S., et al. (1992). Physical chemical characterisation offive earthy-musty- smelling compounds. Water Sci. Technol., 25(2), 81-8.

708

Chapter 26 Adsorption From Aqueous Solutions: Water Purification

66. Vik, E., Storhaug, R., Naes, H., and Utkilen, H. (1988). Pilot plant studies of geosmin and 2-MIB removal. Water Sci. Technol., 20(8-9), 229-36. 67. Nowak, K.O., Cannon, F.S., and Mazyck, D.W. (2004). Enhancing activated carbon adsorption of MIB: Methane and steam treatments. Environ. Sci. Technol., 38,276-84. 68. Gillogly, T. (1999). MIB Adsorption in Drinking Water Treatment. PhD Thesis, University of Illinois, Urbana-Champaign. 69. Newcombe, G. and Cook, D. (2002). Influences on the removal of tastes and odours by PAC.Aqua, 51(8),463-74. 70. Donati, C., Drikas, M., Hayes, R., and Newcombe, G. (1994). Microcystin-LR adsorption by powdered activated carbon. Water Res., 28(8), 1735-42. 71. Cook, D. and Newcombe, G. (2002). Removal of microcystin variants with powdered activated carbon. Water Sci. Technol.: Water Supply, 2(5-6), 201-8. 72. Hart, J. and Stott, P. (1993). Microcystin-LR Removalfrom Water (Report FR0367). Foundation for Water Research. 73. Newcombe, G. and Nicholson, B. (2004). Water treatment options for dissolved cyanotoxins. Aqua, 53, 227-39. 74. Falconer, I., Bartram, J., Chorus, I., et al. (1999). Safe levels and practices. I Toxic Cyanobacteria in Water, A Guide to Their Public Health Consequences, Monitoring and Management (I. Chorus and J. Bartam, eds). E & FN Spon. 75. Mohamed, Z., Carmichael, W., An, J., and EI-Sharouny, H. (1999). Activated carbon removal efficiency of microcystins in an aqueous cell extract of Microcystis aeruginosa and Oscillatoria tenuis strains isolated from Egyptian freshwaters. Environ. Toxicology, 14(1), 197-201. 76. UKWIR Report (1997). Algal toxins, occurrence and treatability of anatoxin a and microcystins. Report Ref 97 IDW107lOS. 77. Newcombe, G., Cook, D., Brooke, S., et al. (2003). Treatment options for microcystin toxins: similarities and differences between variants. Environ. Technol., 24, 299-308. 78. Cook, D. and Newcombe, G. (2002). Effect ofnatural organic matter concentration and character on the adsorption of microcystin analogues onto PAC. Proceedings of the American Water Works Association Water Quality Technology Conference, November 11-13, 2002, Seattle, USA. CD ROM. 79. Jones, G., Minatol, W., Craig, K., and Naylor, R. (1993). Removal of low level cyanobacterial peptide toxins from drinking water using powdered and granular activated carbon and chlorination - results of laboratory and pilot plant studies. Proceedings of the 15th Australian Water & Wastewater Association, Federal Convention, Gold Coast, pp. 339-46. 80. Himberg, K., Keijola, A., Hiisvirta, L., and Sivonen, K. (1989). The effect of water treatment processes on the removal of hepatotoxins from Microcystis and Oscillatoria cyanobacteria: a laboratory study. Water Res., 23(8), 979-84. 81. Craig, K. and Bailey D. (1995). Cyanobacterial toxin microcystin LR removal using activated carbon - Hunter Water Corporation experience. Proceedings of the 16th AWWA Federal Convention, April 1995, Sydney, Australia, pp. 579-86. 82. Newcombe, G. (2002). Removal of algal toxins using ozone and GAC. American Water Works Association Research Foundation Report No. 90904. 83. Carlile, P.R. (1994). Further Studies to Investigate Microcystin-LR and Anatoxin-a Removal from Water (Report FR0458). Marlow, Buckinghamshire: Foundation for Water Research.

References

84. UKWIR Report (1996). Pilot scale GAC tests to evaluate toxin removal. Report Ref No. 96/DW/07/1. 85. Chadik, P.A. and Amy, G.L. (1987). Molecular weight effects on THM control by coagulation and adsorption.]. Environ. Eng., 113(6), 1234-48. 86. Lee, M.C. and Snoeyink, V.L. (1980). Effect of GAC pore size distribution and alum pretreatment on the adsorption of humic substances. Proceedings AWWA Annual Conference. Water for the World - Challenge of the 80's, pp. 319-28. 87. Weber, W.J., Jr, Voice, T.C., and Jodellah, A. (1983). Adsorption of humic substances: the effects of heterogeneity and system characteristics. Am. Water Works Assoc., 75(12), 612-19. 88. Dastgheib, S.A., Karanfil, T., and Cheng, W. (2004). Tailoring activated carbons for enhanced removal of natural organic matter from natural waters. Carbon, 42(3), 547-57. 89. Newcombe, G. (1999). A study of natural organic material and its adsorption onto activated carbon. PhD Dissertation, University of South Australia: Adelaide, Australia. 90. Newcombe, G., Donati, C., Drikas, M., and Hayes, R. (1994). Adsorption onto activated carbon: electrostatic and non-electrostatic interactions. Water Supply, 14, 129-42. 91. Newcombe, G. and Cook, D. (2003). Removal of natural microcontaminants from drinking water using activated carbon. In Encyclopaedia of Colloid and Inteiface Science. (P. Somasundaran, ed.). Marcel Dekker, Inc. pp. 4221-39. 92. Bjelopavlic, M., Newcombe, G., and Hayes, R. (1998). Adsorption of NOM onto activated carbon: effect of surface charge, ionic strength and pore volume distribution.]. Colloid Inteiface Sci., 210, 271-80.

SORPTION OF VISCOUS ORGANICS BY MACROPOROUS CARBONS Michio Inagaki, l Masahiro Toyoda,2 Norio Iwashita,3 and Feiyu Kang4 1 Faculty of Engineering, Aichi Institute of Technology, Yakusa, Toyota, japan 2Faculty of Engineering, Oita University, Dannoharu, Oita, japan 3Nationallnstitute of Advanced Industrial Science and Technology, Onogawa, Tsukuba, japan 4Department of Materials Science and Engineering, Tsinghua University, Beijing, China

Contents 27.1 Introduction 27.2 Macropore Structure of Carbon Materials 27.3 Sorption Capacity for Viscous Organics 27.4 Kinetics of Sorption 27.5 Recovery of Heavy Oils 27.6 Discussion 27.7 Conclusions Acknowledgments References

711

712 716 722 727 73 1 73 2 73 2

73 2

27.1 INTRODUCTION Heavy oil spills result in not only a great deal of damage to the global environment but also a great loss of energy resources. It was claimed that a large amount of heavy oil could be sorbed into exfoliated graphite [1]. A Chinese group carried out studies on sorption of heavy oils into exfoliated graphite, particularly paying attention to its preparation conditions [2]. It was demonstrated by a Japanese group that porous carbon materials with macropores, not only exfoliated graphite but also carbonized fir fibers, are able to sorb a large amount of heavy oil very quickly, more than 80 g of heavy oil per 1 g of carbon Adsorption by Carbons ISBN: 978-0-08-044464-2

© 2008 Elsevier Ltd. All rights reserved.

711

71 2

Chapter 27 Sorption of Viscous Organics by Macroporous Carbons

materials within 1 min [3]. However, microporous carbon materials, such as activated carbons, have only small sorption capacity, as small as a few grams per gram. Dependences of sorption capacity on bulk density of carbon materials and on temperature and viscosity of heavy oils, recovery of sorbed heavy oil from carbon materials, and also recycling of both heavy oils and carbon materials were explored on different carbon materials - exfoliated graphite [3-8], carbonized fir fibers, which are fibrous components extracted from natural fir trees [9, 10], and carbon fiber felts [11]. Some trials for practical applications by using exfoliated graphite packed into plastic bags were also reported [12, 13]. These experimental results were reviewed in different journals [14-19]. Fundamental sorption kinetics of heavy oils into carbons was also studied by using the so-called wicking method [11, 20, 21]. A series of our studies showed that large spaces, which are constructed by the entangled worm-like particles of exfoliated graphite, fibrous particles of carbonized fir fibers, and carbon fibers are mainly responsible for their large sorption capacity. However, a difficulty was pointed out to correctly evaluate these large spaces formed among fragile particles, such as worm-like particles of exfoliated graphite, to reach more realistic value for pore volume in exfoliated graphite. For the characterization of these large spaces, a special dilatometer for the mercury porosimeter [22] and also an impregnation technique ofparaffin [23] were proposed. On the basis of these experimental results on exfoliated graphite, the mechanism of a large sorption capacity of exfoliated graphite was discussed [24]. The works on sorption of exfoliated graphite for heavy oils and biomedical fluids by the Chinese groups were also reviewed [19]. Here, the sorption of viscous organics, heavy oils, different oils such as engine and cooking oils, and also biomedical fluids are discussed on macroporous carbon materials, mainly three kinds of materials, i.e., exfoliated graphite, carbonized fir fibers, and carbon fiber felts. The recovery of sorbed heavy oils from macroporous carbon materials is also discussed.

27.2 MACROPORE STRUCTURE OF (ARBON MATERIALS

Exfoliated graphite was prepared by rapid heating of residue compounds of natural graphite flakes with sulfuric acid and composed of characteristic wormlike particles. In this material, three kinds of macropores have to be identified [23,25-27], as shown in Fig. 27.1(a-c). Ellipsoidal pores inside the worm-like particles (intraparticle pores) (Fig. 27.1 (a)) and crevice-like pores on the surface of the particles (Fig. 27.1 (b)). These two kinds of pores are formed during exfoliation of graphite flakes preferentially along the normal to the basal planes of graphite. Among the worm-like particles, large spaces (interparticle pores) are formed (Fig. 27.1(c)) mainly due to the complicated entanglement of the worm-like particles. Pore structure of exfoliated graphite was recently studied by developing different techniques because of its importance to understand the sorption performance mainly for different heavy oils.

27.2

Macropore Structure of Carbon Materials

Figure

27.1

713

Scanning electron microscope (SEM) images of exfoliated graphite.

In order to evaluate pore structure of exfoliated graphite, exfoliation volume, which is a volume occupied by a lump of exfoliated graphite, or bulk density, which is an inverse of the exfoliation volume, was used. Exfoliation volume includes overall information on the three kinds of pores mentioned above; the exfoliation volume is larger if pore structure is more developed. Information on each pore, however, could not be obtained separately. Two techniques for the evaluation of pores among and inside the worm-like particles were recently developed. The pores inside the particles were evaluated by preparing a fractured cross section of a number of worm-like particles and by determining the different parameters of pores, cross-sectional area, lengths of major and minor axes, aspect ratio, and fractal dimension of pore wall, with the aid of an image processing technique [25]. On large spaces among the particles, mercury porosimetry using a special dilatometer was proposed, by which large pores up to 600 f.1m diameter could be measured [22]. Recently, paraffin impregnation was successfully performed to solidify a lump of fragile worm-like particles to make cutting into thin slices possible [23]. The surfaces of slices were observed under an optical microscope; the black parts corresponded to the cross section occupied by worm-like particles and the white part to paraffin, which is a cross section of large spaces among the worm-like particles. By using the image processing technique, the parameters of large spaces were determined. The volume occupied by the worm-like particles was then obtained by the following equation:

Vw = (Sw/ S )V/11

(27.1)

where Sw is the area of the worm-like particles, i.e., the black part, S and V are the area of the slice used and the whole volume of the solidified block, respectively, and 11 is the shrinkage of paraffin that was measured as 80% in the present work. The volume of the large spaces among the worm-like particles was calculated by subtracting the volume occupied by the particles, Vw , from the exfoliation volume of the exfoliated graphite. The exfoliated graphite that is commercially available and used for the sorption ofviscous organics is discussed in the following sections and the averaged parameters ofpores among and inside the worm-like particles are summarized in Table 27.1. Histograms ofcross-sectional area ofthese pores are shown in Fig. 27.2.

Chapter 27 Sorption of Viscous Organics by Macroporous Carbons

Table 27.1

Parameters for pores among and inside the worm-like particles in a commercially available exfoliated graphite

Cross-sectional area (f..1m2 ) Major axis (f..1m) Minor axis (f..1m) Aspect ratio Fractal dimension

Averaged pore parameters

Number of pores measured

422 32 16

138 X 103

0.53 1.1

0.65 0.77

2286

6300

490

300

(a) Pores inside the worm-like particles

50

100

150

Cross-sectional arealJlm

I

o

!

o o

o

LO

o

o

o

LO f'...

LO

C\I

200 2

LO

Cross-sectional area of pores (11m2)

(b) Pores among the worm-like particles

>.

()

.........

c

Q)

~

:::J

c

C'"

:J

U.

~

Q)

°C\loq-COCOOC\loq-cocoo ..... C\I (Y) oq- co f'o. co C'l 0 C\l 0 0 0 0 0 0 0 0 ..........

CT

~

0000000000

LL

Cross-sectional

arealmm 2

oq-oq-oq-oq-oq-oq-oq-oq-oq-oq-oq-oq-oq-oqC\i~
Cross-sectional \....

arealmm

o

0.16

0.32 0.48

0.64 0.80

0.96

2

1.12 1.28

'\

1.44

Cross-sectional area (mm 2)

Figure 27.2

Histograms of cross-sectional area of pores.

o

LO f'...

o o o

C\I

27.2

Macropore Structure of Carbon Materials

71 5

Pore structures in exfoliated graphite, large spaces among the worm-like particles, and pores inside the particles are known to depend strongly on exfoliation temperature and content of intercalates of the original residue compounds [26-28]. In the present exfoliated graphite, the averaged cross-sectional area of spaces among the particles reaches to about 1.4 x 105 J.1m2 (0.14 mm2 ) , but distributes in a wide range, as seen from histograms in Fig. 27.2(b), where the largest frequency locates in the range of 0.008-0.012 mm2 , but the largest pore reaches to 30 mm2 (3 x 107 J.1m2 ). The sizes of pores inside the particles are as small as 420 J.1m2 on an average and distribute in a range up to 2 x 103 J.1m2 • The aspect ratio is a little different between the two kinds of pores, for the spaces among the particles about 0.65 but for those inside the particles about 0.41 under an approximation of elliptic cross sections, the former being much closer to round cross sections than the latter. The pores inside the particles are clearly seen to be elliptic in Fig. 27.1 (a) and their minor axes are preferentially along the axis of worm-like particle, i.e., the normal to basal plane of pristine graphite flake. Elliptic cross section of spaces among the particles was assumed here, but their shapes were reasonably expected to be more complicated because these pores are formed by and surrounded with worm-like particles. Fractal dimensions for pore walls are quite different between spaces among the particles and pores inside the particles, for the former about 0.77 but for the latter about 1.1. The small value of fractal dimension for spaces among the particles is supposed to be due to the crevice-like V-shaped pores on the surface of worm-like particles. Fibrous components of fir trees were separated from lignin components by treating in saturated water vapor for 1 min and then carbonized at 900°C for 1 h in a flow of a high-purity argon gas. In these carbonized fibers, three kinds of macropores are observed (Fig. 27.3); pores along fiber axis with rectangular cross section (Fig. 27 .3 (a)), small round pores on the wall of fibers (Fig. 27.3(b)), which seem to be connected to the former rectangular pores, and large spaces with different and irregular sizes among fibrous particles (Fig. 27.3 (c)). The first two are intraparticle pores and the last are interparticle ones. In carbon fiber felts, however, only one kind of pores, interparticle pores, are observed among the fibers (Fig. 27.4). The surface of each fiber is smooth and no pores are inside of the fibers. Felts composed of polyacrylonitrile (PAN)-based and isotropic pitch-based carbon fibers were used as sorbents in the present work.

Figure 27.3 Scanning electron microscope (SEM) images of carbonized fir fibers.

716

Chapter 27 Sorption of Viscous Organics by Macroporous Carbons

Figure 27.4 Scanning electron microscope (SEM) image of carbon fiber felt.

27.3

SORPTION CAPACITY FOR VISCOUS ORGANICS

27.3.1 Heavy Oils A small lump of carbon material was added either onto the heavy oil floating on the water or on the heavy oil itself In Fig. 27.5, typical changes in appearance are shown in the case ofsorption ofheavy oil floating on the water by the exfoliated graphite. The A-grade heavy oil floating on the water (Fig. 27.5(a)) was completely sorbed into the added exfoliated graphite (Fig. 27.5(b)). The characteristic brown color of the A-grade heavy oil disappeared within 1 min after the addition of exfoliated graphite, because the amount of heavy oil is less than the sorption capacity of the exfoliated graphite added. The exfoliated graphite-sorbed oil loses its luster and looks a little blacker (Fig. 27.5(b)). After taking out the exfoliated graphite, no contamination appeared in the water and even if it was transferred onto a white filter paper, as shown in Fig. 27.5(c). When the amount of heavy oil was a little larger than the sorption capacity of the exfoliated graphite, the periphery of the exfoliated graphite lump was trimmed by the oil layer. When large excess oil was added, the whole exfoliated

Figure 27.5 Photographs of A-grade heavy oil with exfoliated graphite. (a) Heavy oil floating on water, (b) 1 min after addition of a lump of exfoliated graphite, and (c) after recovery of oil-sorbed exfoliated graphite by filtration.

27.3 Sorption Capacity for Viscous Organics

717

graphite looked wetted and the brown color of the oil remained on the water. Exfoliated graphite-sorbed heavy oil could be separated from water by filtration. When the lump was placed on the surface of the A-grade heavy oil directly, it was picked up by using a stainless-steel mesh after 2 h of immersion and then kept 1 h in order to drain off the excess oil. In the case of the viscous C-grade heavy oil, however, immersion for 15 h and draining-off for 3 h were employed. The sorption capacity was calculated from the mass increase of the lump before and after sorption, by converting the difference to the mass (g) of sorbed heavy oil per 1 g of carbon. When a stainless-steel mesh was used for picking up the carbon materials after sorption of oils, the mass of the oil that adhered onto the mesh was subtracted from the observed mass increase, though it was negligibly small in the case of the A-grade oil. In Fig. 27.6, the dependences of sorption capacity on the bulk density of the three carbon sorbents, exfoliated graphite, carbonized fir fibers, and carbon fiber felts are shown for the A-grade heavy oil whose viscosity is 0.004 Pa s. In Fig. 27.6(b) and (c), representative data for exfoliated graphite and fir fibers are shown for making the comparison easier. It has to be mentioned that sorption capacity of exfoliated graphite and carbonized fir fibers with low bulk density is surprisingly high, e.g., 1 g of exfoliated graphite with bulk density of 7 kg/m 3 can sorb more than 80 g of the A-grade heavy oil, which is much higher than that of conventional sorbents for heavy oils - polyurethane foams (10-30 gig). Sorption capacity decreases markedly with increasing bulk density. Sorption capacity of carbonized fir fibers is a little lower in the low bulk density region in comparison with exfoliated graphite. Carbon fiber felts used had rather high bulk density and so sorption capacity was not high, as shown in Fig. 27.6(c). However, the relations between the sorption capacity for the A-grade heavy oil and the bulk density observed for the three carbon sorbents were almost the same with each other. Sorption capacities of granular activated carbons and activated carbon fibers were measured, but they were relatively low, e.g., 1 gig £Jr activated carbon granules with 1100 m 2 I g surface area and 19 gl g for those with 1220 m 2 I g, and no relation to the Brunauer, Emmett, and Teller (BET) surface area was observed. Therefore, the experimental results on different carbon materials showed that macropores, which make bulk density lower, are mainly responsible for their large sorption capacity. Fibrous particles of carbon may be advantageous for easy deformation of macropores to be suitable for sorption of heavy oils. Sorption capacity for the A-grade heavy oil showed certain correspondence to the pore volume measured by using a new dilatometer of mercury porosimetry, as shown in Fig. 27.7, which was expected to attribute mostly to spaces among the particles. The volume of the large spaces among the particles that was determined by using the paraffin impregnation method was about 75% of the total volume of the lump of exfoliated graphite, and about 68% of the sorbed heavy oil was assumed to occupy these spaces among the worm-like particles [23].

718

Chapter 27 Sorption of Viscous Organics by Macroporous Carbons

(a) Exfoliated graphite

Q) .::£

.........

(b) Carbonized fir fibers

120

90

•

0)

~

80

·0 100 ~ > ~

0)

.::£

Q)

80

.::£

.........

~

~

~

'0 1: ::J

"0 ~

60

~ ()

0

E-

(j)

Fir fibers carbonized at 380°C

•

Exfoliated graphite

•

50

~

40 30

0 (j) 20

DO

20

0

a0

Fir fibers carbonized at 900°C

•

[]

c

40

E c

60

a.

O

~

[J

o

0)

"'C 0)

70

.........

Q)

..c.

[J

10 0

~'b ..

[J

0

0 0

25

50

75

100

125

0

20

3 Bulk density (kg/m )

40

60

80

100

Bulk density (kg/m 3)

(c) Carbon fiber felts

90

~

80 ~

0)

.........

~

"0 ~

a. ~ ()

c

o

Carbon fiber felts

70

•

Firfibers

60

•

Exfoliated graphite EG-1

-,

50 40

0

a0

(j)

~

30 20 10 0 0

~~-

0-

20 40 60 80 100 120 140 160 180 200 Bulk density (kg/m 3)

Figure 27.6 Dependences of sorption capacity for the A-grade heavy oil on bulk density of carbon sorbents.

In Fig. 27.8(a) and (b), the bulk density dependences of the sorption capacity for the viscous C-grade heavy oil, whose viscosity is 0.35 Pa s, are shown on exfoliated graphite and carbonized fibers. In Fig. 27.8(a), the sorption capacity of the B-grade heavy oil with a little lower viscosity (0.27 Pa s) is also plotted. Sorption capacity for the viscous C-grade oil is relatively low and its decrease \vith increasing bulk density is observed markedly for the C-grade than for the less viscous A-grade. No sorption was detected on dense exfoliated graphite, but on carbonized fir fibers a certain capacity could be observed. Sorption capacity

27.3 Sorption Capacity for Viscous Organics

o

100

50

o

Exfoliated graphite

~ Carbonized fir fibers

•

Activated carbon

[] Carbon fiber felt

O - - _......_ _......._ _......II...--._ _

o

50

.....-_-~

100

Pore volume (ml/g)

Figure 27.7 Relation between sorption capacity ofdifferent carbon sorbents for the A-grade heavy oil and pore volume measured by using a new dilatometer for mercury porosimetry.

(a) Exfoliated graphite

(b) Carbonized fir fibers 70 ~

100 [] B-grade heavy oil

0) ~

..........

0'>

\

75

<5

~

40 as as 30 () 0-

~ \

0

0, \

E-

\0 ."

25

\.

\

•

.....0'- - - - ____ --__ -0 __

25

50

75

Bulk density (kg/m 3)

100

-

~

0 125

0._QJ . 0

10 .A.

0

20

<5

Cf)

0, 0

lIP

c:::

'\

Cf)

f.

~

~\ ~\

c:::

• Exfoliated graphite

13

.\

0

E-

0> ~

" ~\ ~\

50

• Fir fiber carbonized at 380 0 e

0, 50

\

~ ~

o Fir fiber carbonized at goooe

[J

60 e-grade heavy oil

C

'0

as 0as ()

<>

0

10 20 30 40 50 60 70 80 90 100

Bulk density (kg/m 3 )

Figure 27.8 Dependences of sorption capacity of exfoliated graphite and carbonized fir fibers for the C- and B-grade heavy oils on bulk density of carbon sorbents.

of exfoliated graphite for the B-grade heavy oil, which is usually a mixture of the less viscous A-grade oil and the viscous C-grade oil, is a little larger than the C-grade, suggesting that viscosity of heavy oils is one of important factors governing their sorption phenomena into porous carbons. In Fig. 27.9(a), the sorption capacity of an exfoliated graphite with bulk density of 7 kg/m3 is plotted against the logarithm of viscosity for four kinds

Chapter 27 Sorption of Viscous Organics by Macroporous Carbons

720

(a) Heavy oils

(b) Oils with different viscosities

100

Oi .::::t:.

~

'0

\A

..,

80

.~o

.......... 0>

~ ~

a. (lj ()

40

a 0

CJ)

C A-grade heavy oil

20

•

Crude oil

1\ B-grade heavy oil

•

0 0.001

~ ~

'0

C-grade heavy oil

0.01

0.1

~ 990 '0.", <>

III

. . o"~11

60

o

.~

It

(lj

\

a. (lj ()

~

0

•

80

0,

~~

•

60

0> .::::t:.

'~

(lj

c:

,•

100

\ 1

c:

40

It

0

a 0

CJ)

10

\

20

0 0.0001

Viscosity 'TJ (Pa s)

0.001

0.01

0.1

10

Viscosity 'TJ (Pa s)

Figure 27.9 Dependences of sorption capacity of exfoliated graphite with a bulk density of 7 kg/m3 on the viscosity of various oils.

of heavy oils, based on the measurements of sorption capacity at different temperatures from O°C to 30°C. Figure 27.9(a) shows a strong dependence of sorption capacity on viscosity of sorbate heavy oils, and their dependence seems to be divided into two; low viscosity region for the A-grade and crude oils and high viscosity region for the B- and C-grade oils. However, the measurements on a wide range of viscosity using various oils show that sorption capacity of the exfoliated graphite levelled off in the intermediate viscosity range, as shown in Fig. 27.9(b), and will be discussed in the next section.

27.3.2 Various Oils Other than Heavy Oils Various oils were selected to cover a wide range ofviscosity as summarized in Table 27.2. The exfoliated graphite used was the same one as above, whose bulk density was about 7 kg/m3 •

Table 27.2

Oils used in the present work

Kerosene Light oil A-grade heavy oil Crude oil Mineral oil Grape seed oil Salad oil

788.3 823.2 852.3 867.7 842.5 919.9 918.3

0.001 0.001 0.004 0.007 0.033 0.052 0.056

Saillower oil Two-cycle motor oil Four-cycle motor oil Diesel oil B-grade heavy oil C-grade heavy oil

914.0 858.3 876.1 877.7 902.7 925.5

0.069 0.118 0.126 0.127 0.160 0.350

27.3 Sorption Capacity for Viscous Organics

721

In Fig. 27.9(b), the sorption capacity is plotted against viscosity 11. The sorption capacity that was determined by direct soaking of an exfoliated graphite lump with a bulk density of 7 kg/m3 into oils at different temperatures show a marked increase at the high-viscosity side and a marked decrease at the lowviscosity side. The sorption capacity value, which levels off at intermediate viscosity, is around 70 gig.

27.3.3 Biomedical Fluids Biomedical molecules are typically large molecular and weak polar materials, for which exfoliated graphite has a large sorption capacity. The sorption performance of exfoliated graphite with different bulk densities was studied on several kinds ofbiomedical molecules, ovalbumin, serum albumin, bovine serum albumin (BSA), lysine, and herring sperm DNA [19]. Changes in absorbed amount of BSA with time showed that sorbed amount increases quickly in the first 20 min, but exfoliated graphite with the higher bulk density quickly reaches saturation at the lower amount. The lower density sample has larger sorption capacity, because ofits larger pore volume for capillary condensation and takes longer time to be saturated. In Fig. 27.10, dependences of sorption capacity on bulk density of exfoliated graphite are compared with three liquids - heavy oil, gasoline, and BSA. Sorption capacity decreases with increasing bulk density of exfoliated graphite for the three liquids, because of the decrease of pore volume, particularly the decrease of large spaces among the particles, in the lump of exfoliated graphite. The characteristics of carbon materials, such as low weight, chemical inertness, excellent compatibility with the human body [29], and also bacteriostasis, led to the new application namely: medical dressing in preventing a traumatized

70 _

..,....----------------t

60

0) -.... -9 50 C

\

~ 40

\

«j ()

c:

o

30

aa 20

\,

\Heavyoil

0

~Gasolin~

-~:q

CJ)

O'Q......

~~[j--D

"'0

<

\ 0

•

T5

10

BSA solution

".--.--["'--. \.::::=..n.-~-=.~=~

°"'-0 --0--0-0-

0'1---.....-.......-........-......---...-...,....---.-......----.....-.....

o

20

40

60

80

100

Bulk density of exfoliated graphite (kg/m 3 )

Figure 27.10 Dependences of sorption capacity of bovine serum albumin (BSA) on the bulk density of exfoliated graphite in comparison with heavy oil and gasoline oil.

Chapter 27 Sorption of Viscous Organics by Macroporous Carbons

722

surface from infection, using large sorption capacity of exfoliated graphite for medical fluids [30].

27.4

KINETICS OF SORPTION

Kinetics of sorption into carbon materials for different oils was studied by using the so-called wicking method [31]. The system for the measurement is schematically shown in Fig. 27.11(a). The mass increase by capillary suction of oils from the bottom into carbon sorbents, either exfoliated graphite or carbonized fir fibers packed into a glass tube with a cross-sectional area of 314 mm2 with different densities or carbon fiber felts cut into similar crosssectional area, was measured at room temperature as a function of time. The change in the mass of carbon sorbents due to the sorption of oils was plotted against time (sorption curve) as shown in Fig. 27.11 (b). Some ofsorption curves for the A- and C-grade heavy oils are shown on exfoliated graphite with different bulk densities in Fig. 27.12(a) and (b), respectively. The initial slope of sorption curves depends strongly on both the bulk density of exfoliated graphite and the viscosity of the heavy oil. For the A-grade heavy oil, gradual suction of the heavy oil is observed on the exfoliated graphite column with a bulk density of 7 kg/m3 , not reaching saturation even after 50 s. For the column with high densities of more than 20 kg/m3 , however, very rapid suction and reaching saturation within lOs were observed (Fig. 27.12(a)). The initial slope of the curves increased with increasing bulk density of the column, but the saturated mass increase showed a maximum at a bulk density of around (b)

(a)

Glass column 10 mm

~

Carbon absorbent

~ ~ Glass filter 20 mm

I

Time

Movable stage

Figure 27.11 Schemes of measurement system for wicking method and sorption curve.

723

27.4 Kinetics of Sorption

(b) C-grade heavy oil

(a) A-grade heavy oil 2.0

2.0

§

§ Q)

en

1.5

Q)

3

20 kg/m 3

1.5

en

co

co

Q)

~

.~

12 kg/m

/"".

<3 .5: 1.0

1.0

en en

en en

~

20

30

40

50

-;:.

0.5

0.0 10

/ . -----

~~"·""·-30kg/m3

co

co ~ 0.5

~~----'-------L_.L..--......L...----L....---L_..L--.......L.-----'

0

1000

2000

3000

4000

5000

Time (s)

Time (s)

Figure 27.12 Sorption curves observed for the A- and C-grade heavy oils using exfoliated graphite with different bulk densities.

12kg/m3 . Very similar dependence of sorption curve on the bulk density of exfoliated graphite column was also observed for the much viscous C-grade heavy oil, but to reach saturation it needed much longer time than the A-grade heavy oil (Fig. 27.12(b)). The sorption curve before saturation is well approximated by the equation: ms -- Kst 1/2 + B ,

(27.2)

where ms is the mass increase per cross-sectional area of the sorbent column, t is the time, Ks is the sorptivity or liquid sorption coefficient, and B is a constant. Ks (kg/m2 s1/ 2 ) is a measure of sorption rate. This equation was theoretically derived for the sorption of a liquid into cylindrical capillary of a porous body [32] on the basis of the law of momentum conservation, Poiseuille's law, and capillary phenomenon, and successfully applied to porous ceramics [33, 34]. In Fig. 27.13(a-c), the plots of ms vs t 1/ 2 for the A-grade heavy oil are shown for the three carbon sorbents - exfoliated graphite, carbonized fir fibers, and carbon fiber felts, respectively, with different bulk densities. The initial slope of these curves, i.e., sorptivity K s ' depends strongly on the carbon sorbent and also its bulk density. The dependences of sorptivity Ks on bulk density of the three carbon sorbents are shown in Fig. 27.14. For the A-grade heavy oil, Ks for carbonized fir fiber drastically increases with increasing its bulk density in the region from 7 to 20 kg/m3 , and the increase in Ks seems to be saturated at around 5.5 kg/m2 Sl/2, when the lump of fibers is densified above 30 kg/m3 . In the case of the carbon fiber felts, which have bulk density higher than 50 kg/m 3 , the value of Ks may be approximated to be a constant of about 5.5 kg/m2 Sl/2, even though there is certain scattering in the experimental points. For the exfoliated graphite, the maximum K s is half lower than those of others with a value of

Chapter 27 Sorption of Viscous Organics by Macroporous Carbons

(b) Carbonized fir fibers

(a) Exfoliated graphite 20

20

15

C\J

..........

31 kg/m 3

C, 10 ..........

13 kg/m 3

E

..........

C)

C,

15

C\J

E

..........

C)

10

CI)

CI)

E

E

5

5

0 0

15

15

(c) Carbon fiber felts 20

C' 15

E

..........

C)

C, 10 .......... CI)

E 5

Figure 27.13 Sorption curves of carbon sorbents with different bulk densities for the Agrade heavy oil. 6

6-

0

[:l

0

~ T'""(J)

C\I

E

.......... C)

0

B

0

B 0

Carbon fiber felt

4

C, ~CI)

~

"> E. 0

en

2

20

40

60

80

Bulk density (kg/m 3 )

Figure 27.14 Dependences of sorptivity Ks on the bulk density of sorbents.

27.4 Kinetics of Sorption

72 5

16 kg/m 3 . The sorptivity Ks was found to be independent of the specimen height, though the saturated values of ms were different. For the viscous C-grade heavy oil, the value of sorptivity K s was so small, about 0.2 kg/m2 Sl/2, that its slight dependence on the bulk density of the two carbon sorbents - carbonized fir fibers and carbon fiber felts - was observed. Sorptivity or liquid sorption coefficient K s is theoretically expressed as follows [32]: (27.3)

where dz is the density, 'Y the surface tension and JL the viscosity of the liquid sorbate, e* the effective sorption porosity, A the average tortuosity factor of the capillaries (A > 1), Yo the average pore radius of the porous sorbent, and () the contact angle of interface between the liquid and the pore wall of sorbent. Thus, in the first bracket in Eqn (27.3) are the parameters based on the sorbates, the second one are the variables for sorbents, and the third one is the parameter for the interface between the sorbate and the sorbent. In order to understand the dependences of the sorptivity Ks on the bulk density of carbon sorbents for the A-grade heavy oil, the first bracket in Eqn (27.3) must be a constant, and also the third bracket can be assumed to be a constant because the contact angle () between the A-grade heavy oil and the pore wall of carbon is not supposed to have much difference among the carbon materials used. Therefore, the sorptivity Ks can be approximated to depend on the three parameters of the carbon sorbent, effective sorption porosity e*, average tortuosity factor A, and average pore radius Yo. The effective sorption porosity, e*, is the volume ratio of macropores directly involved in the sorption and e* is calculated using the value m7 [32], at which the linear relation between ms vs (1/2 is broken away (refer Fig. 27.13) from the equation:

e * =m7 -, Ld}

(27.4)

where L is the height of sorbent. With increasing bulk density of sorbent, the effective sorption porosity e* increases rapidly, but the average pore radius Yo decreases. The tortuosity A is mainly governed by the smoothness of the surface of sorbent particles. In order to have a high sorptivity Ks ' therefore, a low value of A, i.e., smooth surface of particles, and high bulk density where changes in both e* and Yo becomes small, is desired. This occurs in carbon fiber felts among the three carbon sorbents used, as shown in Fig. 27.14. In the case of exfoliated graphite, e* shows a maximum at a bulk density of about 16 kg/m3 , pore size distribution changes markedly, i.e., the average pore radius Yo decreases with increasing bulk density, and the value of A is expected to be the largest among the three sorbents.

Chapter 27 Sorption of Viscous Organics by Macroporous Carbons

72 6

Therefore, the complicated change of K s observed on exfoliated graphite seems to be a result of balancing between the dependences of 8* and Yo on the bulk density of the exfoliated graphite [21]. In the case of carbonized fir fibers, however, a marked dependence of K s on their bulk density was observed, from a low value comparable to exfoliated graphite to a high value comparable to the carbon fiber felts. Their Ks seemed to be mainly governed by 8*, which has also pronounced dependence on bulk density, even though the average pore radius Yo seems to become small with increasing bulk density. For the carbonized fir fibers with high bulk density, 8* tends to be saturated and pore size distribution becomes simple, which seems to lead the value of K s to be a constant near that for carbon fiber felts [11, 21]. A detailed discussion on the dependence of K s on the bulk density of carbon sorbents was presented in our papers [20, 21]. In Fig. 27.15, sorption curves observed on the three heavy oils - the A-, B-, and C-grade oils - and salad oil are compared in order to show the effect of viscosity of oils on their sorption rate. The sorption rate depends strongly on viscosity. Less viscous oil (e.g., A-grade heavy oil and salad oil) reaches saturation very quickly. However, viscous oil (e.g., C-grade heavy oil) is sorbed very slowly into exfoliated graphite. On the other hand, saturated amounts of sorbed oil for the three oils - the A- and B-grade heavy oils and salad oil - reached almost the same value after about 1 h (about 3600 s). For the viscous C-grade heavy oil, however, it took a long time, about 24 h, to reach a saturation, but the saturated amount of oil was a little less than those for other less viscous oils.

5.0

r------~--------------,

A-grade heavy oil

Salad oil

4.0

§ en en ctS E

3.0

"C

Q)

o

.0

2.0

en

<><><>0<><>0

1.0 0°

0 0 <>

<> <>

0

00 <> <> <> 0 C-grade heavy oil

OL-.-l.--.-I---'---'--..L---l._--L---'-~--'-~~"'--I~"-""-~

o

500

1000 Time (s)

Figure 27.15 Sorption curves for different oils.

1500

2000

727

27.5 Recovery of Heavy Oils

8 •

Kerosene

7

-

~

6

en

..........

C\I

E

5

.......... C)

~ ~rn

~ 'S;

a 0

(j)

4 3

2

Salad oil ~ Safflower oil Grape seed '~-~YCle ~otor oil 2-cycle motor oil Diesel 011 . C-grade heavy 011 OI...o-....................--"""..A.Ao......u - .......................---~.....--

0.0001

0.001

0.01

0.1

Viscosity J-L(Pa s)

Figure 27.16 Dependence of sorptivity Ks on the viscosity of oils.

In Fig. 27.16, sorptivity K s is plotted against viscosity JL of oils in logarithmic scale. Ks shows a strong dependence on JL; the oil with the higher viscosity is sorbed into a column of exfoliated graphite with the slower rate.

27.5

RECOVERY OF HEAVY OILS

For heavy oils, their spillage by accidents result in not only the contamination of the environment but also great loss of energy resources. Therefore, their recovery from sorbents is also an important problem to be solved. Recovered heavy oils have to be usable as energy resources and also recycling of the sorbent carbons is strongly desired. From this point of view, cyclic performance of carbon sorbents was examined by different processes: filtration under suction, washing by solvent for heavy oils, centrifugation, etc. Less viscous oils, such as the A-grade and crude oils, could be recovered from all carbon sorbents by a simple filtration under suction. The changes in amounts of sorbed and recovered oils with cycling are shown on the A-grade oil in Fig. 27.17(a-c). On exfoliated graphite, about half of the sorbed oil can be recovered in each cycle of sorption and recovery. The remaining oils in the exfoliated graphite lump disturb the further sorption and so the sorption capacity of the lump decreases roughly by half for each cycle. This decrease in sorption capacity is reasonably supposed to be due to the oils that are trapped in the small crevice-like pores and also in the pores inside the particles.

728

Chapter 27 Sorption of Viscous Organics by Macroporous Carbons

(a) Exfoliated graphite with 7 kg/m 3

(b) Carbonized fir fibers with 5.5 kg/m

3

50

en ::t:. .......... C)

C. .!!2 '0 u (])

~

40

-

c.> ~

Sorption

0

Recovery

~

30

.....


> 0

II

~

~

20

~

u

(])

.0

10

0 en 0 1st

2nd

3rd

4th

5th

1st 2nd 3rd 4th 5th 6th 7th 8th

Cycling time

Cycling time

(c) Carbon fiber felt with 72.6 kg/m 12 . - - - - - -

3

,.......--.---,..---~--.

1st 2nd 3rd 4th 5th 6th 7th 8th

Cycling time

Figure 27.17 Cyclic performance of carbon sorbents for the A-grade heavy oil by filtration under suction.

The performance of sorption/recovery of carbonized fir fibers by filtration under suction is much better than exfoliated graphite as shown in Fig. 27.17 (b). In each cycle, about 80% of sorbed oil is recovered and so the decrease in sorption capacity with cycling is much slow, after eight cycles it becomes about 60% of that of the first cycle. When the fiber lump with a high bulk density was used, the decrease in sorption capacity with cycling is much less, though the absolute value of sorption capacity is less. Although sorption capacity could not be high, the cycling performance of carbon fiber felts was excellent. By filtration under suction, about 90% of the A-grade heavy oil sorbed could be recovered and no reduction in the sorption capacity was observed even after eight cycles, as shown in Fig. 27.17(c).

27.5 Recovery of Heavy Oils

72 9

Viscous oils could not be recovered from either exfoliated graphite or carbonized fir fibers by filtration even under a strong suction. Sorbed heavy oils could be recovered by washing with a solvent, such as n-hexane, but the exfoliated graphite after washing could not be reused as sorbent for heavy oil, mainly because of the destruction of the bulky texture of the exfoliated graphite. From fir fibers and carbon fiber felts, however, the oils, even the viscous C-grade oil, could be washed out using a solvent. In Fig. 27.18(a) and (b), the cycling performances of the carbonized fir fibers and carbon fiber felts, respectively, the for A- and C-grade heavy oils by washing with n-hexane are shown. For the carbon fiber felts, almost 100% recovery and excellent cyclability by washing with n-hexane were obtained for both the A- and C-grade heavy oils. In the

60

(a) Carbonized fir fibers A-grade heavy

01

C-grade heavy oil

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(b) Carbon fiber felt 14 A-grade heavy oil I_ ~

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Figure 27.18 Cyclic performance of carbonized fir fibers and carbon fiber felt for the A- and C-grade heavy oils by washing with n-hexane.

Chapter 27 Sorption of Viscous Organics by Macroporous Carbons

730

case of the C-grade heavy oil, the less viscous A-grade oil can be used as a solvent, this washing process corresponds to the preparation of the B-grade heavy oil. In the case of carbon fiber felts consisting of PAN-based carbon fibers, even centrifuging with 3800 rpm could be applied without any reduction of sorption capacity during the eight cycles (Fig. 27.19). A fair amount of cyclablity was obtained even by squeezing the felt of PAN-based carbon fibers. For the recovered oils, different analyses on chemical composition, hydrocarbon contents, and molecular weights were carried out. No appreciable difference was detected between original and recovered oils. In Table 27.3, the results on the fraction of aromatic hydrocarbons and different molecular weights are summarized for the A-grade, crude, and C-grade oils. These experimental results showed that the recovered oils could be used for all applications.

(b) Bulk density of 85.5 kg/m 3

(a) Bulk density of 63.6 kg/m 3 _

II Sorption

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Cycling time

Figure 27.19

Cyclic performance of carbon fiber felts by centrifuging with 3800 rpm.

Table 27.3

Fractions of aromatic hydrocarbons and averaged molecular weight values measured by field desorption mass spectrometry (FD-MS) analysis on the crude and (-grade oils

1.06 1.06

A-grade heavy oil Original Recovered

4.0 4.2

258 259

274 274

Original Recovered

4.9 4.5

645 672

869 915

1102 1147

1.35 1.36

1.27 1.25

C-grade heavy oil Original Recovered

5.4 4.6

1071 1207

1768 1839

2428 2393

1.65 1.52

1.37 1.30

Crude oil

Farom - fraction of aromatic hydrocarbon, M n - number-averaged molecular weight, Mw - weight-averaged molecular weight, Mz - z-averaged molecular weight.

731

27.6 Discussion

27.6

DISCUSSION

So far, mats of some polymers, such as poly(propylene) and poly(urethane), have been used for the sorption of spilled oil. Their maximum sorption capacity is about 10-30 g of heavy oil per 1 g ofpolymer [35]. However, they sorb water, as well as heavy oil, and show no special selectivity for heavy oils. Therefore, the effective sorption capacity of the polymer mats for heavy oils floating on water must be lower than the figures mentioned above. Some natural sorbents prepared from cotton fibers, milkweed flosses, and kenaf plants were reported to have rather high sorption capacity and certain potential for oil recovery and sorbent reusability [35-41]. The sorption capacity of macroporous carbon materials, exfoliated graphite, and carbonized fir fibers, is very high in comparison with these materials. Preferential sorption of oils is an advantage of carbon materials in addition to their high sorption capacity. It is interesting to point out that most materials, which have either been used or tested for sorption of heavy oils, are composed from fibrous particles, as explained above. Carbon materials, which had interesting results for heavy oil sorption, are also fibrous, worm-like particles in exfoliated graphite having also fibrous morphology. The reason for this is not clear yet, but easy formation of large spaces with appropriate size for heavy oil sorption associated with easy deformation of fiber networks to give appropriate morphology to keep oils might be one of the reasons. For the large sorption capacity of carbon materials, large spaces among fibrous particles are reasonably supposed to be responsible. In the case of the lump of exfoliated graphite, there are at least three kinds of pores - large spaces among entangled worm-like particles with fibrous morphology, crevice-like pores on the surface of worm-like particles, and elliptic pores inside the particles. The large spaces among the particles occupy about 75% of the total volume of the lump of exfoliated graphite and about 70% of the sorbed heavy oil fill these spaces [23]. These large spaces among the particles can be easily destroyed by a slight compression, and, as a consequence, the sorption capacity drops down correspondingly, as shown in Fig. 27.3. However, the other two pores, the crevice-like pores on the surface of particles and the elliptic pores inside the particles, also have important roles for heavy oil sorption. Observations under the optical microscope showed that the oil rose through the edge of the crevices formed on the surface of the particles immediately on pumping heavy oil into the lump of exfoliated graphite [16]. This complicated pore structure in the exfoliated graphite lump may result in rather strong holding of sorbed heavy oils, which did not move to the filter paper during filtration to recover from the water surface, even though sorption rate is low in comparison with carbon fiber felts that have a smooth surface. The same discussion on heavy oil sorption into carbonized fir fibers is reasonably assumed, which have similar pore structure, large spaces among the fibers of fir plants, small pores inside the fibers, and also rough surface of the fibers. In

732

Chapter 27 Sorption of Viscous Organics by Macroporous Carbons

carbon fiber felts, however, only interparticle pores exist, which seems to result in small sorption capacity, but high sorption rate and high recovery ratio. Hydrophobic (oleophilic) nature of the surface of carbon materials seems also to be a factor governing heavy oil sorption, particularly for preferential sorption of heavy oils.

27.7

CONCLUSIONS

All experimental results on the sorption of viscous organics, such as various oils including heavy oils and biomedical fluids, by macroporous carbon materials [2-24] revealed that the sorption of large amount of viscous organics into carbon materials is due to the capillary pumping based on their pore structure; capillary pumping is assisted by intraparticle pores, such as crevice-like on the surface of worm-like particles and ellipsoidal pores in the particles of exfoliated graphite, and most of the organics pumped up are kept in the large interparticle spaces. Certain possibilities of these macroporous carbon materials to be used for the protection of environment from heavy oil pollutions and the reuse of spilled heavy oils were demonstrated.

ACKNOWLEDGMENTS

This series of works on heavy oil sorption and recovery was carried out in the Proposal-Based New Industry Creative Type Technology R&D Promotion Program of New Energy and Industrial Technology Development Organization (NEDO), Japan (No. 98Ec-12-002), and under the Joint Research Program betweenJapan Society for the Promotion of Science aSPS) and National Natural Science Foundation of China (NSFC). The works were partly supported by a grant of Frontier Research Project from Ministry of Education, Japan.

REFERENCES

1. Fujiraito Ind. Co., Ltd. (1979). Japanese Patent Proposal (No. 95333). 2. Cao, N.Z., Shen, W.C., Wen, S.Z., et al. (1996). The adsorption performance of heavy oil on expanded graphite. Carbon '96, New-castle upon Tyne, UK, pp. 114-15.

References

733

3. Toyoda, M., Aizawa, J., and Inagaki, M. (1998). Sorption and recovery of heavy oil by using exfoliated graphite. Desalination, 115, 199-201. 4. Toyoda, M., Moriya, K., and Inagaki, M. (1999). Sorption of heavy oil into exfoliated graphite-influence of bulk density and pore for sorption. TANSO, 187, 96-100 (in Japanese). 5. Toyoda, M., Moriya, K., Aizawa, J., et al. (2000). Sorption and recovery of heavy oils by using exfoliated graphite. Part I: maximum sorption capacity. Desalination, 128, 205-11. 6. Inagaki, M., Konno, H., Toyoda, M., et al. (2000). Sorption and recovery of heavy oils by using exfoliated graphite Part II: recovery of heavy oil and recycling of exfoliated graphite. Desalination, 128, 213-18. 7. Tryba, B., Kalenczuk, R.J., Kang, F., et al. (2000). Studies of exfoliated graphite (EG) for heavy oil sorption. Mol. Cryst. Liq. Cryst., 340, 113-19. 8. Tryba, B., Morawski, A.W., Kalenczuk, R.]., and Inagaki, M. (2003). Exfoliated graphite as a new sorbent for removal of engine oils from wastewater. Spill Sci. Technol. Bull., 8, 569-71. 9. Inagaki, M., Kawahara, A., and Konno, H. (2002). Sorption and recovery of heavy oils using carbonized fir fibers and recycle. Carbon, 40, 105-11. 10. Inagaki, M., Kawahara, A., and Hayashi, T. (2001). Sorption, recovery and recycling of heavy oil by using carbonized fir fibers. Res. Rep. Aichi Inst. Technol., 36, 69-78 (in Japanese). 11. Inagaki, M., Kawahara, A., Iwashita, N., et al. (2002). Heavy oil sorption and recovery by using carbon fiber felts. Carbon, 40, 1487-92. 12. Inagaki, M., Shibata, K., Setoh, S., et al. (2000). Sorption and recovery of heavy oils by using exfoliated graphite part III: trials for practical applications. Desalination, 128, 219-22. 13. Toyoda, M., Dogawa, N., Seki, T., et al. (2001). Sorption and recovery ofA-grade heavy oil by using exfoliated graphite packed in plastic bag - trial for practical applications. TANS 0, 166-9 (in Japanese). 14. Toyoda, M. and Inagaki, M. (2000). Heavy oil sorption using exfoliated graphite. New application of exfoliated graphite to protect heavy oil pollution. Carbon, 38, 199-210. 15. Inagaki, M., Toyoda, M., and Nishi, Y. (2001). Sorption, recovery and recycling of heavy oils by carbon materials. Kagaku Kougaku, 65, 179-82 (in Japanese). 16. Inagaki, M., Toyoda, M., Iwashita, N., et al. (2001). Exfoliated graphite for spilled heavy oil recovery. Carbon Sci., Korea, 2, 1-8. 17. Inagaki, M., T oyoda, M., Iwashita, N., et al. (2002). Sorption, recovery and recycle of spilled heavy oils using carbon materials. TANS 0, 16-25 (in Japanese). 18. Toyoda, M. and Inagaki, M. (2003). Sorption and recovery of heavy oils by using exfoliated graphite. Spill. Sci. Technol. Bull., 8, 467-74. 19. Kang, F., Zheng, Y.P., Zhao, H., et al. (2003). Sorption of heavy oils and biomedicalliquids into exfoliated graphite - researches in China. New Carbon Mater., 18, 161-73. 20. Nishi, Y., Dai, G., Iwashita, N., et al. (2002). Evaluation of sorption behavior of heavy oil into exfoliated graphite by wicking method. Mater. Sci. Res. Int., 8,43-8. 21. Nishi, Y., Iwashita, N., Sawada, Y., and Inagaki, M. (2002). Sorption kinetics of heavy oil into porous carbons. Water Res., 36, 5029-36.

734

Chapter 27 Sorption of Viscous Organics by Macroporous Carbons

22. Nishi, Y., Iwashita, N., and Inagaki, M. (2002). Evaluation of pore structure of exfoliated graphite by mercury porosimeter. TANS 0, 31-4 (inJapanese). 23. Zheng, Y.P., Wang, H.N., Kang, F.Y., et al. (2004). Sorption capacity of exfoliated graphite for oils - sorption in and among worm-like particles. Carbon, 42,2603-7. 24. Toyoda, M., Nishi, Y., Iwashita, N., and Inagaki, M. (2002). Sorption and recovery of heavy oils by using exfoliated graphite. Part IV: discussion on high oil sorption of exfoliated graphite. Desalination, 151, 139-44. 25. Inagaki, M. and Suwa, T. (2001). Pore structure analysis of exfoliated graphite using image processing of scanning electron micrographs. Carbon, 39, 915-20. 26. Kang, F.Y., Zheng, Y.P., Wang, H.N., et al. (2002). Effect of preparation conditions on the characteristics of exfoliated graphite. Carbon, 40, 1575-81. 27. Inagaki, M., Tashiro, R., Toyoda, M., et al. (2004). Pore structure of exfoliated graphite prepared from residue compounds with sulfuric acid. J. Ceram. Soc. Jpn., 112, S1513-16. 28. Inagaki, M., Tashiro, R., Washino, Y., and Toyoda, M. (2004). Exfoliation process of graphite via intercalation compounds. J. Phys. Chem. Solids, 65, 133-7. 29. Bokros, J., LaGrange, L.D., and Shoen, FJ. (1972). Control of structure of carbon for use in bioengineering. In Chemistry and Physics of Carbon, Vol. 9 (P.L. Walker, ed.). New York: Marcel Dekker, pp. 103-71. 30. Cao, N.Z., Shen, W.C., Wen, S.Z., et al. (1996). The adsorption of proteins on expanded graphite. Extended Abstracts of the European Conference, Carbon '96, Newcastle upon Tyne, UK, pp. 258-9. 31. Aggarwal, R. (1977). Evaluation of relative wettability of carbon fibers. Carbon, 15,291-3. 32. Washburn, E.W. (1921). The dynamics of capillary flow. Phys. Rev., 17,273-83. 33. Beltran, V., Escardino, A., Feliu, C., and Rodrigo, M.D. (1988). Liquid suction by porous ceramic materials. Br. Ceram. Trans. J., 87, 64-9. 34. Beltran, V., Barba, A., Rodrigo, M.D., and Escardino, A. (1989). Liquid suction by porous ceramic materials: 2. Influence of pressing conditions. Br. Ceram. Trans. J., 88,219-22. 35. Chol, H.M. and Cloud, R.M. (1992). Natural sorbents in oil spill cleanup. Environ. Sci. Technol., 26, 772-6. 36. Drelich, J., Hupka, J., and Gutkowski, B. (1988). Absorptivity of fibrous mats applied for removing spilt oil. Chemistryfor Protection of the Environment 1987, Studies in Environmental Science. Elsevier, 34, pp. 207-21. 37. Johnson, R.F., Manjrekar, T.G., and Halligan, J.E. (1973). Removal of oil from water surfaces by sorption on unstructured fibers. Environ. Sci. Technol., 7, 439-43. 38. Yamamoto, H. (1998). Manufacturing of oil sorbent from heat treated wood fiber and developing new products. Cellulose Commun., 5, 148-51. 39. Miyata, N. (1999). Oil sorbency ofsorbents prepared from kenaf (Hibiscus cannabinus L.) Plants. Sen'i Gakkaishi, 55, 576-83. 40. Umehara, K., Nakamura, S., and Saito, M. (1997). Sorbents for oils derived from woods. 27th Symposium on Chemical Treatment of Woods, Proceedings, pp. 4957 (in Japanese). 41. Inagaki, M., Nagata, T., Suwa, T.,et al. (2004). Sorption kinetics of various oils into exfoliated graphite. Fresenius Environ. Bull. (in press).

SUBJECT INDEX

activated carbon, 40 acid-basicity, 656 adsorption capacity, 634 influence of operation conditions, 635 catalytic reactions with, 645 caustic-impregnated, 535 for supercapacitors, 609 granular (GAC), prediction of adsorption behavior, 684 ignition of, 551 metal impregnated, 545, 645 nitrogen-containing, 541, 544 photocatalysis with, 646 powdered (PAC), prediction of adsorption behavior, 684 preloading with organic matter, 638 preparation by KOH activation, 610 reaction with oxidants, 641 saturation, 639 surface oxygen complexes in, 539, 544, 547, 584, 642, 645, 657, 659, 663 selection for applications, 553 activated carbon fibers, 40, 431 activation-pore structure relationship in, 444 advantages o£ 431 applications o£ 447 characterization o£ 436 preparation o£ 431 activated mesocarbon microbeads, 113 active surface area, 598 adsorption calorimetry, 57 adsorption energy distribution (AED), 9, 212, 339 adsorption energy surface (AES), 214 thermodynamic meaning o£ 149 adsorption enthalpy, 5, 53, 56, 336, 526, 588

adiabatic, 68 differential, 6, 226 integral, 68 isosteric, 56, 61, 293, 336 isothermal, 67 adsorption from solution, 273 for carbon characterization, 289 isotherm trypes, 291 thermodynamics o£ 290 adsorption hysteresis, 10, 459 adsorption isotherms, types, 7 adsorption potential, 147 distribution (APD), 462, 469 adsorption thermodynamics, 53 classical thermodynamics, 54 statistical mechanics, 59 adsorptive processes, design o£ 585 aging of carbons, 305 albumin adsorption, 358 algal metabolites/toxins adsorption, 696, 699 alkane adsorption, 521 alkanethiol adsorption, 522 alpha plot method, 9, 470 ammonia adsorption, 179 anion exchange properties, 318 argon adsorption, 80, 255, 337, 414 atomic force microscopy (AFM), 516 atrazine adsorption, 690 bacteria adsorption, 671 Barrett, Joyner and Halenda (BJH) method, 246, 461 basic structural unit (BSU), 25 basicity of 1T-electrons, 316 benzene adsorption, 550, 664 biomedical fluids adsorption, 716 bivariate model, 213, 225 bivariate surfaces, 213 boron doping, 504, 604 737

Subject Index

Broekhoff-de Boer method, 246 Brunauer-Emmett-Teller (BET) theory/ equation, 3, 473 C 6o ,329 hydrogenation o£ 348 C 7o ,329 calorimetry, 57 canonical ensemble, 60, 62, 93 capacitance, 607 carbon, 17 allotropes and polytypes, 17 alloys, 21 nanotexture, 16, 28, 38 phase diagram for, 20 structures, 17 carbon anodes, nanostructurated, 597, 602, 607 carbon black, 4, 5, 34, 35, 255, 460, 464 carbon dioxide adsorption, 88, 91, 179, 244, 331, 344, 438 carbon electrodes, biologically active, reactions at, 502 corrosion processes in, 503 chemically modified, 492 electrochemical kinetics on, 494 in molten salts, 504 manufacturing techniques for, 506 modified by transition metal complexes, 499 organic electrochemistry at, 501 oxygen electroreduction (OERR) on, 495 in acid solutions, 498 in alkaline solutions, 497 reactions at, 499 surface oxygen complexes in, 493 surface radical states in, 486 thermodynamics o£ 484 types of carbons for, 485, 486 carbon fibers, 23, 32, 33, 34 carbon membranes, for gas separation, 578 carbon molecular sieves, 7, 572 carbon monoxide adsorption, 343 carbon nanofibers, 32, 403, 406 carbon nanotubes, 16, 187, 369 activated, as electrode materials, 618 as anodes for Li-ion batteries, 600

as electrodes for supercapacitors, 616 functionalization, 617 mUltiwall (MWNT), 30, 407 single-wall (SWNT), 30, 187, 369 axial phase transition in, 194 bundles o£ 188, 369 charging with alkali metals, 373, 383 endohedral adsorption on, 190, 372, 376, 383 exohedral adsorption on, 202 endohedral transitions in, 196 interstitial sites/channels, adsorption on, 198,376 opening o£ 378 carbon surfaces, fractality o£ 490 nitrogen sites in, 322 roughness o£ 489 oxygen complexes in, 305 acidity distribution, 310 characterization, 306, 307 generation, 305, 306 cation exchange properties, 312 CD 4 adsorption, 413 classical thermodynamics, 54 CMK-l, 457, 467 CMK-3, 456, 459, 466, 471, 474 colloid imprinted carbons, 42 computer simulations of adsorption, 77 boundary conditions, selection of, 81 ensemble, selection o£ 82 generating configurations, 83 initialization, 83 potential energy surface, 79 conducting polymers, 619 contact angle, 168 cylindrical pore, 11, 245 grand canonical Monte Carlo (GCMC) simulation o£ 257, 280 dangling bonds, 301, 302 decWorination and decWoramination, 644 density functional theory (DFT), 10, 253 ab initio, 341, 375 nonlocal (NLDFT), 10, 64, 253 application to pore size distribution (PSD) determination, 253, 287 thermodynamic (TDFT), 375

Subject Index

deuterium adsorption, 390, 419 diamond, 17 disordered carbons, 605 doping with heteroatoms, 602 Dubinin theory, 7, 247 Dubinin-Radushkevich equation, 7, 247 characteristic curve, 7, 440 dye adsorption, 666 electrical double layer, 480, 487, 607 electrochemical energy storage, 593 electrochemical interface, 479 electrochemical kinetics, 482 electrodes, adsorption at, 481 electrolyte adsorption, 660 electrophoresis, 319 endotemplating and exotemplating, 456 energetic heterogeneity, 262 energetic topography, 211 and attractive interactions, 228 and repulsive interactions, 227 scaling behavior, 230 temperature dependence, 230 enhanced potential method, 250 ensemble and time averaging, 91 Escherichia coli adsorption, 672, 673 ethylene adsorption, 333 exfoliated graphite, 5, 29, 712 macropore structure in, 713 Frenkel-Halsey-Hill (FHH) equation, 6 fullerene, 35, 37, 329 as phase for cleaning and preconcentrating analytes, 356 defective fullerene, 333 hydrogenation of': 348 lattice hydrogen in, 346 porosity in, 330 water solutions of': 357 fullerene black, 35, 331 gas chromatography, 355 gas mixture adsorption, 59, 65, 69, 334 gas separation, 567 gas-solid adsorption, 3 energetics of': 53 gas-solid virial coefficients, 218 generalized Gaussian model (GGM), 213, 216 comparative test for, 223

739

geosmin adsorption, 696 Gibbs adsorption equation, 170, 480 Gibbs ensemble, 96, 258 glass-like carbon, 37 gold cyanides, adsorption of': 322, 323 grand canonical ensemble, 96 grand canonical Monte Carlo (GCMC), 10,96,121,124,226,257,280,332 graphene, 19, 42, 104, 515 curved graphene structures, 383 graphite, 18, 28, 80, 176 basal plane, 81, 180, 514 ion intercalation in, 490 structure, 18 graphitizable carbons, 23 heavy oil, 711 sorption, 716 factors affecting 71 7 kinetics, 722 recovery, 727 helium adsorption, 337, 417 high-performance liquid chromatography (HPLC), 353 highly oriented pyrolytic graphite (HOPG), 28, 514 superstructures in, 518 hormone adsorption, 695 Horvath-Kawazoe method, 248 humic substances adsorption, 669 hydrated transition metal ions, adsorption of': 322 hydrofullerene, 346 hydrogen adsorption, 346, 369, 419 and hydrogen storage, 346, 370, 403, 404 at cryogenic temperatures, 374 endohedral adsorption, 346, 350, 383 isotopes, 388 modeling of chemisorption, 384 modeling of phyisorption ab initio, 379 with classical potentials, 371 phase transitions, 391 axial, 194 production, from reformer off-gas, by pressure swing adsorption, 574 hydrogen cyanide adsorption, 545 hydrogen sulfide adsorption, 534, 646 adsorption-oxidation mechanism, 536

740 hydrophilic surface sites, 11, 302 hydrophobic carbon surfaces, 302 hysteresis loops, 7, 461 ideal adsorption solution theory (lAST), 70 ideal heterogeneous systems, simulations o£ 221 immersion calorimetry, 274 into pure liquids, 274 setup for nonwetting systems, 278 setup for wetting systems, 276 immersion enthalpy, 282, 663 immersion thermodynamics, 280 infrared spectroscopy of surface species, 343 inorganic gases, adsorption o£ 534 inorganic solutes, adsorption o£ 631 integral equation of adsorption, 151 resolution o£ 152 analytical solutions, 152 numerical solutions, 152 intercalation, 595 internal energy, 66 inverse gas chromatography, 338 iodine adsorption, 296 ionic strength, effect on adsorption, 670 irreversible capacity, 597 isoelectric point, 319, 321 Kelvin equation, 3, 10, 251 krypton adsorption, 409 lead adsorption, 356 Lennard-Jones equation/potential, 79, 108, 148, 213, 241 light oils sorption, 716 lithium insertion, 595 mechanism, 605 lithium-ion battery, 595 mass titration, 320 metal ion adsorption, 632 mechanism, 633 methane adsorption, 175, 205, 409, 412 and methane storage, 587 methyl tertiary-butyl ether (MTBE) adsorption, 693

Subject Index

microbial colonization, 671, 687 microcystins adsorption, 699 nucropore characterization, contribution of activated carbon fibers to, 438 filling, 4, 9 microporous carbons, as supercapacitor electrodes, 609 molecular models for porous carbons, 106 ab initio simulation methods, 119 reconstruction methods for, 107 reverse Monte Carlo (RMC) , 98, 110 constrained reverse Monte Carlo (CRMC), 114 regular porous carbons, 106 semiempirical methods, 119 simple geometric models, for disordered porous carbons, 107 monolayers, self-assembled, 521 molecular dynamics (MD), 83, 337 Monte Carlo method, 10, 85, 257, 471 Metropolis method, 86 grand canonical Monte Carlo (GCMC), 10, 96, 121, 124, 226, 257, 280, 332 naphtalene adsorption, 352 natural gas storage, 587 natural organic matter removal by adsorption, 668, 688, 702 neon adsorption, 203, 422 n-heptane adsorption, 338 nitrogen adsorption, 5, 243, 255, 331, 424, 438, 458 doping,603 production from air, by pressure swing adsorption, 572 nitrogen oxides adsorption, 343, 546 noble gas adsorption, 175, 337, 408 nonelectrolyte adsorption, 658 nongraphitizable carbons, 23, 37 nonporous carbons, physisorption on, 5, 7 multilayer isotherms in, 5 oil spills, remediation o£ 711 ordered mesoporous carbons, 41, 455 analysis o£ by XPS, 467

Subject Index

applications o£ 457 graphitic character of the surface o£ 465, 469 pore size distribution in, 461 ordered microporous carbons, 42 organic solutes, adsorption, 653 oxygen adsorption, 341 path integral Monte Carlo (PIMC) method, 98 pesticide adsorption, 690 pH of carbons, 319 phase transitions, 95 phenol adsorption, 660 mechanisms o£ 661, 663 physisorption, 3 point of zero charge, 320 polarity, 177 polycyclic aromatic hydrocarbons (PAHs) adsorption, 354 pore classification, IUPAC, 4 pore models, 103 pore size, 610 analysis, by adsorption from solution, 295 classification, 240 distribution (PSD), 6, 9, 12, 122, 443, 461 numerical inversion for determining, 262 regularization method for determining, 263 porous carbons confinement in, 125 nanotexture in, 38 porous texture, 239, 273 characterization by gas-solid adsorption, 239 characterization by immersion calorimetry, 286 characterization by liquid-solid adsorption, 273 potential models, 240 fluid-fluid, 241 and solid-fluid potential energy, 244 pressure swing adsorption process, 570, 572, 574, 576 pyrone-like structures, 314

74 1 quantum sieving, quantum molecular sieves, 385 reaction with aqueous bases, 308, 309 reverse Monte Carlo (RMC) method, 98 reversible capacity, origins o£ 595 scanning tunneling microscopy (STM) , 516 schwarzite, 39, 333 slit-shaped pores, 11, 104, 109, 173, 240, 244, 372 grand canonical Monte Carlo (GCMC) simulation o£ 257, 280 small-angle X-ray scattering (SAXS), 445 solvent vapor recovery, by adsorption 570 submonolayers, self-assembled, 521 sulfur atom submonolayers, 522 sulfur dioxide adsorption, 542 adsorption-oxidation mechanism, 542 supercapacitors, electrochemical, 607 superhydrophobicity, 302 surface area, 1, 12, 286, 295, 473 surface chemistry characterization by immersion calorimetry, 283 characterization by liquid-solid adsorption, 273 surface complexation models (SCM), 636 surface heterogeneity, 8, 147, 233 surface tension, 168, 171 surfactant adsorption, 666 taste and odor removal, from potable water, 696 templated carbons, 41, 457 as supercapacitor electrodes, 613 tetrafluoromethane adsorption, 422 thermal swing adsorption process, 570, 571 thiol adsorption, 341 tricholoroethylene (TCE) adsorption, 694 vinyl cWoride monomer, adsorption o£ 581 viscous organics sorption, 711 volatile organic compounds (VOCs), adsorption/removal, 549, 581

Subject Index

74 2 water adsorption, 11, 122, 176,583 water treatment, 631, 679 factors influencing, 681 wettability characterization, 284 wetting isotherm, 172 wetting of solids by liquids, 167

X-ray photoelectron spectroscopy (XPS),467 xenon adsorption, 411, 420 Young equation, 168 zeolite-templated carbons, 42 zeta potential, 319

AUTHOR INDEX

Arvia, AlejandroJ., 479, 513,19,20 Bandosz, TeresaJ., 533, 21 Beguin, Franvois, 593, 23 Bock, Henry, 103, 5 Boehm, Hans-Peter, 301, 13 Bojan, Mary J., 77, 187, 4, 9 Bolzan, Agustin E., 479,19 Bottani, Eduardo J., 53, 3 Calbi, M. Mercedes, 187, 9 Cazorla-Amor6s, Diego, 431, 17 Cole, Milton W., 187,369,9, 15 Darmstadt, Hans, 455, 18 Denoyel, Renaud, 273, 12 Do, Duong D., 239, 11 Do, Ha D., 239, 11 Faur-Brasquet, Catherine, 631, 24 Frackowiak, Elzbieta, 593, 23 Gatica, Silvina M., 187, 9 Gubbins, Keith E., 103, 5

Martinez-Alonso, Amelia, 329, 14 Migone, Aldo D., 403, 16 Moreno-Castilla, Carlos, 653, 25 Newcombe, Gayle, 679,26 Olivier, James P., 147,7 Pikunic, Jorge, 103, 5 Ramirez-Pastor, AntonioJ., 211,10 Riccardo, Jose L., 211, 10 Rouquerol, Franvoise, 273, 12 Rouquerol, Jean, 273, 12 Ryoo, Ryong, 455, 18 Salvarezza, Roberto C., 513, 20 Sing, Kenneth S.W., 3, 1 Sircar, Shivaji, 565, 22 Steele, William A., 77, 167, 4, 8 Suarez-Garcia, Fabian, 329, 14

Inagaki, Michio, 711, 27 Iwashita, Norio, 711, 27

Tasc6n, Juan M.D., 15, 53, 329, 2, 3, 14 Teran Arce, Fernando, 513, 20 Toyoda, Masahiro, 711, 27

Jakubov, Timur S., 133, 6 Johnson, J. Karl, 187, 369, 9, 15

Ustinov, Eugene A., 239, 11

Kang, Feiyu, 711, 27

Vela, Maria E., 513,20

Le Cloirec, Pierre, 631, 24 Linares-Solano, Angel, 431, 17

Zgrablich, Giorgio, 211, 10 Zubimendi, Jose L., 513, 20

735